scientific article case study

Browse All Articles
Newsletter Sign-Up

18 Jun 2024
Research & Ideas

Industrial Decarbonization: Confronting the Hard Challenges of Cement

CEOs in construction and heavy industries must prioritize innovative abatement strategies to meet rising global demand for cement while reducing emissions. Research by Gunther Glenk offers an economic framework for identifying emission reduction options.

11 Jun 2024
In Practice

The Harvard Business School Faculty Summer Reader 2024

What's on your vacation reading list? Harvard Business School faculty members plan to explore not only sober themes, such as philosophy and climate policy, but classic mysteries and hip-hop history.

04 Jun 2024
Cold Call Podcast

How One Insurtech Firm Formulated a Strategy for Climate Change

The Insurtech firm Hippo was facing two big challenges related to climate change: major loss ratios and rate hikes. The company used technologically empowered services to create its competitive edge, along with providing smart home packages, targeting risk-friendly customers, and using data-driven pricing. But now CEO and president Rick McCathron needed to determine how the firm’s underwriting model could account for the effects of high-intensity weather events. Harvard Business School professor Lauren Cohen discusses how Hippo could adjust its strategy to survive a new era of unprecedented weather catastrophes in his case, “Hippo: Weathering the Storm of the Home Insurance Crisis.”

23 Apr 2024

Getting to Net Zero: The Climate Standards and Ecosystem the World Needs Now

What can companies and regulators do as climate predictions grow grimmer? They should measure impact, strengthen environmental institutions, and look to cities to lead, say Robert Kaplan, Shirley Lu, and Rosabeth Moss Kanter.

22 Apr 2024

When Does Impact Investing Make the Biggest Impact?

More investors want to back businesses that contribute to social change, but are impact funds the only approach? Research by Shawn Cole, Leslie Jeng, Josh Lerner, Natalia Rigol, and Benjamin Roth challenges long-held assumptions about impact investing and reveals where such funds make the biggest difference.

18 Mar 2024

When It Comes to Climate Regulation, Energy Companies Take a More Nuanced View

Many assume that major oil and gas companies adamantly oppose climate-friendly regulation, but that's not true. A study of 30 years of corporate advocacy by Jonas Meckling finds that energy companies have backed clean-energy efforts when it aligns with their business interests.

12 Mar 2024

How Used Products Can Unlock New Markets: Lessons from Apple's Refurbished iPhones

The idea of reselling old smartphones might have seemed risky for a company known for high-end devices, but refurbished products have become a major profit stream for Apple and an environmental victory. George Serafeim examines Apple's circular model in a case study, and offers insights for other industries.

27 Feb 2024

How Could Harvard Decarbonize Its Supply Chain?

Harvard University aims to be fossil-fuel neutral by 2026 and totally free of fossil fuels by 2050. As part of this goal, the university is trying to decarbonize its supply chain and considers replacing cement with a low-carbon substitute called Pozzotive®, made with post-consumer recycled glass. A successful pilot project could jump start Harvard’s initiative to reduce embodied carbon emissions, but it first needs credible information about the magnitude and validity of potential carbon reductions. Harvard Business School professor emeritus Robert Kaplan and assistant professor Shirley Lu discuss the flow of emissions along the supply chain of Harvard University’s construction projects, the different methods of measuring carbon emissions, including the E-liability approach, and the opportunity to leverage blockchain technology to facilitate the flow of comparable and reliable emissions information in the case, “Harvard University and Urban Mining Industries: Decarbonizing the Supply Chain.”

30 Jan 2024

Can Second-Generation Ethanol Production Help Decarbonize the World?

Raízen, a bioenergy company headquartered in São Paulo, is Brazil’s leader in sugar and ethanol production and the world’s leading ethanol trader. Since its creation in 2011, the company had primarily produced first-generation ethanol (E1G) from sugarcane, a crop that can also be used to produce sugar. In 2015, Raízen also started to produce second-generation ethanol (E2G), a biofuel derived from residual and waste materials, such as cane bagasse and straw – which don’t compete with food production. The company’s growth strategy focused on developing and boosting a low carbon portfolio that focused on E2G, based on the belief that Raízen—and Brazil—could help the world decarbonize and profit from the energy transition. Paula Kovarsky, Raízen’s chief strategy and sustainability officer, was confident the company could become a global green energy champion. But after the board’s approval for the first round of E2G investments, she faced a complex challenge: how to expand the market for second-generation ethanol and other sugar-cane waste biofuels, in order to ensure Raízen’s long-term growth? Harvard Business School professor Gunnar Trumbull and Kovarsky discuss the company’s strategy for bringing second-generation ethanol to the world in the case, “Raízen: Helping to Decarbonize the World?”

29 Jan 2024

Do Disasters Rally Support for Climate Action? It's Complicated.

Reactions to devastating wildfires in the Amazon show the contrasting realities for people living in areas vulnerable to climate change. Research by Paula Rettl illustrates the political ramifications that arise as people weigh the economic tradeoffs of natural disasters.

17 Jan 2024

Are Companies Getting Away with 'Cheap Talk' on Climate Goals?

Many companies set emissions targets with great fanfare—and never meet them, says research by Shirley Lu and colleagues. But what if investors held businesses accountable for achieving their climate plans?

09 Jan 2024

Could Clean Hydrogen Become Affordable at Scale by 2030?

The cost to produce hydrogen could approach the $1-per-kilogram target set by US regulators by 2030, helping this cleaner energy source compete with fossil fuels, says research by Gunther Glenk and colleagues. But planned global investments in hydrogen production would need to come to fruition to reach full potential.

02 Jan 2024

Should Businesses Take a Stand on Societal Issues?

Should businesses take a stand for or against particular societal issues? And how should leaders determine when and how to engage on these sensitive matters? Harvard Business School Senior Lecturer Hubert Joly, who led the electronics retailer Best Buy for almost a decade, discusses examples of corporate leaders who had to determine whether and how to engage with humanitarian crises, geopolitical conflict, racial justice, climate change, and more in the case, “Deciding When to Engage on Societal Issues.”

10 Trends to Watch in 2024

Employees may seek new approaches to balance, even as leaders consider whether to bring more teams back to offices or make hybrid work even more flexible. These are just a few trends that Harvard Business School faculty members will be following during a year when staffing, climate, and inclusion will likely remain top of mind.

19 Sep 2023

What Chandrayaan-3 Says About India's Entrepreneurial Approach to Space

India reached an unexplored part of the moon despite its limited R&D funding compared with NASA and SpaceX. Tarun Khanna discusses the significance of the landing, and the country's advancements in data and digital technology.

12 Sep 2023
What Do You Think?

Who Gets the Loudest Voice in DEI Decisions?

Business leaders are wrestling with how to manage their organizations' commitment to diversity, equity, and inclusion. If you were a CEO, which constituency would you consider most: your employees, customers, or investors? asks James Heskett. Open for comment; 0 Comments.

26 Jul 2023

STEM Needs More Women. Recruiters Often Keep Them Out

Tech companies and programs turn to recruiters to find top-notch candidates, but gender bias can creep in long before women even apply, according to research by Jacqueline Ng Lane and colleagues. She highlights several tactics to make the process more equitable.

18 Jul 2023

Will Global Demand for Oil Peak This Decade?

The International Energy Agency expects the world's oil demand to start to ebb in the coming years. However, Joseph Lassiter and Lauren Cohen say the outlook will likely be more complex, especially as poor and fast-growing regions seek energy sources for their economies.

28 Apr 2023

Sweden’s Northvolt Electric Battery Maker: A Startup with a Mission

In Stockholm, Sweden an upstart battery maker, Northvolt, is trying to recreate the value chain for European car manufacturers making the switch to EVs. With two founders from Tesla and two experienced financiers at the helm, the company seems bound for success. But can they partner with government, scale fast enough, and truly be part of the climate solution? Harvard Business School professor George Serafeim discusses what it takes to scale a business—the right people, in the right place, at the right time—with the aim of providing a climate solution in the case, “Northvolt, Building Batteries to Fight Climate Change.” As part of a new first-year MBA course at Harvard Business School, this case examines the central question: what is the social purpose of the firm?

18 Apr 2023

What Happens When Banks Ditch Coal: The Impact Is 'More Than Anyone Thought'

Bank divestment policies that target coal reduced carbon dioxide emissions, says research by Boris Vallée and Daniel Green. Could the finance industry do even more to confront climate change?

Get new issue alerts Get alerts
Submit a Manuscript

Secondary Logo

Journal logo.

Colleague's E-mail is Invalid

Your message has been successfully sent to your colleague.

Save my selection

How to Write Case Reports and Case Series

Ganesan, Prasanth

Department of Medical Oncology, Jawaharlal Institute of Postgraduate Medical Education and Research, Puducherry, India

Address for correspondence: Dr. Prasanth Ganesan, Medical Oncology, 3 rd Floor, SSB, Jawaharlal Institute of Postgraduate Medical Education and Research, Dhanvantari Nagar, Puducherry - 605006, India. E-mail: [email protected]

Received March 13, 2022

Received in revised form April 10, 2022

Accepted April 10, 2022

This is an open access journal, and articles are distributed under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike 4.0 License, which allows others to remix, tweak, and build upon the work non-commercially, as long as appropriate credit is given and the new creations are licensed under the identical terms.

Case reports are considered the smallest units of descriptive studies. They serve an important function in bringing out information regarding presentation, management, and/or outcomes of rare diseases. They can also be a starting point in understanding unique associations in clinical medicine and can introduce very effective treatment paradigms. Preparing the manuscript for a case report may be the first exposure to scientific writing for a budding clinician/researcher. This manuscript describes the steps of writing a case report and essential considerations when publishing these articles. Individual components of a case report and the “dos and don'ts” while preparing these components are detailed.

INTRODUCTION

A case report describes several aspects of an individual patient's presentation, investigations, management decisions, and/or outcomes. This is a type of observational study and has been described as the smallest publishable unit in medical literature.[ 1 ] A case series involves a group of patients with similar presentations or treatments. In modern medicine [ Figure 1 ], these publications are categorized as the “lowest level of evidence”.[ 2 ] However, they serve several essential functions. For example, there are rare diseases where large, randomized trials, or even observational studies may not be possible. Medical practice, in these conditions, is often guided by well-presented case reports or series. There are situations where a single case report has heralded an important therapy change.[ 3 ] Further, case reports are often a student's first exposure to manuscript writing. Hence, these serve as training for budding scholars to understand scientific writing, learn the process of manuscript submission, and receive and respond to reviewer comments. This article explains the reasons why case reports are published and provides guidance for writing such type of articles.

WHY ARE CASE REPORTS PUBLISHED?

A case report is often published to highlight the rarity of a particular presentation. However, it may be of much more value if it also informs some aspects of management. This could be in the form of rare expressions of a common disease so that clinicians who read will be aware and can consider additional possibilities and differential diagnoses when encountering similar situations. A new form of evaluation of a patient, either to facilitate the diagnostics or to improve understanding of the disease condition, may stimulate a case report. Novel treatments may be tried, and the results might be necessary to disseminate. This may be encountered either in rare diseases or conditions where treatment options are exhausted. Moreover, randomized trials report outcomes of a group and often do not inform about the individual patient. [ Table 1 ] describes a few examples of case reports/case series which have had a remarkable impact on medical practice.

ETHICAL ISSUES

If there is a possibility of patient identification from the report, it is mandatory to obtain informed consent from the patient while approval from the institutional ethics committee (IEC) may also be needed depending on institutional policies.[ 7 ] If identifying information is absent (or if suitable steps are taken to remove identifying information or hide the identity, (such as by covering the eyes), it may still be required by some journals to obtain ethics committee approval for certain types of case reports. If a case series involves retrospective chart review, “waiver-of-consent” may be sought from the ethics committee. Indian Ethical Guidelines do not separately address this issue in case reports.[ 8 ] The Committee on Publication Ethics has described best practices for journals when publishing case reports which also gives links to model consent forms.[ 9 ]

HOW TO START?

If you are a beginner and you have identified an interesting case which you want to report, the first step would be to sit with your team and discuss the aspects of the case you want to highlight in your publication.[ 10 ] Do a literature search and try to summarize available information before writing the draft. It would also be a good idea to understand which journal you are targeting; this will assist in determining the number of figures, the word limits, and ethical requirements (such as informed consent). Discussions with senior faculty about the authors and their order should also be done at this point to avoid issues later. For a beginner, it would be a good practice to present the case in the department or in an institutional scientific forum before writing up the manuscript.

COMPONENTS OF a CASE REPORT

A case report usually has the following sections: an abstract, a brief introduction, the actual description of the case, and finally, the discussion which highlights the uniqueness of the case and includes a conclusion statement. Many journals these days publish case reports only as a letter to editor; in such cases, an abstract is not usually required.

The title must be informative about the problem being reported. It may refer to the particular issue being highlighted in the report, or it may refer to the educational aspect of that particular report. Catchy titles are often used by authors to trigger interest among the readers and make them want to read the article. Authors may remember to use titles which will help people locate the article when searching the literature.

When writing a title, it may be best to avoid terms such as “case report,” “review of literature,” “unique,” “rare,” “first-report”; these do not add value to the presentation.

Introduction

This must introduce the condition and clearly state why the case report is worth reading. It may also contain a brief mention of the current status of the problem being described with supporting references.

Describing the case

The case must be presented succinctly, in a chronological order, clearly highlighting the salient aspects of the case being reported. Relevant negative findings may be provided. For example, if a case is being reported for elaborating a new type of treatment, then more attention must be given to treatment aspects (e.g., name of the drug, dosage, schedule, dose modifications, or the type of surgery, duration, and type of anesthesia) after briefly describing the presentation and diagnostics. The idea is that the reader must be able to apply the treatment in his/her practice if required.

However, if the case is being presented for diagnostic rarity/unusual clinical features/pathological aspects, then more attention must be given to these aspects. For example, if the emphasis is on tissue pathology, then the description must include details about tissue processing, types of stains, and immunohistochemistry details.

Figures and tables

Figures, as in any publication, should be self-explanatory. A properly constructed figure legend can be used for describing certain aspects of the case much better than long-winded text in the main manuscript. This will also help to reduce the word count in the main manuscript. If there are multiple figures (e.g., follow-up radiology series and response to treatment images), these can be combined as [ Figure 1 ]a, [ Figure 1 ]b, [ Figure 1c ] or [ Figure 1 ]a, [ Figure 1 ]b, [ Figure 1 ]c, [ Figure 1d ]. This will help conform to the figure number limits prescribed by the journal. While preparing the figures, one must ensure that the quality of the art/photograph is not compromised. Further, patient identifying features must be masked, unless necessary to show.

Tables are usually not part of case reports but may be used. One example is presenting the baseline investigations in a tabular format which can facilitate assimilation as well as reduce the word count. Tables are more often used in case series. The most common is a type of table where the features of all the cases included are summarized with each row referring to an individual patient. This usually works for a series of up to ten patients; beyond that, the table may become crowded and difficult to understand. Tables may also be used in the discussion section to summarize related, published reports to date.

Discussion including review

A case report may help to alter the approach to patient management in the clinic or it may even stimulate original research evaluating a new treatment. Thus, the discussion must summarize the unique aspects of the case (why is the case different?) and the essential learning points/implications (how will it change management?/What further research needs to be done?). In addition to stating the differences from existing literature, the discussion should also attempt to explain these differences.

If the condition or treatment approach being focused on is sufficiently rare, reviewing all available cases published until that point is critical. This review may be presented in a table with each case described briefly. A more nuanced study might attempt to summarize the relevant demographics and clinical details of the various cases published to date in the form of a table (e.g., median age, gender distribution, and survival outcomes).

CASE SERIES - WHAT IS DIFFERENT?

There is no formal definition as to what is case series and what would be considered a retrospective cohort study. In general, a case series comprises <10 cases; beyond that, it may be feasible to apply formal statistics and may be considered a cohort study.

Both case reports and case series are descriptive studies. Case series must have similar cases and hence the inclusion must be clearly defined. The interventions must be documented in a way that is reproducible and follow-up of each individual in the report must be available. Although formal statistical analyses are usually not a part of case series, authors may attempt to summarize baseline demographic parameters using descriptive statistics.

ABSTRACT OF a CASE REPORT

As explained earlier, a few journals do not require abstracts for case report submissions. When required, one should try to highlight the salient aspects of the case presented and the reason for the publication within the abstract word limit, which may be as short as 100–200 words. Spend time and effort in writing a good abstract as this is a portion which is usually read by the editor during manuscript screening and may have implications for whether the article progresses to the next stage of editorial processing.

REFERENCES IN a CASE REPORT

One may only cite key references in a case report or series as there is limited scope for elaborate literature search. Most journals have a limit of 10–15 references for case reports; when publishing as a letter to editor (or correspondence), the allowed reference limit may be even lower (five or less for some journals).

CHOOSING THE RIGHT JOURNAL

Many journals have recently stopped publishing case reports and series. This is often an attempt by journals to optimize their resources (space and reviewer time) to attain the highest possible impact. Although this is unfortunate, it is a reality which must be acknowledged. Nonetheless, the advent of online-only journals has led to more options for aspiring authors. Some journals accept case series, whereas others have “sister” journals created to accept case reports and other, less definitive, contributions to the literature.[ 11 ] It is an important exercise to study all available journals accepting case reports of the type being written. The case report must be tailored to the journal's requirements. Many journals may charge an article processing fee; author(s) must consider whether they are willing to pay and publish. Some of these may be predatory journals; authors must be wary of them and scrupulously avoid publishing in such journals as they can permanently stain the publication records of a researcher.

PUBLISHING THE CASE REPORT/SERIES AS a LETTER TO EDITOR/IMAGE SERIES

When the matter to be conveyed is very minimal or is being published mainly for its rarity, letters to editor may be an alternate route to publish case report data. Interesting images may be published in the form of “images” series which is now a part of many journals. The flexibility of web-based publishing also allows interesting videos to be published online.

GUIDELINES FOR CASE REPORTS

There are guidelines which help authors in the preparation and submission of case reports. The CAse REports (CARE) checklist is one such popular guideline. It provides a “checklist” and other resources for authors that can help navigate the process of writing a case report, especially when a person is doing it for the first time.[ 12 ]

AUTHORSHIP IN CASE REPORTS

Although there are no separate guidelines for authorship in “case reports,” general authorship rules follow that for any manuscript. “Gift” authorship must be avoided. All authors must have contributed to the creation of the manuscript in addition to being involved in some aspect of care of the patient being reported. Authorship order should be ideally predecided based on mutual consensus.

CONCLUSIONS

A case report is a useful starting point for one's scientific writing career. There are useful online resources which describe the steps for a newbie writer.[ 13 14 ] [ Table 2 ] summarizes the important components to follow and understand when writing case reports. Although many frontline journals have reduced their acceptance of case reports, these publications continue to serve an essential scientific and academic role.

Financial support and sponsorship

Conflicts of interest.

There are no conflicts of interest.

Case reports; manuscript writing; case series; references

+ Favorites
View in Gallery

Readers Of this Article Also Read

How to revise and resubmit the manuscript after a favorable peer review, glossopharyngeal neuralgia following coronavirus disease 2019 infection, polymorphous adenocarcinoma of the parotid – an uncommon site of occurrence, primary vulval mucinous adenocarcinoma of intestinal type masquerading as..., detection of rare blood group ax phenotype in blood donor.

Perspectives from Researchers on Case Study Design

by Janet Salmons, PhD, Research Community Manager for SAGE Methodspace

Research design is the focus for the first quarter of 2023. Find a post about case study design , and read the unfolding series of posts here .

What is a “case study” research design?

Linda Bloomberg describes a case study as:

An in-depth exploration from multiple perspectives of the richness and complexity of a particular social unit, system, or phenomenon. Its primary purpose is to generate understanding and insights in order to gain knowledge and inform professional practice, policy development, and community or social action. Case study research is typically extensive; it draws on multiple methods of data collection and involves multiple data sources.

The researcher begins by identifying a specific case or set of cases to be studied. Each case is an entity that is described within certain parameters, such as a specific time frame, place, event, and process. Hence, the case becomes a bounded system . Typically, case study researchers analyze the real-life cases that are currently in progress so that they can gather accurate information that is not lost by time.

This method culminates in the production of a detailed description of a setting and its participants, accompanied by an analysis of the data for themes, patterns, and issues. A case study is therefore both a process of inquiry about the case at hand and the product of that inquiry. (Bloomberg, 2018, p. 276)

Case studies use more than one form of data either within a research paradigm (multimodal ), or more than one form of data from different paradigms (mixed methods). As Bloomberg notes, the case study method is employed across disciplines, including education, health care, social work, history, sociology, management studies, and organizational studies. When you look at lists of most-read and most-cited articles you will find that this flexible approach is widely used and published. Here are some open-access articles about multimodal qualitative or mixed methods designs that include both qualitative and quantitative elements.

Qualitative Research with Case Studies

Brannen, J., & Nilsen, A. (2011). Comparative Biographies in Case-based Cross-national Research: Methodological Considerations. Sociology, 45(4), 603–618. https://doi.org/10.1177/0038038511406602

Abstract. This article examines some methodological issues relating to an embedded case study design adopted in a comparative cross-national study of working parents covering three levels of social context: the macro level; the workplace level; and the individual level. It addresses issues of generalizability, in particular the importance of criteria for the selection of cases in the research design and analysis phases. To illustrate the benefits of the design the article focuses on the level of individual biographies. Three exemplars of biographical trajectories and experiences are presented and discussed. It is argued that a multi-tiered design and a comparative biographical approach can add to the understanding of individual experience by placing it in context and thus yield knowledge that is of general sociological relevance by demonstrating the interrelatedness of agency and structure.

Ebneyamini, S., & Sadeghi Moghadam, M. R. (2018). Toward Developing a Framework for Conducting Case Study Research. International Journal of Qualitative Methods, 17(1). https://doi.org/10.1177/1609406918817954

Abstract. This article reviews the use of case study research for both practical and theoretical issues especially in management field with the emphasis on management of technology and innovation. Many researchers commented on the methodological issues of the case study research from their point of view thus, presenting a comprehensive framework was missing. We try representing a general framework with methodological and analytical perspective to design, develop, and conduct case study research. To test the coverage of our framework, we have analyzed articles in three major journals related to the management of technology and innovation to approve our framework. This study represents a general structure to guide, design, and fulfill a case study research with levels and steps necessary for researchers to use in their research.

Flyvbjerg, B. (2006). Five Misunderstandings About Case-Study Research. Qualitative Inquiry, 12(2), 219–245. https://doi.org/10.1177/1077800405284363

Abstract. This article examines five common misunderstandings about case-study research: (a) theoretical knowledge is more valuable than practical knowledge; (b) one cannot generalize from a single case, therefore, the single-case study cannot contribute to scientific development; (c) the case study is most useful for generating hypotheses, whereas other methods are more suitable for hypotheses testing and theory building; (d) the case study contains a bias toward verification; and (e) it is often difficult to summarize specific case studies. This article explains and corrects these misunderstandings one by one and concludes with the Kuhnian insight that a scientific discipline without a large number of thoroughly executed case studies is a discipline without systematic production of exemplars, and a discipline without exemplars is an ineffective one. Social science may be strengthened by the execution of a greater number of good case studies.

Morgan SJ, Pullon SRH, Macdonald LM, McKinlay EM, Gray BV. Case Study Observational Research: A Framework for Conducting Case Study Research Where Observation Data Are the Focus. Qualitative Health Research. 2017;27(7):1060-1068. doi:10.1177/1049732316649160

Abstract. Case study research is a comprehensive method that incorporates multiple sources of data to provide detailed accounts of complex research phenomena in real-life contexts. However, current models of case study research do not particularly distinguish the unique contribution observation data can make. Observation methods have the potential to reach beyond other methods that rely largely or solely on self-report. This article describes the distinctive characteristics of case study observational research, a modified form of Yin’s 2014 model of case study research the authors used in a study exploring interprofessional collaboration in primary care. In this approach, observation data are positioned as the central component of the research design. Case study observational research offers a promising approach for researchers in a wide range of health care settings seeking more complete understandings of complex topics, where contextual influences are of primary concern. Future research is needed to refine and evaluate the approach.

Rule, P., & John, V. M. (2015). A Necessary Dialogue: Theory in Case Study Research. International Journal of Qualitative Methods , 14 (4). https://doi.org/10.1177/1609406915611575

Abstract. This article is premised on the understanding that there are multiple dimensions of the case–theory relation and examines four of these: theory of the case, theory for the case, theory from the case, and a dialogical relation between theory and case. This fourth dimension is the article’s key contribution to theorizing case study. Dialogic engagement between theory and case study creates rich potential for mutual formation and generative tension. The article argues that the process of constructing and conducting the case is theory laden, while the outcomes of the study might also have theoretical implications. Case study research that is contextually sensitive and theoretically astute can contribute not only to the application and revision of existing theory but also to the development of new theory. The case thus provides a potentially generative nexus for the engagement of theory, context, and research.

Thomas, G. (2011). A Typology for the Case Study in Social Science Following a Review of Definition, Discourse, and Structure. Qualitative Inquiry, 17(6), 511–521. https://doi.org/10.1177/1077800411409884

Abstract. The author proposes a typology for the case study following a definition wherein various layers of classificatory principle are disaggregated. First, a clear distinction is drawn between two parts: (1) the subject of the study, which is the case itself, and (2) the object, which is the analytical frame or theory through which the subject is viewed and which the subject explicates. Beyond this distinction the case study is presented as classifiable by its purposes and the approaches adopted— principally with a distinction drawn between theory-centered and illustrative study. Beyond this, there are distinctions to be drawn among various operational structures that concern comparative versus noncomparative versions of the form and the ways that the study may employ time. The typology reveals that there are numerous valid permutations of these dimensions and many trajectories, therefore, open to the case inquirer.

VanWynsberghe, R., & Khan, S. (2007). Redefining Case Study. International Journal of Qualitative Methods , 6 (2), 80–94. https://doi.org/10.1177/160940690700600208

Abstract. In this paper the authors propose a more precise and encompassing definition of case study than is usually found. They support their definition by clarifying that case study is neither a method nor a methodology nor a research design as suggested by others. They use a case study prototype of their own design to propose common properties of case study and demonstrate how these properties support their definition. Next, they present several living myths about case study and refute them in relation to their definition. Finally, they discuss the interplay between the terms case study and unit of analysis to further delineate their definition of case study. The target audiences for this paper include case study researchers, research design and methods instructors, and graduate students interested in case study research.

Mixed Methods Research with Case Studies

Guetterman, T. C., & Fetters, M. D. (2018). Two Methodological Approaches to the Integration of Mixed Methods and Case Study Designs: A Systematic Review. American Behavioral Scientist, 62(7), 900–918. https://doi.org/10.1177/0002764218772641

Abstract. Case study has a tradition of collecting multiple forms of data—qualitative and quantitative—to gain a more complete understanding of the case. Case study integrates well with mixed methods, which seeks a more complete understanding through the integration of qualitative and quantitative research. We identify and characterize “mixed methods–case study designs” as mixed methods studies with a nested case study and “case study–mixed methods designs” as case studies with nested mixed methods. Based on a review of published research integrating mixed methods and case study designs, we describe key methodological features and discuss four exemplar interdisciplinary studies.

Luyt, R. (2012). A Framework for Mixing Methods in Quantitative Measurement Development, Validation, and Revision: A Case Study. Journal of Mixed Methods Research, 6(4), 294–316. https://doi.org/10.1177/1558689811427912

Abstract. A framework for quantitative measurement development, validation, and revision that incorporates both qualitative and quantitative methods is introduced. It extends and adapts Adcock and Collier’s work, and thus, facilitates understanding of quantitative measurement development, validation, and revision as an integrated and cyclical set of procedures best achieved through mixed methods research. It also offers a systematic guide concerning how these procedures may be undertaken through detailing key “stages,” “levels,” and practical “tasks.” A case study illustrates how qualitative and quantitative methods may be mixed through the use of the proposed framework in the cross-cultural content- and construct-related validation and subsequent revision of a quantitative measure. The contribution of this article to mixed methods research literature is briefly discussed.

Mason, W., Morris, K., Webb, C., Daniels, B., Featherstone, B., Bywaters, P., Mirza, N., Hooper, J., Brady, G., Bunting, L., & Scourfield, J. (2020). Toward Full Integration of Quantitative and Qualitative Methods in Case Study Research: Insights From Investigating Child Welfare Inequalities. Journal of Mixed Methods Research, 14(2), 164–183. https://doi.org/10.1177/1558689819857972

Abstract. Delineation of the full integration of quantitative and qualitative methods throughout all stages of multisite mixed methods case study projects remains a gap in the methodological literature. This article offers advances to the field of mixed methods by detailing the application and integration of mixed methods throughout all stages of one such project; a study of child welfare inequalities. By offering a critical discussion of site selection and the management of confirmatory, expansionary and discordant data, this article contributes to the limited body of mixed methods exemplars specific to this field. We propose that our mixed methods approach provided distinctive insights into a complex social problem, offering expanded understandings of the relationship between poverty, child abuse, and neglect.

Onghena, P., Maes, B., & Heyvaert, M. (2019). Mixed Methods Single Case Research: State of the Art and Future Directions. Journal of Mixed Methods Research, 13(4), 461–480. https://doi.org/10.1177/1558689818789530

Abstract. Mixed methods single case research (MMSCR) is research in which single case experimental and qualitative case study methodologies, and their accompanying sets of methods and techniques, are integrated to answer research questions that concern a single case. This article discusses the historical roots and the distinct nature of MMSCR, the kinds of knowledge MMSCR produces, its philosophical underpinnings, examples of MMSCR, and the trustworthiness and validity of MMSCR. Methodological challenges relate to the development of a critical appraisal tool for MMSCR, to the team work that is involved in designing and conducting MMSCR studies, and to the application of mixed methods research synthesis for multiple case studies and single case experiments.

Sharp, J. L., Mobley, C., Hammond, C., Withington, C., Drew, S., Stringfield, S., & Stipanovic, N. (2012). A Mixed Methods Sampling Methodology for a Multisite Case Study. Journal of Mixed Methods Research, 6(1), 34–54. https://doi.org/10.1177/1558689811417133

Abstract. The flexibility of mixed methods research strategies makes such approaches especially suitable for multisite case studies. Yet the utilization of mixed methods to select sites for these studies is rarely reported. The authors describe their pragmatic mixed methods approach to select a sample for their multisite mixed methods case study of a statewide education policy initiative in the United States. The authors designed a four-stage sequential mixed methods site selection strategy to select eight sites in order to capture the broader context of the research, as well as any contextual nuances that shape policy implementation. The authors anticipate that their experience would provide guidance to other mixed methods researchers seeking to maximize the rigor of their multisite case study sampling designs.

Bloomberg, L. (2018). Case study. In B. B. Frey (Ed.), The SAGE encyclopedia of educational research, measurement, and evaluation . https://doi.org/10.4135/9781506326139

Designing Survey Research

Designing research with case study methods.

Have a language expert improve your writing

Run a free plagiarism check in 10 minutes, generate accurate citations for free.

Knowledge Base

Methodology

What Is a Case Study? | Definition, Examples & Methods

What Is a Case Study? | Definition, Examples & Methods

Published on May 8, 2019 by Shona McCombes . Revised on November 20, 2023.

A case study is a detailed study of a specific subject, such as a person, group, place, event, organization, or phenomenon. Case studies are commonly used in social, educational, clinical, and business research.

A case study research design usually involves qualitative methods , but quantitative methods are sometimes also used. Case studies are good for describing , comparing, evaluating and understanding different aspects of a research problem .

When to do a case study, step 1: select a case, step 2: build a theoretical framework, step 3: collect your data, step 4: describe and analyze the case, other interesting articles.

A case study is an appropriate research design when you want to gain concrete, contextual, in-depth knowledge about a specific real-world subject. It allows you to explore the key characteristics, meanings, and implications of the case.

Case studies are often a good choice in a thesis or dissertation . They keep your project focused and manageable when you don’t have the time or resources to do large-scale research.

You might use just one complex case study where you explore a single subject in depth, or conduct multiple case studies to compare and illuminate different aspects of your research problem.

Case study examples
Research question	Case study
What are the ecological effects of wolf reintroduction?	Case study of wolf reintroduction in Yellowstone National Park
How do populist politicians use narratives about history to gain support?	Case studies of Hungarian prime minister Viktor Orbán and US president Donald Trump
How can teachers implement active learning strategies in mixed-level classrooms?	Case study of a local school that promotes active learning
What are the main advantages and disadvantages of wind farms for rural communities?	Case studies of three rural wind farm development projects in different parts of the country
How are viral marketing strategies changing the relationship between companies and consumers?	Case study of the iPhone X marketing campaign
How do experiences of work in the gig economy differ by gender, race and age?	Case studies of Deliveroo and Uber drivers in London

Prevent plagiarism. Run a free check.

Once you have developed your problem statement and research questions , you should be ready to choose the specific case that you want to focus on. A good case study should have the potential to:

Provide new or unexpected insights into the subject
Challenge or complicate existing assumptions and theories
Propose practical courses of action to resolve a problem
Open up new directions for future research

TipIf your research is more practical in nature and aims to simultaneously investigate an issue as you solve it, consider conducting action research instead.

Unlike quantitative or experimental research , a strong case study does not require a random or representative sample. In fact, case studies often deliberately focus on unusual, neglected, or outlying cases which may shed new light on the research problem.

Example of an outlying case studyIn the 1960s the town of Roseto, Pennsylvania was discovered to have extremely low rates of heart disease compared to the US average. It became an important case study for understanding previously neglected causes of heart disease.

However, you can also choose a more common or representative case to exemplify a particular category, experience or phenomenon.

Example of a representative case studyIn the 1920s, two sociologists used Muncie, Indiana as a case study of a typical American city that supposedly exemplified the changing culture of the US at the time.

While case studies focus more on concrete details than general theories, they should usually have some connection with theory in the field. This way the case study is not just an isolated description, but is integrated into existing knowledge about the topic. It might aim to:

Exemplify a theory by showing how it explains the case under investigation
Expand on a theory by uncovering new concepts and ideas that need to be incorporated
Challenge a theory by exploring an outlier case that doesn’t fit with established assumptions

To ensure that your analysis of the case has a solid academic grounding, you should conduct a literature review of sources related to the topic and develop a theoretical framework . This means identifying key concepts and theories to guide your analysis and interpretation.

There are many different research methods you can use to collect data on your subject. Case studies tend to focus on qualitative data using methods such as interviews , observations , and analysis of primary and secondary sources (e.g., newspaper articles, photographs, official records). Sometimes a case study will also collect quantitative data.

Example of a mixed methods case studyFor a case study of a wind farm development in a rural area, you could collect quantitative data on employment rates and business revenue, collect qualitative data on local people’s perceptions and experiences, and analyze local and national media coverage of the development.

The aim is to gain as thorough an understanding as possible of the case and its context.

In writing up the case study, you need to bring together all the relevant aspects to give as complete a picture as possible of the subject.

How you report your findings depends on the type of research you are doing. Some case studies are structured like a standard scientific paper or thesis , with separate sections or chapters for the methods , results and discussion .

Others are written in a more narrative style, aiming to explore the case from various angles and analyze its meanings and implications (for example, by using textual analysis or discourse analysis ).

In all cases, though, make sure to give contextual details about the case, connect it back to the literature and theory, and discuss how it fits into wider patterns or debates.

If you want to know more about statistics , methodology , or research bias , make sure to check out some of our other articles with explanations and examples.

Normal distribution
Degrees of freedom
Null hypothesis
Discourse analysis
Control groups
Mixed methods research
Non-probability sampling
Quantitative research
Ecological validity

Research bias

Rosenthal effect
Implicit bias
Cognitive bias
Selection bias
Negativity bias
Status quo bias

Cite this Scribbr article

If you want to cite this source, you can copy and paste the citation or click the “Cite this Scribbr article” button to automatically add the citation to our free Citation Generator.

McCombes, S. (2023, November 20). What Is a Case Study? | Definition, Examples & Methods. Scribbr. Retrieved July 10, 2024, from https://www.scribbr.com/methodology/case-study/

Is this article helpful?

Shona McCombes

Other students also liked, primary vs. secondary sources | difference & examples, what is a theoretical framework | guide to organizing, what is action research | definition & examples, what is your plagiarism score.

Click through the PLOS taxonomy to find articles in your field.

For more information about PLOS Subject Areas, click here .

Loading metrics

Open Access

Peer-reviewed

Research Article

A case study exploring associations between popular media attention of scientific research and scientific citations

Roles Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Writing – original draft, Writing – review & editing

Affiliation Department of Exercise Sciences, Brigham Young University, Provo, Utah, United States of America

Affiliation Department of Statistics, Brigham Young University, Provo, Utah, United States of America

Roles Conceptualization, Formal analysis, Investigation, Methodology, Writing – original draft, Writing – review & editing

Affiliation University Communications, Brigham Young University, Provo, Utah, United States of America

Roles Conceptualization, Investigation, Methodology, Writing – original draft, Writing – review & editing

Roles Conceptualization, Data curation, Investigation, Methodology, Writing – original draft, Writing – review & editing

Affiliation Harold B. Lee Library, Brigham Young University, Provo, Utah, United States of America

Affiliation School of Communications, Brigham Young University, Provo, Utah, United States of America

Roles Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Project administration, Writing – original draft, Writing – review & editing

* E-mail: [email protected]

P. Sage Anderson,
Aubrey R. Odom,
Hunter M. Gray,
Jordan B. Jones,
William F. Christensen,
Todd Hollingshead,
Joseph G. Hadfield,
Alyssa Evans-Pickett,
Megan Frost,

Published: July 1, 2020
https://doi.org/10.1371/journal.pone.0234912
Reader Comments

The association between mention of scientific research in popular media (e.g., the mainstream media or social media platforms) and scientific impact (e.g., citations) has yet to be fully explored. The purpose of this study was to clarify this relationship, while accounting for some other factors that likely influence scientific impact (e.g., the reputations of the scientists conducting the research and academic journal in which the research was published). To accomplish this purpose, approximately 800 peer-reviewed articles describing original research were evaluated for scientific impact, popular media attention, and reputations of the scientists/authors and publication venue. A structural equation model was produced describing the relationship between non-scientific impact (popular media) and scientific impact (citations), while accounting for author/scientist and journal reputation. The resulting model revealed a strong association between the amount of popular media attention given to a scientific research project and corresponding publication and the number of times that publication is cited in peer-reviewed scientific literature. These results indicate that (1) peer-reviewed scientific publications receiving more attention in non-scientific media are more likely to be cited than scientific publications receiving less popular media attention, and (2) the non-scientific media is associated with the scientific agenda. These results may inform scientists who increasingly use popular media to inform the general public and scientists concerning their scientific work. These results might also inform administrators of higher education and research funding mechanisms, who base decisions partly on scientific impact.

Citation: Anderson PS, Odom AR, Gray HM, Jones JB, Christensen WF, Hollingshead T, et al. (2020) A case study exploring associations between popular media attention of scientific research and scientific citations. PLoS ONE 15(7): e0234912. https://doi.org/10.1371/journal.pone.0234912

Editor: Lutz Bornmann, Max Planck Society, GERMANY

Received: November 28, 2019; Accepted: June 4, 2020; Published: July 1, 2020

Copyright: © 2020 Anderson et al. This is an open access article distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Data Availability: Data are available from Figshare (DOI: https://doi.org/10.6084/m9.figshare.12142572.v7 ).

Funding: The author(s) received no specific funding for this work.

Competing interests: The authors declare that no competing interests exist.

Introduction

Scientific research and the resulting peer-reviewed publications are highly valued in the evaluations of university faculty [ 1 ], as well as in the evaluations of a university’s commitment to research. Research productivity and impact are important factors in decisions that affect faculty hiring and pay, and allocation of ultra-competitive research funds [ 2 – 4 ]. Scientific impact (SI; herein defined generally as the amount of attention given to scientific research by scientists) is difficult to quantify, although SI is often thought to reflect research productivity and prestige. SI is often quantified via different citation counts; e.g., the number of times a scientific publication is cited in peer-reviewed literature, average number of citations for publications within a particular journal, or number of career citations for a specific researcher. Using citation counts to evaluate success of a given publication, journal, or researcher has its limitations because citation counts vary substantially between scientific disciplines [ 5 ] and researcher career stages [ 6 ], making it difficult to compare citation rates across disciplines and investigators. Additionally, a measurement of SI (as previously defined) using citation counts does not account for another important facet of scientific research: non-scientific impact (NSI; herein defined generally as the amount of attention given to scientific research by non-scientists in mainstream news outlets, online blogs, and/or social media). In some ways (as presently defined), NSI reflects the import of scientific research as perceived by members of the lay public. Scientists across various disciplines now increasingly use a wider variety of tools to disseminate scientific results to lay audiences using various media avenues [ 7 ]. Like SI, NSI is difficult to quantify. Further, the relationship between NSI and SI is unclear, although previous research has indicated a potential relationship between the mention of scientific research in popular media (e.g., mainstream news or social media) and scientific impact (e.g., citation count; [ 8 – 14 ]).

Mainstream media coverage of scientific research typically features scientific articles published in academic journals that fit the editorial focus and news values of mainstream media outlets [ 13 , 15 , 16 ]. Prior studies have described two different potential explanations for the relationship between NSI and SI: an earmark hypothesis and a publicity effect. The earmark hypothesis asserts that media outlets cover certain scientific studies because of their intrinsic value and, as a result, it predicts that the publicized studies would have garnered the same amount of SI without the benefit of media exposure [ 10 , 11 ]. The publicity effect proposes that media coverage provides an SI boost for scientific studies that they would not have received on their own [ 10 , 11 , 17 ]. Based on this idea, academic publishers and authors have engaged in systematic public relations efforts to secure media coverage [ 12 , 18 ]. In addition, public relations scholars have found empirical evidence that media coverage can influence perceptions and behavior of media consumers in a variety of different contexts [ 19 – 24 ]. While some researchers have focused upon news media coverage while studying the concept of publicity, other researchers have examined the relationship between social media and SI [ 12 , 25 , 26 ]. However, in the current digital media environment, information flows bidirectionally between traditional news outlets and social media platforms, making it difficult to study media sources in isolation [ 27 , 28 ].

The purpose of this study was to investigate potential relationships between NSI (mainstream news and social media) and SI, with an emphasis on scientific research regarding physical health and exercise. More specifically, we investigated potential relationships between (1) popular (i.e., non-scientific) media attention given to scientific research regarding physical health and exercise, and (2) the attention given by scientists to the same research ( viz , citations). We hypothesized that NSI and SI would be positively correlated; i.e., that scientists (like non-scientific consumers of popular news and social media) are more likely to think, study, and write about issues that either have received, or will yet receive, more attention in the mainstream news and social media. To account for several other factors that likely influence SI (in addition to NSI), we also attempted to quantify relationships between SI and scientific reputation of the scientist/author (AR) and academic journal (JR) in which the scientific research was published.

To accomplish the purpose of this study, 818 peer-reviewed scientific articles describing original research studies were analyzed. All articles were chosen from a single discipline so that discipline-specific metrics associated with publication data (e.g., journal impact factors and author h-index values) were comparable across articles. The year of each publication was either 2007 or 2008. Each publication appeared in one of five prominent academic journals from the Sports Sciences subject category of the Web of Science (WOS; Clarivate Analytics, Philadelphia, PA, USA) scientific citation indexing service; these journals were chosen because we thought they provided a good representation of reputable physical health and exercise journals. Three of the journals ( Medicine and Science in Sports and Exercise , The American Journal of Sports Medicine , and Journal of Applied Physiology ) were first quartile journals in 2007 and 2008. One journal was second quartile in 2007 and 2008 ( European Journal of Applied Physiology ), while one was a third and first quartile journal in 2007 and 2008, respectively ( Journal of Science and Medicine in Sport ). All original research articles published in each journal during 2007 and 2008 were analyzed, except for The Journal of Applied Physiology , which publishes substantially more articles annually than the other journals; 200 articles were randomly sampled from this journal to prevent overrepresentation of this journal. All journal articles were accessed and associated journal article characteristics analyzed between October 2017 and May 2018.

The Altmetric Attention Score (AAS) was used as one of the measures representing NSI. The AAS is a weighted count of various non-scientific mentions of the scientific research/publication, including mainstream news, online blogs, Wikipedia, and Twitter and Facebook [ 29 ]. This approach was chosen because the AAS is a practical, accepted, single count of attention garnered across the presently large [ 30 , 31 ], and still growing, spectrum of different forms of non-scientific media. The AAS was manually obtained for each original research article via the Altmetric bookmarklet, which was downloaded from the altmetric.com website; 74% of the original research articles had an Altmetric score of zero, indicating no measurable online attention. Because the AAS represents a diverse variety of non-scientific sources, it can be difficult to clearly understand the role of specific source types (e.g., social media versus newspaper mentions) within the AAS [ 32 ]. To better understand the specific influence of social media on NSI, separate from the influence of the AAS, we included social media mentions as an additional observed variable, in addition to the AAS. This variable, social media mentions, was represented by an aggregate of two of the most prominent social media platforms, Facebook and Twitter (e.g., 1 Facebook mention + 1 Twitter mention = 2 social media mentions). This information was gathered through the detailed AAS breakdown that is available for each article via the Altmetric bookmarklet.

Citation counts and several other article usage metrics were used to represent SI for each publication. Citation counts reported by both Scopus (Elsevier, Amsterdam, Netherlands) and WOS were used. Journal impact factor and subject category (Sport Sciences) rank were collected via the InCites Journal Citation reports in WOS. The field-weighted citation impact score from Scopus was also used (Orthopedics and Sports Medicine subject area). Journal impact factor, WOS subject category rank, and field-weighted citation count each represent methods designed to quantify journal quality and scientific impact; each method attempts to account for differences across scientific disciplines and publication dates. The Sports Sciences subject category (WOS) is smaller (currently 83 journals) than the Orthopedics and Sports Medicine subject area (Scopus; currently 244 journals). Additionally, counts of individual article abstract views and readers on the reference managing site Mendeley (Elsevier, Amsterdam, Netherlands) were used to help represent SI. These Mendeley values were extracted from the Mendeley website manually using a title search for each analyzed article. In almost every case, searching via the article title yielded the correct article; however, in a few cases, it was necessary to search via the lead author name which yielded the correct result. Whether by title or author search, only one corresponding article was found and recorded for each inquiry. Initially, we intended to collect Mendeley readership data using the Altmetric bookmarklet, but Mendeley readership data were not available for all articles using the bookmarklet.

Because AR and JR likely affect citation counts [ 33 , 34 ], we attempted to account for these factors in the current analysis. AR was evaluated using the WOS h-index for the lead and corresponding authors. Reputation for the lead and corresponding authors’ institution(s) were also used to help represent AR, and these were evaluated based upon research output rankings for the academic institution(s) of the lead and corresponding author at the time of publication; the Academic Ranking of World Universities (Shanghai Ranking) was used to evaluate institutional ranking, which is reputable and publicly available. JR was evaluated via the ranking of the journal within the WOS Sports Science subject category, as well as 1- and 5-year journal impact factors and journal impact factor percentiles (all collected via WOS).

After removing any publication with partially-missing data, 801 of the 818 aforementioned scientific publications remained for analysis. A sample size of 801 with 32 parameters results in a sample-to-parameter ratio of approximately 25, which is larger than necessary for estimation and evaluation of model fit [ 35 , 36 ]. To ensure that observations were optimally suited for structural equation modeling, skewed variables were transformed. A Box-Cox approach was used to find the optimal transformation toward normality [ 37 ]; to avoid computational problems associated with log(0), we used the log(x+1) transformation whenever the Box-Cox procedure selected the log transformation as optimal. Additional details concerning the transformation selected for each variable are presented in Table 1 . The structural equation modeling approach was used to consider the relationships among four latent constructs (factors): AR ( f AR ), JR ( f JR ), NSI ( f NSI ), and SI ( f SI ). Structural equation modeling is an oft used tool for characterizing complex interrelationships among variables within a network of observed or latent variables [ 38 , 39 ]. In order to identify an association between f NSI and f SI , while accounting for potential influence of the f AR and f JR , we chose to model the effects of the first three factors ( f AR , f JR , and f NSI ) on the last factor ( f SI ). As described in the Results section, we found that a latent variable model was a generally illuminating approach, succinctly characterizing the relationships between f SI and each of the other factors ( f AR , f JR , and f NSI ).

PPT PowerPoint slide
PNG larger image
TIFF original image

For each of the 13 variables, the article count, average, standard deviation (SD), median, interquartile range (IQR), and minimum and maximum values are presented. All descriptive statistics are calculated for all journals and within the distinct journal quartiles. As many variables have been transformed, a description of the transformation performed (if any) is also included.

https://doi.org/10.1371/journal.pone.0234912.t001

The structural equation model is shown graphically in Fig 1 . The latent factor f AR , is associated with institution ranking, as well as the lead and corresponding authors’ h-indices. The second latent factor ( f JR ) is the driving factor behind the observed variables of the 1- and 5-year impact factors for the journal, as well as the percentile for the journal impact factor within the exercise and wellness area (a subject category created by WOS). The third latent factor ( f NSI ) is related to AAS and social media mentions, as previously described. Finally, the factor for SI ( f SI ) is associated with the following observable variables: both Scopus and WOS citation counts, Field Weighted Citation Count, as well as counts of individual article abstract views and readers on the reference managing site Mendeley. For each variation of the structural equation model that we fit, we first considered goodness-of-fit indices to assess overall model fit including the χ 2 goodness-of-fit test, root mean square error of approximation (RMSEA) [ 40 ], standardized root mean square residual (SRMR) [ 41 ], and Bentler’s comparative fit index (CFI) [ 42 ]. When using the χ 2 test statistic to assess model fit, the probability of rejecting the proposed model increases with the number of observations, rendering the undesirable property of increasing the chance of rejecting models with reasonable fit as the sample size increases [ 43 ]. Consequently, researchers often rely on goodness-of-fit measures such as RMSEA, SRMR, and CFI to assess model adequacy. The RMSEA metric is calculated using the χ 2 test statistic and quantifies the excess lack of fit for the model. One recommended criterion is that an RMSEA value less than 0.06 represents a good fit [ 44 ]. Other researchers have suggested 0.01, 0.05, and 0.08 to indicate excellent, good, and mediocre fit, respectively [ 45 ]. The SRMR is a second absolute measure of fit that quantifies the difference between the model-predicted covariance matrix for the variables and the sample covariance matrix. An SRMR value of zero indicates a perfect fit and a value of one indicates the opposite. Hu and Bentler suggest that an SRMR value that is less than 0.08 indicates a good fit [ 46 ]. Finally, CFI quantifies the improvement in the χ 2 test statistic when comparing to a baseline model consisting of uncorrelated variables. CFI ranges from zero to one, with a value of one indicating that the chosen model has removed all of the lack of fit associated with the baseline model. Hu and Bentler recommend that CFI values greater than 0.95 indicate a good fit [ 46 ].

Unidirectional relationships are denoted by single headed arrows. Covariances between two factors are shown using double headed arrows. Factors are denoted by bolded oval shapes and observed variables are denoted by rectangles. The model indicates that there is a strong relationship between attention given in non-scientific media ( f NSI ), by the general public, and scientific literature ( f SI ), by scientists.

https://doi.org/10.1371/journal.pone.0234912.g001

Results and discussion

A structural equation model was produced to investigate interrelationships among measurable (i.e., observed) variables associated with NSI and SI, and AR and JR ( Fig 1 ). As was described in more detail in the Methods section, the adequacy of the model was assessed using a suite of goodness-of-fit statistics and corresponding accepted rules of thumb. A general consensus among the following assessments indicated that the model reasonably characterizes relationships among the measurable variables associated with NSI, SI, AR, and JR: RMSEA, SRMR, and Bentler’s CFI (CFI; χ 2 = 453.796, with p value < 0.0001; RMSEA = 0.091; SRMR = 0.057; CFI = 0.951). We considered the three goodness-of-fit metrics of CFI, RMSEA, and SRMR together as a holistic assessment of model fit; because two of the three metrics met our criterion for good fit, we determined that our model was appropriate and adequately fit the data. Descriptive statistics for all involved variables are presented in Table 1 .

The aforementioned structural equation model was fit in Mplus software [ 39 ] (Muthén & Muthén, Los Angeles, CA, USA). Standardized coefficients are reported herein for ease of interpretability. A path diagram for the model is presented in Fig 1 . Important predictive relationships exist (all p values were < 0.001) between each of the exogenous factors ( f AR , f JR , and f NSI ) and the SI factor ( f SI ). Within Fig 1 , unidirectional impacts are indicated by the arrows pointing from f AR , f JR , and f NSI , toward f SI , and also by the arrows relating these factors with their associated observed variables. The curved bi-directional arrows in Fig 1 represent covariances between factors that do not have a direct relationship with each other. The standardized factor loading estimate for NSI onto SI was approximately 0.380, which is nearly twice as large as the standardized factor loading estimate for either of the other two exogenous factors (f AR and f JR ) on SI (0.197 and 0.203, respectively). We interpret these standardized factor loading estimates to indicate that for a scientific publication, a one standard deviation increase in NSI is associated with a 0.380 standard deviation increase in SI for that same publication, holding all other considered factors constant. Similarly, a one standard deviation increase in AR would correspond to a 0.197 standard deviation increase in SI, and a one standard deviation increase in JR would correspond to a 0.203 standard deviation increase in SI, holding all other considered factors constant. By comparing the differences in magnitude between these standardized factor loading estimates, we conclude that NSI has a strong association with SI of an article. Importantly, however, we note that the R 2 value for f SI is 25.2%, meaning that only 25.2% of the variability in SI can be explained by the combination of NSI, AR, and JR.

A strong relationship was observed between each defined variable (shown in the rectangles in Fig 1 ) and its associated factor (shown in the ovals in Fig 1 ). Additionally, all factor loadings exhibited the expected direction: all were positive except for Institutional Ranking, which uses smaller values to represent institutions with better reputations. Each of these loadings had an associated p value of less than 0.001. The relative size of the factor loadings associated with a given factor indicates the relative importance of each observed variable in the definition of the factor. For example, the SI factor loads onto the Scopus and WOS (Clarivate Analytics, Philadelphia, PA, USA) citation count variables most heavily, indicating how each factor is quantifying the notion of SI. Similarly, corresponding author h-index is the most important observed variable in defining f AR , one- and five-year impact factors are the most important components of f JR , and the AAS is most important in defining f NSI . Fig 1 also indicates weak positive correlations among the three exogenous factors: corr ( f AR , f JR ) = 0.049 ( p = 0.167), corr ( f AR , f NSI ) = 0.086 ( p = 0.023), and corr ( f JR , f NSI ) = 0.072 ( p = 0.063).

In review, the purpose of this study was to determine whether non-scientific attention given to scientific research in various forms of popular media (NSI) is related to the amount of attention paid to the same research by fellow scientists, via scientific citations (SI), while accounting for some of the other factors also thought to influence SI. The present results revealed a strong positive association between NSI and SI, indicating that scientific experiments receiving more attention in non-scientific media such as mainstream news and/or social media are cited more in the peer-reviewed scientific literature. The present results demonstrate that news outlets and social media are either discussing the most scientifically impactful papers, or that increased coverage of a scientific article increases the likelihood of an article receiving scientific citations. It was also determined that author and journal reputations are valuable predictors of SI, but the effect size for NSI is roughly equivalent to the combined effect size for the two reputation factors (AR and JR). While the current model looks foremost at unidirectional effects of AR, JR, and NSI, on SI, we cannot confidently assert that these effects are causal, and we cannot speak to the chronology of the present effects which is also a shortcoming of other related previous research [ 10 , 11 , 14 , 17 , 47 ]. Specifically, the current results do not indicate that scientists, or their associated institutions, will experience greater scientific impact by enlarging their media relations staff or expanding their social media outreach. On the other hand, given the strong association between NSI and SI, this research does indicate that scientists and institutions should carefully consider the impact of popular and social media when striving to expand their influence or evaluate the influence of individual scientists. Among other benefits, a clearer understanding of the association between NSI and SI might assist scientists in effectively connecting the general public to the most impactful research.

Again, it is important to not conclude that the present results support a particular temporal sequence of NSI and SI, as has been implied by some previous researchers [ 10 , 11 , 17 ] who discussed a publicity effect of non-scientific media on SI (i.e., non-scientific media boosting subsequent SI). The present model ( Fig 1 ) does not indicate causality and temporal sequence should not be assumed. We conducted a post hoc sub-analysis, as a limited test of temporal sequence, by analyzing dates of the identified non-scientific mentions and scientific citations for 18 of the 801 present scientific publications (six publications from each of the first, second, and third quartiles of the Sports Sciences WOS subject category rank). The results of this sub-analysis are presented in Fig 2 . Generally, the parallel nature of the lines representing NSI and SI ( Fig 2 ) suggest that non-scientific mentions and scientific impact might occur simultaneously, contradicting the ideas that NSI consistently provides a subsequent boost to SI, or vice versa. Although interesting, the results of this sub-analysis represent only a small sample and are otherwise limited. For example, only aggregated data were considered. Scientific citations and media mentions were not linked for individual publications, so the parallel nature of the two lines in Fig 2 might be due to factors not related to a temporal relationship between scientific citations and media mentions. Larger and more comprehensive studies are needed to clearly understand the temporal sequence of non-scientific mentions and scientific impact for research concerning physical health and exercise, and other disciplines.

The observation that the two lines are somewhat parallel indicates no consistent temporal sequence for mentions in popular media and scientific citations; i.e., it is unclear which generally come first (popular media mentions or scientific citations).

https://doi.org/10.1371/journal.pone.0234912.g002

It is important for most scientific research to be generally accessible to a non-specialist audience. Future research should explore potential news values (e.g., significance, prominence, proximity, etc.) inherent in scholarly research that may motivate the news media and science-centric social media accounts to report on some studies while ignoring others (i.e., the earmark hypothesis). While acknowledging that not all important research will be “newsworthy,” as defined by traditional news values, a clear understanding of how producers of popular media select topics to talk and write about can help researchers learn to frame their research for consumption by members of the general society. Future research may assist scientists in knowing how to present their research in palatable ways in mainstream news and social media, making their research both more accessible to the general public as well as actionable for industries associated with the research discipline. Future related research might also help scientists better understand specific motivations and purposes for different users of social media who mention scientific research, as it is known that different social media platforms are sometimes used for different purposes (e.g., societal impact, visibility, or education [ 32 ]). Although limited in some ways, companies such as Kudos Innovations [ 48 ] now offer various ways for scientists to present their research in ways that are more friendly to the lay population.

The present results corroborate the established notion that quantification of SI is difficult. SI is complicated, with multiple dimensions, and the present finite representations of SI do not comprehensively represent this complex concept. This is substantiated by the present finding that the current model (involving NSI, AR, and JR) predicted only slightly more than a quarter of the variance in SI. Despite the complexity and potential misunderstanding of SI, it is commonly and perhaps over-confidently used to inform important decisions in academia, like decisions concerning research funding allocations, and faculty hiring and promotions. Numerous factors influence SI [ 49 ], many of which were not considered in the present analysis. Some of these other factors include but are not limited to article type (e.g., review article, short note, or book chapter) [ 50 ], publication language [ 51 ], number of listed coauthors [ 52 , 53 ], and availability of the publication (i.e., open access or traditional subscription-based journals) [ 54 ]. Even technical problems like incorrect citations within articles [ 55 , 56 ] are (unfortunately) quite common and influence citation rates; one noteworthy study in this area reported that nearly half of all citations in a sample of scientific articles were incorrect [ 55 ].

Although research concerning physical health and exercise is not the primary focus of this paper, the context of physical health and exercise facilitates some valuable discussion. Physical health and exercise are topics that receive vast attention from non-scientific sources, and the appropriateness of some of this attention may be dubious. Similar to research in other disciplines, it is important that, generally speaking, the most meaningful matters of physical health and exercise receive the most attention in non-scientific media; NSI, such as social media and other private media outlets, influences people’s choices related to health. If a research article is having a large impact on society, it probably deserves further attention from researchers. The present findings are important because there is a dearth of research concerning the relationship between SI and NSI in physical health and exercise (although we hypothesize that present research applies to other scientific disciplines). Physical health and exercise are often mentioned in popular media, including mainstream news and social media, and it is not unusual for results from scientific research to be included in these mentions. To ensure the health and safety of the general public, it is imperative to know in what ways popular media impact and scientific impact are related (if at all) for scientific research concerning physical health and exercise. If NSI and SI are unrelated for research concerning physical health and exercise, then there is reason for concern that society consumes research that is not the most important, but merely the most interesting. The idea that the general public is being offered, for consumption, research of less impact, relative to more impactful research is concerning. An example of this, from the physical health and exercise literature, is a study [ 57 ] that received immense media attention (an AAS of 729—top 5% of all research output scored by Altmetric) that was arguably undeserved: the study was a pilot study, and was explicitly described as such. While the result was intriguing, the study involved only six young healthy subjects and was not representative of a large part of the general adult American population.

In addition to the limiting factors already discussed, other limitations exist for the present study. Although we attempted to control for all variables that likely influence NSI and SI, some confounding variables were not completely controlled for, including scientific merit of and popular interest of the observed original research articles. These two confounding variables were considered at the outset of this research, yet completely accounting for these two variables was beyond our means. The establishment of expert committees to evaluate scientific merit and popular interest of each original research study presently analyzed was considered, but the cost of such committees was beyond our budgetary restraints and inherently subjective. Another factor that likely limits current relevance of the present results is our decision to analyze research articles only from the years 2007–08. Social media use has clearly increased since 2007–2008, and current relationships between NSI and SI are likely different. Major social media platforms (e.g., Facebook) were not as prominent in 2007–2008 as they are today, and research performed in 2007–2008 is less likely to appear on social media today, relative to more recent research [ 58 ]. We opted to choose two years (2007–2008) in the recent past that optimized popular media coverage on the internet while also allowing time for some potential scientific citations to accrue, because some researchers have described a risk in citation related research of extracting data before sufficient time has been given for scientific citations to accrue [ 58 ]. This all had to be balanced with an ability to find news media mentions on the internet. To find this coverage, we chose to use data collected by the Altmetric organization, which also presents some limitations. Altmetric did not begin collecting news media coverage for research articles until October 2011 (altmetric.com); thus coverage of research articles deleted by popular news sources prior to October 2011 was not included in our evaluation. Because media sources are most likely to report on recently published research articles [ 59 , 60 ] it is possible that the number of missed sources was not insignificant, and we do not know the number of undetectable media mentions. AAS is not a comprehensive measure and is limited in other ways. For example, approximately three quarters of the articles presently analyzed had AAS’s that equaled zero, while only four of the analyzed articles had Mendeley readership values of zero. Interestingly, related to Mendeley readership, the presently analyzed articles exhibited relatively good coverage: more than 99% of the articles had a non-zero Mendeley readership value, relative to previously reported averages that ranged from 82% in 2013 to 89% in 2009 [ 61 ]. This good coverage existed despite the fact that only one of the five presently analyzed journals belongs to Elsevier (Mendeley was acquired by Elsevier in 2013). Another limitation associated with the use of AAS is due to the heterogeneous nature of the AAS, which limits the ability to understand specific constituents; research aiming to more clearly understand more precise contributions to the AAS obviously is needed and requires additional resources. Another final limitation discussed herein relates to the fact that research articles for this study focused upon the discipline of physical health and exercise. The nature of relationships among media attention, author reputation, journal reputation, and scientific impact may prove to differ across disciplines; however, our study argues that intended and unintended impacts of such relationships should at least be acknowledged when evaluating the scientific impact of articles or authors associated with academic publishing.

Conclusions

In summary, the current results reveal a strong relationship between the (1) amount of attention peer-reviewed scientific research concerning physical health and activity receives through popular media and (2) amount of attention the same research receives from fellow scientists, reflected by number of citations in peer-reviewed scientific literature. The direction of this association, however, cannot be ascertained via the current results; the popular media might capably perceive the most impactful scientific research to report upon, or the popular media attention might cause an increase in subsequent scientific impact. These findings have several potential applications outlined herein. Much remains to be discovered concerning interactions between popular media, generally produced by and for non-scientists, and the scientific literature which has historically been written by and for the scientific community.

View Article
PubMed/NCBI
Google Scholar
8. Promotion of research articles to the lay press: a summary of a three-year project, Wiley-Blackwell, 2012, pp. 207–212.
19. A. Jeffrey, D. Michaelson, D.W. Stacks, 2006. Exploring the link between volume of media coverage and business outcomes. https://instituteforpr.org/wp-content/uploads/Media_Coverage_Business06.pdf .
32. Haustein S., Bowman T.D., Costas R., Interpreting Altmetrics: Viewing Acts on Social Media Through the Lens of Citation and Social Theories, in: Cassidy R.S. (Ed.), Theories of Informetrics and Scholarly Communication, De Gruyter Saur, Berlin, Boston, 2016, pp. 372–405.
35. R.B. Kline, Principles and practice of structural equation modeling, Principles and practice of structural equation modeling., Guilford Press, 1998, p. 112.
38. K.A. Bollen, Structural Equations with Latent Variables, John Wiley & Sons, Incorporated, Somerset, UNITED STATES, 1989.
39. L.K. Muthen, B. Muthen, Muthén, M. Mplus Version 8 User’s Guide, Muthen & Muthen2017.
40. J.H. Steiger, Statistically based tests for the number of common factors, the annual meeting of the Psychometric Society. Iowa City, IA. 1980 (1980). https://ci.nii.ac.jp/naid/10012870999/en/ .
41. Jöreskog K.G., LISREL VI, analysis of linear structural relationships by maximum likelihood, instrumental variables, and least squares methods, in: Sörbom D. (Ed.) Scientific Software, Inc., Mooresville, Ind.:, 1984.
42. P.M. Bentler, EQS Structural Equations Program Manual: Version 3.0, 1989.
43. A.C. Rencher, W.F. Christensen, Confirmatory Factor Analysis, Wiley 2012.
45. R.C. MacCallum, M.W. Browne, H.M. Sugawara, Power analysis and determination of sample size for covariance structure modeling, American Psychological Association, US, 1996, pp. 130–149.

Arts & Culture
Civic Engagement
Economic Development
Environment
Human Rights
Social Services
Water & Sanitation
Foundations
Nonprofits & NGOs
Social Enterprise
Collaboration
Design Thinking
Impact Investing
Measurement & Evaluation
Organizational Development
Philanthropy & Funding
Current Issue
Sponsored Supplements
Global Editions
In-Depth Series
Stanford PACS
Submission Guidelines

Case Study - Articles

An inside look at one organization ( more )

Promoting a Culture of Caring in Education

By Alison Badgett

For the past two decades, the Jed Foundation has led the fight to address the mental health crisis among American youth. Its story highlights the importance of addressing the cultural causes of the mental health crisis through systems change. | Open access to this article is made possible by the Jed Foundation

Metro Rail Comes to Hyderabad

By Ram Nidumolu , Vijaya Sunder M & Pavitra Madhira

One of India’s largest cities launched the world’s biggest public-private partnership metro rail project to construct essential public transit for its bustling metropolis. Its leaders overcame numerous hurdles by cultivating a stakeholder mindset.

The Power of Relationships to Transform Systems

By John Kania & Juanita Zerda 1

Californians for Justice has elevated the power of young people by establishing authentic relationships between them and teachers, educators, and officials. In so doing, it has remade education in the state and crafted a model for broader social change.

The School System Rebuilding Civil Society

By Noor Noman 1

The Citizens Foundation is transforming how education is delivered in Pakistan, with remarkable outcomes for the country’s underprivileged children.

Open Society Under Threat

By Paul Hockenos

After more than three decades of promoting liberal democracy, Open Society Foundations sees itself on the defensive. Can a strategic restructuring and new leadership turn the tide?

Justice for Liberia’s Forgotten War

By Clair MacDougall

Alain Werner and Hassan Bility have teamed up to pursue expat Liberians accused of horrific war crimes. They have succeeded in winning justice abroad, but can they secure justice in Liberia itself?

A Music Industry for Musicians

By Giana Eckhardt & Tom Wagner

Kobalt Music Group is challenging the dominance of the Big Three record labels by harnessing technology to pay musicians more, faster, and with greater transparency. But how far can it reform an industry built on the exploitation of its talent?

Preserving Social Purpose Amid a Global Pandemic

By Gregory C. Unruh & Fernanda Arreola

Mexico’s Pixza began as a social inclusion vehicle for homeless adults through a pizza business. Its evolution demonstrates how social entrepreneurs can leverage purpose to sustain organizations through a crisis and to reengineer business models to foster greater impact.

Waterborne Democracy for Rural India

By Puja Changoiwala 1

For more than four decades, Gram Vikas has been delivering equitable water and sanitation systems to deprived villages in rural India by training and encouraging them to take ownership of their solutions.

National Geographic Reinvents Itself

By Amanda M. Fairbanks

The National Geographic Society began as a Victorian-era institution of white gentlemen explorers dedicated to understanding the globe. To better reflect the world and thrive in the 21st century, it has diversified its leadership, transformed its internal culture, and created a media juggernaut.

SSIR.org and/or its third-party tools use cookies, which are necessary to its functioning and to our better understanding of user needs. By closing this banner, scrolling this page, clicking a link or continuing to otherwise browse this site, you agree to the use of cookies.

Games & Quizzes
History & Society
Science & Tech
Biographies
Animals & Nature
Geography & Travel
Arts & Culture
On This Day
One Good Fact
New Articles
Lifestyles & Social Issues
Philosophy & Religion
Politics, Law & Government
World History
Health & Medicine
Browse Biographies
Birds, Reptiles & Other Vertebrates
Bugs, Mollusks & Other Invertebrates
Environment
Fossils & Geologic Time
Entertainment & Pop Culture
Sports & Recreation
Visual Arts
Demystified
Image Galleries
Infographics
Top Questions
Britannica Kids
Saving Earth
Space Next 50
Student Center
Introduction

The case study creation process

Types of case studies, benefits and limitations.

When did science begin?
Where was science invented?

Blackboard inscribed with scientific formulas and calculations in physics and mathematics

Our editors will review what you’ve submitted and determine whether to revise the article.

Academia - Case Study
Verywell Mind - What is a Case Study?
Simply Psychology - Case Study Research Method in Psychology
CORE - Case study as a research method
National Center for Biotechnology Information - PubMed Central - The case study approach
BMC Journals - Evidence-Based Nursing - What is a case study?
Table Of Contents

case study , detailed description and assessment of a specific situation in the real world created for the purpose of deriving generalizations and other insights from it. A case study can be about an individual, a group of people, an organization, or an event, among other subjects.

By focusing on a specific subject in its natural setting, a case study can help improve understanding of the broader features and processes at work. Case studies are a research method used in multiple fields, including business, criminology , education , medicine and other forms of health care, anthropology , political science , psychology , and social work . Data in case studies can be both qualitative and quantitative. Unlike experiments, where researchers control and manipulate situations, case studies are considered to be “naturalistic” because subjects are studied in their natural context . ( See also natural experiment .)

The creation of a case study typically involves the following steps:

The research question to be studied is defined, informed by existing literature and previous research. Researchers should clearly define the scope of the case, and they should compile a list of evidence to be collected as well as identify the nature of insights that they expect to gain from the case study.
Once the case is identified, the research team is given access to the individual, organization, or situation being studied. Individuals are informed of risks associated with participation and must provide their consent , which may involve signing confidentiality or anonymity agreements.
Researchers then collect evidence using multiple methods, which may include qualitative techniques, such as interviews, focus groups , and direct observations, as well as quantitative methods, such as surveys, questionnaires, and data audits. The collection procedures need to be well defined to ensure the relevance and accuracy of the evidence.
The collected evidence is analyzed to come up with insights. Each data source must be reviewed carefully by itself and in the larger context of the case study so as to ensure continued relevance. At the same time, care must be taken not to force the analysis to fit (potentially preconceived) conclusions. While the eventual case study may serve as the basis for generalizations, these generalizations must be made cautiously to ensure that specific nuances are not lost in the averages.
Finally, the case study is packaged for larger groups and publication. At this stage some information may be withheld, as in business case studies, to allow readers to draw their own conclusions. In scientific fields, the completed case study needs to be a coherent whole, with all findings and statistical relationships clearly documented.

Case studies have been used as a research method across multiple fields. They are particularly popular in the fields of law, business, and employee training; they typically focus on a problem that an individual or organization is facing. The situation is presented in considerable detail, often with supporting data, to discussion participants, who are asked to make recommendations that will solve the stated problem. The business case study as a method of instruction was made popular in the 1920s by instructors at Harvard Business School who adapted an approach used at Harvard Law School in which real-world cases were used in classroom discussions. Other business and law schools started compiling case studies as teaching aids for students. In a business school case study, students are not provided with the complete list of facts pertaining to the topic and are thus forced to discuss and compare their perspectives with those of their peers to recommend solutions.

In criminology , case studies typically focus on the lives of an individual or a group of individuals. These studies can provide particularly valuable insight into the personalities and motives of individual criminals, but they may suffer from a lack of objectivity on the part of the researchers (typically because of the researchers’ biases when working with people with a criminal history), and their findings may be difficult to generalize.

In sociology , the case-study method was developed by Frédéric Le Play in France during the 19th century. This approach involves a field worker staying with a family for a period of time, gathering data on the family members’ attitudes and interactions and on their income, expenditures, and physical possessions. Similar approaches have been used in anthropology . Such studies can sometimes continue for many years.

Case studies provide insight into situations that involve a specific entity or set of circumstances. They can be beneficial in helping to explain the causal relationships between quantitative indicators in a field of study, such as what drives a company’s market share. By introducing real-world examples, they also plunge the reader into an actual, concrete situation and make the concepts real rather than theoretical. They also help people study rare situations that they might not otherwise experience.

Because case studies are in a “naturalistic” environment , they are limited in terms of research design: researchers lack control over what they are studying, which means that the results often cannot be reproduced. Also, care must be taken to stay within the bounds of the research question on which the case study is focusing. Other limitations to case studies revolve around the data collected. It may be difficult, for instance, for researchers to organize the large volume of data that can emerge from the study, and their analysis of the data must be carefully thought through to produce scientifically valid insights. The research methodology used to generate these insights is as important as the insights themselves, for the latter need to be seen in the proper context. Taken out of context, they may lead to erroneous conclusions. Like all scientific studies, case studies need to be approached objectively; personal bias or opinion may skew the research methods as well as the results. ( See also confirmation bias .)

Business case studies in particular have been criticized for approaching a problem or situation from a narrow perspective. Students are expected to come up with solutions for a problem based on the data provided. However, in real life, the situation is typically reversed: business managers face a problem and must then look for data to help them solve it.

An official website of the United States government

The .gov means it’s official. Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site.

The site is secure. The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

Publications
Account settings

Preview improvements coming to the PMC website in October 2024. Learn More or Try it out now .

Advanced Search
Journal List
J Can Chiropr Assoc
v.52(4); 2008 Dec

Guidelines to the writing of case studies

Dr. brian budgell.

* Département chiropratique, Université du Québec à Trois-Rivières, 3351, boul des Forges, Trois-Rivières, Qc, Canada G9A 5H7

An external file that holds a picture, illustration, etc.
Object name is jcca-v52-4-199f1.jpg

Dr. Brian Budgell, DC, PhD, JCCA Editorial Board

Introduction

Case studies are an invaluable record of the clinical practices of a profession. While case studies cannot provide specific guidance for the management of successive patients, they are a record of clinical interactions which help us to frame questions for more rigorously designed clinical studies. Case studies also provide valuable teaching material, demonstrating both classical and unusual presentations which may confront the practitioner. Quite obviously, since the overwhelming majority of clinical interactions occur in the field, not in teaching or research facilities, it falls to the field practitioner to record and pass on their experiences. However, field practitioners generally are not well-practised in writing for publication, and so may hesitate to embark on the task of carrying a case study to publication. These guidelines are intended to assist the relatively novice writer – practitioner or student – in efficiently navigating the relatively easy course to publication of a quality case study. Guidelines are not intended to be proscriptive, and so throughout this document we advise what authors “may” or “should” do, rather than what they “must” do. Authors may decide that the particular circumstances of their case study justify digression from our recommendations.

Additional and useful resources for chiropractic case studies include:

Waalen JK. Single subject research designs. J Can Chirop Assoc 1991; 35(2):95–97.
Gleberzon BJ. A peer-reviewer’s plea. J Can Chirop Assoc 2006; 50(2):107.
Merritt L. Case reports: an important contribution to chiropractic literature. J Can Chiropr Assoc 2007; 51(2):72–74.

Portions of these guidelines were derived from Budgell B. Writing a biomedical research paper. Tokyo: Springer Japan KK, 2008.

General Instructions

This set of guidelines provides both instructions and a template for the writing of case reports for publication. You might want to skip forward and take a quick look at the template now, as we will be using it as the basis for your own case study later on. While the guidelines and template contain much detail, your finished case study should be only 500 to 1,500 words in length. Therefore, you will need to write efficiently and avoid unnecessarily flowery language.

These guidelines for the writing of case studies are designed to be consistent with the “Uniform Requirements for Manuscripts Submitted to Biomedical Journals” referenced elsewhere in the JCCA instructions to authors.

After this brief introduction, the guidelines below will follow the headings of our template. Hence, it is possible to work section by section through the template to quickly produce a first draft of your study. To begin with, however, you must have a clear sense of the value of the study which you wish to describe. Therefore, before beginning to write the study itself, you should gather all of the materials relevant to the case – clinical notes, lab reports, x-rays etc. – and form a clear picture of the story that you wish to share with your profession. At the most superficial level, you may want to ask yourself “What is interesting about this case?” Keep your answer in mind as your write, because sometimes we become lost in our writing and forget the message that we want to convey.

Another important general rule for writing case studies is to stick to the facts. A case study should be a fairly modest description of what actually happened. Speculation about underlying mechanisms of the disease process or treatment should be restrained. Field practitioners and students are seldom well-prepared to discuss physiology or pathology. This is best left to experts in those fields. The thing of greatest value that you can provide to your colleagues is an honest record of clinical events.

Finally, remember that a case study is primarily a chronicle of a patient’s progress, not a story about chiropractic. Editorial or promotional remarks do not belong in a case study, no matter how great our enthusiasm. It is best to simply tell the story and let the outcome speak for itself. With these points in mind, let’s begin the process of writing the case study:

Title: The title page will contain the full title of the article. Remember that many people may find our article by searching on the internet. They may have to decide, just by looking at the title, whether or not they want to access the full article. A title which is vague or non-specific may not attract their attention. Thus, our title should contain the phrase “case study,” “case report” or “case series” as is appropriate to the contents. The two most common formats of titles are nominal and compound. A nominal title is a single phrase, for example “A case study of hypertension which responded to spinal manipulation.” A compound title consists of two phrases in succession, for example “Response of hypertension to spinal manipulation: a case study.” Keep in mind that titles of articles in leading journals average between 8 and 9 words in length.
Other contents for the title page should be as in the general JCCA instructions to authors. Remember that for a case study, we would not expect to have more than one or two authors. In order to be listed as an author, a person must have an intellectual stake in the writing – at the very least they must be able to explain and even defend the article. Someone who has only provided technical assistance, as valuable as that may be, may be acknowledged at the end of the article, but would not be listed as an author. Contact information – either home or institutional – should be provided for each author along with the authors’ academic qualifications. If there is more than one author, one author must be identified as the corresponding author – the person whom people should contact if they have questions or comments about the study.
Key words: Provide key words under which the article will be listed. These are the words which would be used when searching for the article using a search engine such as Medline. When practical, we should choose key words from a standard list of keywords, such as MeSH (Medical subject headings). A copy of MeSH is available in most libraries. If we can’t access a copy and we want to make sure that our keywords are included in the MeSH library, we can visit this address: http://www.ncbi.nlm.nih.gov:80/entrez/meshbrowser.cgi

A narrative abstract consists of a short version of the whole paper. There are no headings within the narrative abstract. The author simply tries to summarize the paper into a story which flows logically.

A structured abstract uses subheadings. Structured abstracts are becoming more popular for basic scientific and clinical studies, since they standardize the abstract and ensure that certain information is included. This is very useful for readers who search for articles on the internet. Often the abstract is displayed by a search engine, and on the basis of the abstract the reader will decide whether or not to download the full article (which may require payment of a fee). With a structured abstract, the reader is more likely to be given the information which they need to decide whether to go on to the full article, and so this style is encouraged. The JCCA recommends the use of structured abstracts for case studies.

Since they are summaries, both narrative and structured abstracts are easier to write once we have finished the rest of the article. We include a template for a structured abstract and encourage authors to make use of it. Our sub-headings will be:

Introduction: This consists of one or two sentences to describe the context of the case and summarize the entire article.
Case presentation: Several sentences describe the history and results of any examinations performed. The working diagnosis and management of the case are described.
Management and Outcome: Simply describe the course of the patient’s complaint. Where possible, make reference to any outcome measures which you used to objectively demonstrate how the patient’s condition evolved through the course of management.
Discussion: Synthesize the foregoing subsections and explain both correlations and apparent inconsistencies. If appropriate to the case, within one or two sentences describe the lessons to be learned.
Introduction: At the beginning of these guidelines we suggested that we need to have a clear idea of what is particularly interesting about the case we want to describe. The introduction is where we convey this to the reader. It is useful to begin by placing the study in a historical or social context. If similar cases have been reported previously, we describe them briefly. If there is something especially challenging about the diagnosis or management of the condition that we are describing, now is our chance to bring that out. Each time we refer to a previous study, we cite the reference (usually at the end of the sentence). Our introduction doesn’t need to be more than a few paragraphs long, and our objective is to have the reader understand clearly, but in a general sense, why it is useful for them to be reading about this case.

The next step is to describe the results of our clinical examination. Again, we should write in an efficient narrative style, restricting ourselves to the relevant information. It is not necessary to include every detail in our clinical notes.

If we are using a named orthopedic or neurological test, it is best to both name and describe the test (since some people may know the test by a different name). Also, we should describe the actual results, since not all readers will have the same understanding of what constitutes a “positive” or “negative” result.

X-rays or other images are only helpful if they are clear enough to be easily reproduced and if they are accompanied by a legend. Be sure that any information that might identify a patient is removed before the image is submitted.

At this point, or at the beginning of the next section, we will want to present our working diagnosis or clinical impression of the patient.

It is useful for the reader to know how long the patient was under care and how many times they were treated. Additionally, we should be as specific as possible in describing the treatment that we used. It does not help the reader to simply say that the patient received “chiropractic care.” Exactly what treatment did we use? If we used spinal manipulation, it is best to name the technique, if a common name exists, and also to describe the manipulation. Remember that our case study may be read by people who are not familiar with spinal manipulation, and, even within chiropractic circles, nomenclature for technique is not well standardized.

We may want to include the patient’s own reports of improvement or worsening. However, whenever possible we should try to use a well-validated method of measuring their improvement. For case studies, it may be possible to use data from visual analogue scales (VAS) for pain, or a journal of medication usage.

It is useful to include in this section an indication of how and why treatment finished. Did we decide to terminate care, and if so, why? Did the patient withdraw from care or did we refer them to another practitioner?

Discussion: In this section we may want to identify any questions that the case raises. It is not our duty to provide a complete physiological explanation for everything that we observed. This is usually impossible. Nor should we feel obligated to list or generate all of the possible hypotheses that might explain the course of the patient’s condition. If there is a well established item of physiology or pathology which illuminates the case, we certainly include it, but remember that we are writing what is primarily a clinical chronicle, not a basic scientific paper. Finally, we summarize the lessons learned from this case.
Acknowledgments: If someone provided assistance with the preparation of the case study, we thank them briefly. It is neither necessary nor conventional to thank the patient (although we appreciate what they have taught us). It would generally be regarded as excessive and inappropriate to thank others, such as teachers or colleagues who did not directly participate in preparation of the paper.

A popular search engine for English-language references is Medline: http://www.ncbi.nlm.nih.gov/entrez/query.fcgi

Legends: If we used any tables, figures or photographs, they should be accompanied by a succinct explanation. A good rule for graphs is that they should contain sufficient information to be generally decipherable without reference to a legend.
Tables, figures and photographs should be included at the end of the manuscript.
Permissions: If any tables, figures or photographs, or substantial quotations, have been borrowed from other publications, we must include a letter of permission from the publisher. Also, if we use any photographs which might identify a patient, we will need their written permission.

In addition, patient consent to publish the case report is also required.

Running Header:

Name, academic degrees and affiliation

Name, address and telephone number of corresponding author

Disclaimers

Statement that patient consent was obtained

Sources of financial support, if any

Key words: (limit of five)

Abstract: (maximum of 150 words)

Case Presentation
Management and Outcome

Introduction:

Provide a context for the case and describe any similar cases previously reported.

Case Presentation:

Introductory sentence: e.g. This 25 year old female office worker presented for the treatment of recurrent headaches.
Describe the essential nature of the complaint, including location, intensity and associated symptoms: e.g. Her headaches are primarily in the suboccipital region, bilaterally but worse on the right. Sometimes there is radiation towards the right temple. She describes the pain as having an intensity of up to 5 out of ten, accompanied by a feeling of tension in the back of the head. When the pain is particularly bad, she feels that her vision is blurred.
Further development of history including details of time and circumstances of onset, and the evolution of the complaint: e.g. This problem began to develop three years ago when she commenced work as a data entry clerk. Her headaches have increased in frequency in the past year, now occurring three to four days per week.
Describe relieving and aggravating factors, including responses to other treatment: e.g. The pain seems to be worse towards the end of the work day and is aggravated by stress. Aspirin provides some relieve. She has not sought any other treatment.
Include other health history, if relevant: e.g. Otherwise the patient reports that she is in good health.
Include family history, if relevant: e.g. There is no family history of headaches.
Summarize the results of examination, which might include general observation and postural analysis, orthopedic exam, neurological exam and chiropractic examination (static and motion palpation): e.g. Examination revealed an otherwise fit-looking young woman with slight anterior carriage of the head. Cervical active ranges of motion were full and painless except for some slight restriction of left lateral bending and rotation of the head to the left. These motions were accompanied by discomfort in the right side of the neck. Cervical compression of the neck in the neutral position did not create discomfort. However, compression of the neck in right rotation and extension produced some right suboccipital pain. Cranial nerve examination was normal. Upper limb motor, sensory and reflex functions were normal. With the patient in the supine position, static palpation revealed tender trigger points bilaterally in the cervical musculature and right trapezius. Motion palpation revealed restrictions of right and left rotation in the upper cervical spine, and restriction of left lateral bending in the mid to lower cervical spine. Blood pressure was 110/70. Houle’s test (holding the neck in extension and rotation for 30 seconds) did not produce nystagmus or dizziness. There were no carotid bruits.
The patient was diagnosed with cervicogenic headache due to chronic postural strain.

Management and Outcome:

Describe as specifically as possible the treatment provided, including the nature of the treatment, and the frequency and duration of care: e.g. The patient undertook a course of treatment consisting of cervical and upper thoracic spinal manipulation three times per week for two weeks. Manipulation was accompanied by trigger point therapy to the paraspinal muscles and stretching of the upper trapezius. Additionally, advice was provided concerning maintenance of proper posture at work. The patient was also instructed in the use of a cervical pillow.
If possible, refer to objective measures of the patient’s progress: e.g. The patient maintained a headache diary indicating that she had two headaches during the first week of care, and one headache the following week. Furthermore the intensity of her headaches declined throughout the course of treatment.
Describe the resolution of care: e.g. Based on the patient’s reported progress during the first two weeks of care, she received an additional two treatments in each of the subsequent two weeks. During the last week of care she experienced no headaches and reported feeling generally more energetic than before commencing care. Following a total of four weeks of care (10 treatments) she was discharged.

Discussion:

Synthesize foregoing sections: e.g. The distinction between migraine and cervicogenic headache is not always clear. However, this case demonstrates several features …

Summarize the case and any lessons learned: e.g. This case demonstrates a classical presentation of cervicogenic headache which resolved quickly with a course of spinal manipulation, supportive soft-tissue therapy and postural advice.

References: (using Vancouver style) e.g.

1 Terret AGJ. Vertebrogenic hearing deficit, the spine and spinal manipulation therapy: a search to validate the DD Palmer/Harvey Lillard experience. Chiropr J Aust 2002; 32:14–26.

Legends: (tables, figures or images are numbered according to the order in which they appear in the text.) e.g.

Figure 1: Intensity of headaches as recorded on a visual analogue scale (vertical axis) versus time (horizontal axis) during the four weeks that the patient was under care. Treatment was given on days 1, 3, 5, 8, 10, 12, 15, 18, 22 and 25. Headache frequency and intensity is seen to fall over time.

ORIGINAL RESEARCH article

What affected the vitality of high-speed rail station areas a case study of chengdu-chongqing urban agglomeration, china.

1 School of Architecture, Southwest Jiaotong University, Chengdu, China
2 College of Environment and Civil Engineering, Chengdu University of Technology, Chengdu, China

With the rapid expansion of high-speed rail (HSR), the HSR station areas are often the key development areas of the cities and the gateways to display the cities’ image. However, the problem of lack of vitality in these areas has emerged. Limited studies have quantified the vitality of HSR station areas and examined the factors influencing it. The purpose of this study is to assess the impact of various factors on the vitality of HSR station areas. To accomplish this objective, we propose a method for measuring the vitality of HSR station areas using Baidu’s real-time user density data. We demonstrate the method through the case study of 91 HSR station areas in the Chengdu-Chongqing urban agglomeration in China. We construct structural equation models using a Bayesian approach to test the effects of intercity accessibility, intracity accessibility, surrounding area density, and local socio-economic development on the vitality of HSR station areas. The results show that (1) Intracity accessibility, surrounding area density, and local socioeconomic development have significant positive effects on the vitality density of HSR station areas. Intercity accessibility has a negative effect on the vitality density of HSR station areas. (2) Surrounding area density positively influences the stability of weekday and weekend vitality in HSR station areas. Local socio-economic development negatively impacts the stability of weekend vitality in HSR station areas. (3) High-vitality HSR station areas are mostly located in Chengdu and Chongqing, both megacities. Station areas with low vitality are primarily located in small cities. This study’s findings can be used to guide the planning and decision-making of HSR station areas aimed at enhancing their vitality.

1 Introduction

As one of the most critical innovations in the railway system, high-speed rail is expanding rapidly worldwide. HSR’s high capacity and speed can facilitate rapid population movement and economic activity between cities. Not only are HSR stations important hubs for regional intercity transportation, but their surrounding areas also play a significant role in interpersonal exchanges and interactions. The areas surrounding HSR stations tend to be key development areas for cities. In particular, China is rapidly expanding its HSR network and has constructed many new HSR stations at the city fringes or periphery. The local governments believe that the HSR will stimulate development around the stations, so they have built numerous new zones around the stations in order to create a vibrant environment. Creating a vibrant HSR station area is expected to increase the area’s commercial value, improve public space efficiency, and enhance the city’s image ( Jacobs, 1992 ).

In practice, however, HSR station areas are not always vibrant. For example, many of the new HSR zones planned around HSR stations in China have remained vacant for long periods and have become HSR ghost towns ( Zhao and Ma, 2017 ; Dong L. et al., 2021 ). Additionally, several businesses near HSR stations have difficulty developing ( Facchinetti-Mannone, 2009 ; Vickerman, 2015 ). Identifying the factors that influence the vitality of HSR station areas is essential to promoting their vitality. There are several uses for investigating the factors influencing the vitality of these areas: (1) It can be used as a guide for the regeneration of HSR station areas to increase their vibrancy; (2) It can be used as a basis to determine the locations of HSR stations; (3) It can be used to provide recommendations concerning commercial projects surrounding HSR stations.

However, research on this topic is scarce at present. Most studies of urban vitality have focused on entire cities or neighbourhoods, including streets, parks, communities, metro station areas, and more ( Kang, 2020 ; Guo et al., 2021 ; Xiao et al., 2021 ). A limited number of studies have examined vitality at the local scale of HSR station areas. Wang et al. (2022a) investigated the vitality of the Yangtze River Delta’s HSR station areas and factors affecting it. However, the study quantified the vitality of HSR station areas using built environment and socioeconomic indicators. The vitality of population flow in HSR station areas and the factors affecting it were not assessed. Urban vitality is generally defined as the spatial distribution of people flows and activities ( Jacobs, 1992 ). People flow and activity data with spatial and temporal dimensions can more accurately reflect the vitality of HSR station areas. Therefore, it is essential to quantify the vitality of HSR station areas and identify the factors that influence it from the perspective of population vitality. In addition, most current studies used traditional regression models to investigate urban vitality factors ( Yu et al., 2022 ). However, this approach makes constructing complex causal relationships between multiple variables difficult. It cannot be utilised to examine the relationships between space vitality and unobservable variables, such as intercity and intracity accessibility ( Liu et al., 2021 ). Several studies have shown a significant correlation between intercity accessibility, intracity accessibility, and the development of HSR station areas ( Deng et al., 2020 ). Nevertheless, research has yet to investigate how these unobservable variables causally affect the vitality of HSR station areas.

In order to fill this research gap, this study employs structural equation modelling, which enables the analysis of complex causal relationships between multiple variables that cannot be directly observed and dependent variables ( Hoyle, 1995 ). This method has been employed in recent years to study urban spaces and their vitality ( Liu et al., 2021 ; van de Coevering et al., 2021 ; Prithviraj and Sundaram, 2023 ). The Chengdu-Chongqing agglomeration (CCUA) is employed as a case study in this study with the objective of examining the impact of intercity accessibility, intracity accessibility, surrounding area density, and local socio-economic development on population vitality in HSR station areas. The study will address three research questions: (1) How can the vitality of HSR station areas be quantified? (2) What factors affect the vitality of HSR station areas? (3) What is the relationship between the various factors affecting HSR station area vitality?

Furthermore, the following three contributions are made by this study. First, we quantified the population vitality of HSR station areas using real-time Baidu user density (RBUD) data. Second, we examined the causal relationships between the unobservable variables of intercity accessibility, intracity accessibility, surrounding area density, local socio-economic development, and the vitality of HSR station areas. Finally, we provided insights for planning and decision-making in HSR station areas to enhance vitality.

In this paper, following the introduction ( Section 1 ), Section 2 reviews the research on urban vitality and the factors affecting the development and vitality of HSR station areas. Section 3 introduces the study area, methods, and data sources. Section 4 presents the results of the analysis. Section 5 discusses the conclusions of the analysis and practical applications. Section 6 concludes the study and discusses future directions for research.

2 Literature review

2.1 high-speed rail station areas and urban vitality.

Many researchers have examined how HSR affects host cities from various perspectives, including accessibility, economic development, and labour migration ( Garmendia et al., 2012 ; Vickerman, 2018 ). However, only a few studies have been conducted at the local scale in HSR station areas ( Yin et al., 2015 ). Research in HSR station areas focused on land use ( Wenner and Thierstein, 2022 ), economic development ( Kim et al., 2018 ), transportation and land use integration ( Wei and Wang, 2022 ), quality of place ( Du J. et al., 2021 ), and planning decision-making mechanisms ( Dai, 2015 ). Few studies have been conducted on urban vitality in HSR station areas. Wang L. et al. (2022) measured the vitality of HSR station areas using several built environment and socio-economic indicators. According to their study, the vitality of HSR station areas was positively influenced by factors such as station-city connectivity and city administrative level. However, the urban vitality index used in the study was not constructed from the perspective of people flows and activities. As HSR station areas are considered to be important places for human interaction ( Bertolini, 1999 ), it is essential to conduct vitality research from this perspective.

According to Jacobs (1992) , urban vitality can be defined as the interaction between human activities and the environment. It has been demonstrated that a vibrant and high-quality area can spontaneously draw a variety of individuals to visit and engage in social activities during differing periods ( Gehl, 2011 ). Consequently, the study defines the vitality of HSR station areas through the intensity and stability of population activities within each unit of the environment.

Currently, methods for measuring population vitality can be broadly categorised as field survey methods and big data methods. Field survey methods include interviews, questionnaires, on-site observation, instrumental monitoring, etc. These methods are time-consuming, require much human support, and are more appropriate for measuring urban vitality on a small scale and for a short period ( Liu et al., 2023 ). Location-based services (LBS) data were mainly used in big data methods. There are several advantages to using this type of data. These include its large scale, large time span, ease of access, and ability to reflect spatial and temporal distribution patterns of population activities. This method is more appropriate for studies involving large geographical areas and local areas of multiple cities. The use of real-time LBS data has become increasingly popular in the study of urban vitality recently ( Kang, 2020 ; Jiang et al., 2022 ), including Tencent user density data, mobile phone signalling data, and Sina Weibo data. For instance, Liu et al. (2021) investigated Huangpu River waterfront vitality in Shanghai based on Tencent user density data and analysed the factors that influence it. Xia et al. (2022) used mobile phone signal data to evaluate Changsha’s spatial vitality. However, a study that measures the vitality of HSR station areas in multiple cities has yet to be conducted using real-time LBS data. Therefore, appropriate technological methods are needed to measure population vitality in HSR station areas.

2.2 Factors influencing the development and vitality of HSR station areas

Few studies examined the factors influencing the vitality of HSR station areas. Nevertheless, some studies have investigated factors affecting the vitality of other types of public transportation station areas ( Dong Y.-H. et al., 2021 ; Xu and Chen, 2021 ; Tu et al., 2022 ). These studies can provide insight into the selection of factors that influence the vitality of HSR station areas in the following section. For instance, Tu et al. (2022) found a significant relationship between local socio-economic development, transport facilities, the built environment, and the vitality of subway station areas. Xu and Chen (2021) also found a correlation between transport accessibility and underground space vitality in metro stations. Wang et al. (2022b) found that multiple POI types have a positive effect on population vitality in metro station areas.

In addition, there have been some studies on the effects of HSR on neighbouring areas and the development of HSR station areas. These studies mainly discussed the intercity accessibility ( Wang et al., 2013 ; Moyano et al., 2019b ; Huang and Zong, 2020 ), intracity accessibility ( Wang et al., 2013 ; Moyano et al., 2018 ; Zhao et al., 2018 ; Moyano et al., 2019a ; Moyano et al., 2019b ; Yang et al., 2019 ), the built environment of the neighbouring areas ( Du J. et al., 2021 ; Wenner and Thierstein, 2022 ), local socio-economic development ( Pol, 2003 ; Kim et al., 2018 ; Deng et al., 2020 ; Zhao et al., 2023 ) and other factors ( Sun, 2016 ; Wang et al., 2021 ) of HSR stations ( Table 1 ). According to these literatures, several factors have been found to be positively correlated with the development of HSR station areas. These factors include the level of local socio-economic development, the frequency of station services, transport connections to the city, HSR station operating times, and city administration levels ( Deng et al., 2020 ; Wang L. et al., 2022 ). A negative correlation exists between the development of HSR station areas and the distance between the station and the city center ( Deng et al., 2020 ; Wang L. et al., 2022 ). The studies serve as the basis for selecting factors influencing the vitality of HSR station areas in the later section.

Table 1 . Factors associated with the vitality of HSR station areas in theoretical and empirical studies.

Despite this, empirical research regarding how HSR station areas influence vitality remains contentious and insufficiently explored. First, according to Du Z. et al. (2021) , the frequency of train service positively correlated with nightlight brightness in HSR station areas. However, the study by Wang L. et al. (2022) did not find that frequency of train service had a significant effect on HSR station areas’ vitality. There is a need to investigate the causal relationship between train service frequency and the vitality of HSR station areas. Second, the causal relationship between intercity accessibility, intracity accessibility, surrounding area density, local socio-economic development, and the vitality of HSR station areas has not yet been fully explored. Meanwhile, the LBS data has not yet been used in studies to quantify the population vitality of the HSR station areas. Lastly, many studies have used regression models to analyse factors affecting urban vitality but have not explored the impact of multiple unobservable variables on the vitality of HSR station areas.

3 Data and methods

3.1 study area.

The study used 91 HSR station areas in the CCUA in China as a case study. The urban agglomeration is the most densely populated area in western China. There are two megacities with a population of 10 million or more in the urban agglomeration, Chengdu and Chongqing, as well as six large cities with a population of one million or more and more than 20 small and medium-sized cities ( Figure 1 ). In 2022, the urban agglomeration had a total area of 185,000 square kilometres, a population of 97 million residents, and a gross regional product of 770 million yuan, ranking fourth in China. In addition, the urban agglomeration has formed a radial HSR network structure with Chengdu and Chongqing as the core, operating 91 HSR stations.

Figure 1 . Location of the study area.

Notably, HSR station areas in the urban agglomeration are generally large and diverse in type, and spatial and temporal distributions of population activity are evident. These HSR stations consist of stations converted from old rail stations and newly built stations. There are HSR stations in the city centre and stations on the edge and periphery of cities. The cities in which they are located also have different economic and social conditions. Therefore, the case study of HSR station areas in the urban agglomeration represents the study of the vitality of HSR station areas. The study’s results can also provide a reference for the vitality-oriented regeneration of HSR station areas in other regions.

To quantify the vitality of the HSR station areas and explore the factors influencing the areas’ vitality, we defined the HSR station area as the area formed by the 1500-m road network surrounding the station from its entrance and exit. The reasons for this definition are as follows: (1) The area delineated by the extent of the road network is more precise than the circular extent delineated by previous studies ( Yang et al., 2022 ). The area of the road network excludes areas such as water and mountains, which is a better depiction of what pedestrians can access. (2) Previous studies indicated that the 1500-m road network area was acceptable for most pedestrians travelling from an HSR station to nearby destinations. Based on a survey of 2,991 passengers at HSR stations, 84.05% of respondents were willing to walk less than 20 min to reach the vicinity of the HSR station ( Lin, 2011 ). Assuming a walking speed of 4.5 km/h, the distance of the road network in 20 min would be 1,500 m (3) The 1500-m range is consistent with the range defined in other studies of HSR station areas ( Wei and Wang, 2022 ; Wenner and Thierstein, 2022 ).

3.2 Data sources

3.2.1 rbud data.

The data provide a new method for measuring population vitality in HSR station areas. The data are a type of LBS data obtained from the Baidu Huiyan interface ( https://huiyan.baidu.com/ ). The data were generated by users who used Baidu Corporation products through active access or passively when parked or moving slowly. The Baidu Corporation is the largest internet search engine company in China. It has developed many Baidu products and services, with monthly active users of the Baidu app reaching 663 million in September 2023 ( Baidu, 2023 ). The RBUD data are suitable for studying vitality at a number of HSR station areas across multiple cities because of their high quality, broad coverage, and extensive capacity. In addition, the data have gradually been used to study urban vitality and have been shown to reflect population activity patterns spatially and temporally ( Zhao et al., 2022 ; Jiao and Bao, 2023 ). This study used RBUD data every hour between 6 a.m. and 11 p.m. from 10–16 April 2023 (1 week). Of the 7 days, April 15 and 16 are weekend days, and the rest are weekdays.

3.2.2 Data on points of interest (POIs), the road network, and railway lines

The data were obtained from the Gaode Open Platform ( https://lbs.amap.com/ ) in April 2023. POI points have their name, latitude, longitude, and attribute classification information. In China, Gaode Open Platform is the leading LBS provider. POIs on the platform cover a wide range of categories, including business services and public facilities. We excluded broad categories of POIs that do not reflect the functions or facilities associated with the land, such as roadside facilities, place names and addresses, and event activities. In addition, we verified the road and railway data using the latest Google satellite imagery to ensure accuracy.

3.2.3 HSR timetable data

The data were collected from the Ctrip website ( https://trains.ctrip.com/ ) between 17 and 23 December 2022 (1 week). Ctrip.com , one of China’s most extensive online travel services, provides train timetable information that corresponds with China’s official train ticket sales website.

3.2.4 Data of other types

The population data for HSR station areas were obtained from Worldpop ( https://www.worldpop.org/ ). These data are raster data with a resolution of 100 m by 100 m. The data on feeder traffic near HSR stations were collected from the Baidu Encyclopedia ( https://baike.baidu.com/ ) and Baidu Map ( https://map.baidu.com ). Data on economic development and population for the cities served by the HSR stations were obtained from the Sichuan Statistical Yearbook and the Chongqing Statistical Yearbook for 2022.

3.3 Model construction and research hypotheses

3.3.1 theoretical model construction.

Structural equation modelling can establish, estimate, and test complex causal relationships between observable and latent variables ( Bowen and Guo, 2011 ). This study has a limited sample size, which makes it difficult to apply generalised least squares or great likelihood estimates to determine the extent to which the attributes of the HSR stations affect the vitality of their areas. Therefore, we used a structural equation model based on Bayesian estimation. In contrast to traditional algorithms, the Bayesian method of estimation relies on the Markov chain Monte Carlo method rather than the asymptotic theory for sample generation. For small sample data, Bayesian structural equation modelling would provide more reliable parameter estimation ( Rupp et al., 2004 ; Kruschke et al., 2012 ).

We constructed a structural equation model using Amos 26.0 to test the relationships between the vitality of HSR station areas and several variables, using the CCUA as the case study ( Figure 2 ). The model is composed of a measurement model as well as a structural model. In this model, weekday and weekend vitality were used as endogenous variables. Based on existing studies ( Table 1 ), we chose intercity accessibility, intracity accessibility, surrounding area density, and local socio-economic development as exogenous variables.

Figure 2 . Conceptual structural equation model.

3.3.2 Research hypotheses

The study proposed four hypotheses based on existing research. In this study, intercity accessibility is defined as the ease of access to HSR stations via the rail network. According to an existing study on the night-time lighting of HSR station areas ( Du Z. et al., 2021 ), the higher the intercity accessibility of an HSR station, the more dense and stable population activities may exist in the HSR station area. Therefore, the following hypothesis was proposed.

Hypothesis 1. The higher the intercity accessibility of an HSR station, the more vibrant the HSR station area.

Intracity accessibility refers to the ease of travelling between the HSR station and the destination within the host city. Several studies have demonstrated that the closer an HSR station is to the city centre and the better station-city transit connectivity it has, the better developed its surroundings will be ( Deng et al., 2020 ; Wang L. et al., 2022 ). Therefore, the following hypothesis was proposed.

Hypothesis 2. The higher the intracity accessibility of an HSR station, the more vibrant the HSR station area.

The density of the surrounding area is indicative of the possibility of population activity in the area adjacent to the HSR station. Previous studies have found a significant positive correlation ( Shi et al., 2023 ) and a positive causal relationship ( Li and Zhao, 2023 ) between population density and urban vitality. The density of POIs has also been shown to affect urban vitality positively ( Li et al., 2022 ; Li and Zhao, 2023 ). Furthermore, nearby POIs have also been found to be positively correlated with metro station vitality ( Wang L. et al., 2022 ). Consequently, the following hypothesis was proposed.

Hypothesis 3. The higher the density of the area surrounding an HSR station, the more vibrant the HSR station area.

Local socio-economic development refers to the social and economic development level in the area served by the HSR station. Previous studies found that the more economically developed and populated the city where the HSR station is situated, the more developed the station area ( Deng et al., 2020 ; Wang L. et al., 2022 ). Thus, the following hypothesis was proposed.

Hypothesis 4. The higher the level of local socio-economic development, the more vibrant the HSR station area.

3.3.3 Variable setting

In this study, the endogenous variable is the vitality of HSR station areas. Vitality refers to the continuity and intensity of population and activity presence over time. It can be measured by the density of population and activities per unit area, as well as the stability of their changes ( Liu et al., 2021 ; Xia et al., 2022 ). As a result, we constructed two observable variables, vitality density and vitality stability, to measure the vitality of HSR station areas. The vitality density was used to estimate the static intensity of vitality per unit area. The vitality stability was used to assess vitality dynamics over time.

Moreover, vitality density was negatively associated with vitality stability in this study. A considerable portion of vitality studies constructs vitality variables separately for weekdays and weekends because vitality is generally different on weekdays and weekends. Therefore, we separately evaluated vitality density and vitality stability on weekdays and weekends ( Table 2 ).

Table 2 . Endogenous variables measure the vitality of HSR station areas.

3.3.3.1 Vitality density

The vitality density is the population density of the HSR station area at a given time. The variable was measured by the ratio of the average number of users per hour between 6 a.m. and 11 p.m. to the area of the HSR station area. A higher value of this variable indicates a higher vitality level in the HSR station area. Table 2 presents the calculation of vitality density.

3.3.3.2 Vitality stability

Vitality stability refers to the dynamic change in population density over time. The standard deviation of user density from 6 a.m. to 11 p.m. was used to calculate this variable. The variable was normalised for the following research. The higher the value of this variable, the more stable the HSR station area’s vitality. The calculation of vitality stability is shown in Table 2 .

In this study, intercity accessibility, intracity accessibility, surrounding area density, and local socio-economic development of the HSR station are exogenous variables.

3.3.3.3 Intercity accessibility

An HSR station’s intercity accessibility refers to its ability to access other rail stations on the rail network. Therefore, we measured intercity accessibility using indicators of the number of stations within 1 hour, the number of end stations reachable by train, and transfer centrality. Table 3 shows descriptions of the indicators and their calculation methods.

Table 3 . Exogenous variables measure the attributes of HSR stations.

3.3.3.4 Intracity accessibility

Intracity accessibility refers to how easily one can travel between the HSR station and various destinations within the host city. The study by Deng et al. (2020) found that the closer an HSR station is located in the city centre, the better developed the area surrounding the station will be. This study did not use the variable distance between the HSR station and the city centre since it has a factor loading of less than 0.5. We used the number of feeder transport modes and the number of nearby public transport stations to measure intracity accessibility. Table 3 describes the indicators and the calculation method.

3.3.3.5 Surrounding area density

The density of the surrounding area refers to the density of the built environment and population in an HSR station area. We utilised two variables to assess the area’s density around HSR stations—the surrounding POI density and the surrounding population density. Table 3 describes the indicators and their calculation.

3.3.3.6 Local socio-economic development

Local socio-economic development refers to the degree of economic and social development in the areas served by the HSR station. We measured local economic and social development using the local gross domestic product (GDP) and the number of residents. A description of the indicators and their calculation method is shown in Table 3 .

Since the distributions of the variables above deviate from normality, we referred to existing studies ( Li et al., 2020 ) and used the natural logarithm of these variables for the subsequent analyses. Figure 3 shows the spatial distribution of the above-observed variables.

Figure 3 . Spatial distribution of observed variables.

4.1 Spatial and temporal distribution of vitality in HSR station areas

To compare vitality density differences between weekdays and weekends, we used the same interval classification method to categorise vitality density values in the HSR station areas into six levels. The vitality density is represented by levels 1–6 ( Figure 4 ). Red indicates high vitality density values in the HSR station areas, whereas green indicates low vitality density values.

Figure 4 . Weekday vitality density (left) and weekend vitality density (right) in the HSR station areas.

The spatial pattern of vitality density in the HSR station areas of the CCUA is similar during weekdays and weekends. HSR station areas with high vitality density values are primarily found in Chengdu and Chongqing, two megacities. Most HSR station areas with low vitality density values are in small cities, such as Qingshen County and Qianwei County. Regarding the time dimension, most HSR stations have the same level of vitality density on weekdays and weekends. A few HSR station areas differ in vitality density by one level. Among them, Jianyangnan Station and Tongnan Station have higher vitality densities on weekends. Wusheng Station and Nixi Station have higher vitality densities on weekdays. In general, vitality density in the HSR station areas varies little between the weekdays and weekends.

In addition, we classified vitality stability into six levels using the same interval classification method. There are six levels of vitality stability, ranging from low to high ( Figure 5 ). Most HSR station areas have higher vitality stability levels on weekdays and weekends. Most HSR station areas with high vitality stability are in Chengdu and Chongqing, two megacities. Most areas with low vitality stability can be found at small HSR stations, such as Qing Shen Station, Buxingjie Station, and Ande Station.

Figure 5 . Weekday vitality stability (left) and weekend vitality stability (right) in the HSR station areas.

The vitality stability of most HSR station areas is at the same level on weekdays and weekends, with very little difference between them. In some HSR station areas, vitality stability differs by one level between weekdays and weekends. Among them, the weekend stability is more robust in HSR station areas such as Wanzhoubei Station, Dianjiang Station, and Changshoubei Station. The weekday stability is more excellent in HSR station areas such as Tongnan Station, Wusheng Station, and Tuxi Station.

4.2 Reliability and validity test results

To ensure the validity of the model fit assessment and hypothesis testing, we checked the reliability and validity of the models and variables. Cronbach’s coefficient alpha (CCA) tests the internal consistency of observed variables of the same dimension in the study. CCA values greater than 0.6 are generally considered to be acceptable. Table 4 illustrates that all latent variables have a CCA greater than 0.7, and the CCA value for all the observed variables is 0.831, which indicates good internal consistency.

Table 4 . Reliability and validity tests for all variables (N = 91).

Composite reliability (CR) measures the consistency between a group of observations to assess the reliability of a latent variable. The greater the CR value, the greater the correlation between observed variables within a group. There is generally good composite reliability when the latent variable has a CR value of 0.7 or higher. In Table 4 , CR values for all latent variables greater than 0.7 indicate that internal consistency is good.

Average variance extracted (AVE) measures how well latent variables can be distinguished from each other. In order to determine this, the square root of each latent variable’s AVE was compared with its correlation coefficient with other latent variables. Moreover, the AVE value should be greater than 0.5. In Table 4 , all AVE values are greater than 0.5. According to Table 5 , the square root of each latent variable’s AVE is greater than its correlation coefficient with the other latent variables, indicating good discriminant validity.

Table 5 . Results of the discriminant validity test.

Factor loadings indicate the contribution of each observed variable in explaining the latent variable. Generally, a factor loading of greater than 0.5 is considered an acceptable value. A factor loading of greater than 0.7 indicates that the observed variable can effectively represent its corresponding latent variable. Table 4 shows that the factor loadings for all the observed variables are greater than 0.7 and significant ( p < 0.001), indicating a strong association between the observed variables and their corresponding latent variables.

4.3 Model fit results

In this study, vitality density and vitality stability have an opposite spatial relationship. A significant strong correlation was observed between weekday vitality density and weekend vitality density ( r > 0.9), as well as between weekday vitality stability and weekend vitality stability ( r > 0.9). To ensure the accuracy of the model analysis, four independent models were constructed for weekday vitality density (Model 1), weekend vitality density (Model 2), weekday vitality stability (Model 3), and weekend vitality stability (Model 4), consistent with the study of Xia et al. (2022) .

We analysed the model’s goodness of fit. The goodness of fit of a model is assessed using seven main indices ( Ao et al., 2024 ). Table 6 shows the goodness of fit indices for the Models 1 to 4. Models 1 to 4 indices are within the SEM recommended thresholds, indicating a satisfactory fit between the models and the data.

Table 6 . Model fit indices.

4.4 Path analysis results

Bayesian estimation can provide more robust model results when applied to structural equation modelling of small samples than great likelihood estimation or generalised least squares estimation ( Rupp et al., 2004 ; Kruschke et al., 2012 ). For this reason, we employed Bayesian estimation of structural equation models. The results of Model 1 were calculated based on 9,127 simulated analysis samples with a convergence statistic 1.0001. The results of Model 2 were calculated based on 9,500 simulated analysis samples, and a convergence statistic of 1.0001 was obtained. The results of Model 3 were calculated based on 9,001 simulated analysis samples, and a convergence statistic of 1.0002 was obtained. The results of Model 4 were calculated based on 9,423 simulated analysis samples, and a convergence statistic of 1.0001 was obtained.

A convergence statistic equal to 1.0000 is the most perfect convergence criterion. Generally, a convergence statistic less than or equal to 1.10 generates sufficient samples ( Gelman and Rubin, 1992 ). It can be assumed that the results of Models 1 to 4 converged to a satisfactory level (different initial values resulted in slightly different results for each run of the Bayesian structural equation model, but overall, it was very stable). The results of the analyses for Models 1 to 4 are presented in Table 7 and Figure 6 .

Table 7 . The standardised path coefficients and results of the tested hypotheses.

Figure 6 . Graphical results of Bayesian structural equation models 1 to 4.

5 Discussion

5.1 analysing the factors influencing the vitality of hsr station areas, 5.1.1 intercity accessibility.

Based on the results of Models 1 to 4 ( Table 7 ), the direct effect of intercity accessibility on weekday and weekend vitality density in the HSR station areas is −0.122 ( p < 0.05) and −0.121 ( p < 0.05), respectively. In other words, the greater the intercity accessibility of an HSR station, the lower the vitality density of the HSR station area. Moreover, there was no correlation between intercity accessibility and the vitality stability of HSR station areas ( p > 0.05).

This phenomenon may be caused by following several factors. First, HSR stations with high intercity accessibility in the study areas function as large-scale transport hubs. In order to accommodate the emergency evacuation of large passenger flows, large plazas were constructed in front of these HSR stations. Due to the enormous size of these plazas and the lack of facilities designed to attract people, people rarely stay in them when not in an emergency. Second, to facilitate the rapid evacuation of vehicles, expressways were often built around HSR stations with high intercity accessibility. These expressways and large plazas isolate the HSR stations from the surrounding urban areas, making it difficult to attract people and activities from surrounding areas. Lastly, a high-capacity interchange facility, such as a metro, is available at HSR stations with high intercity accessibility. Passenger traffic can be dispersed quickly through these high-capacity interchange facilities, resulting in passengers spending less time at HSR stations. As a result, the greater the intercity accessibility, the lower the vitality density performance of HSR station areas. The existing study also supported this finding ( Lu and Zhao, 2023 ). The existing study found that travellers frequently used other modes of transportation for quick transfers and stayed for a shorter period. In the HSR station areas, there was not a high level of vitality.

5.1.2 Intracity accessibility

Based on the model results ( Table 7 ), the direct effect of intracity accessibility on weekday and weekend vitality density of HSR station areas is 0.265 ( p < 0.001) and 0.255 ( p < 0.001), respectively. This means that the greater the accessibility to the HSR station within a city, the higher the vitality density in that area. Moreover, no correlation was found between intracity accessibility and the vitality stability of HSR station areas ( p > 0.05).

Two variables related to intracity accessibility positively impact the vitality density of HSR station areas—the number of feeder transport modes and the number of nearby public transport stations. This may be because the more feeder transportation modes and nearby public transportation stations there are, the greater the number of available feeder transportation stations. Transportation station areas serve as places for interpersonal communication and interaction that are often attractive for population activities and vibrant ( Xu and Chen, 2022 ). Furthermore, according to the traditional view of urban vitality, accessibility within a city facilitates the interaction between the urban population and the environment ( Yang et al., 2021 ). Consequently, the greater the intracity accessibility, the higher the vitality density at the HSR station areas.

5.1.3 Surrounding area density

The results of the models ( Table 7 ) show that the density of the surrounding area has the greatest influence on the weekday and weekend vitality density of the HSR station areas, with a direct effect of 0.617 ( p < 0.001) and 0.612 ( p < 0.001), respectively. The direct impact of surrounding area density on weekday and weekend vitality stability is 0.481 ( p < 0.001) and 0.523 ( p < 0.001), respectively. In other words, the higher the density of the surrounding area of the HSR stations, the higher the density and stability of vitality at the HSR station areas.

According to this study, two variables representing the density of the surrounding area positively affected the density and stability of vitality in the HSR station areas - the density of the surrounding population and the density of the surrounding POIs. Regarding the surrounding population density, this may be because areas with a high population density tend to have intensified activity. Additionally, HSR stations with a high surrounding population density tend to be less impacted by passenger traffic, which results in excellent vitality stability. As for the density of the surrounding POIs, this may be explained by the fact that denser businesses and amenities tend to attract more significant and stable populations ( Liu et al., 2019 ). Population and POI density have been shown to positively affect urban vitality in other urban areas ( Liu et al., 2021 ; Shi et al., 2023 ).

5.1.4 Local socio-economic development

According to the results of the models ( Table 7 ), local socio-economic development has a direct impact on HSR station areas’ weekday and weekend vitality density by 0.274 ( p < 0.001) and 0.294 ( p < 0.001), respectively. Put another way, the more economically and socially developed the local area is, the higher the vitality density in the HSR station area. Both Deng et al. (2020) and Wang L. et al. (2022) found similar results, concluding that local socio-economic development positively affects the development of HSR station areas. It may be because, on the one hand, the more economically and socially developed a city is, the more tax revenue the local government receives. More likely, substantial funding will be allocated to the construction and development of the HSR station area. On the other hand, a city with a higher level of economic and social development is generally more attractive in terms of population and resources. Its HSR station area is generally more vibrant and has greater development potential. Moreover, the finding is in line with a study on metro station area vitality, which found that more affluent urban areas have higher levels of metro station area vitality ( Tu et al., 2022 ).

The results of the models ( Table 7 ) indicate that local socio-economic development has a direct effect on weekend vitality stability of −0.366 ( p < 0.05). There was no correlation between the local socio-economic development and the weekday vitality stability of the HSR station areas ( p > 0.05). In other words, the higher the level of local socio-economic development, the less stable the vitality of HSR station areas on weekends. On the one hand, it may be explained by the fact that the higher the local socio-economic development level, the more passengers use the HSR during the weekend. In the meantime, a substantial portion of passengers travelling on the HSR show a relatively consistent schedule. Individuals traveling for purposes such as sightseeing or visiting relatives usually depart on Saturday mornings or middays and return on Sunday afternoons or evenings. A higher traffic flow may result during these times ( Yue et al., 2023 ), resulting in a less stable vitality throughout the day. On the other hand, a higher level of local socio-economic development generally results in more visitor-attracting amenities in an HSR station area. Particularly on weekends, people may engage in a lot of commercial, social, and other activities in this area, causing its vitality to become more unstable.

5.2 Implications for HSR station planning and decision-making

The study found that intracity accessibility, surrounding area density, and local socio-economic development positively impact the vitality density of HSR station areas. In contrast, intercity accessibility is associated with a negative impact. The density of the surrounding area positively influences the stability of vitality in the HSR station areas. Local socio-economic development has a negative effect on the stability of weekend vitality. In light of these findings, we put forth the following planning strategies.

Firstly, it is recommended that priority be given to upgrading existing stations in or near the city centre to HSR stations rather than constructing new HSR stations on the city’s edges or periphery. This is because the areas surrounding these existing stations are often more developed, with a higher population and greater facility density. The higher population and facility density near HSR stations are conducive to commercial success, generating stable and dense vitality.

Secondly, developing new zones and large commercial projects around HSR stations should be carefully considered in cities with low economic and social development. It is evident that HSR station areas in these cities are experiencing difficulties attracting people and activities. In economically developing and more populous cities, especially those with upgraded HSR stations, the areas surrounding HSR stations should consider increasing building density and developing large-scale commercial and business projects to enhance their spatial vitality.

Furthermore, the station squares of the HSR stations in the study area are typically expansive yet fail to attract a considerable number of people or activities. In addition to its use for evacuation at special times, the station square should also be considered as a means of reflecting the city’s image during normal times and be developed into a vibrant public space. The installation of leisure and rest facilities, such as seating and pavilions, in the square could be considered, as well as implementing urban cultural and commercial activities on weekends. Moreover, constructing a large road encircling the station square should be avoided, as this would result in isolation from the surrounding urban areas. Enhancing the walkability between the station square and the surrounding areas would also be beneficial.

Lastly, HSR stations can accommodate a variety of transport interchanges, such as intercity bus stations and coach stations. Moreover, commercial and service facilities can be built in the areas, which have also been shown to attract more people and activities.

6 Conclusion and limitations

6.1 conclusion.

For the purpose of exploring the factors that affect HSR station areas’ vitality, the study uses the RBUD data to present the vitality density and stability, utilising 91 HSR stations within the CCUA for analysis. Through this method, spatial and temporal characteristics of HSR station area vitality can be represented. Furthermore, the method can identify HSR station areas exhibiting insufficient vitality. As the data are relatively accessible, the method can also be employed to quantify the vitality of HSR station areas in other regions.

Furthermore, the study fills a gap in the existing research. The study employs Bayesian structural equation modelling to comprehensively examine the causal relationships between unobservable variables: intercity accessibility, intracity accessibility, surrounding area density, local socio-economic development, and the vitality of HSR station areas. Consequently, the study can be classified as an explanatory study, with the objective of exploring the causal relationships between multiple factors that influence vitality. The study reveals that intracity accessibility, surrounding area density, and local socio-economic development positively influence the vitality density of HSR station areas. Conversely, intercity accessibility negatively impacts the vitality density of HSR station areas. Moreover, the surrounding area density exerts a positive effect on the stability of vitality in HSR station areas. Conversely, local socio-economic development has a negative effect on the stability of weekend vitality. The findings can be used as a basis for the location of HSR stations as well as for the planning and decision-making of HSR station areas with the objective of increasing vitality.

6.2 Limitations and research perspectives

It should be noted that the study is not without limitations. The study selected the HSR station areas in the CCUA in China as a case study. It remains to be seen whether the conclusions of this study can be applied to HSR station areas in other city clusters or regions, given the different economic and social development conditions. Furthermore, Baidu’s real-time data on user density does not include infants, older people, and individuals not using Baidu’s mobile applications. This may result in a lack of vitality data for these groups.

Further studies should examine the spatial and temporal dynamics of different types of populations (e.g., travellers and residents) in HSR station areas, as well as the factors that influence their vitality. Moreover, future studies could employ nonlinear research methods to investigate potential causal relationships between micro-factors, such as the design and land use of HSR station areas, and their vitality.

Data availability statement

The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.

Author contributions

XY: Conceptualization, Data curation, Formal Analysis, Methodology, Software, Visualization, Writing–original draft, Writing–review and editing. YY: Conceptualization, Funding acquisition, Project administration, Supervision, Validation, Writing–review and editing. PP: Methodology, Validation, Writing–review and editing. CL: Visualization, Writing–review and editing.

The author(s) declare that financial support was received for the research, authorship, and/or publication of this article. This study is supported by the National Natural Science Foundation of China (Grant Number 52178059) and the Soft Science Project of Sichuan Provincial Science and Technology (Grant Number 24RKX0585).

Conflict of interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Publisher’s note

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

Ao, Y., Peng, P., Li, M., Li, J., Wang, Y., and Martek, I. (2024). Empowering architecture, engineering and construction students through building information modeling competitions: a deep dive into behavioral motivation. Eng. Constr. Archit. Manage . ahead-of-print (ahead-of-print). doi:10.1108/ECAM-10-2023-1076

CrossRef Full Text | Google Scholar

Baidu (2023). Baidu announces third quarter 2023 results. Available at: https://ir.baidu.com/static-files/f4006310-1a98-4d86-89a1-edfea1ef5d0e (Accessed January 28, 2024).

Google Scholar

Bertolini, L. (1999). Spatial development patterns and public transport: the application of an analytical model in The Netherlands. Plan. Pract. Res. 14 (2), 199–210. doi:10.1080/02697459915724

Bowen, N. K., and Guo, S. (2011). Structural equation modeling . New York, NY, USA: Oxford University Press .

Curtis, C., and Scheurer, J. (2010). Planning for sustainable accessibility: developing tools to aid discussion and decision-making. Prog. Plan. 74 (2), 53–106. doi:10.1016/j.progress.2010.05.001

Dai, G. (2015). The impact of policy networks on the urbanisation around high-speed railway stations in China: the case of wuhan. Environ. Plan. C-Gov. Policy 33 (3), 533–551. doi:10.1177/0263774x15594016

Deng, T., Gan, C., Perl, A., and Wang, D. (2020). What caused differential impacts on high-speed railway station area development? Evidence from global nighttime light data. Cities 97, 102568. doi:10.1016/j.cities.2019.102568

Dong, L., Du, R., Kahn, M., Ratti, C., and Zheng, S. (2021a). “Ghost cities” versus boom towns: do China's high-speed rail new towns thrive? Reg. Sci. Urban Econ. 89, 103682. doi:10.1016/j.regsciurbeco.2021.103682

Dong, Y.-H., Peng, F.-L., and Guo, T.-F. (2021b). Quantitative assessment method on urban vitality of metro-led underground space based on multi-source data: a case study of shanghai inner ring area. Tunn. Undergr. Space Technol. 116, 104108. doi:10.1016/j.tust.2021.104108

Du, J., van Wesemael, P., and Druta, O. (2021a). Place quality in high-speed rail station areas: concept definition. J. Transp. Land Use 14 (1), 1165–1186. doi:10.5198/jtlu.2021.1820

Du, Z., Wu, W., Liu, Y., Zhi, W., and Lu, W. (2021b). Evaluation of China's high-speed rail station development and nearby human activity based on nighttime light images. Int. J. Environ. Res. Public Health 18 (2), 557. doi:10.3390/ijerph18020557

PubMed Abstract | CrossRef Full Text | Google Scholar

Facchinetti-Mannone, V. (2009). “Location of high speed rail stations in French medium-size city and their mobility and territorial implications,” in City futures 09. (Madrid, Spain: city futures 09) (Spain: Madrid ).

Garmendia, M., Ribalaygua, C., and Ureña, J. M. (2012). High speed rail: implication for cities. Cities 29, S26–S31. doi:10.1016/j.cities.2012.06.005

Gehl, J. (2011). Life between buildings . Washington, DC, USA: Island Press .

Gelman, A., and Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences. Stat. Sci. 7 (4), 457–472. doi:10.1214/ss/1177011136

Guo, X., Chen, H., and Yang, X. (2021). An evaluation of street dynamic vitality and its influential factors based on multi-source big data. ISPRS Int. J. Geo-Inf. 10 (3), 143. doi:10.3390/ijgi10030143

Hoyle, R. H. (1995). Structural equation modeling: concepts, issues, and applications . Thousand Oaks, CA, USA: Sage .

Huang, Y., and Zong, H. (2020). The spatial distribution and determinants of China’s high-speed train services. Transp. Res. Pt. A-Policy Pract. 142, 56–70. doi:10.1016/j.tra.2020.10.009

Jacobs, J. (1992). The death and life of great american cities 1961 . New York, NY, USA: Vintage .

Jiang, Y., Han, Y., Liu, M., and Ye, Y. (2022). Street vitality and built environment features: a data-informed approach from fourteen Chinese cities. Sustain. Cities Soc. 79, 103724. doi:10.1016/j.scs.2022.103724

Jiao, H., and Bao, L. (2023). Optimization path of carbon offsetting in negative urban spaces under dual carbon goals. J. Comput. Methods Sci. Eng. 23 (6), 3055–3069. doi:10.3233/jcm-226997

Kang, C.-D. (2020). Effects of the human and built environment on neighborhood vitality: evidence from seoul, korea, using mobile phone data. J. Urban Plann. Dev. 146 (4), 05020024. doi:10.1061/(ASCE)UP.1943-5444.0000620

Kim, H., Sultana, S., and Weber, J. (2018). A geographic assessment of the economic development impact of Korean high-speed rail stations. Transp. Policy 66, 127–137. doi:10.1016/j.tranpol.2018.02.008

Kruschke, J. K., Aguinis, H., and Joo, H. (2012). The time has come:Bayesian methods for data analysis in the organizational sciences. Organ Res. Methods 15 (4), 722–752. doi:10.1177/1094428112457829

Li, J., Auchincloss, A. H., Yang, Y., Rodriguez, D. A., and Sanchez, B. N. (2020). Neighborhood characteristics and transport walking: exploring multiple pathways of influence using a structural equation modeling approach. J. Transp. Geogr. 85, 102703. doi:10.1016/j.jtrangeo.2020.102703

Li, Q., Cui, C., Liu, F., Wu, Q., Run, Y., and Han, Z. (2022). Multidimensional urban vitality on streets: spatial patterns and influence factor identification using multisource urban data. ISPRS Int. J. Geo-Inf. 11 (1), 2. doi:10.3390/ijgi11010002

Li, Z., and Zhao, G. (2023). Revealing the spatio-temporal heterogeneity of the association between the built environment and urban vitality in shenzhen. ISPRS Int. J. Geo-Inf. 12 (10), 433. doi:10.3390/ijgi12100433

Lin, C. (2011). Research of impact factors of high-speed railways hub area development in China. Urban Plann.Int. 26 (06), 72–77.

Liu, S., Ge, J., Ye, X., Wu, C., and Bai, M. (2023). Urban vitality assessment at the neighborhood scale with geo-data: a review toward implementation. J. Geog. Sci. 33 (7), 1482–1504. doi:10.1007/s11442-023-2139-1

Liu, S., Lai, S.-Q., Liu, C., and Jiang, L. (2021). What influenced the vitality of the waterfront open space? A case study of huangpu river in shanghai, China. Cities 114, 103197. doi:10.1016/j.cities.2021.103197

Liu, S., Zhang, L., and Long, Y. (2019). Urban vitality area identification and pattern analysis from the perspective of time and space fusion. Sustainability 11 (15), 4032. doi:10.3390/su11154032

Lu, Y., and Zhao, Z. (2023). On the spatial development characteristics and optimization strategies of high-speed rail station area in northeast China. Low. Temp. Archit. Technol. 45 (02), 1–6. doi:10.13905/j.cnki.dwjz.2023.2.001

Moyano, A., Coronado, J. M., Ruiz, R., and Romero, V. (2019a). Station avenue: high-speed rail’s missing link. Assessing pedestrian city-station routes for edge stations in Spanish small cities. J. Hous. Built Environ. 34, 175–193. doi:10.1007/s10901-018-9621-6

Moyano, A., Moya-Gómez, B., and Gutiérrez, J. (2018). Access and egress times to high-speed rail stations: a spatiotemporal accessibility analysis. J. Transp. Geogr. 73, 84–93. doi:10.1016/j.jtrangeo.2018.10.010

Moyano, A., Rivas, A., and Coronado, J. M. (2019b). Business and tourism high-speed rail same-day trips: factors influencing the efficiency of high-speed rail links for Spanish cities. Eur. Plan. Stud. 27 (3), 533–554. doi:10.1080/09654313.2018.1562657

Pol, P. M. (2003). “The economic impact of the high-speed train on urban regions,” in 43rd congress of the European regional science association: "peripheries, centres, and spatial development in the new europe (Belgium: Louvain-la-Neuve ).

Prithviraj, D., and Sundaram, L. (2023). Exploring the walkability of senior citizens in a densely populated neighborhood of Chennai, India—a structural equation modeling approach. Sustainability 15 (18), 13868. doi:10.3390/su151813868

Rupp, A. A., Dey, D. K., and Zumbo, B. D. (2004). To bayes or not to bayes, from whether to when: applications of bayesian methodology to modeling. Struct. Equ. Model. A Multidiscip. J. 11 (3), 424–451. doi:10.1207/s15328007sem1103_7

Shi, Y., Zheng, J., and Pei, X. (2023). Measurement method and influencing mechanism of urban subdistrict vitality in shanghai based on multisource data. Remote Sens. 15 (4), 932. doi:10.3390/rs15040932

Sun, H. (2016). Study on the correlation between the hierarchical urban system and high-speed railway network planning in China. Front. Archit. Res. 5 (3), 301–318. doi:10.1016/j.foar.2016.04.003

Tu, W., Zhu, T., Zhong, C., Zhang, X., Xu, Y., and Li, Q. (2022). Exploring metro vibrancy and its relationship with built environment: a cross-city comparison using multi-source urban data. Geo-spatial Inf. Sci. 25 (2), 182–196. doi:10.1080/10095020.2021.1996212

van de Coevering, P., Maat, K., and van Wee, B. (2021). Causes and effects between attitudes, the built environment and car kilometres: a longitudinal analysis. J. Transp. Geogr. 91, 102982. doi:10.1016/j.jtrangeo.2021.102982

Vickerman, R. (2015). High-speed rail and regional development: the case of intermediate stations. J. Transp. Geogr. 42, 157–165. doi:10.1016/j.jtrangeo.2014.06.008

Vickerman, R. (2018). Can high-speed rail have a transformative effect on the economy? Transp. Policy 62, 31–37. doi:10.1016/j.tranpol.2017.03.008

Wang, D., Dewancker, B., Duan, Y., and Zhao, M. (2022a). Exploring spatial features of population activities and functional facilities in rail transit station realm based on real-time positioning data: a case of xi’an metro line 2. ISPRS Int. J. Geo-Inf 11, 485. doi:10.3390/ijgi11090485

Wang, D., Wei, Y. D., and Deng, T. (2021). Transportation development, spatiotemporal convergence, and urban land use: study of the opening of high-speed rails in the yangtze river delta, China. J. Urban Plann. Dev. 147 (3), 05021023. doi:10.1061/(asce)up.1943-5444.0000732

Wang, D., Xu, Y., and Zhao, M. (2022b). Spatial differentiation and influence mechanism of the connection-distribution performance of urban high-speed railway hub in the yangtze river economic belt. J. Geog. Sci. 32 (12), 2475–2502. doi:10.1007/s11442-022-2057-7

Wang, J. J., Xu, J., and He, J. (2013). Spatial impacts of high-speed railways in China: a total-travel-time approach. Environ. Plan. A 45 (9), 2261–2280. doi:10.1068/a45289

Wang, L., and Duan, X. (2018). High-speed rail network development and winner and loser cities in megaregions: the case study of yangtze river delta, China. Cities 83, 71–82. doi:10.1016/j.cities.2018.06.010

Wang, L., Zheng, W., He, S., and Wei, S. (2022c). Assessing urban vitality and its determinants in high-speed rail station areas in the yangtze river delta, China. J. Transp. Land Use 15 (1), 333–354. doi:10.5198/jtlu.2022.2010

Wei, S., and Wang, L. (2022). Classifying high-speed rail stations in the yangtze river delta, China: the node-place modelling approach. Appl. Spat. Anal. Policy 16 (2), 625–646. doi:10.1007/s12061-022-09492-w

Wenner, F., and Thierstein, A. (2022). High speed rail as urban generator? An analysis of land use change around european stations. Eur. Plan. Stud. 30 (2), 227–250. doi:10.1080/09654313.2021.1946485

Xia, X., Zhang, Y., Zhang, Y., and Rao, T. (2022). The spatial pattern and influence mechanism of urban vitality: a case study of changsha, China. Front. Environ. Sci. 10, 942577. doi:10.3389/fenvs.2022.942577

Xiao, L., Lo, S., Liu, J., Zhou, J., and Li, Q. (2021). Nonlinear and synergistic effects of tod on urban vibrancy: applying local explanations for gradient boosting decision tree. Sustain. Cities Soc. 72, 103063. doi:10.1016/j.scs.2021.103063

Xu, Y., and Chen, X. (2021). Quantitative analysis of spatial vitality and spatial characteristics of urban underground space (uus) in metro area. Tunn. Undergr. Space Technol. 111, 103875. doi:10.1016/j.tust.2021.103875

Xu, Y., and Chen, X. (2022). The spatial vitality and spatial environments of urban underground space (uus) in metro area based on the spatiotemporal analysis. Tunn. Undergr. Space Technol. 123, 104401. doi:10.1016/j.tust.2022.104401

Yang, H., Dijst, M., Feng, J., and Ettema, D. (2019). Mode choice in access and egress stages of high-speed railway travelers in China. J. Transp. Land Use 12 (1), 701–721. doi:10.5198/jtlu.2019.1420

Yang, X., Yang, Y., and Zhou, R. (2022). Research progress of the node-place model abroad and its enlightenments: applications, extensions and systematic development. Urban Plann.Int. , 1–17. doi:10.19830/j.upi.2022.013

Yang, Y., Ma, Y., and Jiao, H. (2021). Exploring the correlation between block vitality and block environment based on multisource big data: taking wuhan city as an example. Land 10 (9), 984. doi:10.3390/land10090984

Yin, M., Bertolini, L., and Duan, J. (2015). The effects of the high-speed railway on urban development: international experience and potential implications for China. Prog. Plan. 98, 1–52. doi:10.1016/j.progress.2013.11.001

Yu, B., Cui, X., Liu, R., Luo, P., Tian, F., and Yang, T. (2022). Intergenerational differences in the urban vibrancy of tod: impacts of the built environment on the activities of different age groups. Front. Public Health 10, 994835. doi:10.3389/fpubh.2022.994835

Yue, Y., Chen, J., Feng, T., Wang, W., Wang, C., and Ma, X. (2023). New classification scheme and evolution characteristics analysis of high-speed railway stations using large-scale mobile phone data: a case study in jiangsu, China. J. Transp. Eng. Pt A-Syst. 149 (11), 04023108. doi:10.1061/jtepbs.Teeng-7855

Zhao, C., Bai, Y., and Guo, D. (2023). How does the opening of China's high-speed rail affect the spatial mismatch of haze pollution and economic growth? Environ. Sci. Pollut. Res. Int. 30 (38), 88387–88405. doi:10.1007/s11356-023-28525-6

Zhao, L., Tang, X., Xing, X., and Cai, C. (2022). Big data analysis of park and green space serviceability for elderly population--case study of core area of beijing. Sens. Mater. 34, 4369–4380. doi:10.18494/SAM4127

Zhao, S., and Ma, D. (2017). Ghost city phenomenon along China's high-speed railway grid. Int. J. Sustain. Soc. 9 (3), 210–225. doi:10.1504/ijssoc.2017.088307

Zhao, S., Wu, N., and Wang, X. (2018). Impact of feeder accessibility on high-speed rail share: wuhan–guangzhou corridor, China. J. Urban Plann. Dev. 144 (4), 04018029. doi:10.1061/(ASCE)UP.1943-5444.0000475

Keywords: vibrancy, station area, high-speed rail, environmental impact, big data, urban planning

Citation: Yang X, Yu Y, Peng P and Liu C (2024) What affected the vitality of high-speed rail station areas? A case study of Chengdu-Chongqing urban agglomeration, China. Front. Environ. Sci. 12:1401310. doi: 10.3389/fenvs.2024.1401310

Received: 15 March 2024; Accepted: 21 June 2024; Published: 11 July 2024.

Reviewed by:

Copyright © 2024 Yang, Yu, Peng and Liu. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

*Correspondence: Yang Yu, [email protected]

Disclaimer: All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article or claim that may be made by its manufacturer is not guaranteed or endorsed by the publisher.

Open access
Published: 27 June 2011

The case study approach

Sarah Crowe 1 ,
Kathrin Cresswell 2 ,
Ann Robertson 2 ,
Guro Huby 3 ,
Anthony Avery 1 &
Aziz Sheikh 2

BMC Medical Research Methodology volume 11 , Article number: 100 ( 2011 ) Cite this article

789k Accesses

40 Altmetric

Metrics details

The case study approach allows in-depth, multi-faceted explorations of complex issues in their real-life settings. The value of the case study approach is well recognised in the fields of business, law and policy, but somewhat less so in health services research. Based on our experiences of conducting several health-related case studies, we reflect on the different types of case study design, the specific research questions this approach can help answer, the data sources that tend to be used, and the particular advantages and disadvantages of employing this methodological approach. The paper concludes with key pointers to aid those designing and appraising proposals for conducting case study research, and a checklist to help readers assess the quality of case study reports.

Peer Review reports

Introduction

The case study approach is particularly useful to employ when there is a need to obtain an in-depth appreciation of an issue, event or phenomenon of interest, in its natural real-life context. Our aim in writing this piece is to provide insights into when to consider employing this approach and an overview of key methodological considerations in relation to the design, planning, analysis, interpretation and reporting of case studies.

The illustrative 'grand round', 'case report' and 'case series' have a long tradition in clinical practice and research. Presenting detailed critiques, typically of one or more patients, aims to provide insights into aspects of the clinical case and, in doing so, illustrate broader lessons that may be learnt. In research, the conceptually-related case study approach can be used, for example, to describe in detail a patient's episode of care, explore professional attitudes to and experiences of a new policy initiative or service development or more generally to 'investigate contemporary phenomena within its real-life context' [ 1 ]. Based on our experiences of conducting a range of case studies, we reflect on when to consider using this approach, discuss the key steps involved and illustrate, with examples, some of the practical challenges of attaining an in-depth understanding of a 'case' as an integrated whole. In keeping with previously published work, we acknowledge the importance of theory to underpin the design, selection, conduct and interpretation of case studies[ 2 ]. In so doing, we make passing reference to the different epistemological approaches used in case study research by key theoreticians and methodologists in this field of enquiry.

This paper is structured around the following main questions: What is a case study? What are case studies used for? How are case studies conducted? What are the potential pitfalls and how can these be avoided? We draw in particular on four of our own recently published examples of case studies (see Tables 1 , 2 , 3 and 4 ) and those of others to illustrate our discussion[ 3 – 7 ].

What is a case study?

A case study is a research approach that is used to generate an in-depth, multi-faceted understanding of a complex issue in its real-life context. It is an established research design that is used extensively in a wide variety of disciplines, particularly in the social sciences. A case study can be defined in a variety of ways (Table 5 ), the central tenet being the need to explore an event or phenomenon in depth and in its natural context. It is for this reason sometimes referred to as a "naturalistic" design; this is in contrast to an "experimental" design (such as a randomised controlled trial) in which the investigator seeks to exert control over and manipulate the variable(s) of interest.

Stake's work has been particularly influential in defining the case study approach to scientific enquiry. He has helpfully characterised three main types of case study: intrinsic , instrumental and collective [ 8 ]. An intrinsic case study is typically undertaken to learn about a unique phenomenon. The researcher should define the uniqueness of the phenomenon, which distinguishes it from all others. In contrast, the instrumental case study uses a particular case (some of which may be better than others) to gain a broader appreciation of an issue or phenomenon. The collective case study involves studying multiple cases simultaneously or sequentially in an attempt to generate a still broader appreciation of a particular issue.

These are however not necessarily mutually exclusive categories. In the first of our examples (Table 1 ), we undertook an intrinsic case study to investigate the issue of recruitment of minority ethnic people into the specific context of asthma research studies, but it developed into a instrumental case study through seeking to understand the issue of recruitment of these marginalised populations more generally, generating a number of the findings that are potentially transferable to other disease contexts[ 3 ]. In contrast, the other three examples (see Tables 2 , 3 and 4 ) employed collective case study designs to study the introduction of workforce reconfiguration in primary care, the implementation of electronic health records into hospitals, and to understand the ways in which healthcare students learn about patient safety considerations[ 4 – 6 ]. Although our study focusing on the introduction of General Practitioners with Specialist Interests (Table 2 ) was explicitly collective in design (four contrasting primary care organisations were studied), is was also instrumental in that this particular professional group was studied as an exemplar of the more general phenomenon of workforce redesign[ 4 ].

What are case studies used for?

According to Yin, case studies can be used to explain, describe or explore events or phenomena in the everyday contexts in which they occur[ 1 ]. These can, for example, help to understand and explain causal links and pathways resulting from a new policy initiative or service development (see Tables 2 and 3 , for example)[ 1 ]. In contrast to experimental designs, which seek to test a specific hypothesis through deliberately manipulating the environment (like, for example, in a randomised controlled trial giving a new drug to randomly selected individuals and then comparing outcomes with controls),[ 9 ] the case study approach lends itself well to capturing information on more explanatory ' how ', 'what' and ' why ' questions, such as ' how is the intervention being implemented and received on the ground?'. The case study approach can offer additional insights into what gaps exist in its delivery or why one implementation strategy might be chosen over another. This in turn can help develop or refine theory, as shown in our study of the teaching of patient safety in undergraduate curricula (Table 4 )[ 6 , 10 ]. Key questions to consider when selecting the most appropriate study design are whether it is desirable or indeed possible to undertake a formal experimental investigation in which individuals and/or organisations are allocated to an intervention or control arm? Or whether the wish is to obtain a more naturalistic understanding of an issue? The former is ideally studied using a controlled experimental design, whereas the latter is more appropriately studied using a case study design.

Case studies may be approached in different ways depending on the epistemological standpoint of the researcher, that is, whether they take a critical (questioning one's own and others' assumptions), interpretivist (trying to understand individual and shared social meanings) or positivist approach (orientating towards the criteria of natural sciences, such as focusing on generalisability considerations) (Table 6 ). Whilst such a schema can be conceptually helpful, it may be appropriate to draw on more than one approach in any case study, particularly in the context of conducting health services research. Doolin has, for example, noted that in the context of undertaking interpretative case studies, researchers can usefully draw on a critical, reflective perspective which seeks to take into account the wider social and political environment that has shaped the case[ 11 ].

How are case studies conducted?

Here, we focus on the main stages of research activity when planning and undertaking a case study; the crucial stages are: defining the case; selecting the case(s); collecting and analysing the data; interpreting data; and reporting the findings.

Defining the case

Carefully formulated research question(s), informed by the existing literature and a prior appreciation of the theoretical issues and setting(s), are all important in appropriately and succinctly defining the case[ 8 , 12 ]. Crucially, each case should have a pre-defined boundary which clarifies the nature and time period covered by the case study (i.e. its scope, beginning and end), the relevant social group, organisation or geographical area of interest to the investigator, the types of evidence to be collected, and the priorities for data collection and analysis (see Table 7 )[ 1 ]. A theory driven approach to defining the case may help generate knowledge that is potentially transferable to a range of clinical contexts and behaviours; using theory is also likely to result in a more informed appreciation of, for example, how and why interventions have succeeded or failed[ 13 ].

For example, in our evaluation of the introduction of electronic health records in English hospitals (Table 3 ), we defined our cases as the NHS Trusts that were receiving the new technology[ 5 ]. Our focus was on how the technology was being implemented. However, if the primary research interest had been on the social and organisational dimensions of implementation, we might have defined our case differently as a grouping of healthcare professionals (e.g. doctors and/or nurses). The precise beginning and end of the case may however prove difficult to define. Pursuing this same example, when does the process of implementation and adoption of an electronic health record system really begin or end? Such judgements will inevitably be influenced by a range of factors, including the research question, theory of interest, the scope and richness of the gathered data and the resources available to the research team.

Selecting the case(s)

The decision on how to select the case(s) to study is a very important one that merits some reflection. In an intrinsic case study, the case is selected on its own merits[ 8 ]. The case is selected not because it is representative of other cases, but because of its uniqueness, which is of genuine interest to the researchers. This was, for example, the case in our study of the recruitment of minority ethnic participants into asthma research (Table 1 ) as our earlier work had demonstrated the marginalisation of minority ethnic people with asthma, despite evidence of disproportionate asthma morbidity[ 14 , 15 ]. In another example of an intrinsic case study, Hellstrom et al.[ 16 ] studied an elderly married couple living with dementia to explore how dementia had impacted on their understanding of home, their everyday life and their relationships.

For an instrumental case study, selecting a "typical" case can work well[ 8 ]. In contrast to the intrinsic case study, the particular case which is chosen is of less importance than selecting a case that allows the researcher to investigate an issue or phenomenon. For example, in order to gain an understanding of doctors' responses to health policy initiatives, Som undertook an instrumental case study interviewing clinicians who had a range of responsibilities for clinical governance in one NHS acute hospital trust[ 17 ]. Sampling a "deviant" or "atypical" case may however prove even more informative, potentially enabling the researcher to identify causal processes, generate hypotheses and develop theory.

In collective or multiple case studies, a number of cases are carefully selected. This offers the advantage of allowing comparisons to be made across several cases and/or replication. Choosing a "typical" case may enable the findings to be generalised to theory (i.e. analytical generalisation) or to test theory by replicating the findings in a second or even a third case (i.e. replication logic)[ 1 ]. Yin suggests two or three literal replications (i.e. predicting similar results) if the theory is straightforward and five or more if the theory is more subtle. However, critics might argue that selecting 'cases' in this way is insufficiently reflexive and ill-suited to the complexities of contemporary healthcare organisations.

The selected case study site(s) should allow the research team access to the group of individuals, the organisation, the processes or whatever else constitutes the chosen unit of analysis for the study. Access is therefore a central consideration; the researcher needs to come to know the case study site(s) well and to work cooperatively with them. Selected cases need to be not only interesting but also hospitable to the inquiry [ 8 ] if they are to be informative and answer the research question(s). Case study sites may also be pre-selected for the researcher, with decisions being influenced by key stakeholders. For example, our selection of case study sites in the evaluation of the implementation and adoption of electronic health record systems (see Table 3 ) was heavily influenced by NHS Connecting for Health, the government agency that was responsible for overseeing the National Programme for Information Technology (NPfIT)[ 5 ]. This prominent stakeholder had already selected the NHS sites (through a competitive bidding process) to be early adopters of the electronic health record systems and had negotiated contracts that detailed the deployment timelines.

It is also important to consider in advance the likely burden and risks associated with participation for those who (or the site(s) which) comprise the case study. Of particular importance is the obligation for the researcher to think through the ethical implications of the study (e.g. the risk of inadvertently breaching anonymity or confidentiality) and to ensure that potential participants/participating sites are provided with sufficient information to make an informed choice about joining the study. The outcome of providing this information might be that the emotive burden associated with participation, or the organisational disruption associated with supporting the fieldwork, is considered so high that the individuals or sites decide against participation.

In our example of evaluating implementations of electronic health record systems, given the restricted number of early adopter sites available to us, we sought purposively to select a diverse range of implementation cases among those that were available[ 5 ]. We chose a mixture of teaching, non-teaching and Foundation Trust hospitals, and examples of each of the three electronic health record systems procured centrally by the NPfIT. At one recruited site, it quickly became apparent that access was problematic because of competing demands on that organisation. Recognising the importance of full access and co-operative working for generating rich data, the research team decided not to pursue work at that site and instead to focus on other recruited sites.

Collecting the data

In order to develop a thorough understanding of the case, the case study approach usually involves the collection of multiple sources of evidence, using a range of quantitative (e.g. questionnaires, audits and analysis of routinely collected healthcare data) and more commonly qualitative techniques (e.g. interviews, focus groups and observations). The use of multiple sources of data (data triangulation) has been advocated as a way of increasing the internal validity of a study (i.e. the extent to which the method is appropriate to answer the research question)[ 8 , 18 – 21 ]. An underlying assumption is that data collected in different ways should lead to similar conclusions, and approaching the same issue from different angles can help develop a holistic picture of the phenomenon (Table 2 )[ 4 ].

Brazier and colleagues used a mixed-methods case study approach to investigate the impact of a cancer care programme[ 22 ]. Here, quantitative measures were collected with questionnaires before, and five months after, the start of the intervention which did not yield any statistically significant results. Qualitative interviews with patients however helped provide an insight into potentially beneficial process-related aspects of the programme, such as greater, perceived patient involvement in care. The authors reported how this case study approach provided a number of contextual factors likely to influence the effectiveness of the intervention and which were not likely to have been obtained from quantitative methods alone.

In collective or multiple case studies, data collection needs to be flexible enough to allow a detailed description of each individual case to be developed (e.g. the nature of different cancer care programmes), before considering the emerging similarities and differences in cross-case comparisons (e.g. to explore why one programme is more effective than another). It is important that data sources from different cases are, where possible, broadly comparable for this purpose even though they may vary in nature and depth.

Analysing, interpreting and reporting case studies

Making sense and offering a coherent interpretation of the typically disparate sources of data (whether qualitative alone or together with quantitative) is far from straightforward. Repeated reviewing and sorting of the voluminous and detail-rich data are integral to the process of analysis. In collective case studies, it is helpful to analyse data relating to the individual component cases first, before making comparisons across cases. Attention needs to be paid to variations within each case and, where relevant, the relationship between different causes, effects and outcomes[ 23 ]. Data will need to be organised and coded to allow the key issues, both derived from the literature and emerging from the dataset, to be easily retrieved at a later stage. An initial coding frame can help capture these issues and can be applied systematically to the whole dataset with the aid of a qualitative data analysis software package.

The Framework approach is a practical approach, comprising of five stages (familiarisation; identifying a thematic framework; indexing; charting; mapping and interpretation) , to managing and analysing large datasets particularly if time is limited, as was the case in our study of recruitment of South Asians into asthma research (Table 1 )[ 3 , 24 ]. Theoretical frameworks may also play an important role in integrating different sources of data and examining emerging themes. For example, we drew on a socio-technical framework to help explain the connections between different elements - technology; people; and the organisational settings within which they worked - in our study of the introduction of electronic health record systems (Table 3 )[ 5 ]. Our study of patient safety in undergraduate curricula drew on an evaluation-based approach to design and analysis, which emphasised the importance of the academic, organisational and practice contexts through which students learn (Table 4 )[ 6 ].

Case study findings can have implications both for theory development and theory testing. They may establish, strengthen or weaken historical explanations of a case and, in certain circumstances, allow theoretical (as opposed to statistical) generalisation beyond the particular cases studied[ 12 ]. These theoretical lenses should not, however, constitute a strait-jacket and the cases should not be "forced to fit" the particular theoretical framework that is being employed.

When reporting findings, it is important to provide the reader with enough contextual information to understand the processes that were followed and how the conclusions were reached. In a collective case study, researchers may choose to present the findings from individual cases separately before amalgamating across cases. Care must be taken to ensure the anonymity of both case sites and individual participants (if agreed in advance) by allocating appropriate codes or withholding descriptors. In the example given in Table 3 , we decided against providing detailed information on the NHS sites and individual participants in order to avoid the risk of inadvertent disclosure of identities[ 5 , 25 ].

What are the potential pitfalls and how can these be avoided?

The case study approach is, as with all research, not without its limitations. When investigating the formal and informal ways undergraduate students learn about patient safety (Table 4 ), for example, we rapidly accumulated a large quantity of data. The volume of data, together with the time restrictions in place, impacted on the depth of analysis that was possible within the available resources. This highlights a more general point of the importance of avoiding the temptation to collect as much data as possible; adequate time also needs to be set aside for data analysis and interpretation of what are often highly complex datasets.

Case study research has sometimes been criticised for lacking scientific rigour and providing little basis for generalisation (i.e. producing findings that may be transferable to other settings)[ 1 ]. There are several ways to address these concerns, including: the use of theoretical sampling (i.e. drawing on a particular conceptual framework); respondent validation (i.e. participants checking emerging findings and the researcher's interpretation, and providing an opinion as to whether they feel these are accurate); and transparency throughout the research process (see Table 8 )[ 8 , 18 – 21 , 23 , 26 ]. Transparency can be achieved by describing in detail the steps involved in case selection, data collection, the reasons for the particular methods chosen, and the researcher's background and level of involvement (i.e. being explicit about how the researcher has influenced data collection and interpretation). Seeking potential, alternative explanations, and being explicit about how interpretations and conclusions were reached, help readers to judge the trustworthiness of the case study report. Stake provides a critique checklist for a case study report (Table 9 )[ 8 ].

Conclusions

The case study approach allows, amongst other things, critical events, interventions, policy developments and programme-based service reforms to be studied in detail in a real-life context. It should therefore be considered when an experimental design is either inappropriate to answer the research questions posed or impossible to undertake. Considering the frequency with which implementations of innovations are now taking place in healthcare settings and how well the case study approach lends itself to in-depth, complex health service research, we believe this approach should be more widely considered by researchers. Though inherently challenging, the research case study can, if carefully conceptualised and thoughtfully undertaken and reported, yield powerful insights into many important aspects of health and healthcare delivery.

Yin RK: Case study research, design and method. 2009, London: Sage Publications Ltd., 4

Google Scholar

Keen J, Packwood T: Qualitative research; case study evaluation. BMJ. 1995, 311: 444-446.

Article CAS PubMed PubMed Central Google Scholar

Sheikh A, Halani L, Bhopal R, Netuveli G, Partridge M, Car J, et al: Facilitating the Recruitment of Minority Ethnic People into Research: Qualitative Case Study of South Asians and Asthma. PLoS Med. 2009, 6 (10): 1-11.

Article Google Scholar

Pinnock H, Huby G, Powell A, Kielmann T, Price D, Williams S, et al: The process of planning, development and implementation of a General Practitioner with a Special Interest service in Primary Care Organisations in England and Wales: a comparative prospective case study. Report for the National Co-ordinating Centre for NHS Service Delivery and Organisation R&D (NCCSDO). 2008, [ http://www.sdo.nihr.ac.uk/files/project/99-final-report.pdf ]

Robertson A, Cresswell K, Takian A, Petrakaki D, Crowe S, Cornford T, et al: Prospective evaluation of the implementation and adoption of NHS Connecting for Health's national electronic health record in secondary care in England: interim findings. BMJ. 2010, 41: c4564-

Pearson P, Steven A, Howe A, Sheikh A, Ashcroft D, Smith P, the Patient Safety Education Study Group: Learning about patient safety: organisational context and culture in the education of healthcare professionals. J Health Serv Res Policy. 2010, 15: 4-10. 10.1258/jhsrp.2009.009052.

Article PubMed Google Scholar

van Harten WH, Casparie TF, Fisscher OA: The evaluation of the introduction of a quality management system: a process-oriented case study in a large rehabilitation hospital. Health Policy. 2002, 60 (1): 17-37. 10.1016/S0168-8510(01)00187-7.

Stake RE: The art of case study research. 1995, London: Sage Publications Ltd.

Sheikh A, Smeeth L, Ashcroft R: Randomised controlled trials in primary care: scope and application. Br J Gen Pract. 2002, 52 (482): 746-51.

PubMed PubMed Central Google Scholar

King G, Keohane R, Verba S: Designing Social Inquiry. 1996, Princeton: Princeton University Press

Doolin B: Information technology as disciplinary technology: being critical in interpretative research on information systems. Journal of Information Technology. 1998, 13: 301-311. 10.1057/jit.1998.8.

George AL, Bennett A: Case studies and theory development in the social sciences. 2005, Cambridge, MA: MIT Press

Eccles M, the Improved Clinical Effectiveness through Behavioural Research Group (ICEBeRG): Designing theoretically-informed implementation interventions. Implementation Science. 2006, 1: 1-8. 10.1186/1748-5908-1-1.

Article PubMed Central Google Scholar

Netuveli G, Hurwitz B, Levy M, Fletcher M, Barnes G, Durham SR, Sheikh A: Ethnic variations in UK asthma frequency, morbidity, and health-service use: a systematic review and meta-analysis. Lancet. 2005, 365 (9456): 312-7.

Sheikh A, Panesar SS, Lasserson T, Netuveli G: Recruitment of ethnic minorities to asthma studies. Thorax. 2004, 59 (7): 634-

CAS PubMed PubMed Central Google Scholar

Hellström I, Nolan M, Lundh U: 'We do things together': A case study of 'couplehood' in dementia. Dementia. 2005, 4: 7-22. 10.1177/1471301205049188.

Som CV: Nothing seems to have changed, nothing seems to be changing and perhaps nothing will change in the NHS: doctors' response to clinical governance. International Journal of Public Sector Management. 2005, 18: 463-477. 10.1108/09513550510608903.

Lincoln Y, Guba E: Naturalistic inquiry. 1985, Newbury Park: Sage Publications

Barbour RS: Checklists for improving rigour in qualitative research: a case of the tail wagging the dog?. BMJ. 2001, 322: 1115-1117. 10.1136/bmj.322.7294.1115.

Mays N, Pope C: Qualitative research in health care: Assessing quality in qualitative research. BMJ. 2000, 320: 50-52. 10.1136/bmj.320.7226.50.

Mason J: Qualitative researching. 2002, London: Sage

Brazier A, Cooke K, Moravan V: Using Mixed Methods for Evaluating an Integrative Approach to Cancer Care: A Case Study. Integr Cancer Ther. 2008, 7: 5-17. 10.1177/1534735407313395.

Miles MB, Huberman M: Qualitative data analysis: an expanded sourcebook. 1994, CA: Sage Publications Inc., 2

Pope C, Ziebland S, Mays N: Analysing qualitative data. Qualitative research in health care. BMJ. 2000, 320: 114-116. 10.1136/bmj.320.7227.114.

Cresswell KM, Worth A, Sheikh A: Actor-Network Theory and its role in understanding the implementation of information technology developments in healthcare. BMC Med Inform Decis Mak. 2010, 10 (1): 67-10.1186/1472-6947-10-67.

Article PubMed PubMed Central Google Scholar

Malterud K: Qualitative research: standards, challenges, and guidelines. Lancet. 2001, 358: 483-488. 10.1016/S0140-6736(01)05627-6.

Article CAS PubMed Google Scholar

Yin R: Case study research: design and methods. 1994, Thousand Oaks, CA: Sage Publishing, 2

Yin R: Enhancing the quality of case studies in health services research. Health Serv Res. 1999, 34: 1209-1224.

Green J, Thorogood N: Qualitative methods for health research. 2009, Los Angeles: Sage, 2

Howcroft D, Trauth E: Handbook of Critical Information Systems Research, Theory and Application. 2005, Cheltenham, UK: Northampton, MA, USA: Edward Elgar

Book Google Scholar

Blakie N: Approaches to Social Enquiry. 1993, Cambridge: Polity Press

Doolin B: Power and resistance in the implementation of a medical management information system. Info Systems J. 2004, 14: 343-362. 10.1111/j.1365-2575.2004.00176.x.

Bloomfield BP, Best A: Management consultants: systems development, power and the translation of problems. Sociological Review. 1992, 40: 533-560.

Shanks G, Parr A: Positivist, single case study research in information systems: A critical analysis. Proceedings of the European Conference on Information Systems. 2003, Naples

Pre-publication history

The pre-publication history for this paper can be accessed here: http://www.biomedcentral.com/1471-2288/11/100/prepub

Download references

Acknowledgements

We are grateful to the participants and colleagues who contributed to the individual case studies that we have drawn on. This work received no direct funding, but it has been informed by projects funded by Asthma UK, the NHS Service Delivery Organisation, NHS Connecting for Health Evaluation Programme, and Patient Safety Research Portfolio. We would also like to thank the expert reviewers for their insightful and constructive feedback. Our thanks are also due to Dr. Allison Worth who commented on an earlier draft of this manuscript.

Author information

Authors and affiliations.

Division of Primary Care, The University of Nottingham, Nottingham, UK

Sarah Crowe & Anthony Avery

Centre for Population Health Sciences, The University of Edinburgh, Edinburgh, UK

Kathrin Cresswell, Ann Robertson & Aziz Sheikh

School of Health in Social Science, The University of Edinburgh, Edinburgh, UK

You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sarah Crowe .

Additional information

Competing interests.

The authors declare that they have no competing interests.

Authors' contributions

AS conceived this article. SC, KC and AR wrote this paper with GH, AA and AS all commenting on various drafts. SC and AS are guarantors.

Rights and permissions

This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License ( http://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Reprints and permissions

About this article

Cite this article.

Crowe, S., Cresswell, K., Robertson, A. et al. The case study approach. BMC Med Res Methodol 11 , 100 (2011). https://doi.org/10.1186/1471-2288-11-100

Download citation

Received : 29 November 2010

Accepted : 27 June 2011

Published : 27 June 2011

DOI : https://doi.org/10.1186/1471-2288-11-100

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Case Study Approach
Electronic Health Record System
Case Study Design
Case Study Site
Case Study Report

BMC Medical Research Methodology

ISSN: 1471-2288

General enquiries: [email protected]

Information

Author Services

Initiatives

You are accessing a machine-readable page. In order to be human-readable, please install an RSS reader.

All articles published by MDPI are made immediately available worldwide under an open access license. No special permission is required to reuse all or part of the article published by MDPI, including figures and tables. For articles published under an open access Creative Common CC BY license, any part of the article may be reused without permission provided that the original article is clearly cited. For more information, please refer to https://www.mdpi.com/openaccess .

Feature papers represent the most advanced research with significant potential for high impact in the field. A Feature Paper should be a substantial original Article that involves several techniques or approaches, provides an outlook for future research directions and describes possible research applications.

Feature papers are submitted upon individual invitation or recommendation by the scientific editors and must receive positive feedback from the reviewers.

Editor’s Choice articles are based on recommendations by the scientific editors of MDPI journals from around the world. Editors select a small number of articles recently published in the journal that they believe will be particularly interesting to readers, or important in the respective research area. The aim is to provide a snapshot of some of the most exciting work published in the various research areas of the journal.

Original Submission Date Received: .

Active Journals
Find a Journal
Proceedings Series
For Authors
For Reviewers
For Editors
For Librarians
For Publishers
For Societies
For Conference Organizers
Open Access Policy
Institutional Open Access Program
Special Issues Guidelines
Editorial Process
Research and Publication Ethics
Article Processing Charges
Testimonials
Preprints.org
SciProfiles
Encyclopedia

Article Menu

Subscribe SciFeed
Recommended Articles
Author Biographies
Google Scholar
on Google Scholar
Table of Contents

Find support for a specific problem in the support section of our website.

Please let us know what you think of our products and services.

Visit our dedicated information section to learn more about MDPI.

JSmol Viewer

Dead on the beach predicting the drift of whale remains improves management for offshore disposal.

1. Introduction

1.1. large whale offshore disposal and decomposition, 1.2. modelling drift, 2. materials and methods, 2.1. whale remains and position tracking, 2.2. drift trajectory modelling, 2.3. search object database, 2.4. environmental data, 2.5. dispersion parameters, 2.6. comparison of simulated trajectory and satellite track, 4. discussion, 4.1. offshore whale carcass disposal enhanced through modelling drift, 4.2. study limitations, 5. conclusions, supplementary materials, author contributions, institutional review board statement, informed consent statement, data availability statement, acknowledgments, conflicts of interest.

Click here to enlarge figure

Action	Benefits	Disadvantages/Difficulties	Most Feasible
Landfill	(1) reduced biohazard	(1) Costly (2) transportation, truck and excavator needed (3) road hazard (4) risk of handling for workers (5) unethical and culturally controversial	Public beaches that are accessible with landfill or holding facility in proximity
Rendering and composting	Turned into compost or biodiesel Reducing health hazards	(1) Costly (2) transportation, truck and excavator needed (3) road hazard (4) risk of handling for workers (5) culturally controversial	Public beaches that are accessible with landfill or holding facility in proximity
Burial on beach	(1) Nutrient enrichment for shore environment (2) reduction of biological hazard and smell	(1) Changes in groundwater quality (2) possible shark attraction to the surf zone (3) contamination from euthanasia (4) long decomposition time (5) earth moving equipment, cranes, trained operators required (6) risk for workers	Areas with foredunes, remote or less public beaches with access
Natural Decomposition	(1) Cost effective (2) decomposition through natural processes (insects, scavengers) (3) provision of food for beach organism and nutrient enrichment	(1) Changes in groundwater quality (2) unpleasant sight and smell (3) possible shark attraction to the surf zone (4) possible contamination from euthanasia (5) risk of biological contamination (6) possible refloating and washing up to a populated area	Remote areas, inaccessible locations and with smaller cetaceans
Towing out to sea	(1) Sustainable recycling nutrients at sea (2) food source for marine species in surface waters, and benthic environment (3) ethical sensible (4) potential carbon removal (5) reduced biohazard	(1) Can wash ashore again (2) expertise and knowledge required (3) suitable vessel and weather conditions needed (4) potential navigational hazard (5) unclear jurisdictional responsibilities (6) potential navigation hazard	Floating carcasses, calm weather conditions
Sinking	(1) Potential for carbon removal (2) nutrient enrichment and recycle to marine environment (3) reduced risk of navigational hazard (4) reduced biohazard	(1) Refloats (2) weights left at sea (3) expertise and knowledge required (4) less cost effective	Floating carcasses, calm weather conditions
Explosives	(1) Forced break down into smaller pieces (2) prevention of accidental, naturally occurring rupture	(1) Biohazard (2) safety hazard (3) risk of uncontrolled dispersion	Remote areas

Giardino, G.V.; Gana, J.C.; De León, M.C.; Mandiola, M.A.; Dassis, M.; Denuncio, P.; Elissamburu, A.; Morón, S.; Rodríguez Heredia, S.; Alvarez, C.K. Occurrence and anthropogenic-derived mortality of humpback whales ( Megaptera novaeangliae ) along the northern coast of Argentina, 2003–2021. N. Z. J. Mar. Freshw. Res. 2022 , 58 , 73–88. [ Google Scholar ] [ CrossRef ]
Vermeulen, E.; Jouve, E.; Best, P.; Cliff, G.; Dicken, M.; Kotze, D.; McCue, S.; Meÿer, M.; Seakamela, M.; Thompson, G. Mortalities of southern right whales ( Eubalaena australis ) and related anthropogenic factors in South African waters, 1999–2019. J. Cetacean Res. Manag. 2022 , 23 , 149–169. [ Google Scholar ] [ CrossRef ]
van Weelden, C.; Towers, J.R.; Bosker, T. Impacts of climate change on cetacean distribution, habitat and migration. Clim. Chang. Ecol. 2021 , 1 , 100009. [ Google Scholar ] [ CrossRef ]
Parsons, E.; Dolman, S.J.; Wright, A.J.; Rose, N.A.; Burns, W. Navy sonar and cetaceans: Just how much does the gun need to smoke before we act? Mar. Pollut. Bull. 2008 , 56 , 1248–1257. [ Google Scholar ] [ CrossRef ] [ PubMed ]
Moore, M.J.; Mitchell, G.H.; Rowles, T.K.; Early, G. Dead cetacean? Beach, bloat, float, sink. Front. Mar. Sci. 2020 , 7 , 333. [ Google Scholar ] [ CrossRef ]
Tucker, J.P.; Santos, I.R.; Crocetti, S.; Butcher, P. Whale carcass strandings on beaches: Management challenges, research needs, and examples from Australia. Ocean Coast. Manag. 2018 , 163 , 323–338. [ Google Scholar ] [ CrossRef ]
Quaggiotto, M.-M.; Sánchez-Zapata, J.A.; Bailey, D.M.; Payo-Payo, A.; Navarro, J.; Brownlow, A.; Deaville, R.; Lambertucci, S.A.; Selva, N.; Cortés-Avizanda, A. Past, present and future of the ecosystem services provided by cetacean carcasses. Ecosyst. Serv. 2022 , 54 , 101406. [ Google Scholar ] [ CrossRef ]
Tucker, J.P.; Santos, I.R.; Davis, K.L.; Butcher, P.A. Whale carcass leachate plumes in beach groundwater: A potential shark attractant to the surf? Mar. Pollut. Bull. 2019 , 140 , 219–226. [ Google Scholar ] [ CrossRef ] [ PubMed ]
Heiss, J.W. Whale burial and organic matter impacts on biogeochemical cycling in beach aquifers and leachate fluxes to the nearshore zone. J. Contam. Hydrol. 2020 , 233 , 103656. [ Google Scholar ] [ CrossRef ]
Clua, E.; Chauvet, C.; Read, T.; Werry, J.M.; Lee, S.Y. Behavioural patterns of a tiger shark ( Galeocerdo cuvier ) feeding aggregation at a blue whale carcass in Prony Bay, New Caledonia. Mar. Freshw. Behav. Physiol. 2013 , 46 , 1–20. [ Google Scholar ] [ CrossRef ]
Nowacek, D.P.; Johnson, M.P.; Tyack, P.L.; Shorter, K.A.; McLellan, W.A. Buoyant balaenids: The ups and downs of buoyancy in right whales. Proc. R. Soc. Lond. Ser. B Biol. Sci. 2001 , 268 , 1811–1816. [ Google Scholar ] [ CrossRef ] [ PubMed ]
Geraci, J.R.; Anderson, D.M.; Timperi, R.J.; Aubin, D.J.S.; Early, G.A.; Prescott, J.H.; Mayo, C.A. Humpback Whales ( Megaptera novaeangliae ) Fatally Poisoned by Dinoflagellate Toxin. Can. J. Fish. Aquat. Sci. 1989 , 46 , 1895–1898. [ Google Scholar ] [ CrossRef ]
Tønnessen, J.N.; Johnsen, A.O. The History of Modern Whaling ; University of California Press: Berkeley, CA, USA, 1982. [ Google Scholar ]
Lea, J.S.E.; Daly, R.; Leon, C.; Daly, C.A.K.; Clarke, C.R. Life after death: Behaviour of multiple shark species scavenging a whale carcass. Mar. Freshw. Res. 2019 , 70 , 302–306. [ Google Scholar ] [ CrossRef ]
Curtis, T.H.; Kelly, J.T.; Menard, K.L.; Laroche, R.K.; Jones, R.E.; Klimley, A.P. Observations on the behavior of white sharks scavenging from a whale carcass at Point Reyes, California. Calif. Fish Game 2006 , 92 , 113. [ Google Scholar ]
Fallows, C.; Gallagher, A.J.; Hammerschlag, N. White sharks ( Carcharodon carcharias ) scavenging on whales and its potential role in further shaping the ecology of an apex predator. PLoS ONE 2013 , 8 , e60797. [ Google Scholar ] [ CrossRef ] [ PubMed ]
McAuley, R.B.; Bruce, B.D.; Keay, I.S.; Mountford, S.; Pinnell, T.; Whoriskey, F.G. Broad-scale coastal movements of white sharks off Western Australia described by passive acoustic telemetry data. Mar. Freshw. Res. 2017 , 68 , 1518–1531. [ Google Scholar ] [ CrossRef ]
Daniel, P.; Jan, G.; Cabioc’h, F.; Landau, Y.; Loiseau, E. Drift modeling of cargo containers. Spill Sci. Technol. Bull. 2002 , 7 , 279–288. [ Google Scholar ] [ CrossRef ]
Peltier, H.; Dabin, W.; Daniel, P.; Van Canneyt, O.; Dorémus, G.; Huon, M.; Ridoux, V. The significance of stranding data as indicators of cetacean populations at sea: Modelling the drift of cetacean carcasses. Ecol. Indic. 2012 , 18 , 278–290. [ Google Scholar ] [ CrossRef ]
Nero, R.W.; Cook, M.; Coleman, A.T.; Solangi, M.; Hardy, R. Using an ocean model to predict likely drift tracks of sea turtle carcasses in the north central Gulf of Mexico. Endanger. Species Res. 2013 , 21 , 191–203. [ Google Scholar ] [ CrossRef ]
Małyszko, M. Assessment of the potential effectiveness of the WIG craft in search action at sea using SARMAP software. TransNav Int. J. Mar. Navig. Saf. Sea Transp. 2019 , 13 , 437–442. [ Google Scholar ] [ CrossRef ]
Bell, M.; Charles-Edwards, E.; Wilson, T.; Cooper, J. Demographic futures for South East Queensland. Aust. Plan. 2010 , 47 , 126–134. [ Google Scholar ] [ CrossRef ]
Heidemann, H.; Ribbe, J. Marine Heat Waves and the Influence of El Niño off Southeast Queensland, Australia. Front. Mar. Sci. 2019 , 6 , 56. [ Google Scholar ] [ CrossRef ]
Oke, P.R.; Roughan, M.; Cetina-Heredia, P.; Pilo, G.S.; Ridgway, K.R.; Rykova, T.; Archer, M.R.; Coleman, R.C.; Kerry, C.G.; Rocha, C.; et al. Revisiting the circulation of the East Australian Current: Its path, separation, and eddy field. Prog. Oceanogr. 2019 , 176 , 102139. [ Google Scholar ] [ CrossRef ]
Azis Ismail, M.F.; Ribbe, J.; Karstensen, J.; Lemckert, C.; Lee, S.; Gustafson, J. The Fraser Gyre: A cyclonic eddy off the coast of eastern Australia. Estuar. Coast. Shelf Sci. 2017 , 192 , 72–85. [ Google Scholar ] [ CrossRef ]
Hunt, S.; Stuart, G.; Reed, R.; Mirfanderesk, H.; Tomlinson, R. Managing Coastal Disasters on Australia’s Gold Coast. In Solutions to Coastal Disasters 2008 ; Amer Society of Civil Engineers: Reston, VA, USA, 2008; pp. 699–712. [ Google Scholar ]
Spaulding, M.L.; Isaji, T.; Hall, P.; Allen, A.A. A hierarchy of stochastic particle models for search and rescue (SAR): Application to predict surface drifter trajectories using HF radar current forcing. J. Mar. Environ. Eng. 2006 , 8 , 181. [ Google Scholar ]
Spaulding, M.L.; Anderson, E.; Howlett, E.; Mendelsohn, D.; Opishinski, T. Application of OILMAP and SIMAP to predict the transport and fate of the North Cape Spill. In Proceedings of the 19th Arctic and Marine Oil Spill Program, Technical Seminar, Calgary, AB, Canada, 12–14 June 1996. [ Google Scholar ]
Chu, T.-N.; Tsai, C.-H. Drift track simulation for past marine incidents using SARMAP. In Proceedings of the OCEANS’10 IEEE SYDNEY, Sydney, Australia, 24–27 May 2010; pp. 1–4. [ Google Scholar ]
Spaulding, M.; Howlett, E. Application of SARMAP to estimate probable seach area for objects lost at sea. Oceanogr. Lit. Rev. 1997 , 5 , 523. [ Google Scholar ]
Brushett, B.A.; King, B.A.; Lemckert, C. Evaluation of met-ocean forecast data effectiveness for tracking drifters deployed during operational oil spill response in Australian waters. J. Coast. Res. 2011 , 64 , 991–994. [ Google Scholar ]
Brushett, B.A.; King, B.A.; Lemckert, C.J. Assessment of ocean forecast models for search area prediction in the eastern Indian Ocean. Ocean Model. 2016 , 97 , 1–15. [ Google Scholar ] [ CrossRef ]
Brushett, B.A.; Allen, A.A.; King, B.A.; Lemckert, C.J. Application of leeway drift data to predict the drift of panga skiffs: Case study of maritime search and rescue in the tropical pacific. Appl. Ocean Res. 2017 , 67 , 109–124. [ Google Scholar ] [ CrossRef ]
Mu, L.; Tu, H.; Geng, X.; Qiao, F.; Chen, Z.; Jia, S.; Zhu, R.; Zhang, T.; Chen, Z. Research on the Drift Prediction of Marine Floating Debris: A Case Study of the South China Sea Maritime Drift Experiment. J. Mar. Sci. Eng. 2024 , 12 , 357. [ Google Scholar ] [ CrossRef ]
Breivik, Ø.; Allen, A.A.; Maisondieu, C.; Olagnon, M. Advances in search and rescue at sea. Ocean Dyn. 2013 , 63 , 83–88. [ Google Scholar ] [ CrossRef ]
Davies, A. The numerical solution of the three-dimensional hydrodynamic equations, using a B-spline representation of the vertical current profile. In Elsevier Oceanography Series ; Elsevier: Amsterdam, The Netherlands, 1977; Volume 19, pp. 1–25. [ Google Scholar ]
Lellouche, J.-M.; Greiner, E.; Le Galloudec, O.; Garric, G.; Regnier, C.; Drevillon, M.; Benkiran, M.; Testut, C.-E.; Bourdalle-Badie, R.; Gasparin, F. Recent updates to the Copernicus Marine Service global ocean monitoring and forecasting real-time 1/12° high-resolution system. Ocean Sci. 2018 , 14 , 1093–1126. [ Google Scholar ] [ CrossRef ]
Tucker, J.P.; Vercoe, B.; Santos, I.R.; Dujmovic, M.; Butcher, P.A. Whale carcass scavenging by sharks. Glob. Ecol. Conserv. 2019 , 19 , e00655. [ Google Scholar ] [ CrossRef ]
Dicken, M. First observations of young of the year and juvenile great white sharks ( Carcharodon carcharias ) scavenging from a whale carcass. Mar. Freshw. Res. 2008 , 59 , 596–602. [ Google Scholar ] [ CrossRef ]
Reisdorf, A.G.; Bux, R.; Wyler, D.; Benecke, M.; Klug, C.; Maisch, M.W.; Fornaro, P.; Wetzel, A. Float, explode or sink: Postmortem fate of lung-breathing marine vertebrates. Palaeobiodivers. Palaeoenviron. 2012 , 92 , 67–81. [ Google Scholar ] [ CrossRef ]
Dudley, S.F.J.; Anderson-Reade, M.D.; Thompson, G.; McMullen, P.B.; Sharks, N. Concurrent scavenging off a whale carcass by great white sharks, Carcharodon carcharias, and tiger sharks, Galeocerdo cuvier. Fish. Bull.-Natl. Ocean. Atmos. Adm. 2000 , 98 , 646–649. [ Google Scholar ]
Lockyer, C. Body weights of some species of large whales. ICES J. Mar. Sci. 1976 , 36 , 259–273. [ Google Scholar ] [ CrossRef ]
Ward, S.; Robins, P.; Owen, A.; Demmer, J.; Jenkins, S. The importance of resolving nearshore currents in coastal dispersal models. Ocean Model. 2023 , 183 , 102181. [ Google Scholar ] [ CrossRef ]
Meynecke, J.-O.; Samanta, S.; de Bie, J.; Seyboth, E.; Prakash Dey, S.; Fearon, G.; Vichi, M.; Findlay, K.; Roychoudhury, A.; Mackey, B. Do whales really increase the oceanic removal of atmospheric carbon? Front. Mar. Sci. 2023 , 10 , 1117409. [ Google Scholar ] [ CrossRef ]
Smith, C.R.; Bernardino, A.F.; Baco, A.; Hannides, A.; Altamira, I. Seven-year enrichment: Macrofaunal succession in deep-sea sediments around a 30 tonne whale fall in the Northeast Pacific. Mar. Ecol. Prog. Ser. 2014 , 515 , 133–149. [ Google Scholar ] [ CrossRef ]

Model	Provider	Horizontal Resolution	Vertical Coordinates	Forecast Length (h)	Time Step (h)	Wind Forcing	Grid Limits
Blue Link	BOM	0.1° × 0.1° (10 km × 10 km)	51 z layers	96	3	ACCESS-G	Global [−74.90 to 75.00]° N, [−180 to 180]° E
HYCOM	NOAA	1/12° (~9 km)	32 hybrid layers	144	3	NOAA	Global
Copernicus	CMEMS	0.083° × 0.083° (~9 km × ~9 km)	75 layers	240	1	ECMWF	Global

Date	Time	Location of Whale Remains	Lat/Long	Distance Drifted (km)	Average Speed (km/h)	Activity on Whale Remains
16 July 2023	4:00 p.m.	South of Noosa Heads	−26.48183 153.33417	-	-	First sighted by Coastguard
17 July 2023	1:45 p.m.	North of Noosa Heads	−26.3402 153.12417	26.2	1.2	Sighted and fitted with tracker
18 July 2023	7:09 a.m.	East of Cooloola beach	−26.17422 153.10828	17.5	1.1	Sighted and towed offshore
18 July 2023	1:40 p.m.	Offshore of Coloola beach	−26.12883 153.11145	27.5	4.1	Repositioned offshore
20 July 2023	1:04 p.m.	East of Double Island Point	−25.87401 153.2444	37.3	0.8	Loss of satellite tag signal for 11 h
25 July 2023	3:00 a.m.	South of Fraser Island	−25.76318 153.12045	114	0.7	Loss of satellite tag signal

The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

Share and Cite

Meynecke, J.-O.; Zigic, S.; Perez, L.; Dunn, R.J.K.; Benfer, N.; Gustafson, J.; Bosshard, S. Dead on the Beach? Predicting the Drift of Whale Remains Improves Management for Offshore Disposal. J. Mar. Sci. Eng. 2024 , 12 , 1156. https://doi.org/10.3390/jmse12071156

Meynecke J-O, Zigic S, Perez L, Dunn RJK, Benfer N, Gustafson J, Bosshard S. Dead on the Beach? Predicting the Drift of Whale Remains Improves Management for Offshore Disposal. Journal of Marine Science and Engineering . 2024; 12(7):1156. https://doi.org/10.3390/jmse12071156

Meynecke, Jan-Olaf, Sasha Zigic, Larissa Perez, Ryan J. K. Dunn, Nathan Benfer, Johan Gustafson, and Simone Bosshard. 2024. "Dead on the Beach? Predicting the Drift of Whale Remains Improves Management for Offshore Disposal" Journal of Marine Science and Engineering 12, no. 7: 1156. https://doi.org/10.3390/jmse12071156

Article Metrics

Article access statistics, supplementary material.

ZIP-Document (ZIP, 16439 KiB)

Further Information

Mdpi initiatives, follow mdpi.

Subscribe to receive issue release notifications and newsletters from MDPI journals

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

View all journals
Explore content
About the journal
Publish with us
Sign up for alerts
Open access
Published: 10 July 2024

Fast-moving stars around an intermediate-mass black hole in ω Centauri

Maximilian Häberle ORCID: orcid.org/0000-0002-5844-4443 1 ,
Nadine Neumayer ORCID: orcid.org/0000-0002-6922-2598 1 ,
Anil Seth ORCID: orcid.org/0000-0003-0248-5470 2 ,
Andrea Bellini ORCID: orcid.org/0000-0003-3858-637X 3 ,
Mattia Libralato ORCID: orcid.org/0000-0001-9673-7397 4 , 5 ,
Holger Baumgardt ORCID: orcid.org/0000-0002-1959-6946 6 ,
Matthew Whitaker ORCID: orcid.org/0009-0007-3015-9900 2 ,
Antoine Dumont ORCID: orcid.org/0000-0003-0234-3376 1 ,
Mayte Alfaro-Cuello ORCID: orcid.org/0000-0002-1212-2844 7 ,
Jay Anderson ORCID: orcid.org/0000-0003-2861-3995 3 ,
Callie Clontz ORCID: orcid.org/0009-0005-8057-0031 1 , 2 ,
Nikolay Kacharov ORCID: orcid.org/0000-0002-6072-6669 8 ,
Sebastian Kamann ORCID: orcid.org/0000-0001-6604-0505 9 ,
Anja Feldmeier-Krause ORCID: orcid.org/0000-0002-0160-7221 1 , 10 ,
Antonino Milone ORCID: orcid.org/0000-0001-7506-930X 11 ,
Maria Selina Nitschai ORCID: orcid.org/0000-0002-2941-4480 1 ,
Renuka Pechetti ORCID: orcid.org/0000-0002-1670-0808 9 &
Glenn van de Ven ORCID: orcid.org/0000-0003-4546-7731 10

Nature volume 631 , pages 285–288 ( 2024 ) Cite this article

Metrics details

Compact astrophysical objects
Galaxies and clusters

Black holes have been found over a wide range of masses, from stellar remnants with masses of 5–150 solar masses ( M ☉ ), to those found at the centres of galaxies with M > 10 5 M ☉ . However, only a few debated candidate black holes exist between 150 M ☉ and 10 5 M ☉ . Determining the population of these intermediate-mass black holes is an important step towards understanding supermassive black hole formation in the early universe 1 , 2 . Several studies have claimed the detection of a central black hole in ω Centauri, the most massive globular cluster of the Milky Way 3 , 4 , 5 . However, these studies have been questioned because of the possible mass contribution of stellar mass black holes, their sensitivity to the cluster centre and the lack of fast-moving stars above the escape velocity 6 , 7 , 8 , 9 . Here we report the observations of seven fast-moving stars in the central 3 arcsec (0.08 pc) of ω Centauri. The velocities of the fast-moving stars are significantly higher than the expected central escape velocity of the star cluster, so their presence can be explained only by being bound to a massive black hole. From the velocities alone, we can infer a firm lower limit of the black hole mass of about 8,200 M ☉ , making this a good case for an intermediate-mass black hole in the local universe.

Most nearby young star clusters formed in three massive complexes

A supra-massive population of stellar-mass black holes in the globular cluster Palomar 5

A wide star–black-hole binary system from radial-velocity measurements

ω Centauri (ω Cen) is a special case among the globular clusters of the Milky Way. Owing to its high mass, complex stellar populations and kinematics, ω Cen is widely accepted as the stripped nucleus of an accreted dwarf galaxy 10 , 11 . These factors combined with its proximity ( D = 5.43 kiloparsec (kpc); ref. 12 ) have made it a prime target for searching for an intermediate-mass black hole (IMBH). As part of the oMEGACat project 13 , 14 , we recently constructed an updated proper-motion catalogue of the inner regions of ω Cen, on the basis of more than 500 Hubble Space Telescope (HST) archival images taken over a time span of 20 years. The unprecedented depth and precision of this catalogue have enabled us to discover a statistically significant overdensity of fast-moving stars in the centre of the cluster (Fig. 1 and Extended Data Fig. 1 ). In total, we find seven stars with a total proper motion higher than 2.41 mas yr −1 within 3″ of the centre determined in refs. 6 , 15 (hereafter AvdM10 centre). At a cluster distance of 5.43 kpc (ref. 12 ), this corresponds to projected two-dimensional (2D) velocities higher than the escape velocity of the cluster if no IMBH is present ( v esc = 62 km s −1 ; ref. 16 ; Methods ). Here we show that the presence of these stars strongly indicates a massive black hole, similar to the S-stars in the Galactic centre 17 . A list of the fast-moving stars is provided in Extended Data Table 1 , and we label the fast-moving stars with letters from A to G, sorted by their proximity to the AvdM10 centre. All these stars lie along the cluster main sequence in the colour–magnitude diagram (CMD) (Fig. 2 ). The fastest and the centremost star (Fig. 1 , star A) has a 2D proper motion of 4.41 ± 0.08 mas yr −1 (113.0 ± 1.1 km s −1 ). The motion of this star was measured over 286 epochs and a full 20.6-year time baseline (Fig. 3 ). We run extensive quality checks to ensure that the astrometry of the discovered fast-moving stars is reliable. To ensure the cleanest possible dataset, we limit our analysis to stars whose velocity is at least 3 σ above the escape velocity. This leads to the exclusion of stars B and G; however, this has negligible influence on the determined IMBH constraints.

a , Solid grey markers indicate all stars with a high-quality (HQ) proper motion measurement in our new catalogue within a 40″ × 40″ region centred on the AvdM10 centre 6 . Well-measured stars with velocities higher than the cluster escape velocity (62 km s −1 ) and lying on the cluster main sequence in the colour-magnitude diagram (Fig. 2 ) are marked in pink. We use filled markers for stars that are at least 3 σ above the escape velocity, and open markers for all other stars above the escape velocity. b , Stacked image of the innermost region of ω Cen using all observations in the WFC3/UVIS F606W filter. The fast-moving stars and their proper-motion vectors are shown in pink. The arrows indicate the stellar motion over 100 years. We also list the measured individual velocities. The cyan cross indicates the photometric centre of ω Cen measured by ref. 6 , with the dashed circle indicating the 1″ error reported for this centre; the orange cross marks the centre, allowing for the lowest IMBH mass; and the blue cross marks the most likely position of an IMBH given the Markov chain Monte Carlo (MCMC) analysis of the acceleration limits of the fast-moving stars. Dec, declination; RA, right ascension, min., minimum.

The CMD locations of all fast-moving stars are marked with pink symbols, with their photometric 1 σ errors marked with error bars. All of them lie on the main sequence, showing that they are probably members of ω Cen. The stars are labelled from A to G, sorted by their distance from the AvdM10 centre.

a , Individual measured positions with 1 σ error bars. b , Multi-epoch HST imaging for star A, the fastest ( v projected = 113.0 ± 1.1 km s −1 ) and centremost of the seven fast-moving stars discovered in the centre of ω Cen. The star is indicated with a pink marker on the images and its motion over 21 years with a line. This plot shows the notable astrometric quality and the long temporal baseline we have in our unique dataset. Similar plots for all other stars are shown in Extended Data Fig. 2 . Dec, declination; RA, right ascension; FOV, field of view.

Four of the fast-moving stars, including the three fastest in the sample, are found within the centremost arcsecond ( r projected < 0.03 pc or r projected < 0.09 ly). These four innermost stars are all fainter than m F606W > 22.7, which is unlikely ( P = 0.013) to be a random occurrence given the overall distribution of stellar magnitudes in the centre of ω Cen. Moreover, all of them lie towards the blue side of the main sequence. Both these properties could have interesting physical implications on the mechanism involved in capturing these stars or on their tidal interactions with the IMBH.

We expect a certain number of Milky Way stars in our field of view, and because they have a large proper motion with respect to ω Cen, they can mimic fast-moving cluster stars. On the basis of the number density of fast-moving stars at larger radii (Extended Data Fig. 1 ), we estimate the rate of contaminants to be 0.0026 arcsec −2 , which is consistent with the expectations from the Besançon Milky Way model 18 . This number density gives an expected average value of only 0.074 foreground stars in the inner 3-arcsec radius. A detection of five such stars by a pure coincidence can, therefore, strongly be ruled out by simple Poisson statistics ( P = 1.7 × 10 −8 ) (ref. 19 ). Having two or more random contaminants within our five-star sample can also be ruled out at the 3 σ level ( P = 0.0026). We also show in the Methods that these stars cannot be explained by objects bound to stellar mass ( ≲ 100 M ☉ ) black holes and that ejections from three-body interactions or an IMBH are not plausible.

Therefore, the presence of the seven central stars moving faster than the escape velocity of the cluster can be explained only if they are bound to a compact massive object near the centre, raising the local escape velocity. If no massive object was present, their velocities would cause them to leave the central region in less than 1,000 years, and then eventually escape the cluster. These fast-moving stars are a predicted consequence of an IMBH, but these stars are not expected from mass-segregated stellar-mass black holes 9 .

We do not know several parameters of the system, including the mass and exact location of this massive object, the relative line-of-sight (LOS) distance between the object and the stars, and the LOS velocity of the stars. Despite this, we can calculate a lower limit on the mass of the dark object using the 2D velocities of the fast-moving stars, assuming only that they are bound to it. The combined constraint from the velocities of the five robustly measured fast-moving stars is about 8,200 M ☉ , thus making an IMBH the only plausible solution. The position of the IMBH requiring the lowest mass is only 0.3 arcsec away from the AvdM10 (ref. 6 ) centre, in agreement with the ±1″ error on the AvdM10 centre. Further details of this calculation can be found in the Methods .

Although the linear motion and the velocity of the stars can be measured with great precision, the expected acceleration signal from an IMBH is considerably weaker and harder to detect. However, even a non-detection of acceleration could provide useful constraints on the mass and location of the IMBH. The accelerations of all stars are consistent with zero within 3 σ , but two stars have more than 2 σ acceleration measurements. We model both the velocity and the acceleration measurements to further constrain the IMBH properties ( Methods ); this calculation increases the lower limit on the black hole mass to 21,100 M ☉ (99% confidence) and gives a preferred position for the IMBH 0.77″ northeast of the AvdM10 centre.

Apart from these constraints that are purely based on the assumed escape velocity and our astrometric data of the five robustly measured fast-moving stars, we also compared the full velocity distribution observed in the inner 10″ of ω Cen to already existing state-of-the-art N -body models 5 with various IMBH masses. Models with no IMBH, a stellar mass black hole cluster or an IMBH with a mass greater than 50,000 M ☉ are all strongly ruled out, whereas models with an IMBH mass of 39,000 M ☉ and 47,000 M ☉ are most consistent with the fraction of fast-moving stars and the observed velocity distribution. However, we caution that our comparisons show that low number statistics limit these comparisons, and mismatches with the overall velocity distribution suggest a need for improved modelling (see Methods for more details).

The detection of fast-moving stars in the centre of ω Cen strengthens the evidence for an IMBH in this cluster. Owing to the probable origin of ω Cen as the nucleus of the Gaia–Enceladus–Sausage dwarf galaxy 20 , 21 , this black hole provides an important data point in the study of black hole demographics in low-mass galaxies, along with other black holes that have been detected in more massive globular clusters and stripped nuclei around M31 such as G1 ( M ≈ 20,000 M ☉ ) (refs. 22 , 23 ) or B023-G078 ( M ≈ 100,000 M ☉ ) (ref. 24 ). Moreover, this black hole provides the closest massive black hole and only the second after Sgr A* for which we can study the motion of multiple individual bound stellar companions. A comparison with the motion of the stars in the Galactic centre is shown in the Methods and Extended Data Fig. 8 .

A more precise estimate of the black hole mass requires dynamical modelling of all newly available kinematic data using models that include the impact of both an IMBH and mass-segregated dark remnants. The exact properties of the orbits of the fast-moving stars have to be determined by deep, pin-pointed follow-up observational studies. Spectroscopic observations with integral-field-unit instruments such as VLT MUSE 25 or JWST NIRSpec IFU 26 could yield LOS velocities for the fast-moving stars. Even more precise and deeper astrometric measurements with existing (VLTI GRAVITY+ 27 , JWST NIRCam 28 ) or future (ELT MICADO 29 , VLT MAVIS 30 ) instruments could enable the detection of additional tightly bound stars, and the measurements of accelerations, key for obtaining direct measurements of the black hole mass. Our results also motivate revisiting the other likely accreted nuclear star clusters of the Milky Way 21 , with M54 being the clearest case. For the search for IMBHs in other globular clusters, our results indicate that it may be necessary to extend kinematic studies to the faintest stars, which is observationally challenging for clusters at larger distances and with high central densities.

Discussion of previous IMBH detections in ω Centauri

The debate about an IMBH in ω Cen dates back almost two decades but has remained controversial. Early dynamical modelling based on LOS integrated-light velocity dispersion measurements suggested an IMBH mass of ${M}_{{\bf{IMBH}}}=\left({4.0}_{-1.0}^{+0.75}\right)\times {10}^{4}{M}_{\odot }$ (ref. 3 ). These results were challenged with a precise redetermination of the centre of the cluster 6 and dynamical modelling of proper motions 7 measured from multi-epoch HST imaging observations that placed an upper limit of 1.2 × 10 4 M ☉ on the IMBH. Using additional integrated light observations and a centre based on the maximum LOS velocity dispersion, a best-fit IMBH mass of ${M}_{{\bf{IMBH}}}=\left(4.7\pm 1.0\right)\times {10}^{4}{M}_{\odot }$ was obtained in ref. 4 . When assuming the AvdM10 centre, the IMBH mass was slightly lower, ${M}_{{\bf{IMBH}}}=\left(3.0\pm 0.4\right)\times {10}^{4}{M}_{\odot }$ .

Subsequent comparisons of both proper motions and LOS velocities to N -body simulations continued to show evidence for an approximately 4.0 × 10 4 M ☉ IMBH 31 , 32 . However, these observations were also shown to be fully consistent with a dark cluster of stellar mass black holes in the central region of ω Cen 8 . The lack of fast-moving stars in previous proper-motion catalogues supported this scenario over an IMBH 9 . Other works noted the influence of radial velocity anisotropy on dynamical mass estimates 33 , 34 .

Most recently, the discovery of a counter-rotating core using VLT MUSE LOS velocity measurements of individual stars 35 highlighted once again the kinematic complexity of the centremost region of ω Cen. The centre of this counter-rotation coincides with the AvdM10 centre within about 5″ but is incompatible with the centres used in refs. 3 , 4 .

Previous accretion constraints in context

With the detection of a 10 4−5 M ☉ IMBH, the upper limits on any accretion signal at X-ray 36 and radio 37 wavelengths make this the most weakly accreting black hole known. Deep, 291 ksec Chandra observations place an upper limit of the 0.5–7 keV luminosity of around 10 30 ergs s −1 (ref. 36 ), roughly 12 orders of magnitude below the Eddington limit. The radio upper limit implies an even fainter source, with the 5 GHz upper limit of 1.3 × 10 27 ergs s −1 (ref. 37 ) corresponding to an implied X-ray luminosity using the fundamental plane of about 10 29 ergs s −1 (ref. 38 ). Assuming standard bolometric corrections of about 10 (ref. 39 ), this X-ray luminosity upper limit suggests an Eddington ratio of $\log ({L}_{{\rm{bol}}}/{L}_{{\rm{edd}}}) < -12$ , far fainter than that for Sgr A* 40 or any other known black hole. This faint signal could be because of a combination of low surrounding gas density, a low accretion rate of that gas and/or a low radiative efficiency 37 . Low-luminosity active galactic nuclei including Sgr A* are brightest at infra-red and sub-millimetre wavelengths most likely because of synchrotron emission from compact jets 41 , 42 . Therefore, future observations with the James Webb Space Telescope or the Atacama Large Millimeter array would provide the highest sensitivity to any emission from the IMBH of ω Cen. Any detection would reveal the location of the IMBH as well as provide valuable constraints on the black hole accretion in this extremely faint source.

Proper-motion measurements and sample selection

Our proper-motion measurements are based on the reduction of archival HST data of the central region of ω Cen, taken over a time span of more than 20 years. We used the state-of-the-art photometry tool KS2 (ref. 32 ) for the source detection and the astro-photometric measurements, and the established procedure described in refs. 43 , 44 , 45 , 46 to measure proper motions relative to the bulk motion of the cluster. The result of this extensive study is a proper-motion catalogue with high-precision measurements for 1.4 million stars out to the half-light radius of ω Cen with a typical temporal baseline of more than 20 years. Owing to the large number of observations (in total we reduced over 500 images and some stars in the central region have up to 467 individual astrometric measurements) the catalogue reaches unprecedented depth and precision. The highest precision is achieved in the well-covered centre of the cluster, in which our proper motions have a median error of only about 6.6 µ as yr −1 (0.17 km s −1 ) per component for bright stars.

The catalogue is larger than any other kinematic catalogue published for a globular cluster and significantly extends previous proper-motion catalogues for ω Cen 6 , 32 , 47 . A detailed comparison with other proper-motion datasets is published along with the catalogue 14 . In a following section and in Extended Data Fig. 3 , we compare the completeness of the different catalogues to show that it is plausible that the fast-moving stars have been missed in previous searches.

We use a high-quality subset of the proper-motion catalogue to search for real fast-moving stars and limit spurious astrometric measurements (for example, two sources that are falsely identified as one) that can have apparent high proper-motion measurements. Our criteria for this subset are based on the amount of available data for the measurements. Specifically, we used only sources that had at least 20 astrometric measurements covering a temporal baseline of at least 20 years and a fraction of rejected measurements (based on sigma clipping) of less than 15%. We also made cuts on the quality of the proper-motion fit requiring both a proper-motion error less than 0.194 mas yr −1 ≈ 5 km s −1 and a reduced χ 2 < 10 for the linear proper-motion fit for both the right ascension (RA) and declination (Dec) measurements. Apart from these quality selections, we also required the star to lie on the CMD sequence in an HST-based CMD (Fig. 2 ). These cuts help to drastically reduce the number of contaminants. These criteria are met uniformly out to a radius of about 90 arcsec; at larger radii they lead to selection effects due to reduced observational coverage. A total of 157,320 out of 241,133 (65.2%) entries of the proper-motion catalogue within r < 90″ match the combined criteria. Extended Data Table 1b shows the individual measured proper-motion components for the seven fast-moving stars. We note that for this analysis we have not applied the local a posteriori proper-motion corrections provided with the catalogue 14 , as we are studying the central region that is well dithered and observed with various rotation angles. We verified that applying these corrections would neither change our fast-moving star sample nor alter our conclusions.

Details on verification for fast-moving stars

The criteria detailed above should lead to a clean dataset with very few spurious proper-motion measurements. To ensure that the measurements for the fast-moving stars are reliable, we inspected each of them carefully.

As a first step, we tested the quality of the raw astrometric measurements by studying several goodness-of-fit parameters and photometric quality indicators for the point-spread-function fits used to measure stellar positions (Extended Data Fig. 3 ). We performed this analysis for the WFC3/UVIS F606W filter as it is the most used filter in the centre of ω Cen, and each star has at least 195 measurements in this filter. To verify the goodness of fit, we used the mean of the so-called quality-of-fit (QFIT) flag and the radial excess value, both of which take into account the residuals of the point-spread-function fit. Furthermore, we looked at the mean of the ratio of source flux with respect to the flux of neighbouring sources within its fit aperture. All five stars used for our analysis behave typically for well-measured stars of their magnitude and none of them show extreme values that would indicate problems with the photometry. It is noteworthy that the two stars excluded from our analysis based on their velocities being less than 3 σ above the escape velocity show some deviations. Star B has a relatively low mean QFIT value and high radial excess. Star G is the only one in the sample for which the neighbour flux to star flux ratio is larger than 1.

As a second step, we looked at the stars in several stacked HST images taken at various epochs ranging from 2002 to 2023. The extensive multi-epoch imaging is demonstrated in Extended Data Fig. 2 . The proper motion of a star at the escape velocity (62 km s −1 ) is 2.41 mas yr −1 . Therefore, we expect to see a displacement of at least 50 mas over 21 years, which corresponds to 1.25 WFC3/UVIS pixels. This motion can be seen by eye for all seven stars in the multi-epoch images. Again the excluded stars B and G stick out, that is, that they are partially blended with the neighbouring stars, thus explaining their larger astrometric errors.

Finally, we tested the reliability of our proper-motion measurements by limiting the raw position measurements to different subsets and redoing both the linear and quadratic fits to the motion of the stars. The first test run included only high signal-to-noise measurements. The second test run included only measurements taken with the WFC3/UVIS F606W filter. By using only one filter, we are immune to colour-induced effects such as a partially resolved blend between two differently coloured stars. The proper motions of all fast-moving stars are consistent within the measurement uncertainties using both methods.

Comparison with other proper-motion datasets

Before our analysis, two other high-precision proper-motion catalogues based on HST data have been published 6 , 32 covering the centre of ω Cen. Both datasets were searched for central high proper-motion stars, but none of the stars in our sample have been reported before. To understand why this is the case, we compare the completeness of the different catalogues. Extended Data Fig. 3a shows histograms of the magnitudes of stars with measured proper motions. In the inner 20″, our new catalogue contains more than three times the number of stars of the literature catalogues and extends to significantly fainter magnitudes. The newly detected fast-moving stars all lie at faint magnitudes, in which the completeness of the older catalogues is significantly lower than in the new proper-motion catalogue. This is because of the larger amount of data and the updated source-finding algorithms in the new catalogue, which explains the previous non-detection of the fast-moving stars.

Discussion of photometric errors

Apart from the astrometric reliability, we also studied the quality of the photometric measurements used to locate the stars in the CMD. Although the innermost stars are faint, their statistical photometric errors are small because of the large number of individual photometric measurements combined to a weighted mean value. The statistical errors range from 0.004 mag to 0.037 mag and are given in Extended Data Table 1c . However, especially for faint stars, this statistical error is not able to capture systematic issues caused, for example, by the influence of brighter neighbouring stars. These issues can be identified only by verifying the quality of the point-spread-function fit used to determine the individual photometric measurements. We report the mean quality of fit, radial excess and neighbour flux to source flux ratio flags for both filters in Extended Data Table 1c and compare them with those of stars at similar (Δ m < 0.5) magnitudes in Extended Data Fig. 3 . All stars in the robustly measured sample show typical quality of fit for their respective magnitude. We note that stars B and G (which were excluded from the analysis) show comparatively poor QFIT. Stars E and G show a possible flux contribution from a neighbouring source (indicated by a high radial excess value and a high neighbour flux to source flux ratio). This can be confirmed by the stacked images shown in Extended Data Fig. 2 , in which these stars show a close neighbour. Owing to the relatively bright magnitude of star E and the low astrometric scatter, we still consider its measurement valid.

Density of Milky Way contaminants versus fast-star background

To quantify our expected level of contamination from Milky Way foreground and background stars, we compared our results with those of a Besançon model 18 . Using the m1612 model, we simulate a 1 square degree patch centred on ω Cen retrieving Johnson colours and kinematics. We then transform the model Johnson V and I magnitudes into F606W and F814W magnitudes using linear relations fitted to Padova models 48 between V–I of 0 and 2. We use the same colour cuts and consider stars between F606W of 16–24. We then count the number of stars with a total proper motion above 2.41 mas yr −1 (equivalent to our velocity cutoff at the escape velocity v esc = 62 km s −1 ). These would appear as contaminants in our fast-moving star sample. We find a density of 0.0039 stars per arcsec 2 . This is somewhat higher than the 0.0026 ± 0.0003 stars per arcsec 2 found as the background level in our observations. This discrepancy is alleviated by considering only 65.2% of all stars within our catalogue meet the high-quality criteria used for our fast-moving star selection (see above). Correcting for this factor, we get an expected background of 0.0025 stars per arcsec 2 , perfectly matching the observed background density (Extended Data Fig. 1 ). This suggests that our background level is consistent with being predominantly Milky Way contaminants. Relaxing our requirement that stars be more than 3 σ above the escape velocity results in a higher observed background level of 0.0042 stars per arcsec 2 , no longer consistent with the Milky Way background. This suggests that our stricter definition of a fast-moving star reduces contamination from poorly measured stars in ω Cen to a negligible level.

Other scenarios that could explain the fast-moving stars

A complete contamination of our sample by Milky Way foreground and background stars that are non-members of ω Cen can be ruled out statistically. We now explore and rule out alternative scenarios to the fast-moving stars being bound to an IMBH. One alternative explanation for stars with a high velocity is to have them bound in a close orbit with a stellar-mass black hole. This scenario can be ruled out for BHs less than 100 M ☉ , as the periods required to reach the observed velocities are less than 10 years, which is well within the 20-year span over which we have observed linear motions.

Another scenario could be that the stars are actually unbound from the cluster and have recently been accelerated by three-body interactions, either with stellar-mass black hole binaries or with an IMBH. Ejection by an IMBH in the centre of the cluster can be ruled out by the very high rate of ejections necessary to sustain the observed number of fast-moving stars within the centre and the absence of observed fast-moving stars at larger radii. To sustain a density of 0.18 fast-moving stars per arcsec 2 in the inner 3 arcsec (equivalent to our conservative sample of five stars) moving with at least 2.4 mas yr −1 would require ejections with a rate of 0.004 stars per year. This would lead to about 117 additional fast-moving stars at larger radii (20″ < r < 90″), apart from around 60 foreground stars expected from the (completeness corrected) Besançon Milky Way model. In our dataset, we find 61 fast-moving stars between 20″ < r < 90″, consistent with the expected Milky Way background but not consistent with a substantial number of additional ejected stars. Moreover, a high hypothetical ejection rate of 0.004 stars per year would deplete all of the about 10 million stars of ω Cen in just 2.5 Gyr. If no IMBH is present, accelerations of stars above the escape velocity are still possible by three- or four-body interactions between stellar or compact object binaries 49 . However, these interactions would not be limited to the innermost few arcseconds of the cluster because of the slowly varying stellar density in the core of ω Cen. Furthermore, the expected rate of these ejection events is of the order of less than one ejection per 1 million years, around 1,000 times lower than needed to explain the observed number of fast-moving stars in the centre of ω Cen 49 , 50 .

Search for the fast-moving stars in recent LOS velocity data

Line-of-sight (LOS) velocities of the fast-moving stars could help to exclude contaminants and provide further constraints on the orbits of the stars and the mass and position of the IMBH. The deepest and most extensive spectroscopic catalogue of stars in ω Cen is part I of our recently published oMEGACat 13 . This catalogue was created using a large mosaic of observations with the VLT MUSE integral field spectrograph and contains both LOS velocity measurements and metallicities for more than 300,000 stars within the half-light radius of ω Cen. Although we could successfully cross-match five of the seven fast-moving stars, their signal-to-noise ratio is typically too low (about 2) for reliable velocity measurements, in particular for the four fastest, innermost stars.

We could, however, obtain an LOS velocity value for star E ( v LOS = 261.7 ± 2.7 km s −1 ) and star F ( v LOS = 232.5 ± 4.0 km s −1 ). These velocities are very close to the systemic LOS velocity of ω Cen (232.99 ± 0.06 km s −1 ; ref. 13 ), confirming their membership in the cluster, as the Milky Way foreground is centred at v LOS ≈ 0 with a dispersion of 70 km s −1 (ref. 18 ). However, as the relative LOS velocity with respect to the cluster is low and we have only those two velocities for these outer stars, the LOS velocities do not add stronger constraints on the IMBH. For this reason, we did not include them in the rest of our analysis.

Testing the robustness of the assumed escape velocity

Varying the parameters of the n -body models.

Because we use the escape velocity of ω Cen (assuming no IMBH is present) as the threshold for determining whether a star is considered fast or not, it is important to verify the robustness of the escape velocity value. We adopt an escape velocity v esc = 62 km s −1 (ref. 16 ); we have verified this value based on fitting similar N -body models to several state-of-the-art datasets, including MUSE LOS velocity dispersion measurements 51 and HST proper-motion-based dispersion measurements 52 for the central kinematics and Gaia DR3 53 measurements at larger radii using an assumed distance of 5.43 kpc. We varied both the assumed initial stellar mass function (using either the canonical Kroupa IMF 54 or the bottom-light IMF derived in ref. 55 ) and the black hole retention fraction (assuming values of 10%, 30%, 50% or 100%). Despite changes to the central mass-to-light ( M / L ) ratio between the models, the central escape velocity changes only minimally, with a range of values from 61.1 km s −1 to 64.8 km s −1 . Adopting any of these values leaves our sample of seven central stars above the escape velocity unchanged.

An independent test using surface-brightness profiles

As a second test, independent of the N -body models, we calculated an escape velocity profile based on a surface brightness profile using various surface brightness profiles and dynamical models from the literature. We started by parameterizing the surface brightness profile using multi-Gaussian expansion (MGE) 56 models. We then converted the surface brightness to a mass density using several mass-to-light ratios and distances used in the literature. From the mass density, we can derive the gravitational potential ( Φ ( r )). The escape velocity profile is then given by

with the tidal radius r tidal = 48.6′ ≈ 74.6 pc from refs. 57 , 58 .

These tests showed that the central escape velocity does not depend strongly on the stellar mass distribution in the centremost region, instead it is dominated by the global M / L ratio and the assumed distance. The early dynamical models in the IMBH debate assumed both a distance of 4.8 kpc (ref. 59 ) and an M / L of 2.6 (vdMA10; ref. 7 ) or 2.7 (N08; refs. 3 , 4 ). With these values our tests give a central escape velocity of 55.4 km s −1 (vdMA10) and 56.9 km s −1 (N08). If we would also use the 4.8 kpc distance to scale the proper motions, this gives a cutoff of 2.43 mas yr −1 (vdMA10) and 2.48 mas yr −1 (N08), close to the adopted cutoff at 2.41 mas yr −1 and not changing the sample of the seven fast-moving stars detected. Owing to the parallax measurements of the Gaia satellite and updated kinematic distance measurements, the distance to ω Cen was robustly redetermined and larger values have been found (5.24 ± 0.11 kpc; ref. 60 ; 5.43 ± 0.05; ref. 12 ). A dynamical model using the same surface brightness profile as ref. 3 but a larger distance of ${5.14}_{-0.24}^{+0.25}\,{\rm{kpc}}$ was presented in ref. 8 ; this study found an M / L of ${2.55}_{-0.28}^{+0.35}$ . Using these values, the central escape velocity derived from the surface brightness profile is 61.1 km s −1 (equivalent to a proper motion of 2.51 mas yr −1 ); again not changing our fast-moving stars sample. Finally, varying the distance of any model by 0.2 kpc while holding the M / L constant results in variation in the escape velocity of the order of ±3 km s −1 . These results show that our fast-moving star limit ( v esc = 62 km s −1 at a distance of 5.43 kpc) is consistent with the escape velocity values directly derived from surface-brightness profiles and several dynamically estimated M / L values. To visualize the escape velocity, we calculated the escape velocity using the surface-brightness profile in ref. 3 , an M / L of 2.4, and a distance of 5.43 kpc as found from the N -body models with a cluster of stellar mass black holes. The resulting profile is shown in Extended Data Fig. 5f . The predicted escape velocity is flat out to approximately 50″, a property shared by all of the calculated escape velocity profiles. This makes the detection of the fast-moving stars only in the central few arcseconds more compelling.

An empirical confirmation of the central escape velocity

We make one final, and relatively model-independent, empirical confirmation of the central escape velocity based on the distribution of 2D velocities in the innermost region of ω Cen (Extended Data Fig. 4 ). As we have seen in the analysis above, the escape velocity varies only slightly within the inner about 50″ of the core of ω Cen. Furthermore, the velocity dispersion profile is relatively flat in the innermost 10″, with a value of about 20 km s −1 (refs. 6 , 35 , 52 ). Therefore, we would expect rather similar distributions of stellar velocities in both the centre (0″ < r < 3″) and an outer ring at (3″ < r < 10″). Although we observe a clear excess of fast-moving stars in the inner 3 arcsec, there is a sharp cutoff very close to the adopted escape velocity in the (3″ < r < 10″) bin. Although there is a total of 2,090 stars, there is only one star with a velocity significantly faster than the escape velocity (instead of 17 stars expected from a 2D Maxwell–Boltzmann distribution with σ 1D = 20 km s −1 ). This suggests that the stars with these velocities have escaped the central region. This outer fast-moving star has a 2D velocity of 75.8 km s −1 and is at a radius of r = 9.5″. From the density of Milky Way contaminants with apparent velocities above the escape velocity, we would expect about 0.7 foreground stars in the (3″ < r < 10″) region; therefore, this fast-moving star is consistent with being a Milky Way foreground star.

The escape velocity provides a minimum black hole mass

The escape velocity for an isolated black hole is given by

In ω Cen, we have to take into account the potential of the globular cluster as well. If we assume this to be constant over the very small region in which we found the fast-moving stars (an assumption that agrees with the published surface brightness profiles, see Extended Data Fig. 6f ), we obtain

If a star at the distance of r 3 D with a velocity v 3 D is bound to the black hole, we can calculate the following lower limit on the black hole mass:

A lower limit can also be calculated if the LOS velocity and distance are not known, as v 3 D ≥ v 2 D and r 3 D ≥ r 2 D . As we do not know the exact 2D position of the black hole relative to the fast-moving stars, we calculated this lower limit for all stars and a grid of assumed 2D locations around the AvdM10 centre 6 . Each individual star alone would allow for a very low mass, as the location of the black hole could coincide with the star (Extended Data Fig. 5a–d ). However, combining these limits for all stars gives a higher minimum black hole mass (Extended Data Fig. 5e ). If we assume that all five robustly detected stars are bound to the black hole, the lower limit is about 8,200 M ☉ and the minimum mass location is only 0.3″ away from the AvdM10 (ref. 6 ) centre at the location RA = 201.6967370° and Dec = −47.4795066°. If we assume that the two most constraining stars are just random foreground contaminants, which is ruled out at the 3 σ level ( P = 0.0026), this limit drops to about 4,100 M ☉ , still well within the IMBH range.

Acceleration measurements

The astrometric analysis in the catalogue 14 considered only linear motions of the stars. If there is a massive black hole present near the centre, we might also be able to measure accelerated motion of the closest stars, allowing for a direct mass measurement of the black hole. With an IMBH mass of 40,000 M ☉ and at a radius of 0.026 pc (1″ on the sky), the acceleration of a star would be 0.25 km s −1 yr −1 (or 0.01 mas yr −2 ). This is at the limit of the precision of our current dataset. With a 20-year baseline, we expect only a deviation of 0.05 pixel from a linear motion. For bright stars, the astrometric uncertainty can be as low as 0.01 pixel; however, for the faint fast-moving stars we have detected, the errors are significantly larger.

To constrain these possible accelerations, we repeated the fit of the motion of each star enabling the addition of a quadratic component. The results for this fit are shown in Extended Data Table 1 . The accelerations of the stars are consistent with zero within 3 σ , but two stars have more than 2 σ acceleration measurements. The errors on our acceleration measurements lie between 0.004 mas yr −2 and 0.03 mas yr −2 and are, therefore, of a magnitude similar to the expected acceleration signal. The strongest acceleration is shown by star B, which has been excluded from the robust subset of fast-moving stars because its proper motion is not 3 σ above the escape velocity. Owing to the proximity of a bright neighbour star, we do not deem this acceleration measurement to be reliable.

As the LOS distances to the fast-moving stars are unknown, it is not possible to place direct constraints on the IMBH mass using the upper limits on accelerations. If no acceleration is detected, as is the case for the centremost star A, this could mean that either the black hole is not very massive or the LOS distance of star A to the black hole is large. Combining the measurements for the ensemble of fast-moving stars and making some assumptions on their spatial distribution still enables us to use the acceleration limits to place further constraints on the black hole mass and its location. This is described in the next section.

Markov chain Monte Carlo fitting of the acceleration data

Assuming the fast-moving stars are bound to the IMBH, we can model the stars as being on Keplerian orbits around the IMBH. We used Bayesian analysis to sample the posterior distribution for the unknown mass and position of the black hole. In this analysis, there were eight free parameters: black hole mass; its on-sky x - and y -positions; and five LOS distances between the black hole and each fast-moving star. This analysis makes use of the available astrometric observations but stops short of modelling individual stellar orbits that would introduce more free parameters.

We use a likelihood function with these eight free parameters and give the likelihood based on the observed on-sky x - and y -acceleration, proper motion and position of the five robustly measured fast-moving stars. For each star, we calculated a first likelihood term based on the modelled acceleration a modelled using a Gaussian distribution with mean a observed and width equal to the acceleration uncertainty. The second term in the likelihood accounts for the escape velocity constraints and is kept constant if the observed 2D velocity of the star is below the modelled escape velocity. For stars with 2D velocities above the modelled escape velocity, the likelihood is a Gaussian distribution with mean v 2D − v esc total and width equal to the uncertainty in observed proper motion.

We make these assumptions about the model: (1) The black hole mass is between 1 M ☉ and 100,000 M ☉ , because a black hole mass beyond this upper limit is ruled out by our N -body models. (2) The black hole is located within the distribution of the fast-moving stars. We use a Gaussian prior in the black hole x - and y -positions with a mean equal to the mean position of the fast-moving stars and width equal to their one-dimensional positional standard deviation, σ stars = 0.0221 pc; we also use a cutoff at ±0.16 pc. (3) The stellar positions are isotropically distributed around the black hole. We model the LOS positions of the stars relative to the black hole using a Gaussian distribution with mean 0 and width σ stars .

The posterior was sampled using a Markov chain Monte Carlo (MCMC) ensemble sampler implemented using the package emcee 61 using recommended burn-in and autocorrelation corrections. We show the posterior distribution for the black hole mass in Extended Data Fig. 6a . The 99% confidence lower limit (21,100 M ☉ ) is significantly higher than that derived from escape velocity constraints alone, whereas the upper limit on the mass is not well constrained. We also find a position for the black hole east of the AvdM10 centre, with $\varDelta x={-0.017}_{-0.031}^{+0.017}\,{\rm{pc}}$ and $\varDelta y={0.011}_{-0.025\,}^{+0.011}{\rm{p}}{\rm{c}}$ (Extended Data Fig. 6b ). The coordinates of the MCMC based centre estimate are RA = 201.6970128° and Dec = −47.4794533°. We note that the black hole location estimate is dominated by the marginal 2 σ acceleration signal of star D, which is the faintest star in the sample; follow-up studies are required to obtain more precise acceleration measurements.

N -body models

Apart from the analysis of stars with velocities above the escape velocity, we also used a set of existing N -body models with and without central IMBHs to get further constraints on the IMBH mass. We compared the simulations to the full velocity dispersion and surface density profile of ω Cen to determine the best-fitting model and the mass of a central IMBH. The set of models and the details of the fitting procedure are described in detail in refs. 5 , 9 . We note that these models have been presented already in the literature, but the fits to these models have been updated to incorporate the most recent Gaia DR3 data.

In short, the models started from King profiles 62 with central concentrations between c = 0.2 and c = 2.5 and initial half-mass radii between r h = 2 pc and r h = 35 pc. In the models with an IMBH, we varied the mass of the IMBH so that it contains either 0.5%, 1%, 2% or 5% of the cluster mass at T = 12 Gyr when the simulations were stopped. The models with an IMBH assumed a retention fraction of stellar-mass black holes of 10%, whereas in the models without an IMBH we varied the assumed retention fraction of stellar-mass black holes between 10% and 100%. At the end of the simulations, we calculated surface density and velocity dispersion profiles for each N -body model and then determined the best-fitting model by interpolation in our grid of models and using χ 2 minimization against the observed velocity and surface density profile of ω Cen.

The velocity distributions from observations and the models are shown in Extended Data Fig. 7 . We compare the distribution of measured 2D stellar velocities in the inner 10″ of ω Cen with the various models using a Kolmogorov–Smirnov test. Moreover, we compare the fraction of fast-moving stars in the innermost 3 arcsec (Extended Data Table 2 ). Models without an IMBH and with a 20,000 M ☉ IMBH are both strongly excluded by both the overall velocity distribution and the complete lack of fast-moving stars. The overall velocity distribution is in best agreement with the 47,000 M ☉ distribution, whereas the fraction of fast-moving stars is best matched by the 39,000 M ☉ simulation. This tension might be alleviated in future models that contain both an IMBH and a cluster of stellar mass black holes. We caution that these simulations have smaller numbers of stars than observed and that there can be substantial variations in the distribution of central stars due to strong encounters with remnants and binaries. Nonetheless, the simulations suggest that black holes with masses of M ≲ 50,000 M ☉ are consistent with the observed distribution of central velocities and fast-moving stars, whereas the no-IMBH case and significantly more massive black holes are disfavoured because of an overprediction of fast-moving stars. Updated N -body models fit to the oMEGACat kinematic data and dynamical modelling of these same datasets with Jeans models are currently underway.

Comparison with S-stars in the Galactic centre

The black hole indicated by our fast-moving star detection is only the second after Sgr A*, for which we can study the motion of multiple individual bound stellar companions. Therefore, the extensively measured stars around Sgr A* provide a unique comparison point to our fast-moving star sample. We compare the motions of the stars in the S-star catalogue in ref. 17 with our ω Cen fast-moving star sample in Extended Data Fig. 8 . When taking into account the different distances and the approximate black hole mass ratio of 100, the motions show similar amplitudes. However, the density of tracers in ω Cen is significantly lower, despite the greater depth of the observations.

Data availability

The data used in this paper are based on archival observations taken with the HST that are freely available in the Mikulski Archive for Space Telescopes. All used observations have been grouped under a DOI ( https://doi.org/10.17909/26QJ-G090 ) 63 . Moreover, the full proper-motion catalogue is made public along with the respective publication 14 .

Code availability

We used the following Python packages to perform the analysis: matplotlib 64 , scipy 65 , numpy 66 , astropy 67 and emcee 61 . The N -body simulations were run with the publicly available NBODY6 code 68 . We can share the code used in the data analysis upon request.

Greene, J. E., Strader, J. & Ho, L. C. Intermediate-mass black holes. Annu. Rev. Astron. Astrophys. 58 , 257–312 (2020).

Article ADS CAS Google Scholar

Inayoshi, K., Visbal, E. & Haiman, Z. The assembly of the first massive black holes. Annu. Rev. Astron. Astrophys. 58 , 27–97 (2020).

Noyola, E., Gebhardt, K. & Bergmann, M. Gemini and Hubble Space Telescope evidence for an intermediate-mass black hole in ω Centauri. Astrophys. J. 676 , 1008–1015 (2008).

Article ADS Google Scholar

Noyola, E. et al. Very large telescope kinematics for omega Centauri: further support for a central black hole. Astrophys. J. Lett. 719 , L60–L64 (2010).

Baumgardt, H. N -body modelling of globular clusters: masses, mass-to-light ratios and intermediate-mass black holes. Mon. Not. R. Astron. Soc. 464 , 2174–2202 (2017).

Anderson, J. & van der Marel, R. P. New limits on an intermediate-mass black hole in omega Centauri. I. Hubble Space Telescope photometry and proper motions. Astrophys. J. 710 , 1032–1062 (2010).

van der Marel, R. P. & Anderson, J. New limits on an intermediate-mass black hole in omega Centauri. II. Dynamical models. Astrophys. J. 710 , 1063–1088 (2010).

Zocchi, A., Gieles, M. & Hénault-Brunet, V. The effect of stellar-mass black holes on the central kinematics of ω Cen: a cautionary tale for IMBH interpretations. Mon. Not. R. Astron. Soc. 482 , 4713–4725 (2019).

Baumgardt, H. et al. No evidence for intermediate-mass black holes in the globular clusters ω Cen and NGC 6624. Mon. Not. R. Astron. Soc. 488 , 5340–5351 (2019).

Hilker, M. & Richtler, T. ω Centauri – a former nucleus of a dissolved dwarf galaxy? New evidence from Strömgren photometry. Astron. Astrophys. 362 , 895–909 (2000).

ADS CAS Google Scholar

Ibata, R. A., Bellazzini, M., Malhan, K., Martin, N. & Bianchini, P. Identification of the long stellar stream of the prototypical massive globular cluster ω Centauri. Nat. Astron. 3 , 667–672 (2019).

Baumgardt, H. & Vasiliev, E. Accurate distances to galactic globular clusters through a combination of Gaia EDR3, HST, and literature data. Mon. Not. R. Astron. Soc. 505 , 5957–5977 (2021).

Nitschai, M. S. et al. oMEGACat. I. MUSE spectroscopy of 300,000 stars within the half-light radius of ω Centauri. Astrophys. J. 958 , 8 (2023).

Häberle, M. et al. oMEGACat II – Photometry and proper motions for 1.4 million stars in Omega Centauri and its rotation in the plane of the sky. Preprint at https://arxiv.org/abs/2404.03722 (2024).

Goldsbury, R. et al. The ACS survey of galactic globular clusters. X. New determinations of centers for 65 clusters. Astron. J . 140 , 1830–1837 (2010).

Baumgardt, H. & Hilker, M. A catalogue of masses, structural parameters, and velocity dispersion profiles of 112 Milky Way globular clusters. Mon. Not. R. Astron. Soc. 478 , 1520–1557 (2018).

Gillessen, S. et al. An update on monitoring stellar orbits in the galactic center. Astrophys. J. 837 , 30 (2017).

Robin, A. C., Reylé, C., Derrière, S. & Picaud, S. A synthetic view on structure and evolution of the Milky Way. Astron. Astrophys. 409 , 523–540 (2003).

Gehrels, N. Confidence limits for small numbers of events in astrophysical data. Astrophys. J. 303 , 336–346 (1986).

Massari, D., Koppelman, H. H. & Helmi, A. Origin of the system of globular clusters in the Milky Way. Astron. Astrophys. 630 , L4 (2019).

Pfeffer, J., Lardo, C., Bastian, N., Saracino, S. & Kamann, S. The accreted nuclear clusters of the Milky Way. Mon. Not. R. Astron. Soc. 500 , 2514–2524 (2021).

Gebhardt, K., Rich, R. M. & Ho, L. C. A 20,000 M ☉ black hole in the stellar cluster G1. Astrophys. J. Lett. 578 , L41–L45 (2002).

Gebhardt, K., Rich, R. M. & Ho, L. C. An intermediate-mass black hole in the globular cluster G1: improved significance from new Keck and Hubble Space Telescope observations. Astrophys. J. 634 , 1093–1102 (2005).

Pechetti, R. et al. Detection of a 100,000 M ☉ black hole in M31’s most massive globular cluster: a tidally stripped nucleus. Astrophys. J. 924 , 48 (2022).

Bacon, R. et al. The MUSE second-generation VLT instrument. In Proc. SPIE Astronomical Telescopes + Instrumentation Vol. 7735 (eds McLean, I. S. et al.) 773508 (SPIE, 2010).

Böker, T. et al. The Near-Infrared Spectrograph (NIRSpec) on the James Webb Space Telescope. III. Integral-field spectroscopy. Astron. Astrophys. 661 , A82 (2022).

Article Google Scholar

GRAVITY Collaboration. et al. First light for GRAVITY: phase referencing optical interferometry for the Very Large Telescope Interferometer. Astron. Astrophys. 602 , A94 (2017).

Rieke, M. J. et al. Performance of NIRCam on JWST in flight. Publ. Astron. Soc. Pac. 135 , 028001 (2023).

Davies, R. et al. MICADO: the Multi-Adaptive Optics Camera for Deep Observations. Messenger 182 , 17–21 (2021).

ADS Google Scholar

Rigaut, F. et al. MAVIS on the VLT: a powerful, synergistic ELT complement in the visible. Messenger 185 , 7–11 (2021).

Jalali, B. et al. A dynamical N -body model for the central region of ω Centauri. Astron. Astrophys. 538 , A19 (2012).

Bellini, A. et al. The state-of-the-art HST astro-photometric analysis of the core of ω Centauri. I. The catalog. Astrophys. J. 842 , 6 (2017).

Zocchi, A., Gieles, M. & Hénault-Brunet, V. Radial anisotropy in ω Cen limiting the room for an intermediate-mass black hole. Mon. Not. R. Astron. Soc. 468 , 4429–4440 (2017).

Aros, F. I. et al. Dynamical modelling of globular clusters: challenges for the robust determination of IMBH candidates. Mon. Not. R. Astron. Soc. 499 , 4646–4665 (2020).

Pechetti, R. et al. ω Centauri: a MUSE discovery of a counter-rotating core. Mon. Not. R. Astron. Soc. 528 , 4941–4957 (2024).

Haggard, D. et al. A deep Chandra X-ray limit on the putative IMBH in omega Centauri. Astrophys. J. Lett. 773 , L31 (2013).

Tremou, E. et al. The MAVERIC Survey: still no evidence for accreting intermediate-mass black holes in globular clusters. Astrophys. J. 862 , 16 (2018).

Plotkin, R. M., Markoff, S., Kelly, B. C., Körding, E. & Anderson, S. F. Using the fundamental plane of black hole activity to distinguish X-ray processes from weakly accreting black holes. Mon. Not. R. Astron. Soc. 419 , 267–286 (2012).

Duras, F. et al. Universal bolometric corrections for active galactic nuclei over seven luminosity decades. Astron. Astrophys. 636 , A73 (2020).

Event Horizon Telescope Collaboration. et al. First Sagittarius A* Event Horizon Telescope results. V. Testing astrophysical models of the galactic center black hole. Astrophys. J. Lett. 930 , L16 (2022).

GRAVITY Collaboration. et al. The flux distribution of Sgr A*. Astron. Astrophys. 638 , A2 (2020).

Fernández-Ontiveros, J. A., López-López, X. & Prieto, A. Compact jets dominate the continuum emission in low-luminosity active galactic nuclei. Astron. Astrophys. 670 , A22 (2023).

Bellini, A. et al. Hubble Space Telescope Proper Motion (HSTPROMO) catalogs of galactic globular clusters. I. Sample selection, data reduction, and NGC 7078 results. Astrophys. J. 797 , 115 (2014).

Bellini, A. et al. The HST large programme on ω Centauri. II. Internal kinematics. Astrophys. J. 853 , 86 (2018).

Libralato, M. et al. Hubble Space Telescope Proper Motion (HSTPROMO) catalogs of galactic globular cluster. VI. Improved data reduction and internal-kinematic analysis of NGC 362. Astrophys. J. 861 , 99 (2018).

Libralato, M. et al. The Hubble Space Telescope UV Legacy Survey of Galactic Globular Clusters. XXIII. Proper-motion catalogs and internal kinematics. Astrophys. J. 934 , 150 (2022).

Gaia Collaboration, et al. Gaia focused product release: sources from service interface function image analysis. Half a million new sources in omega Centauri. Astron. Astrophys. 680 , A35 (2023).

Bressan, A. et al. PARSEC: stellar tracks and isochrones with the PAdova and TRieste Stellar Evolution Code. Mon. Not. R. Astron. Soc. 427 , 127–145 (2012).

Weatherford, N. C. et al. Stellar escape from globular clusters. I. Escape mechanisms and properties at ejection. Astrophys. J. 946 , 104 (2023).

Cabrera, T. & Rodriguez, C. L. Runaway and hypervelocity stars from compact object encounters in globular clusters. Astrophys. J. 953 , 19 (2023).

Kamann, S. et al. A stellar census in globular clusters with MUSE: the contribution of rotation to cluster dynamics studied with 200000 stars. Mon. Not. R. Astron. Soc. 473 , 5591–5616 (2018).

Watkins, L. L., van der Marel, R. P., Bellini, A. & Anderson, J. Hubble Space Telescope Proper Motion (HSTPROMO) catalogs of galactic globular clusters. II. Kinematic profiles and maps. Astrophys. J. 803 , 29 (2015).

Gaia Collaboration. et al. Gaia Data Release 3. Summary of the content and survey properties. Astron. Astrophys. 674 , A1 (2023).

Kroupa, P. On the variation of the initial mass function. Mon. Not. R. Astron. Soc. 322 , 231–246 (2001).

Baumgardt, H., Hénault-Brunet, V., Dickson, N. & Sollima, A. Evidence for a bottom-light initial mass function in massive star clusters. Mon. Not. R. Astron. Soc. 521 , 3991–4008 (2023).

Emsellem, E., Monnet, G. & Bacon, R. The multi-Gaussian expansion method: a tool for building realistic photometric and kinematical models of stellar systems I. The formalism. Astron. Astrophys. 285 , 723–738 (1994).

Harris, W. E. A catalog of parameters for globular clusters in the Milky Way. Astron. J. 112 , 1487 (1996).

Harris, W. E. A new catalog of globular clusters in the Milky Way. Preprint at https://doi.org/10.48550/arXiv.1012.3224 (2010).

van de Ven, G., van den Bosch, R. C. E., Verolme, E. K. & de Zeeuw, P. T. The dynamical distance and intrinsic structure of the globular cluster ω Centauri. Astron. Astrophys. 445 , 513–543 (2006).

Soltis, J., Casertano, S. & Riess, A. G. The parallax of ω Centauri measured from Gaia EDR3 and a direct, geometric calibration of the tip of the red giant branch and the Hubble constant. Astrophys. J. Lett. 908 , L5 (2021).

Foreman-Mackey, D., Hogg, D. W., Lang, D. & Goodman, J. emcee: the MCMC hammer. Publ. Astron. Soc. Pac. 125 , 306 (2013).

King, I. The structure of star clusters. I. an empirical density law. Astron. J. 67 , 471 (1962).

Häberle, M. Data from Paper “oMEGACat II - Photometry and proper motions for 1.4 million stars in Omega Centauri and its rotation in the plane of the sky” https://doi.org/10.17909/26QJ-G090 (MAST archive at Space Telescope Science Institute, 2024).

Hunter, J. D. Matplotlib: a 2D graphics environment. Comput. Sci. Eng. 9 , 90–95 (2007).

Virtanen, P. et al. SciPy 1.0: fundamental algorithms for scientific computing in Python. Nat. Methods 17 , 261–272 (2020).

Article CAS PubMed PubMed Central Google Scholar

Harris, C. R. et al. Array programming with NumPy. Nature 585 , 357–362 (2020).

Article ADS CAS PubMed PubMed Central Google Scholar

Astropy Collaboration. et al. The Astropy Project: sustaining and growing a community-oriented open-source project and the latest major release (v5.0) of the core package. Astrophys. J. 935 , 167 (2022).

Nitadori, K. & Aarseth, S. J. Accelerating NBODY6 with graphics processing units. Mon. Not. R. Astron. Soc. 424 , 545–552 (2012).

Download references

Acknowledgements

This study is based on the observations with the NASA/ESA HST, obtained at the Space Telescope Science Institute, which is operated by AURA, under NASA contract NAS 5-26555. S.K. acknowledges funding from UKRI in the form of a Future Leaders Fellowship (grant no. MR/T022868/1). A.S., M.W. and A.B. acknowledge support from HST grant GO-16777. A.B. acknowledges support from STScI grants GO-15857 and AR-17033. A.F.K. acknowledges funding from the Austrian Science Fund (FWF) ( https://doi.org/10.55776/ESP542 ). M.A.C. acknowledges support from Fondecyt Postdoctorado, project no. 3230727. A.M. acknowledges funding from PRIN 2022 2022MMEB9W (principal investigator: A. F. Marino).

Open access funding provided by Max Planck Society.

Author information

Authors and affiliations.

Max Planck Institute for Astronomy, Heidelberg, Germany

Maximilian Häberle, Nadine Neumayer, Antoine Dumont, Callie Clontz, Anja Feldmeier-Krause & Maria Selina Nitschai

Department of Physics and Astronomy, University of Utah, Salt Lake City, UT, USA

Anil Seth, Matthew Whitaker & Callie Clontz

Space Telescope Science Institute, Baltimore, MD, USA

Andrea Bellini & Jay Anderson

AURA for the European Space Agency (ESA), Space Telescope Science Institute, Baltimore, MD, USA

Mattia Libralato

INAF, Osservatorio Astronomico di Padova, Padova, Italy

School of Mathematics and Physics, The University of Queensland, St Lucia, Queensland, Australia

Holger Baumgardt

Facultad de Ingeniería y Arquitectura, Universidad Central de Chile, La Serena, Chile

Mayte Alfaro-Cuello

Leibniz Institute for Astrophysics, Potsdam, Germany

Nikolay Kacharov

Astrophysics Research Institute, Liverpool John Moores University, Liverpool, United Kingdom

Sebastian Kamann & Renuka Pechetti

Department of Astrophysics, University of Vienna, Wien, Austria

Anja Feldmeier-Krause & Glenn van de Ven

Dipartimento di Fisica e Astronomia ‘Galileo Galilei’, Università Degli Studi di Padova, Padova, Italy

Antonino Milone

You can also search for this author in PubMed Google Scholar

Contributions

All authors helped with the interpretation of the data and provided comments on the paper. M.H. has led the analysis of the data and is the main author of the text. A.S. and N.N. designed the overall project with significant contributions from A.B., G.v.d.V. and S.K.; A.S., N.N., H.B., M.W. and A.D. contributed to the text. A.S. determined the expected density of Milky Way contaminants. A.B., M.L. and J.A. provided their expertise on astrometric measurements with the HST. H.B. provided and fitted the N -body models for the analysis. M.W. ran the Bayesian analysis used to constrain the IMBH mass and position. A.D. performed the surface-brightness-profile-based calculations. S.K. and M.S.N. helped to find available LOS data for the stars.

Corresponding author

Correspondence to Maximilian Häberle .

Ethics declarations

Competing interests.

The authors declare no competing interests.

Peer review

Peer review information.

Nature thanks Karl Gebhardt, Darryl Haggard and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data figures and tables

Extended data fig. 1 number density of fast-moving stars..

The black markers with errorbars (1 σ ; based on Poisson statistics) show the measured number density of robustly detected fast-moving stars determined in radial bins with respect to ω Cen’s center. A constant density of Galactic fore-/background stars is expected, but we see a strong and statistically significant rise of the density towards the AvdM10 6 centre. Based on the number density of fast-moving stars at large radii (which is consistent with predictions from a Besançon Milky Way model, dashed line), only ∼ 0.073 fast-moving stars are expected within the central 3″ compared to the 5 observed stars.

Extended Data Fig. 2 Astrometry and multi epoch imaging for all fast-moving stars.

Each row ( a–g ) shows the astrometry and imaging for one of the seven fast-moving stars. The left column shows the raw astrometric measurements used to determine the proper motions, colour-coded by the epoch of their observation. The centre column shows the linear and quadratic fits to both the R.A. and Dec. position change of the stars. Errorbars correspond to the 1 σ error on the individual position measurements. The right column shows stacked images from 2002 (ACS/WFC F625W) and 2023 (WFC3/UVIS F606W); the positions of the fast stars are marked with a pink open circle.

Extended Data Fig. 3 Completeness of the catalogue and photometric diagnostics.

Panel a compares the completeness of the various available proper motion datasets for the core of ω Cen, using histograms of the magnitude distribution. The new oMEGACat 14 has significantly higher completeness and reaches fainter magnitudes than the literature catalogues even if we apply the strict quality criteria used in this work. This explains why previous catalogues have not found the faint fast-moving stars (marked with vertical lines) we detect here. The grey dots in b – d show the mean of photometric diagnostics for the raw PSF photometry measurements for the fast-moving stars compared with the bulk of stars in the catalogue. The first panel shows the QFIT parameter, given by the linear correlation function between the PSF and the pixel values in the image. The second panel shows the radial excess parameter, a parameter that compares the residual flux inside versus outside of the fit aperture. The third panel shows the flux ratio between the flux of a star itself and its neighbouring sources. All five robustly measured stars show typical behaviour for their magnitude, while the excluded fast-moving stars (B, G) are influenced by bright neighbouring sources.

Extended Data Fig. 4 Empirical verification of the escape velocity.

Panels a and b show histograms of the observed 2D velocity distribution in the very centre (0″ <r < 3″; c ) and in an outer ring (3″ <r < 10″; d ). While the lower velocities are well described by a 2D Maxwell-Boltzmann distribution with σ 1D = 20 km s −1 (marked with a solid black line, the dashed black lines refer to alternative distributions with σ 1D = 17 km s −1 and σ 1D = 23 km s −1 ), there are clearly notable differences at higher velocities. Those become especially visible in the cumulative normalized histogram shown in d and the zoom-in in e : while the distribution between (0″ <r < 3″, blue line) shows an excess of fast-moving stars, the distribution at larger radii (3″ <r < 10″, orange line) shows a clear deficit of stars at velocities larger than the escape velocity, making the used escape velocity threshold very plausible. Even though the sample is ten times larger, there is only a single star with a velocity significantly larger than v esc . This star has a 2D velocity of 75.8 km s −1 and is at a radius of r = 9.5″. It is consistent with being a Milky Way foreground star.

Extended Data Fig. 5 Determination of a lower limit on the IMBH mass using the escape velocity.

The presence of stars with velocities above the escape velocity of the cluster indicates that they are bound to a massive object. Since we neither know the mass nor the exact position of the object, we can only infer a lower mass limit for each possible 2D location. The four left plots ( a–d ) show the contours of the minimum black hole mass indicated by the four centremost robustly measured fast-moving stars. By combining the minimum black hole mass constraints from each of the fast-moving stars, we can find the position that allows for the lowest IMBH mass ( e ). This analysis indicates a firm lower limit of around 8,200 M ☉ . Our minimum mass location only differs by ∼ 0.3 arcsec from the AvdM10 6 centre. This result does not significantly change if we assume that some of the fast-moving stars are contaminants and remove them from the analysis. Panel f shows the results for a surface brightness profile based escape velocity profile in blue, using the surface brightness profile from 3 and the dynamical distance (5.43 kpc) and M/L ratio (2.4) derived from N-body models, either without any IMBH, with a 8,200 M ☉ IMBH, or a 40,000 M ☉ IMBH. The radii are measured with respect to the minimum mass centre shown in e . The shaded regions indicate the uncertainty introduced by an assumed error of ±0.2 kpc on the distance. The surface-brightness profile based escape velocity is compatible with the adopted value of v esc . = 62 km s −1 . The profile without an IMBH is also nearly flat in the inner ∼ 50″, justifying the assumption of a flat profile in the innermost region.

Extended Data Fig. 6 Constraints on the IMBH using the acceleration measurements.

Taking into account the limits on the accelerations gives us additional constraints on black hole mass ( a ) and on-sky position ( b ). The contours shown correspond to the 1-, 2-, and 3-sigma levels of the distribution. This analysis using both escape velocity and acceleration measurements from the five robustly measured fast stars constrains the minimum IMBH mass stronger than escape velocity constraints alone. Both plots also show the distribution from an MCMC run including stars B and G.

Extended Data Fig. 7 Comparison of the observed velocity distribution with N-Body models.

a , 2D velocity distribution for the stars in the inner 10 arcseconds of ω Cen. We show the observed data in grey, the results for an N-body model without an IMBH in black, and the results for a model with an 47,000 M ☉ IMBH in blue (based on the models of ref. 9 ). The N-body model without an IMBH predicts no stars above the escape velocity; the 47,000 M ⊙ model predicts a number close to our observations. b , Comparison of the normalized, cumulative distribution of stellar velocities for our data and five different N-body models.

Extended Data Fig. 8 Comparison with the Galactic Centre.

In this figure we compare the observed physical motion of our fast star sample with the stars orbiting the black hole Sgr A* in the Galactic Center 17 . The physical scale probed by the fast-moving stars is similar to that probed by the S stars in the Milky Way centre; however, the density of these tracers is lower. Owing to the approximately ∼ 100 times higher black hole mass of Sgr A*, we expect the motions to be ∼ 10 times faster and periods of the stars to be ∼ 10 times shorter, and thus show the motion for 2 years for the S stars to compare to the 20 year time span we observe the stars in ω Cen.

Supplementary information

Peer review file, rights and permissions.

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ .

Reprints and permissions

About this article

Cite this article.

Häberle, M., Neumayer, N., Seth, A. et al. Fast-moving stars around an intermediate-mass black hole in ω Centauri. Nature 631 , 285–288 (2024). https://doi.org/10.1038/s41586-024-07511-z

Download citation

Received : 15 December 2023

Accepted : 02 May 2024

Published : 10 July 2024

Issue Date : 11 July 2024

DOI : https://doi.org/10.1038/s41586-024-07511-z

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

By submitting a comment you agree to abide by our Terms and Community Guidelines . If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Quick links

Explore articles by subject
Guide to authors
Editorial policies

Suggestions or feedback?

MIT News | Massachusetts Institute of Technology

Machine learning
Social justice
Black holes
Classes and programs

Departments

Aeronautics and Astronautics
Brain and Cognitive Sciences
Architecture
Political Science
Mechanical Engineering

Centers, Labs, & Programs

Abdul Latif Jameel Poverty Action Lab (J-PAL)
Picower Institute for Learning and Memory
Lincoln Laboratory
School of Architecture + Planning
School of Engineering
School of Humanities, Arts, and Social Sciences
Sloan School of Management
School of Science
MIT Schwarzman College of Computing

A prosthesis driven by the nervous system helps people with amputation walk naturally

Press contact :.

A person wears a prosthetic leg with a circuit board while walking up stairs in a lab.

Previous image Next image

State-of-the-art prosthetic limbs can help people with amputations achieve a natural walking gait, but they don’t give the user full neural control over the limb. Instead, they rely on robotic sensors and controllers that move the limb using predefined gait algorithms.

Using a new type of surgical intervention and neuroprosthetic interface, MIT researchers, in collaboration with colleagues from Brigham and Women’s Hospital, have shown that a natural walking gait is achievable using a prosthetic leg fully driven by the body’s own nervous system. The surgical amputation procedure reconnects muscles in the residual limb, which allows patients to receive “proprioceptive” feedback about where their prosthetic limb is in space.

In a study of seven patients who had this surgery, the MIT team found that they were able to walk faster, avoid obstacles, and climb stairs much more naturally than people with a traditional amputation.

“This is the first prosthetic study in history that shows a leg prosthesis under full neural modulation, where a biomimetic gait emerges. No one has been able to show this level of brain control that produces a natural gait, where the human’s nervous system is controlling the movement, not a robotic control algorithm,” says Hugh Herr, a professor of media arts and sciences, co-director of the K. Lisa Yang Center for Bionics at MIT, an associate member of MIT’s McGovern Institute for Brain Research, and the senior author of the new study.

Patients also experienced less pain and less muscle atrophy following this surgery, which is known as the agonist-antagonist myoneural interface (AMI). So far, about 60 patients around the world have received this type of surgery, which can also be done for people with arm amputations.

Hyungeun Song, a postdoc in MIT’s Media Lab, is the lead author of the paper , which appears today in Nature Medicine .

Sensory feedback

Most limb movement is controlled by pairs of muscles that take turns stretching and contracting. During a traditional below-the-knee amputation, the interactions of these paired muscles are disrupted. This makes it very difficult for the nervous system to sense the position of a muscle and how fast it’s contracting — sensory information that is critical for the brain to decide how to move the limb.

People with this kind of amputation may have trouble controlling their prosthetic limb because they can’t accurately sense where the limb is in space. Instead, they rely on robotic controllers built into the prosthetic limb. These limbs also include sensors that can detect and adjust to slopes and obstacles.

To try to help people achieve a natural gait under full nervous system control, Herr and his colleagues began developing the AMI surgery several years ago. Instead of severing natural agonist-antagonist muscle interactions, they connect the two ends of the muscles so that they still dynamically communicate with each other within the residual limb. This surgery can be done during a primary amputation, or the muscles can be reconnected after the initial amputation as part of a revision procedure.

“With the AMI amputation procedure, to the greatest extent possible, we attempt to connect native agonists to native antagonists in a physiological way so that after amputation, a person can move their full phantom limb with physiologic levels of proprioception and range of movement,” Herr says.

In a 2021 study , Herr’s lab found that patients who had this surgery were able to more precisely control the muscles of their amputated limb, and that those muscles produced electrical signals similar to those from their intact limb.

After those encouraging results, the researchers set out to explore whether those electrical signals could generate commands for a prosthetic limb and at the same time give the user feedback about the limb’s position in space. The person wearing the prosthetic limb could then use that proprioceptive feedback to volitionally adjust their gait as needed.

In the new Nature Medicine study, the MIT team found this sensory feedback did indeed translate into a smooth, near-natural ability to walk and navigate obstacles.

“Because of the AMI neuroprosthetic interface, we were able to boost that neural signaling, preserving as much as we could. This was able to restore a person's neural capability to continuously and directly control the full gait, across different walking speeds, stairs, slopes, even going over obstacles,” Song says.

A natural gait

For this study, the researchers compared seven people who had the AMI surgery with seven who had traditional below-the-knee amputations. All of the subjects used the same type of bionic limb: a prosthesis with a powered ankle as well as electrodes that can sense electromyography (EMG) signals from the tibialis anterior the gastrocnemius muscles. These signals are fed into a robotic controller that helps the prosthesis calculate how much to bend the ankle, how much torque to apply, or how much power to deliver.

The researchers tested the subjects in several different situations: level-ground walking across a 10-meter pathway, walking up a slope, walking down a ramp, walking up and down stairs, and walking on a level surface while avoiding obstacles.

In all of these tasks, the people with the AMI neuroprosthetic interface were able to walk faster — at about the same rate as people without amputations — and navigate around obstacles more easily. They also showed more natural movements, such as pointing the toes of the prosthesis upward while going up stairs or stepping over an obstacle, and they were better able to coordinate the movements of their prosthetic limb and their intact limb. They were also able to push off the ground with the same amount of force as someone without an amputation.

“With the AMI cohort, we saw natural biomimetic behaviors emerge,” Herr says. “The cohort that didn’t have the AMI, they were able to walk, but the prosthetic movements weren’t natural, and their movements were generally slower.”

These natural behaviors emerged even though the amount of sensory feedback provided by the AMI was less than 20 percent of what would normally be received in people without an amputation.

“One of the main findings here is that a small increase in neural feedback from your amputated limb can restore significant bionic neural controllability, to a point where you allow people to directly neurally control the speed of walking, adapt to different terrain, and avoid obstacles,” Song says.

“This work represents yet another step in us demonstrating what is possible in terms of restoring function in patients who suffer from severe limb injury. It is through collaborative efforts such as this that we are able to make transformational progress in patient care,” says Matthew Carty, a surgeon at Brigham and Women’s Hospital and associate professor at Harvard Medical School, who is also an author of the paper.

Enabling neural control by the person using the limb is a step toward Herr’s lab’s goal of “rebuilding human bodies,” rather than having people rely on ever more sophisticated robotic controllers and sensors — tools that are powerful but do not feel like part of the user’s body.

“The problem with that long-term approach is that the user would never feel embodied with their prosthesis. They would never view the prosthesis as part of their body, part of self,” Herr says. “The approach we’re taking is trying to comprehensively connect the brain of the human to the electromechanics.”

The research was funded by the MIT K. Lisa Yang Center for Bionics and the Eunice Kennedy Shriver National Institute of Child Health and Human Development.

Hugh Herr, who wears two prosthetic legs, speaks to someone holding a prosthetic leg.

Previous item Next item

Share this news article on:

Press mentions.

Researchers at MIT have developed a novel surgical technique that could “dramatically improve walking for people with below-the-knee amputations and help them better control their prosthetics,” reports Timmy Broderick for STAT . “With our patients, even though their limb is made of titanium and silicone, all these various electromechanical components, the limb feels natural, and it moves naturally, without even conscious thought," explains Prof. Hugh Herr.

Financial Times

A new surgical approach developed by MIT researchers enables a bionic leg driven by the body’s nervous system to restore a natural walking gait more effectively than other prosthetic limbs, reports Clive Cookson for the Financial Times . “The approach we’re taking is trying to comprehensively connect the brain of the human to the electro-mechanics,” explains Prof. Hugh Herr.

The Washington Post

A new surgical procedure and neuroprosthetic interface developed by MIT researchers allows people with amputations to control their prosthetic limbs with their brains, “a significant scientific advance that allows for a smoother gait and enhanced ability to navigate obstacles,” reports Lizette Ortega for The Washington Post . “We’re starting to get a glimpse of this glorious future wherein a person can lose a major part of their body, and there’s technology available to reconstruct that aspect of their body to full functionality,” explains Prof. Hugh Herr.

The Guardian

MIT scientists have conducted a trial of a brain controlled bionic limb that improves gait, stability and speed over a traditional prosthetic, reports Hannah Devlin for The Guardian . Prof. Hugh Herr says with natural leg connections preserved, patients are more likely to feel the prosthetic as a natural part of their body. “When the person can directly control and feel the movement of the prosthesis it becomes truly part of the person’s anatomy,” Herr explains.

The Economist

Using a new surgical technique, MIT researchers have developed a bionic leg that can be controlled by the body’s own nervous system, reports The Economist . The surgical technique “involved stitching together the ends of two sets of leg muscles in the remaining part of the participants’ legs,” explains The Economist . “Each of these new connections forms a so-called agonist-antagonist myoneural interface, or AMI. This in effect replicates the mechanisms necessary for movement as well as the perception of the limb’s position in space. Traditional amputations, in contrast, create no such pairings.”

The Boston Globe

Researchers at MIT and Brigham and Women’s Hospital have created a new surgical technique and neuroprosthetic interface for amputees that allows a natural walking gait driven by the body’s own nervous system, reports Adam Piore for The Boston Globe . “We found a marked improvement in each patient’s ability to walk at normal levels of speed, to maneuver obstacles, as well as to walk up and down steps and slopes," explains Prof. Hugh Herr. “I feel like I have my leg — like my leg hasn’t been amputated,” shares Amy Pietrafitta, a participant in the clinical trial testing the new approach.

Magnetic sensors track muscle length

New surgery may enable better control of prosthetic limbs

Making prosthetic limbs feel more natural

More mit news.

Study finds health risks in switching ships from diesel to ammonia fuel

Read full story →

Making meaningful climate change through novel technologies

Five students converse around a whiteboard.

Empowering future innovators through a social impact lens

Woman with a patterned cloth face mask sits at a market stall in Kampala, Uganda. Most other people in the market are also wearing masks

Researchers study differences in attitudes toward Covid-19 vaccines between women and men in Africa

A woman and three men flank the microbioreactor system, which is about the size of a small printer

A new way to miniaturize cell production for cancer treatment

Deborah Fitzgerald stands at a lectern with an open laptop and some papers in front of her

Investigating the past to see technology’s future

More news on MIT News homepage →

Massachusetts Institute of Technology 77 Massachusetts Avenue, Cambridge, MA, USA

Map (opens in new window)
Events (opens in new window)
People (opens in new window)
Careers (opens in new window)
Accessibility
Social Media Hub
MIT on Facebook
MIT on YouTube
MIT on Instagram

share this!

July 10, 2024

This article has been reviewed according to Science X's editorial process and policies . Editors have highlighted the following attributes while ensuring the content's credibility:

fact-checked

trusted source

Study explores long-term impacts of ponderosa pine restoration treatment

by Northern Arizona University

In 1996, a group of researchers from NAU's Ecological Research Institute (ERI) embarked on an ambitious mission to study restoration across 5,224 acres of dense ponderosa pine forests on the Arizona Strip, a dry region of northern Arizona located between the Grand Canyon and the Utah state boundary line.

After more than 20 years of hands-on investigation, monitoring the dry landscape with evolving fieldwork technologies and high crew turnover rates, these same ecologists successfully decreased the area's tree density and vulnerability to wildfire.

They recently published their findings on the effort's long-term effects in the journal Restoration Ecology .

The ERI has led countless research expeditions to revitalize and protect local ecosystems from unnatural wildfires. In the past, limited time, human effort and study-specific data collection restrictions constricted these experiments to studies covering less than 1,000 acres.

As wildfires throughout the western United States grew more intense, and as counterproductive fire exclusion measures led to overly dense forests at greater risk of drought, competition, pathogens and fires that spread at the top of the forest canopy, the ERI saw a need to expand its forest restoration research across thousands of additional acres.

"Back in 1996, there were a couple of fires that were about 10,000 acres that were considered huge at the time," said John Paul Roccaforte, an ERI research associate and the study's lead author. "A few years after that, we're talking about a few million acres. Our approach was that we needed to have our studies scale up as well."

The opportunity to expand their research presented itself when the Bureau of Land Management (BLM) proposed a collaborative study: applying prescribed burns and mechanically thinning trees across a study site of ponderosa pine and Gambel oak forest in the Grand Canyon-Parashant National Monument.

Working with BLM crew members, NAU researchers installed 221 permanent plots in the area at the start of the experiment in 1996, setting aside about 1,200 acres as an untreated control area. They then helped train additional fire units and machine operators to complete tree thinning and prescribed burns until 2005.

The ERI used a unique thinning technique designed to protect older trees and return the monument landscape to its historically open conditions. Instead of thinning a consistent number of trees per acre, the ERI identified pre-settlement ponderosa pines, identifiable based on their unique yellow color, and pines with breast height diameters greater than 70 centimeters. These trees were then protected during thinning and burning.

Additionally, per ERI's restoration principles, teams retained an additional one-to-three replacement trees wherever they encountered evidence of a deceased historical tree.

"Something about fire is just really fun," Roccaforte said. "You can plan things on paper, but it's really exciting to get out on the ground from time to time and be really involved in the implementation part of it. Just being out there lighting stuff on fire and watching fuels get consumed, it's like helping restoration happen right before your eyes."

Until the study's conclusion in 2018, researchers routinely tracked forest structure, regeneration, old-tree mortality and tree growth in the area. Two crews of five researchers each would incrementally visit the site for eight days at a time, collecting measurements and comparing photographs to identify prominent changes in the terrain.

Researchers found the treatments decreased the forest's density by more than 50% while almost doubling the growth rates of individual trees, showcasing a newfound resilience against wildfire and variation in canopy coverage beneficial for wildlife. They also observed additional hardwood tree patches in place of pines after treatment, a phenomenon common in dry conifer forests with fewer resource competitors.

To ensure the long-term effectiveness of restoration strategies in similar dry climates, the study indicates forestry managers should routinely embrace fire as a tool to aid restoration instead of depending on other preventative measures. This way, patches of dense hardwood or vulnerable older oak trees responding to prescribed burns can be identified and monitored depending on each forest's goals.

"Before fire exclusion in the late 1800s, fires burned very frequently through these areas," Roccaforte said. "Fires would maintain and keep tree regeneration at bay. If we don't keep up on frequent low-intensity burning, then we could be right back in the same place we were to begin with in terms of overly dense stands, whether that be ponderosa pine or hardwood."

While no plans for further site research have been confirmed, Roccaforte said the permanent plots established in this study could be used for additional investigation. ERI and BLM will conduct joint investigations in the future.

To learn more about ERI and ponderosa pine restoration, visit eri.nau.edu .

Provided by Northern Arizona University

Explore further

Feedback to editors

Air pollution harms pollinators more than pests, study finds

17 minutes ago

Hexagonal metallic-mean approximants help bridge gap between quasicrystals and modulated structures

Opening the right doors: New work reveals 'jumping gene' control mechanisms

Researchers develop model to study heavy-quark recombination in quark-gluon plasma

57 minutes ago

A new species of extinct crocodile relative rewrites life on the Triassic coastline

12 hours ago

New method achieves tenfold increase in quantum coherence time via destructive interference of correlated noise

Mars likely had cold and icy past, new study finds

Study: Nanoparticle vaccines enhance cross-protection against influenza viruses

New tools are needed to make water affordable, says study

13 hours ago

Researchers demonstrate how to build 'time-traveling' quantum sensors

Relevant physicsforums posts, is meat broth really nutritious.

16 hours ago

Havana Syndrome

18 hours ago

Innovative ideas and technologies to help folks with disabilities

Jul 7, 2024

COVID Virus Lives Longer with Higher CO2 In the Air

Conflicting interpretations of rosemary oil study.

Jul 3, 2024

Who chooses official designations for individual dolphins, such as FB15, F153, F286?

Jun 26, 2024

Science review shows fuel treatments reduce future wildfire severity

Jun 24, 2024

Efforts to restore federal forests in eastern Oregon are working, research shows

Sep 6, 2023

Twenty-year study confirms California forests are healthier when burned, or thinned

Dec 13, 2023

Thinning forests, prescribed fire before drought reduced tree loss

May 29, 2019

Tree-regeneration decline and type-conversion after high-severity fires likely to cause little forest loss

Nov 1, 2023

Thinning and prescribed fire treatments reduce tree mortality

Oct 15, 2020

Recommended for you

Lion with nine lives breaks record with longest swim in predator-infested waters

14 hours ago

Wolves' return has had only small impact on deer populations in Washington state, study shows

17 hours ago

Tiny TnpB: The next-generation genome editing tool for plants unveiled

21 hours ago

From bands to spots, the secrets of the leopard gecko's skin

Energy-saving technique used by world's largest bats revealed

19 hours ago

Rising sea levels spell danger for shorebirds such as the oystercatcher

Let us know if there is a problem with our content.

Use this form if you have come across a typo, inaccuracy or would like to send an edit request for the content on this page. For general inquiries, please use our contact form . For general feedback, use the public comments section below (please adhere to guidelines ).

Please select the most appropriate category to facilitate processing of your request

Thank you for taking time to provide your feedback to the editors.

Your feedback is important to us. However, we do not guarantee individual replies due to the high volume of messages.

E-mail the story

Your email address is used only to let the recipient know who sent the email. Neither your address nor the recipient's address will be used for any other purpose. The information you enter will appear in your e-mail message and is not retained by Phys.org in any form.

Newsletter sign up

Get weekly and/or daily updates delivered to your inbox. You can unsubscribe at any time and we'll never share your details to third parties.

More information Privacy policy

Donate and enjoy an ad-free experience

We keep our content available to everyone. Consider supporting Science X's mission by getting a premium account.

E-mail newsletter

Environmental Science: Nano

Overlooked impact of surface hydroxylation on the solubility of less-soluble compounds: a case study of ceo 2 †.

* Corresponding authors

a Lomonosov Moscow State University, Department of Chemistry, Leninskie Gory 1/3, 119991 Moscow, Russia E-mail: [email protected]

b Kurnakov Institute of General and Inorganic Chemistry of the Russian Academy of Sciences, Leninskii prosp. 31, 117901 Moscow, Russia

c National Research Centre “Kurchatov Institute”, Akademika Kurchatova pl. 1, 123182 Moscow, Russia

d Max Planck Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart, Germany

e National Research University Higher School of Economics, Myasnitskaya st. 20, 101000 Moscow, Russia

Unexpectedly, the solubility of CeO 2 nanoparticles (NPs) at 25 °C does not depend on particle size, but is significantly affected by the sample's thermal pre-treatment. The classical interpretation of NPs' solubility proposed by the Gibbs–Thompson or Kelvin equations fails to describe the experimental data on CeO 2 solubility obtained in this study. Thermal treatment did not change the samples' morphological characteristics, while slightly affecting NP hydroxylation and local crystallinity. The differences in the solubility of dried and non-treated CeO 2 particles were most noticeable at pH < 4, and dissolved cerium concentration was much lower in the case of the dried sample. After prolonged storage (up to 4.5 years) of CeO 2 NPs in aqueous media, the solubility of dried samples gradually increased, while for non-treated samples it remained unchanged. Based on the example of CeO 2 , the dissolution laws of other less soluble nanomaterials should be reconsidered.

Graphical abstract: Overlooked impact of surface hydroxylation on the solubility of less-soluble compounds: a case study of CeO2

Supplementary files

Supplementary information PDF (1514K)

Article information

Download citation, permissions.

Overlooked impact of surface hydroxylation on the solubility of less-soluble compounds: a case study of CeO 2

T. V. Plakhova, A. Yu. Romanchuk, A. D. Konyukhova, I. F. Seregina, A. E. Baranchikov, R. D. Svetogorov, M. W. Terban, V. K. Ivanov and S. N. Kalmykov, Environ. Sci.: Nano , 2024, Advance Article , DOI: 10.1039/D4EN00014E

To request permission to reproduce material from this article, please go to the Copyright Clearance Center request page .

If you are an author contributing to an RSC publication, you do not need to request permission provided correct acknowledgement is given.

If you are the author of this article, you do not need to request permission to reproduce figures and diagrams provided correct acknowledgement is given. If you want to reproduce the whole article in a third-party publication (excluding your thesis/dissertation for which permission is not required) please go to the Copyright Clearance Center request page .

Read more about how to correctly acknowledge RSC content .

Social activity

Search articles by author.

This article has not yet been cited.

Search Menu
Sign in through your institution
Computer Science
Earth Sciences
Information Science
Life Sciences
Materials Science
Science Policy
Advance Access
Special Topics
Author Guidelines
Submission Site
Open Access Options
Self-Archiving Policy
About National Science Review
Editorial Board
Advertising and Corporate Services
Journals Career Network
Dispatch Dates
Journals on Oxford Academic
Books on Oxford Academic

Article Contents

Powerful qtl mapping and favorable allele mining in an all-in-one population: a case study of heading date.

These authors equally contributed to this work

Article contents
Figures & tables
Supplementary Data

Pengfei Wang, Ying Yang, Daoyang Li, Zhichao Yu, Bo zhang, Xiangchun Zhou, Lizhong Xiong, Jianwei Zhang, Yongzhong Xing, Powerful QTL mapping and favorable allele mining in an all-in-one population: a case study of heading date, National Science Review , 2024;, nwae222, https://doi.org/10.1093/nsr/nwae222

Permissions Icon Permissions

The multiparent advanced generation intercross (MAGIC) population is characterized with great potentials in power and resolution of QTL mapping, but SNP-based GWAS does not fully play its potential. In this study, a MAGIC population of 1021 lines was developed from four Xian and four Geng varieties from 5 subgroups of rice. A total of 44,000 genes showed functional polymorphisms among eight parents, including frameshift variations or premature stop codon variations, which provides the potential to map almost all genes of the MAGIC population. Principal component analysis results showed that the MAGIC population had a weak population structure. A high-density bin map of 24,414 bins was constructed. Segregation distortion occurred in the regions possessing the genes underlying genetic incompatibility and gamete development. SNP-based association analysis and bin-based linkage analysis identified 25 significant loci and 47 QTLs for heading date, including 14 known heading date genes. The mapping resolution of genes is dependent on genetic effects with offset distances of less than 55 kb for major effect genes and less than 123 kb for moderate effect genes. Four causal variants and noncoding structure variants were identified to be associated with heading date. Three to four types of alleles with strong, intermediate, weak, and no genetic effects were identified from eight parents, providing flexibility for the improvement of rice heading date. In most cases, japonica rice carries weak alleles, and indica rice carries strong alleles and nonfunctional alleles. These results confirmed that the MAGIC population provides the exceptional opportunity to detect QTLs, and its use is encouraged for mapping genes and mining favorable alleles for breeding.

Author notes

Month:	Total Views:
June 2024	144
July 2024	151

Email alerts

Citing articles via.

Recommend to Your Librarian

Affiliations

Online ISSN 2053-714X
Print ISSN 2095-5138
About Oxford Academic
Publish journals with us
University press partners
What we publish
New features
Open access
Institutional account management
Rights and permissions
Get help with access
Accessibility
Advertising
Media enquiries
Oxford University Press
Oxford Languages
University of Oxford

Oxford University Press is a department of the University of Oxford. It furthers the University's objective of excellence in research, scholarship, and education by publishing worldwide

Cookie settings
Cookie policy
Privacy policy
Legal notice

This Feature Is Available To Subscribers Only

This PDF is available to Subscribers Only

For full access to this pdf, sign in to an existing account, or purchase an annual subscription.

Foreign desk: What Really Fueled Ukraine War

“Could it be the Ukraine war is about fighting for people?” asks Ivan Krastev at The Spectator World .

Months before he invaded, Vladimir Putin lamented Russia’s population decline, vowing to do everything possible to reverse it.

By 2039, Russia’s population is projected to fall to less than 140 million, smaller than Nigeria, Brazil, Pakistan or Ethiopia.

And “Russia’s war in Ukraine has involved the large-scale abduction of children, particularly orphans, who have been forcibly transported to Russia and adopted by Russian parents.”

Indeed: “These so-called ‘new Russians’ were central to the way Putin was defining the objectives of his ‘special military operation.’”

Yet Russia has lost 150,000 soldiers in the war, plus 600,000 Russians who’ve fled.

A prolonged war will devastate Russia “economically and demographically.” So those saying Putin could be ready to end the war next year “are probably not entirely wrong.”

Eye on DC: A Case Study in Enabling

In early June Sen. Patty Murray slammed the Wall Street Journal exposé on President Biden’s rapid decline as a “hit piece,” reports the Washington Examiner’s Byron York .

But “after the disastrous June 27 debate exposed Biden’s infirmities for the world to see, Murray is singing a different tune,” namely that “President Biden must do more to demonstrate he can campaign strong enough to beat Donald Trump.”

York sums up: Only once “Murray’s voters could see for themselves what bad shape the president was in” was she “ready to show Biden the door.”

“Multiply that many times over” to include other lawmakers plus “compliant reporters” and “Democratic politicos” who also “had plenty of reason to know the president is not up to the job.”

Get opinions and commentary from our columnists

Subscribe to our daily Post Opinion newsletter!

Thanks for signing up!

Please provide a valid email address.

By clicking above you agree to the Terms of Use and Privacy Policy .

Never miss a story.

Physician: Jha’s Mandate Gaslighting

White House COVID czar Ashish Jha just “admitted that although he supported vaccine mandates, they did harm as well,” gripes Vinay Prasad at his Substack .

Yet Jha is still “gaslighting” by claiming that “mandates saved a lot of lives.”

No: “Perhaps as little as 1-2% of US people got a dose of the vaccine due to the mandate,” and both young people and those who’d already had COVID gained minimal added protection.

Yet “vaccine mandates cost lives by pushing people out of the work force — a socioeconomic death penalty. It also cost lives by breeding distrust.”

Jha is still “covering up for his own errors in judgment.”

Conservative: Extremism Won in France

“Far-left socialist Jean-Luc Melenchon now leads the largest [bloc] in the French National Assembly,” notes Commentary’s Seth Mandel — yet he’s an “authoritarian populist who wears his disgust for Jews on his sleeve.”

(For example, he “coolly asserted in an interview that the Jews killed Jesus.”)

So much for the “celebratory attitude” of “post-election discourse”: “Extremists weren’t thwarted. No, one extremist was thwarted through the elevation of a politician no less extreme.”

And “the extremist supported by all the ‘moderate’ commentators luxuriates in the kind of Jew-baiting that is practiced in the classrooms and the cafes and op-ed pages of mainstream publications.”

“The willingness of those in France to partner with Melenchon, and those in the West to advocate for such an alliance, was revelatory.”

From the right: Joe’s Inflation Ignorance

“The price controls they enacted that decade failed miserably, leading to shortages and other market disruptions,” groans City Journal’s Allison Schrager of “how poorly policymakers understood” 1970s inflation.

Yet President Biden’s new “plan to bring down food prices” just “repeats these past mistakes.”

Recent “inflation was caused initially by a combination of pandemic-driven supply constraints and elevated demand from federal transfer payments,” not greedy corporations.

Biden’s proposal ignores “basic economic realities,” “proposes cracking down on corporations” and “doling out money to consumers,” which could worsen inflation.

Rather than pushing “price controls or pressure campaigns on grocers,” Biden “should curb spending and let wages grow, allowing more Americans to weather the disastrous results of the past four years.”

— Compiled by The Post Editorial Board

IMAGES

(PDF) How to write a laboratory-based case study for the Journal
(PDF) Scientific Article Writing: An Overview
Social and Basic Sciences Research Review Template
How to structure your scientific article (Part 4: The result section
Understanding Health Research · How to read a scientific paper
Case Study Instructions

VIDEO

Cockatoos are trash burglars
My scientific article #61 ready!
Pulling ideas from the brain
Case Study: Social Media Growth and Sales Boost
Article writing Guidelines
Science of the Pandemic: What We’ve Learned, Challenges that Remain

COMMENTS

Continuing to enhance the quality of case study methodology in health
Purpose of case study methodology. Case study methodology is often used to develop an in-depth, holistic understanding of a specific phenomenon within a specified context. 11 It focuses on studying one or multiple cases over time and uses an in-depth analysis of multiple information sources. 16,17 It is ideal for situations including, but not limited to, exploring under-researched and real ...
Case Study Methodology of Qualitative Research: Key Attributes and
A case study is one of the most commonly used methodologies of social research. This article attempts to look into the various dimensions of a case study research strategy, the different epistemological strands which determine the particular case study type and approach adopted in the field, discusses the factors which can enhance the effectiveness of a case study research, and the debate ...
The case study approach
A case study is a research approach that is used to generate an in-depth, multi-faceted understanding of a complex issue in its real-life context. It is an established research design that is used extensively in a wide variety of disciplines, particularly in the social sciences. A case study can be defined in a variety of ways (Table.
Case Study Method: A Step-by-Step Guide for Business Researchers
Although case studies have been discussed extensively in the literature, little has been written about the specific steps one may use to conduct case study research effectively (Gagnon, 2010; Hancock & Algozzine, 2016).Baskarada (2014) also emphasized the need to have a succinct guideline that can be practically followed as it is actually tough to execute a case study well in practice.
Distinguishing case study as a research method from case reports as a
VARIATIONS ON CASE STUDY METHODOLOGY. Case study methodology is evolving and regularly reinterpreted. Comparative or multiple case studies are used as a tool for synthesizing information across time and space to research the impact of policy and practice in various fields of social research [].Because case study research is in-depth and intensive, there have been efforts to simplify the method ...
Case Study Methods and Examples
The purpose of case study research is twofold: (1) to provide descriptive information and (2) to suggest theoretical relevance. Rich description enables an in-depth or sharpened understanding of the case. It is unique given one characteristic: case studies draw from more than one data source. Case studies are inherently multimodal or mixed ...
Toward Developing a Framework for Conducting Case Study Research
The guide for the case study report is often omitted from case study plans because investigators view the reporting phase as being far in the future. Yin (1994) proposed that the report is planned at the start. Case studies do not have a widely accepted reporting format - hence the experience of the investigator is a key factor (Tellis, 1997).
Science: Articles, Research, & Case Studies on Science
by Desmond Dodd. Many assume that major oil and gas companies adamantly oppose climate-friendly regulation, but that's not true. A study of 30 years of corporate advocacy by Jonas Meckling finds that energy companies have backed clean-energy efforts when it aligns with their business interests. 12 Mar 2024. HBS Case.
Case study research for better evaluations of complex interventions
The Design of Case Study Research in Health Care (DESCARTE) model suggests a series of questions to be asked of a case study researcher (including clarity about the philosophy underpinning their research), study design (with a focus on case definition) and analysis (to improve process). The model resembles toolkits for enhancing the quality and ...
How to Write Case Reports and Case Series
can introduce very effective treatment paradigms. Preparing the manuscript for a case report may be the first exposure to scientific writing for a budding clinician/researcher. This manuscript describes the steps of writing a case report and essential considerations when publishing these articles. Individual components of a case report and the "dos and don'ts" while preparing these ...
Perspectives from Researchers on Case Study Design
This article examines five common misunderstandings about case-study research: (a) theoretical knowledge is more valuable than practical knowledge; (b) one cannot generalize from a single case, therefore, the single-case study cannot contribute to scientific development; (c) the case study is most useful for generating hypotheses, whereas other ...
Google Scholar
Google Scholar provides a simple way to broadly search for scholarly literature. Search across a wide variety of disciplines and sources: articles, theses, books, abstracts and court opinions.
What Is a Case Study?
Revised on November 20, 2023. A case study is a detailed study of a specific subject, such as a person, group, place, event, organization, or phenomenon. Case studies are commonly used in social, educational, clinical, and business research. A case study research design usually involves qualitative methods, but quantitative methods are ...
(PDF) The case study as a type of qualitative research
Abstract. This article presents the case study as a type of qualitative research. Its aim is to give a detailed description of a case study - its definition, some classifications, and several ...
Scientists' attitudes on science and values: Case studies and survey
This article examines the relevance of survey data of scientists' attitudes about science and values to case studies in philosophy of science. We describe two methodological challenges confronting such case studies: 1) small samples, and 2) potential for bias in selection, emphasis, and interpretation.
A case study exploring associations between popular media attention of
The association between mention of scientific research in popular media (e.g., the mainstream media or social media platforms) and scientific impact (e.g., citations) has yet to be fully explored. The purpose of this study was to clarify this relationship, while accounting for some other factors that likely influence scientific impact (e.g., the reputations of the scientists conducting the ...
Case Study
The Power of Relationships to Transform Systems. By John Kania & Juanita Zerda 1. Californians for Justice has elevated the power of young people by establishing authentic relationships between them and teachers, educators, and officials. In so doing, it has remade education in the state and crafted a model for broader social change.
Case study
A case study is a detailed description and assessment of a specific situation in the real world, often for the purpose of deriving generalizations and other insights about the subject of the case study. Case studies can be about an individual, a group of people, an organization, or an event, and they are used in multiple fields, including business, health care, anthropology, political science ...
Single case studies vs. multiple case studies: A comparative study
Also, the more case studies a scientific article has, the less observation time the writer has studied the case studies. But the more likely it is, that the case studies are confident in their representativeness (Gerring, 2004). If the researcher only wants to study one single thing (for example a person from a specific group) or a single group ...
Guidelines to the writing of case studies
It is best to simply tell the story and let the outcome speak for itself. With these points in mind, let's begin the process of writing the case study: Title page: Title: The title page will contain the full title of the article. Remember that many people may find our article by searching on the internet.
What affected the vitality of high-speed rail station areas? A case
The author(s) declare that financial support was received for the research, authorship, and/or publication of this article. This study is supported by the National Natural Science Foundation of China (Grant Number 52178059) and the Soft Science Project of Sichuan Provincial Science and Technology (Grant Number 24RKX0585). Conflict of interest
The case study approach
The case study approach allows in-depth, multi-faceted explorations of complex issues in their real-life settings. The value of the case study approach is well recognised in the fields of business, law and policy, but somewhat less so in health services research. ... Implementation Science. 2006, 1: 1-8. 10.1186/1748-5908-1-1. Article PubMed ...
JMSE
This case study illustrated that wind was the foremost driver of carcass drift due to the surface area above the water surface. ... Offshore disposal of whale carcasses is a sustainable practice but requires good planning and scientific assessment. Whale mortality and strandings have increased in recent years, with deceased whales often brought ...
Fast-moving stars around an intermediate-mass black hole in ω ...
Several studies have claimed the detection of a central black hole in ω Centauri, the most massive globular cluster of the Milky Way3-5. ... making this a good case for an intermediate-mass ...
A prosthesis driven by the nervous system helps people with amputation
"This is the first prosthetic study in history that shows a leg prosthesis under full neural modulation, where a biomimetic gait emerges. No one has been able to show this level of brain control that produces a natural gait, where the human's nervous system is controlling the movement, not a robotic control algorithm," says Hugh Herr, a professor of media arts and sciences, co-director ...
What Is a Case, and What Is a Case Study?
Résumé. Case study is a common methodology in the social sciences (management, psychology, science of education, political science, sociology). A lot of methodological papers have been dedicated to case study but, paradoxically, the question "what is a case?" has been less studied.
Study explores long-term impacts of ponderosa pine restoration treatment
In 1996, a group of researchers from NAU's Ecological Research Institute (ERI) embarked on an ambitious mission to study restoration across 5,224 acres of dense ponderosa pine forests on the ...
Overlooked impact of surface hydroxylation on the solubility of less
The differences in the solubility of dried and non-treated CeO 2 particles were most noticeable at pH < 4, and dissolved cerium concentration was much lower in the case of the dried sample. After prolonged storage (up to 4.5 years) of CeO 2 NPs in aqueous media, the solubility of dried samples gradually increased, while for non-treated samples ...
Powerful QTL mapping and favorable allele mining in an all-in-one
In this study, a MAGIC population of 1021 lines was developed from four Xian and four Geng varieties from 5 subgroups of rice. A total of 44,000 genes showed functional polymorphisms among eight parents, including frameshift variations or premature stop codon variations, which provides the potential to map almost all genes of the MAGIC population.
What really fueled Ukraine war, a case study in enabling and other
Eye on DC: A Case Study in Enabling In early June Sen. Patty Murray slammed the Wall Street Journal exposé on President Biden's rapid decline as a "hit piece," reports the Washington ...

Industrial Decarbonization: Confronting the Hard Challenges of Cement

The Harvard Business School Faculty Summer Reader 2024

How One Insurtech Firm Formulated a Strategy for Climate Change

Getting to Net Zero: The Climate Standards and Ecosystem the World Needs Now

When Does Impact Investing Make the Biggest Impact?

When It Comes to Climate Regulation, Energy Companies Take a More Nuanced View

How Used Products Can Unlock New Markets: Lessons from Apple's Refurbished iPhones

How Could Harvard Decarbonize Its Supply Chain?

Can Second-Generation Ethanol Production Help Decarbonize the World?

Do Disasters Rally Support for Climate Action? It's Complicated.

Are Companies Getting Away with 'Cheap Talk' on Climate Goals?

Could Clean Hydrogen Become Affordable at Scale by 2030?

Should Businesses Take a Stand on Societal Issues?

10 Trends to Watch in 2024

What Chandrayaan-3 Says About India's Entrepreneurial Approach to Space

Who Gets the Loudest Voice in DEI Decisions?

STEM Needs More Women. Recruiters Often Keep Them Out

Will Global Demand for Oil Peak This Decade?

Sweden’s Northvolt Electric Battery Maker: A Startup with a Mission

What Happens When Banks Ditch Coal: The Impact Is 'More Than Anyone Thought'

Secondary Logo

How to Write Case Reports and Case Series

INTRODUCTION

WHY ARE CASE REPORTS PUBLISHED?

ETHICAL ISSUES

HOW TO START?

COMPONENTS OF a CASE REPORT

Introduction

Describing the case

Figures and tables

Discussion including review

CASE SERIES - WHAT IS DIFFERENT?

ABSTRACT OF a CASE REPORT

REFERENCES IN a CASE REPORT

CHOOSING THE RIGHT JOURNAL

PUBLISHING THE CASE REPORT/SERIES AS a LETTER TO EDITOR/IMAGE SERIES

GUIDELINES FOR CASE REPORTS

AUTHORSHIP IN CASE REPORTS

CONCLUSIONS

Financial support and sponsorship

Readers Of this Article Also Read

Perspectives from Researchers on Case Study Design

What is a “case study” research design?

Qualitative Research with Case Studies

Mixed Methods Research with Case Studies

More Posts about Research Design

Designing Survey Research

Have a language expert improve your writing

What Is a Case Study? | Definition, Examples & Methods

Table of contents

Prevent plagiarism. Run a free check.

Cite this Scribbr article

Is this article helpful?

Shona McCombes

A case study exploring associations between popular media attention of scientific research and scientific citations

Introduction

Results and discussion

Conclusions

Case Study - Articles

Promoting a Culture of Caring in Education

Metro Rail Comes to Hyderabad

The Power of Relationships to Transform Systems

The School System Rebuilding Civil Society

Open Society Under Threat

Justice for Liberia’s Forgotten War

A Music Industry for Musicians

Preserving Social Purpose Amid a Global Pandemic

Waterborne Democracy for Rural India

National Geographic Reinvents Itself

The case study creation process

Guidelines to the writing of case studies

General Instructions

ORIGINAL RESEARCH article

1 Introduction

2 Literature review

2.2 Factors influencing the development and vitality of HSR station areas

3 Data and methods

3.2 Data sources

3.2.2 Data on points of interest (POIs), the road network, and railway lines

3.2.3 HSR timetable data