research abstract model

Writing an Abstract for Your Research Paper

Definition and Purpose of Abstracts

An abstract is a short summary of your (published or unpublished) research paper, usually about a paragraph (c. 6-7 sentences, 150-250 words) long. A well-written abstract serves multiple purposes:

• an abstract lets readers get the gist or essence of your paper or article quickly, in order to decide whether to read the full paper;
• an abstract prepares readers to follow the detailed information, analyses, and arguments in your full paper;
• and, later, an abstract helps readers remember key points from your paper.

It’s also worth remembering that search engines and bibliographic databases use abstracts, as well as the title, to identify key terms for indexing your published paper. So what you include in your abstract and in your title are crucial for helping other researchers find your paper or article.

If you are writing an abstract for a course paper, your professor may give you specific guidelines for what to include and how to organize your abstract. Similarly, academic journals often have specific requirements for abstracts. So in addition to following the advice on this page, you should be sure to look for and follow any guidelines from the course or journal you’re writing for.

The Contents of an Abstract

Abstracts contain most of the following kinds of information in brief form. The body of your paper will, of course, develop and explain these ideas much more fully. As you will see in the samples below, the proportion of your abstract that you devote to each kind of information—and the sequence of that information—will vary, depending on the nature and genre of the paper that you are summarizing in your abstract. And in some cases, some of this information is implied, rather than stated explicitly. The Publication Manual of the American Psychological Association , which is widely used in the social sciences, gives specific guidelines for what to include in the abstract for different kinds of papers—for empirical studies, literature reviews or meta-analyses, theoretical papers, methodological papers, and case studies.

Here are the typical kinds of information found in most abstracts:

• the context or background information for your research; the general topic under study; the specific topic of your research
• the central questions or statement of the problem your research addresses
• what’s already known about this question, what previous research has done or shown
• the main reason(s) , the exigency, the rationale , the goals for your research—Why is it important to address these questions? Are you, for example, examining a new topic? Why is that topic worth examining? Are you filling a gap in previous research? Applying new methods to take a fresh look at existing ideas or data? Resolving a dispute within the literature in your field? . . .
• your research and/or analytical methods
• your main findings , results , or arguments
• the significance or implications of your findings or arguments.

Your abstract should be intelligible on its own, without a reader’s having to read your entire paper. And in an abstract, you usually do not cite references—most of your abstract will describe what you have studied in your research and what you have found and what you argue in your paper. In the body of your paper, you will cite the specific literature that informs your research.

When to Write Your Abstract

Although you might be tempted to write your abstract first because it will appear as the very first part of your paper, it’s a good idea to wait to write your abstract until after you’ve drafted your full paper, so that you know what you’re summarizing.

What follows are some sample abstracts in published papers or articles, all written by faculty at UW-Madison who come from a variety of disciplines. We have annotated these samples to help you see the work that these authors are doing within their abstracts.

Choosing Verb Tenses within Your Abstract

The social science sample (Sample 1) below uses the present tense to describe general facts and interpretations that have been and are currently true, including the prevailing explanation for the social phenomenon under study. That abstract also uses the present tense to describe the methods, the findings, the arguments, and the implications of the findings from their new research study. The authors use the past tense to describe previous research.

The humanities sample (Sample 2) below uses the past tense to describe completed events in the past (the texts created in the pulp fiction industry in the 1970s and 80s) and uses the present tense to describe what is happening in those texts, to explain the significance or meaning of those texts, and to describe the arguments presented in the article.

The science samples (Samples 3 and 4) below use the past tense to describe what previous research studies have done and the research the authors have conducted, the methods they have followed, and what they have found. In their rationale or justification for their research (what remains to be done), they use the present tense. They also use the present tense to introduce their study (in Sample 3, “Here we report . . .”) and to explain the significance of their study (In Sample 3, This reprogramming . . . “provides a scalable cell source for. . .”).

Sample Abstract 1

From the social sciences.

Reporting new findings about the reasons for increasing economic homogamy among spouses

Gonalons-Pons, Pilar, and Christine R. Schwartz. “Trends in Economic Homogamy: Changes in Assortative Mating or the Division of Labor in Marriage?” Demography , vol. 54, no. 3, 2017, pp. 985-1005.

Sample Abstract 2

From the humanities.

Analyzing underground pulp fiction publications in Tanzania, this article makes an argument about the cultural significance of those publications

Emily Callaci. “Street Textuality: Socialism, Masculinity, and Urban Belonging in Tanzania’s Pulp Fiction Publishing Industry, 1975-1985.” Comparative Studies in Society and History , vol. 59, no. 1, 2017, pp. 183-210.

Sample Abstract/Summary 3

From the sciences.

Reporting a new method for reprogramming adult mouse fibroblasts into induced cardiac progenitor cells

Lalit, Pratik A., Max R. Salick, Daryl O. Nelson, Jayne M. Squirrell, Christina M. Shafer, Neel G. Patel, Imaan Saeed, Eric G. Schmuck, Yogananda S. Markandeya, Rachel Wong, Martin R. Lea, Kevin W. Eliceiri, Timothy A. Hacker, Wendy C. Crone, Michael Kyba, Daniel J. Garry, Ron Stewart, James A. Thomson, Karen M. Downs, Gary E. Lyons, and Timothy J. Kamp. “Lineage Reprogramming of Fibroblasts into Proliferative Induced Cardiac Progenitor Cells by Defined Factors.” Cell Stem Cell , vol. 18, 2016, pp. 354-367.

Sample Abstract 4, a Structured Abstract

Reporting results about the effectiveness of antibiotic therapy in managing acute bacterial sinusitis, from a rigorously controlled study

Note: This journal requires authors to organize their abstract into four specific sections, with strict word limits. Because the headings for this structured abstract are self-explanatory, we have chosen not to add annotations to this sample abstract.

Wald, Ellen R., David Nash, and Jens Eickhoff. “Effectiveness of Amoxicillin/Clavulanate Potassium in the Treatment of Acute Bacterial Sinusitis in Children.” Pediatrics , vol. 124, no. 1, 2009, pp. 9-15.

“OBJECTIVE: The role of antibiotic therapy in managing acute bacterial sinusitis (ABS) in children is controversial. The purpose of this study was to determine the effectiveness of high-dose amoxicillin/potassium clavulanate in the treatment of children diagnosed with ABS.

METHODS : This was a randomized, double-blind, placebo-controlled study. Children 1 to 10 years of age with a clinical presentation compatible with ABS were eligible for participation. Patients were stratified according to age (<6 or ≥6 years) and clinical severity and randomly assigned to receive either amoxicillin (90 mg/kg) with potassium clavulanate (6.4 mg/kg) or placebo. A symptom survey was performed on days 0, 1, 2, 3, 5, 7, 10, 20, and 30. Patients were examined on day 14. Children’s conditions were rated as cured, improved, or failed according to scoring rules.

RESULTS: Two thousand one hundred thirty-five children with respiratory complaints were screened for enrollment; 139 (6.5%) had ABS. Fifty-eight patients were enrolled, and 56 were randomly assigned. The mean age was 6630 months. Fifty (89%) patients presented with persistent symptoms, and 6 (11%) presented with nonpersistent symptoms. In 24 (43%) children, the illness was classified as mild, whereas in the remaining 32 (57%) children it was severe. Of the 28 children who received the antibiotic, 14 (50%) were cured, 4 (14%) were improved, 4(14%) experienced treatment failure, and 6 (21%) withdrew. Of the 28children who received placebo, 4 (14%) were cured, 5 (18%) improved, and 19 (68%) experienced treatment failure. Children receiving the antibiotic were more likely to be cured (50% vs 14%) and less likely to have treatment failure (14% vs 68%) than children receiving the placebo.

CONCLUSIONS : ABS is a common complication of viral upper respiratory infections. Amoxicillin/potassium clavulanate results in significantly more cures and fewer failures than placebo, according to parental report of time to resolution.” (9)

Some Excellent Advice about Writing Abstracts for Basic Science Research Papers, by Professor Adriano Aguzzi from the Institute of Neuropathology at the University of Zurich:

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What this handout is about

This handout provides definitions and examples of the two main types of abstracts: descriptive and informative. It also provides guidelines for constructing an abstract and general tips for you to keep in mind when drafting. Finally, it includes a few examples of abstracts broken down into their component parts.

What is an abstract?

An abstract is a self-contained, short, and powerful statement that describes a larger work. Components vary according to discipline. An abstract of a social science or scientific work may contain the scope, purpose, results, and contents of the work. An abstract of a humanities work may contain the thesis, background, and conclusion of the larger work. An abstract is not a review, nor does it evaluate the work being abstracted. While it contains key words found in the larger work, the abstract is an original document rather than an excerpted passage.

Why write an abstract?

You may write an abstract for various reasons. The two most important are selection and indexing. Abstracts allow readers who may be interested in a longer work to quickly decide whether it is worth their time to read it. Also, many online databases use abstracts to index larger works. Therefore, abstracts should contain keywords and phrases that allow for easy searching.

Say you are beginning a research project on how Brazilian newspapers helped Brazil’s ultra-liberal president Luiz Ignácio da Silva wrest power from the traditional, conservative power base. A good first place to start your research is to search Dissertation Abstracts International for all dissertations that deal with the interaction between newspapers and politics. “Newspapers and politics” returned 569 hits. A more selective search of “newspapers and Brazil” returned 22 hits. That is still a fair number of dissertations. Titles can sometimes help winnow the field, but many titles are not very descriptive. For example, one dissertation is titled “Rhetoric and Riot in Rio de Janeiro.” It is unclear from the title what this dissertation has to do with newspapers in Brazil. One option would be to download or order the entire dissertation on the chance that it might speak specifically to the topic. A better option is to read the abstract. In this case, the abstract reveals the main focus of the dissertation:

This dissertation examines the role of newspaper editors in the political turmoil and strife that characterized late First Empire Rio de Janeiro (1827-1831). Newspaper editors and their journals helped change the political culture of late First Empire Rio de Janeiro by involving the people in the discussion of state. This change in political culture is apparent in Emperor Pedro I’s gradual loss of control over the mechanisms of power. As the newspapers became more numerous and powerful, the Emperor lost his legitimacy in the eyes of the people. To explore the role of the newspapers in the political events of the late First Empire, this dissertation analyzes all available newspapers published in Rio de Janeiro from 1827 to 1831. Newspapers and their editors were leading forces in the effort to remove power from the hands of the ruling elite and place it under the control of the people. In the process, newspapers helped change how politics operated in the constitutional monarchy of Brazil.

From this abstract you now know that although the dissertation has nothing to do with modern Brazilian politics, it does cover the role of newspapers in changing traditional mechanisms of power. After reading the abstract, you can make an informed judgment about whether the dissertation would be worthwhile to read.

Besides selection, the other main purpose of the abstract is for indexing. Most article databases in the online catalog of the library enable you to search abstracts. This allows for quick retrieval by users and limits the extraneous items recalled by a “full-text” search. However, for an abstract to be useful in an online retrieval system, it must incorporate the key terms that a potential researcher would use to search. For example, if you search Dissertation Abstracts International using the keywords “France” “revolution” and “politics,” the search engine would search through all the abstracts in the database that included those three words. Without an abstract, the search engine would be forced to search titles, which, as we have seen, may not be fruitful, or else search the full text. It’s likely that a lot more than 60 dissertations have been written with those three words somewhere in the body of the entire work. By incorporating keywords into the abstract, the author emphasizes the central topics of the work and gives prospective readers enough information to make an informed judgment about the applicability of the work.

When do people write abstracts?

• when submitting articles to journals, especially online journals
• when applying for research grants
• when writing a book proposal
• when completing the Ph.D. dissertation or M.A. thesis
• when writing a proposal for a conference paper
• when writing a proposal for a book chapter

Most often, the author of the entire work (or prospective work) writes the abstract. However, there are professional abstracting services that hire writers to draft abstracts of other people’s work. In a work with multiple authors, the first author usually writes the abstract. Undergraduates are sometimes asked to draft abstracts of books/articles for classmates who have not read the larger work.

Types of abstracts

There are two types of abstracts: descriptive and informative. They have different aims, so as a consequence they have different components and styles. There is also a third type called critical, but it is rarely used. If you want to find out more about writing a critique or a review of a work, see the UNC Writing Center handout on writing a literature review . If you are unsure which type of abstract you should write, ask your instructor (if the abstract is for a class) or read other abstracts in your field or in the journal where you are submitting your article.

Descriptive abstracts

A descriptive abstract indicates the type of information found in the work. It makes no judgments about the work, nor does it provide results or conclusions of the research. It does incorporate key words found in the text and may include the purpose, methods, and scope of the research. Essentially, the descriptive abstract describes the work being abstracted. Some people consider it an outline of the work, rather than a summary. Descriptive abstracts are usually very short—100 words or less.

Informative abstracts

The majority of abstracts are informative. While they still do not critique or evaluate a work, they do more than describe it. A good informative abstract acts as a surrogate for the work itself. That is, the writer presents and explains all the main arguments and the important results and evidence in the complete article/paper/book. An informative abstract includes the information that can be found in a descriptive abstract (purpose, methods, scope) but also includes the results and conclusions of the research and the recommendations of the author. The length varies according to discipline, but an informative abstract is rarely more than 10% of the length of the entire work. In the case of a longer work, it may be much less.

Here are examples of a descriptive and an informative abstract of this handout on abstracts . Descriptive abstract:

The two most common abstract types—descriptive and informative—are described and examples of each are provided.

Informative abstract:

Abstracts present the essential elements of a longer work in a short and powerful statement. The purpose of an abstract is to provide prospective readers the opportunity to judge the relevance of the longer work to their projects. Abstracts also include the key terms found in the longer work and the purpose and methods of the research. Authors abstract various longer works, including book proposals, dissertations, and online journal articles. There are two main types of abstracts: descriptive and informative. A descriptive abstract briefly describes the longer work, while an informative abstract presents all the main arguments and important results. This handout provides examples of various types of abstracts and instructions on how to construct one.

Which type should I use?

Your best bet in this case is to ask your instructor or refer to the instructions provided by the publisher. You can also make a guess based on the length allowed; i.e., 100-120 words = descriptive; 250+ words = informative.

How do I write an abstract?

The format of your abstract will depend on the work being abstracted. An abstract of a scientific research paper will contain elements not found in an abstract of a literature article, and vice versa. However, all abstracts share several mandatory components, and there are also some optional parts that you can decide to include or not. When preparing to draft your abstract, keep the following key process elements in mind:

• Reason for writing: What is the importance of the research? Why would a reader be interested in the larger work?
• Problem: What problem does this work attempt to solve? What is the scope of the project? What is the main argument/thesis/claim?
• Methodology: An abstract of a scientific work may include specific models or approaches used in the larger study. Other abstracts may describe the types of evidence used in the research.
• Results: Again, an abstract of a scientific work may include specific data that indicates the results of the project. Other abstracts may discuss the findings in a more general way.
• Implications: What changes should be implemented as a result of the findings of the work? How does this work add to the body of knowledge on the topic?

(This list of elements is adapted with permission from Philip Koopman, “How to Write an Abstract.” )

All abstracts include:

• A full citation of the source, preceding the abstract.
• The most important information first.
• The same type and style of language found in the original, including technical language.
• Key words and phrases that quickly identify the content and focus of the work.
• Clear, concise, and powerful language.

Abstracts may include:

• The thesis of the work, usually in the first sentence.
• Background information that places the work in the larger body of literature.
• The same chronological structure as the original work.

How not to write an abstract:

• Do not refer extensively to other works.
• Do not add information not contained in the original work.
• Do not define terms.

If you are abstracting your own writing

When abstracting your own work, it may be difficult to condense a piece of writing that you have agonized over for weeks (or months, or even years) into a 250-word statement. There are some tricks that you could use to make it easier, however.

Reverse outlining:

This technique is commonly used when you are having trouble organizing your own writing. The process involves writing down the main idea of each paragraph on a separate piece of paper– see our short video . For the purposes of writing an abstract, try grouping the main ideas of each section of the paper into a single sentence. Practice grouping ideas using webbing or color coding .

For a scientific paper, you may have sections titled Purpose, Methods, Results, and Discussion. Each one of these sections will be longer than one paragraph, but each is grouped around a central idea. Use reverse outlining to discover the central idea in each section and then distill these ideas into one statement.

Cut and paste:

To create a first draft of an abstract of your own work, you can read through the entire paper and cut and paste sentences that capture key passages. This technique is useful for social science research with findings that cannot be encapsulated by neat numbers or concrete results. A well-written humanities draft will have a clear and direct thesis statement and informative topic sentences for paragraphs or sections. Isolate these sentences in a separate document and work on revising them into a unified paragraph.

If you are abstracting someone else’s writing

When abstracting something you have not written, you cannot summarize key ideas just by cutting and pasting. Instead, you must determine what a prospective reader would want to know about the work. There are a few techniques that will help you in this process:

Identify key terms:

Search through the entire document for key terms that identify the purpose, scope, and methods of the work. Pay close attention to the Introduction (or Purpose) and the Conclusion (or Discussion). These sections should contain all the main ideas and key terms in the paper. When writing the abstract, be sure to incorporate the key terms.

Highlight key phrases and sentences:

Instead of cutting and pasting the actual words, try highlighting sentences or phrases that appear to be central to the work. Then, in a separate document, rewrite the sentences and phrases in your own words.

Don’t look back:

After reading the entire work, put it aside and write a paragraph about the work without referring to it. In the first draft, you may not remember all the key terms or the results, but you will remember what the main point of the work was. Remember not to include any information you did not get from the work being abstracted.

Revise, revise, revise

No matter what type of abstract you are writing, or whether you are abstracting your own work or someone else’s, the most important step in writing an abstract is to revise early and often. When revising, delete all extraneous words and incorporate meaningful and powerful words. The idea is to be as clear and complete as possible in the shortest possible amount of space. The Word Count feature of Microsoft Word can help you keep track of how long your abstract is and help you hit your target length.

Example 1: Humanities abstract

Kenneth Tait Andrews, “‘Freedom is a constant struggle’: The dynamics and consequences of the Mississippi Civil Rights Movement, 1960-1984” Ph.D. State University of New York at Stony Brook, 1997 DAI-A 59/02, p. 620, Aug 1998

This dissertation examines the impacts of social movements through a multi-layered study of the Mississippi Civil Rights Movement from its peak in the early 1960s through the early 1980s. By examining this historically important case, I clarify the process by which movements transform social structures and the constraints movements face when they try to do so. The time period studied includes the expansion of voting rights and gains in black political power, the desegregation of public schools and the emergence of white-flight academies, and the rise and fall of federal anti-poverty programs. I use two major research strategies: (1) a quantitative analysis of county-level data and (2) three case studies. Data have been collected from archives, interviews, newspapers, and published reports. This dissertation challenges the argument that movements are inconsequential. Some view federal agencies, courts, political parties, or economic elites as the agents driving institutional change, but typically these groups acted in response to the leverage brought to bear by the civil rights movement. The Mississippi movement attempted to forge independent structures for sustaining challenges to local inequities and injustices. By propelling change in an array of local institutions, movement infrastructures had an enduring legacy in Mississippi.

Now let’s break down this abstract into its component parts to see how the author has distilled his entire dissertation into a ~200 word abstract.

What the dissertation does This dissertation examines the impacts of social movements through a multi-layered study of the Mississippi Civil Rights Movement from its peak in the early 1960s through the early 1980s. By examining this historically important case, I clarify the process by which movements transform social structures and the constraints movements face when they try to do so.

How the dissertation does it The time period studied in this dissertation includes the expansion of voting rights and gains in black political power, the desegregation of public schools and the emergence of white-flight academies, and the rise and fall of federal anti-poverty programs. I use two major research strategies: (1) a quantitative analysis of county-level data and (2) three case studies.

What materials are used Data have been collected from archives, interviews, newspapers, and published reports.

Conclusion This dissertation challenges the argument that movements are inconsequential. Some view federal agencies, courts, political parties, or economic elites as the agents driving institutional change, but typically these groups acted in response to movement demands and the leverage brought to bear by the civil rights movement. The Mississippi movement attempted to forge independent structures for sustaining challenges to local inequities and injustices. By propelling change in an array of local institutions, movement infrastructures had an enduring legacy in Mississippi.

Keywords social movements Civil Rights Movement Mississippi voting rights desegregation

Example 2: Science Abstract

Luis Lehner, “Gravitational radiation from black hole spacetimes” Ph.D. University of Pittsburgh, 1998 DAI-B 59/06, p. 2797, Dec 1998

The problem of detecting gravitational radiation is receiving considerable attention with the construction of new detectors in the United States, Europe, and Japan. The theoretical modeling of the wave forms that would be produced in particular systems will expedite the search for and analysis of detected signals. The characteristic formulation of GR is implemented to obtain an algorithm capable of evolving black holes in 3D asymptotically flat spacetimes. Using compactification techniques, future null infinity is included in the evolved region, which enables the unambiguous calculation of the radiation produced by some compact source. A module to calculate the waveforms is constructed and included in the evolution algorithm. This code is shown to be second-order convergent and to handle highly non-linear spacetimes. In particular, we have shown that the code can handle spacetimes whose radiation is equivalent to a galaxy converting its whole mass into gravitational radiation in one second. We further use the characteristic formulation to treat the region close to the singularity in black hole spacetimes. The code carefully excises a region surrounding the singularity and accurately evolves generic black hole spacetimes with apparently unlimited stability.

This science abstract covers much of the same ground as the humanities one, but it asks slightly different questions.

Why do this study The problem of detecting gravitational radiation is receiving considerable attention with the construction of new detectors in the United States, Europe, and Japan. The theoretical modeling of the wave forms that would be produced in particular systems will expedite the search and analysis of the detected signals.

What the study does The characteristic formulation of GR is implemented to obtain an algorithm capable of evolving black holes in 3D asymptotically flat spacetimes. Using compactification techniques, future null infinity is included in the evolved region, which enables the unambiguous calculation of the radiation produced by some compact source. A module to calculate the waveforms is constructed and included in the evolution algorithm.

Results This code is shown to be second-order convergent and to handle highly non-linear spacetimes. In particular, we have shown that the code can handle spacetimes whose radiation is equivalent to a galaxy converting its whole mass into gravitational radiation in one second. We further use the characteristic formulation to treat the region close to the singularity in black hole spacetimes. The code carefully excises a region surrounding the singularity and accurately evolves generic black hole spacetimes with apparently unlimited stability.

Keywords gravitational radiation (GR) spacetimes black holes

Works consulted

We consulted these works while writing this handout. This is not a comprehensive list of resources on the handout’s topic, and we encourage you to do your own research to find additional publications. Please do not use this list as a model for the format of your own reference list, as it may not match the citation style you are using. For guidance on formatting citations, please see the UNC Libraries citation tutorial . We revise these tips periodically and welcome feedback.

Belcher, Wendy Laura. 2009. Writing Your Journal Article in Twelve Weeks: A Guide to Academic Publishing Success. Thousand Oaks, CA: Sage Press.

Koopman, Philip. 1997. “How to Write an Abstract.” Carnegie Mellon University. October 1997. http://users.ece.cmu.edu/~koopman/essays/abstract.html .

Lancaster, F.W. 2003. Indexing And Abstracting in Theory and Practice , 3rd ed. London: Facet Publishing.

You may reproduce it for non-commercial use if you use the entire handout and attribute the source: The Writing Center, University of North Carolina at Chapel Hill

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• How to Write an Abstract

Expedite peer review, increase search-ability, and set the tone for your study

The abstract is your chance to let your readers know what they can expect from your article. Learn how to write a clear, and concise abstract that will keep your audience reading.

How your abstract impacts editorial evaluation and future readership

After the title , the abstract is the second-most-read part of your article. A good abstract can help to expedite peer review and, if your article is accepted for publication, it’s an important tool for readers to find and evaluate your work. Editors use your abstract when they first assess your article. Prospective reviewers see it when they decide whether to accept an invitation to review. Once published, the abstract gets indexed in PubMed and Google Scholar , as well as library systems and other popular databases. Like the title, your abstract influences keyword search results. Readers will use it to decide whether to read the rest of your article. Other researchers will use it to evaluate your work for inclusion in systematic reviews and meta-analysis. It should be a concise standalone piece that accurately represents your research. 

What to include in an abstract

The main challenge you’ll face when writing your abstract is keeping it concise AND fitting in all the information you need. Depending on your subject area the journal may require a structured abstract following specific headings. A structured abstract helps your readers understand your study more easily. If your journal doesn’t require a structured abstract it’s still a good idea to follow a similar format, just present the abstract as one paragraph without headings. 

Background or Introduction – What is currently known? Start with a brief, 2 or 3 sentence, introduction to the research area. 

Objectives or Aims – What is the study and why did you do it? Clearly state the research question you’re trying to answer.

Methods – What did you do? Explain what you did and how you did it. Include important information about your methods, but avoid the low-level specifics. Some disciplines have specific requirements for abstract methods. 

• CONSORT for randomized trials.
• STROBE for observational studies
• PRISMA for systematic reviews and meta-analyses

Results – What did you find? Briefly give the key findings of your study. Include key numeric data (including confidence intervals or p values), where possible.

Conclusions – What did you conclude? Tell the reader why your findings matter, and what this could mean for the ‘bigger picture’ of this area of research. 

Writing tips

The main challenge you may find when writing your abstract is keeping it concise AND convering all the information you need to.

• Keep it concise and to the point. Most journals have a maximum word count, so check guidelines before you write the abstract to save time editing it later.
• Write for your audience. Are they specialists in your specific field? Are they cross-disciplinary? Are they non-specialists? If you’re writing for a general audience, or your research could be of interest to the public keep your language as straightforward as possible. If you’re writing in English, do remember that not all of your readers will necessarily be native English speakers.
• Focus on key results, conclusions and take home messages.
• Write your paper first, then create the abstract as a summary.
• Check the journal requirements before you write your abstract, eg. required subheadings.
• Include keywords or phrases to help readers search for your work in indexing databases like PubMed or Google Scholar.
• Double and triple check your abstract for spelling and grammar errors. These kind of errors can give potential reviewers the impression that your research isn’t sound, and can make it easier to find reviewers who accept the invitation to review your manuscript. Your abstract should be a taste of what is to come in the rest of your article.

Don’t

• Sensationalize your research.
• Speculate about where this research might lead in the future.
• Use abbreviations or acronyms (unless absolutely necessary or unless they’re widely known, eg. DNA).
• Repeat yourself unnecessarily, eg. “Methods: We used X technique. Results: Using X technique, we found…”
• Contradict anything in the rest of your manuscript.
• Include content that isn’t also covered in the main manuscript.
• Include citations or references.

Tip: How to edit your work

Editing is challenging, especially if you are acting as both a writer and an editor. Read our guidelines for advice on how to refine your work, including useful tips for setting your intentions, re-review, and consultation with colleagues.

• How to Write a Great Title
• How to Write Your Methods
• How to Report Statistics
• How to Write Discussions and Conclusions
• How to Edit Your Work

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Research Paper Abstract – Writing Guide and Examples

Table of Contents

Research Paper Abstract

Research Paper Abstract is a brief summary of a research pape r that describes the study’s purpose, methods, findings, and conclusions . It is often the first section of the paper that readers encounter, and its purpose is to provide a concise and accurate overview of the paper’s content. The typical length of an abstract is usually around 150-250 words, and it should be written in a concise and clear manner.

Research Paper Abstract Structure

The structure of a research paper abstract usually includes the following elements:

• Background or Introduction: Briefly describe the problem or research question that the study addresses.
• Methods : Explain the methodology used to conduct the study, including the participants, materials, and procedures.
• Results : Summarize the main findings of the study, including statistical analyses and key outcomes.
• Conclusions : Discuss the implications of the study’s findings and their significance for the field, as well as any limitations or future directions for research.
• Keywords : List a few keywords that describe the main topics or themes of the research.

How to Write Research Paper Abstract

Here are the steps to follow when writing a research paper abstract:

• Start by reading your paper: Before you write an abstract, you should have a complete understanding of your paper. Read through the paper carefully, making sure you understand the purpose, methods, results, and conclusions.
• Identify the key components : Identify the key components of your paper, such as the research question, methods used, results obtained, and conclusion reached.
• Write a draft: Write a draft of your abstract, using concise and clear language. Make sure to include all the important information, but keep it short and to the point. A good rule of thumb is to keep your abstract between 150-250 words.
• Use clear and concise language : Use clear and concise language to explain the purpose of your study, the methods used, the results obtained, and the conclusions drawn.
• Emphasize your findings: Emphasize your findings in the abstract, highlighting the key results and the significance of your study.
• Revise and edit: Once you have a draft, revise and edit it to ensure that it is clear, concise, and free from errors.
• Check the formatting: Finally, check the formatting of your abstract to make sure it meets the requirements of the journal or conference where you plan to submit it.

Research Paper Abstract Examples

Research Paper Abstract Examples could be following:

Title : “The Effectiveness of Cognitive-Behavioral Therapy for Treating Anxiety Disorders: A Meta-Analysis”

Abstract : This meta-analysis examines the effectiveness of cognitive-behavioral therapy (CBT) in treating anxiety disorders. Through the analysis of 20 randomized controlled trials, we found that CBT is a highly effective treatment for anxiety disorders, with large effect sizes across a range of anxiety disorders, including generalized anxiety disorder, panic disorder, and social anxiety disorder. Our findings support the use of CBT as a first-line treatment for anxiety disorders and highlight the importance of further research to identify the mechanisms underlying its effectiveness.

Title : “Exploring the Role of Parental Involvement in Children’s Education: A Qualitative Study”

Abstract : This qualitative study explores the role of parental involvement in children’s education. Through in-depth interviews with 20 parents of children in elementary school, we found that parental involvement takes many forms, including volunteering in the classroom, helping with homework, and communicating with teachers. We also found that parental involvement is influenced by a range of factors, including parent and child characteristics, school culture, and socio-economic status. Our findings suggest that schools and educators should prioritize building strong partnerships with parents to support children’s academic success.

Title : “The Impact of Exercise on Cognitive Function in Older Adults: A Systematic Review and Meta-Analysis”

Abstract : This paper presents a systematic review and meta-analysis of the existing literature on the impact of exercise on cognitive function in older adults. Through the analysis of 25 randomized controlled trials, we found that exercise is associated with significant improvements in cognitive function, particularly in the domains of executive function and attention. Our findings highlight the potential of exercise as a non-pharmacological intervention to support cognitive health in older adults.

When to Write Research Paper Abstract

The abstract of a research paper should typically be written after you have completed the main body of the paper. This is because the abstract is intended to provide a brief summary of the key points and findings of the research, and you can’t do that until you have completed the research and written about it in detail.

Once you have completed your research paper, you can begin writing your abstract. It is important to remember that the abstract should be a concise summary of your research paper, and should be written in a way that is easy to understand for readers who may not have expertise in your specific area of research.

Purpose of Research Paper Abstract

The purpose of a research paper abstract is to provide a concise summary of the key points and findings of a research paper. It is typically a brief paragraph or two that appears at the beginning of the paper, before the introduction, and is intended to give readers a quick overview of the paper’s content.

The abstract should include a brief statement of the research problem, the methods used to investigate the problem, the key results and findings, and the main conclusions and implications of the research. It should be written in a clear and concise manner, avoiding jargon and technical language, and should be understandable to a broad audience.

The abstract serves as a way to quickly and easily communicate the main points of a research paper to potential readers, such as academics, researchers, and students, who may be looking for information on a particular topic. It can also help researchers determine whether a paper is relevant to their own research interests and whether they should read the full paper.

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Writing an Abstract for a Research Paper: Guidelines, Examples, and Templates

There are six steps to writing a standard abstract. (1) Begin with a broad statement about your topic. Then, (2) state the problem or knowledge gap related to this topic that your study explores. After that, (3) describe what specific aspect of this problem you investigated, and (4) briefly explain how you went about doing this. After that, (5) describe the most meaningful outcome(s) of your study. Finally, (6) close your abstract by explaining the broad implication(s) of your findings.

In this article, I present step-by-step guidelines for writing an abstract for an academic paper. These guidelines are fo llowed by an example of a full abstract that follows these guidelines and a few fill-in-the-blank templates that you can use to write your own abstract.

Guidelines for Writing an Abstract

The basic structure of an abstract is illustrated below.

A standard abstract starts with a very general statement and becomes more specific with each sentence that follows until once again making a broad statement about the study’s implications at the end. Altogether, a standard abstract has six functions, which are described in detail below.

Start by making a broad statement about your topic.

The first sentence of your abstract should briefly describe a problem that is of interest to your readers. When writing this first sentence, you should think about who comprises your target audience and use terms that will appeal to this audience. If your opening sentence is too broad, it might lose the attention of potential readers because they will not know if your study is relevant to them.

Too broad : Maintaining an ideal workplace environment has a positive effect on employees.

The sentence above is so broad that it will not grab the reader’s attention. While it gives the reader some idea of the area of study, it doesn’t provide any details about the author’s topic within their research area. This can be fixed by inserting some keywords related to the topic (these are underlined in the revised example below).

Improved : Keeping the workplace environment at an ideal temperature positively affects the overall health of employees.

The revised sentence is much better, as it expresses two points about the research topic—namely, (i) what aspect of workplace environment was studied, (ii) what aspect of employees was observed. The mention of these aspects of the research will draw the attention of readers who are interested in them.

Describe the general problem that your paper addresses.

After describing your topic in the first sentence, you can then explain what aspect of this topic has motivated your research. Often, authors use this part of the abstract to describe the research gap that they identified and aimed to fill. These types of sentences are often characterized by the use of words such as “however,” “although,” “despite,” and so on.

However, a comprehensive understanding of how different workplace bullying experiences are associated with absenteeism is currently lacking.

The above example is typical of a sentence describing the problem that a study intends to tackle. The author has noticed that there is a gap in the research, and they briefly explain this gap here.

Although it has been established that quantity and quality of sleep can affect different types of task performance and personal health, the interactions between sleep habits and workplace behaviors have received very little attention.

The example above illustrates a case in which the author has accomplished two tasks with one sentence. The first part of the sentence (up until the comma) mentions the general topic that the research fits into, while the second part (after the comma) describes the general problem that the research addresses.

Express the specific problem investigated in your paper.

After describing the general problem that motivated your research, the next sentence should express the specific aspect of the problem that you investigated. Sentences of this type are often indicated by the use of phrases like “the purpose of this research is to,” “this paper is intended to,” or “this work aims to.”

Uninformative : However, a comprehensive understanding of how different workplace bullying experiences are associated with absenteeism is currently lacking. The present article aimed to provide new insights into the relationship between workplace bullying and absenteeism .

The second sentence in the above example is a mere rewording of the first sentence. As such, it adds nothing to the abstract. The second sentence should be more specific than the preceding one.

Improved : However, a comprehensive understanding of how different workplace bullying experiences are associated with absenteeism is currently lacking. The present article aimed to define various subtypes of workplace bullying and determine which subtypes tend to lead to absenteeism .

The second sentence of this passage is much more informative than in the previous example. This sentence lets the reader know exactly what they can expect from the full research article.

Explain how you attempted to resolve your study’s specific problem.

In this part of your abstract, you should attempt to describe your study’s methodology in one or two sentences. As such, you must be sure to include only the most important information about your method. At the same time, you must also be careful not to be too vague.

Too vague : We conducted multiple tests to examine changes in various factors related to well-being.

This description of the methodology is too vague. Instead of merely mentioning “tests” and “factors,” the author should note which specific tests were run and which factors were assessed.

Improved : Using data from BHIP completers, we conducted multiple one-way multivariate analyses of variance and follow-up univariate t-tests to examine changes in physical and mental health, stress, energy levels, social satisfaction, self-efficacy, and quality of life.

This sentence is very well-written. It packs a lot of specific information about the method into a single sentence. Also, it does not describe more details than are needed for an abstract.

Briefly tell the reader what you found by carrying out your study.

This is the most important part of the abstract—the other sentences in the abstract are there to explain why this one is relevant. When writing this sentence, imagine that someone has asked you, “What did you find in your research?” and that you need to answer them in one or two sentences.

Too vague : Consistently poor sleepers had more health risks and medical conditions than consistently optimal sleepers.

This sentence is okay, but it would be helpful to let the reader know which health risks and medical conditions were related to poor sleeping habits.

Improved : Consistently poor sleepers were more likely than consistently optimal sleepers to suffer from chronic abdominal pain, and they were at a higher risk for diabetes and heart disease.

This sentence is better, as the specific health conditions are named.

Finally, describe the major implication(s) of your study.

Most abstracts end with a short sentence that explains the main takeaway(s) that you want your audience to gain from reading your paper. Often, this sentence is addressed to people in power (e.g., employers, policymakers), and it recommends a course of action that such people should take based on the results.

Too broad : Employers may wish to make use of strategies that increase employee health.

This sentence is too broad to be useful. It does not give employers a starting point to implement a change.

Improved : Employers may wish to incorporate sleep education initiatives as part of their overall health and wellness strategies.

This sentence is better than the original, as it provides employers with a starting point—specifically, it invites employers to look up information on sleep education programs.

Abstract Example

The abstract produced here is from a paper published in Electronic Commerce Research and Applications . I have made slight alterations to the abstract so that this example fits the guidelines given in this article.

(1) Gamification can strengthen enjoyment and productivity in the workplace. (2) Despite this, research on gamification in the work context is still limited. (3) In this study, we investigated the effect of gamification on the workplace enjoyment and productivity of employees by comparing employees with leadership responsibilities to those without leadership responsibilities. (4) Work-related tasks were gamified using the habit-tracking game Habitica, and data from 114 employees were gathered using an online survey. (5) The results illustrated that employees without leadership responsibilities used work gamification as a trigger for self-motivation, whereas employees with leadership responsibilities used it to improve their health. (6) Work gamification positively affected work enjoyment for both types of employees and positively affected productivity for employees with leadership responsibilities. (7) Our results underline the importance of taking work-related variables into account when researching work gamification.

In Sentence (1), the author makes a broad statement about their topic. Notice how the nouns used (“gamification,” “enjoyment,” “productivity”) are quite general while still indicating the focus of the paper. The author uses Sentence (2) to very briefly state the problem that the research will address.

In Sentence (3), the author explains what specific aspects of the problem mentioned in Sentence (2) will be explored in the present work. Notice that the mention of leadership responsibilities makes Sentence (3) more specific than Sentence (2). Sentence (4) gets even more specific, naming the specific tools used to gather data and the number of participants.

Sentences (5) and (6) are similar, with each sentence describing one of the study’s main findings. Then, suddenly, the scope of the abstract becomes quite broad again in Sentence (7), which mentions “work-related variables” instead of a specific variable and “researching” instead of a specific kind of research.

Abstract Templates

Copy and paste any of the paragraphs below into a word processor. Then insert the appropriate information to produce an abstract for your research paper.

Template #1

Researchers have established that [Make a broad statement about your area of research.] . However, [Describe the knowledge gap that your paper addresses.] . The goal of this paper is to [Describe the purpose of your paper.] . The achieve this goal, we [Briefly explain your methodology.] . We found that [Indicate the main finding(s) of your study; you may need two sentences to do this.] . [Provide a broad implication of your results.] .

Template #2

It is well-understood that [Make a broad statement about your area of research.] . Despite this, [Describe the knowledge gap that your paper addresses.] . The current research aims to [Describe the purpose of your paper.] . To accomplish this, we [Briefly explain your methodology.] . It was discovered that [Indicate the main finding(s) of your study; you may need two sentences to do this.] . [Provide a broad implication of your results.] .

Template #3

Extensive research indicates that [Make a broad statement about your area of research.] . Nevertheless, [Describe the knowledge gap that your paper addresses.] . The present work is intended to [Describe the purpose of your paper.] . To this end, we [Briefly explain your methodology.] . The results revealed that [Indicate the main finding(s) of your study; you may need two sentences to do this.] . [Provide a broad implication of your results.] .

• How to Write an Abstract

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How to write a good abstract for a scientific paper or conference presentation

Chittaranjan andrade.

Department of Psychopharmacology, National Institute of Mental Health and Neurosciences, Bangalore, Karnataka, India

Abstracts of scientific papers are sometimes poorly written, often lack important information, and occasionally convey a biased picture. This paper provides detailed suggestions, with examples, for writing the background, methods, results, and conclusions sections of a good abstract. The primary target of this paper is the young researcher; however, authors with all levels of experience may find useful ideas in the paper.

INTRODUCTION

This paper is the third in a series on manuscript writing skills, published in the Indian Journal of Psychiatry . Earlier articles offered suggestions on how to write a good case report,[ 1 ] and how to read, write, or review a paper on randomized controlled trials.[ 2 , 3 ] The present paper examines how authors may write a good abstract when preparing their manuscript for a scientific journal or conference presentation. Although the primary target of this paper is the young researcher, it is likely that authors with all levels of experience will find at least a few ideas that may be useful in their future efforts.

The abstract of a paper is the only part of the paper that is published in conference proceedings. The abstract is the only part of the paper that a potential referee sees when he is invited by an editor to review a manuscript. The abstract is the only part of the paper that readers see when they search through electronic databases such as PubMed. Finally, most readers will acknowledge, with a chuckle, that when they leaf through the hard copy of a journal, they look at only the titles of the contained papers. If a title interests them, they glance through the abstract of that paper. Only a dedicated reader will peruse the contents of the paper, and then, most often only the introduction and discussion sections. Only a reader with a very specific interest in the subject of the paper, and a need to understand it thoroughly, will read the entire paper.

Thus, for the vast majority of readers, the paper does not exist beyond its abstract. For the referees, and the few readers who wish to read beyond the abstract, the abstract sets the tone for the rest of the paper. It is therefore the duty of the author to ensure that the abstract is properly representative of the entire paper. For this, the abstract must have some general qualities. These are listed in Table 1 .

General qualities of a good abstract

SECTIONS OF AN ABSTRACT

Although some journals still publish abstracts that are written as free-flowing paragraphs, most journals require abstracts to conform to a formal structure within a word count of, usually, 200–250 words. The usual sections defined in a structured abstract are the Background, Methods, Results, and Conclusions; other headings with similar meanings may be used (eg, Introduction in place of Background or Findings in place of Results). Some journals include additional sections, such as Objectives (between Background and Methods) and Limitations (at the end of the abstract). In the rest of this paper, issues related to the contents of each section will be examined in turn.

This section should be the shortest part of the abstract and should very briefly outline the following information:

• What is already known about the subject, related to the paper in question
• What is not known about the subject and hence what the study intended to examine (or what the paper seeks to present)

In most cases, the background can be framed in just 2–3 sentences, with each sentence describing a different aspect of the information referred to above; sometimes, even a single sentence may suffice. The purpose of the background, as the word itself indicates, is to provide the reader with a background to the study, and hence to smoothly lead into a description of the methods employed in the investigation.

Some authors publish papers the abstracts of which contain a lengthy background section. There are some situations, perhaps, where this may be justified. In most cases, however, a longer background section means that less space remains for the presentation of the results. This is unfortunate because the reader is interested in the paper because of its findings, and not because of its background.

A wide variety of acceptably composed backgrounds is provided in Table 2 ; most of these have been adapted from actual papers.[ 4 – 9 ] Readers may wish to compare the content in Table 2 with the original abstracts to see how the adaptations possibly improve on the originals. Note that, in the interest of brevity, unnecessary content is avoided. For instance, in Example 1 there is no need to state “The antidepressant efficacy of desvenlafaxine (DV), a dual-acting antidepressant drug , has been established…” (the unnecessary content is italicized).

Examples of the background section of an abstract

The methods section is usually the second-longest section in the abstract. It should contain enough information to enable the reader to understand what was done, and how. Table 3 lists important questions to which the methods section should provide brief answers.

Questions regarding which information should ideally be available in the methods section of an abstract

Carelessly written methods sections lack information about important issues such as sample size, numbers of patients in different groups, doses of medications, and duration of the study. Readers have only to flip through the pages of a randomly selected journal to realize how common such carelessness is.

Table 4 presents examples of the contents of accept-ably written methods sections, modified from actual publications.[ 10 , 11 ] Readers are invited to take special note of the first sentence of each example in Table 4 ; each is packed with detail, illustrating how to convey the maximum quantity of information with maximum economy of word count.

Examples of the methods section of an abstract

The results section is the most important part of the abstract and nothing should compromise its range and quality. This is because readers who peruse an abstract do so to learn about the findings of the study. The results section should therefore be the longest part of the abstract and should contain as much detail about the findings as the journal word count permits. For example, it is bad writing to state “Response rates differed significantly between diabetic and nondiabetic patients.” A better sentence is “The response rate was higher in nondiabetic than in diabetic patients (49% vs 30%, respectively; P <0.01).”

Important information that the results should present is indicated in Table 5 . Examples of acceptably written abstracts are presented in Table 6 ; one of these has been modified from an actual publication.[ 11 ] Note that the first example is rather narrative in style, whereas the second example is packed with data.

Information that the results section of the abstract should ideally present

Examples of the results section of an abstract

CONCLUSIONS

This section should contain the most important take-home message of the study, expressed in a few precisely worded sentences. Usually, the finding highlighted here relates to the primary outcome measure; however, other important or unexpected findings should also be mentioned. It is also customary, but not essential, for the authors to express an opinion about the theoretical or practical implications of the findings, or the importance of their findings for the field. Thus, the conclusions may contain three elements:

• The primary take-home message
• The additional findings of importance
• The perspective

Despite its necessary brevity, this section has the most impact on the average reader because readers generally trust authors and take their assertions at face value. For this reason, the conclusions should also be scrupulously honest; and authors should not claim more than their data demonstrate. Hypothetical examples of the conclusions section of an abstract are presented in Table 7 .

Examples of the conclusions section of an abstract

MISCELLANEOUS OBSERVATIONS

Citation of references anywhere within an abstract is almost invariably inappropriate. Other examples of unnecessary content in an abstract are listed in Table 8 .

Examples of unnecessary content in a abstract

It goes without saying that whatever is present in the abstract must also be present in the text. Likewise, whatever errors should not be made in the text should not appear in the abstract (eg, mistaking association for causality).

As already mentioned, the abstract is the only part of the paper that the vast majority of readers see. Therefore, it is critically important for authors to ensure that their enthusiasm or bias does not deceive the reader; unjustified speculations could be even more harmful. Misleading readers could harm the cause of science and have an adverse impact on patient care.[ 12 ] A recent study,[ 13 ] for example, concluded that venlafaxine use during the second trimester of pregnancy may increase the risk of neonates born small for gestational age. However, nowhere in the abstract did the authors mention that these conclusions were based on just 5 cases and 12 controls out of the total sample of 126 cases and 806 controls. There were several other serious limitations that rendered the authors’ conclusions tentative, at best; yet, nowhere in the abstract were these other limitations expressed.

As a parting note: Most journals provide clear instructions to authors on the formatting and contents of different parts of the manuscript. These instructions often include details on what the sections of an abstract should contain. Authors should tailor their abstracts to the specific requirements of the journal to which they plan to submit their manuscript. It could also be an excellent idea to model the abstract of the paper, sentence for sentence, on the abstract of an important paper on a similar subject and with similar methodology, published in the same journal for which the manuscript is slated.

Source of Support: Nil

Conflict of Interest: None declared.

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Abstracts - A Guide to Writing

What is an abstract.

Abstracts act as concise surrogates or representations of research projects. Abstracts precede papers in research journals and appear in programs of scholarly conferences. They should be brief, concise, and use clear language. A researcher reading an abstract should have a clear idea of what the research project is about after reading an abstract. 

Abstracts allow readers to grasp the purpose and major ideas of a paper, poster, or presentation. A great abstract will be packed with information on the research project and will let other researchers know whether reading the entire paper or attending a presentation is worthwhile.

Why write an abstract?

Abstracts often serve as the advertisement of a research project. They allow readers to quickly scan a small amount of text and to make a decision as to whether the work will satisfy their information needs. If a researcher is interested, he or she will continue on to read the entire document or attend the session.

Many online databases use abstracts to index larger research projects. Using keywords from your research project in your abstract will ensure your project is easily searched.

Types of abstracts

Different academic disciplines have different research methods and requirements.  For example, social sciences or hard science abstracts will typically include the parts of a research experiment; whereas abstracts in the humanities will often discuss the hypothesis being investigated and the conclusion.  Conferences and journals may have specific requirements for abstract submissions, so be sure to review the requirements prior to writing an abstract for your project.

Informative abstracts

Informative abstracts are generally used for documents pertaining to experimental investigations, inquiries, or surveys. The original document is condensed reflecting its form and content and provides quantitative and qualitative information.

Informative Example

Daidzic, N. E. (2015). Efficient general computational method for estimation of standard atmosphere parameters.  International Journal of Aviation, Aeronautics, and Aerospace, 2 (1).  https://doi.org/10.15394/ijaaa.2015.1053

Knowledge of standard air temperature, pressure, density, speed of sound, and viscosity as a function of altitude is essential information in aircraft design, performance testing, pressure altimeter calibration, and several other aeronautical engineering and aviation science applications. A new efficient computational method for rapid calculations of standard atmospheric parameters up to 86 orthometric km is presented. Additionally, mass and weight of each standard atmospheric layer were calculated using a numerical integration method. The sum of all fractional masses and weights represents the total mass and weight of Earth’s atmosphere. The results obtained here agree well with measurements and models of the real atmosphere. Various ISA scale heights were estimated from numerical integration of atmospheric masses and weights. The nature of the geopotential and the orthometric heights and the definition of MSL have been explained. Essential thermodynamic considerations of still and dry air were highlighted. In addition to general working equations for air pressure and density vertical distribution for each atmospheric layer an extensive table of calculated values up to 86 km has been provided in appendix. Several models of air viscosity were also compared. It was found that simple Granger’s model agrees well with the widely accepted Sutherland-type viscosity equation. All computations were performed with the fourteen significant-digits accuracy although only seven significant digits were typically presented in tables.

Indicative abstracts

Indicative abstracts simply describe what the research project is about.

Indicative Example

Porter, L. (2014). Benedict Cumberbatch, transition completed: Films, fame, fans . MX Publishing. Abstract retrieved from https://works.bepress.com/lynnette_porter/3/

Star Trek: Into Darkness, The Fifth Estate, 12 Years a Slave, August: Osage County, The Hobbit: The Desolation of Smaug—these would be milestones in most actors’ entire career. For Benedict Cumberbatch, roles in these films are merely a year’s additions to his already-vast resume. 2013 proved to be the final step in Cumberbatch’s transition from respected working actor to bona fide worldwide celebrity and recipient of BAFTA Los Angeles’ Britannia Award for British Artist of the Year. Like its predecessor, Benedict Cumberbatch, In Transition (MX Publishing, 2013), Benedict Cumberbatch, Transition Completed: Films, Fame, Fans explores the nature of Cumberbatch’s fame and fandom while analysing his most recent roles. This in-depth performance biography does more than critique the actor’s radio, stage, film, and television performances—especially his star turn in the long-awaited yet controversial third series of Sherlock. It also analyses how and why the actor’s work is so memorable in each role, a perspective unique to this performance biography. Cumberbatch’s role in popular culture, as much as his acting in multiple media, is well worth such scrutiny to illustrate that Benedict Cumberbatch represents both the best of acting and of the power of celebrity.

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Writing an abstract - a six point checklist (with samples)

Posted in: abstract , dissertations

The abstract is a vital part of any research paper. It is the shop front for your work, and the first stop for your reader. It should provide a clear and succinct summary of your study, and encourage your readers to read more. An effective abstract, therefore should answer the following questions:

• Why did you do this study or project?
• What did you do and how?
• What did you find?
• What do your findings mean?

So here's our run down of the key elements of a well-written abstract.

• Size - A succinct and well written abstract should be between approximately 100- 250 words.
• Background - An effective abstract usually includes some scene-setting information which might include what is already known about the subject, related to the paper in question (a few short sentences).
• Purpose  - The abstract should also set out the purpose of your research, in other words, what is not known about the subject and hence what the study intended to examine (or what the paper seeks to present).
• Methods - The methods section should contain enough information to enable the reader to understand what was done, and how. It should include brief details of the research design, sample size, duration of study, and so on.
• Results - The results section is the most important part of the abstract. This is because readers who skim an abstract do so to learn about the findings of the study. The results section should therefore contain as much detail about the findings as the journal word count permits.
• Conclusion - This section should contain the most important take-home message of the study, expressed in a few precisely worded sentences. Usually, the finding highlighted here relates to the primary outcomes of the study. However, other important or unexpected findings should also be mentioned. It is also customary, but not essential, to express an opinion about the theoretical or practical implications of the findings, or the importance of their findings for the field. Thus, the conclusions may contain three elements:
• The primary take-home message.
• Any additional findings of importance.
• Implications for future studies.

Example Abstract 2: Engineering Development and validation of a three-dimensional finite element model of the pelvic bone.

Abstract from: Dalstra, M., Huiskes, R. and Van Erning, L., 1995. Development and validation of a three-dimensional finite element model of the pelvic bone. Journal of biomechanical engineering, 117(3), pp.272-278.

And finally...  A word on abstract types and styles

Abstract types can differ according to subject discipline. You need to determine therefore which type of abstract you should include with your paper. Here are two of the most common types with examples.

Informative Abstract

The majority of abstracts are informative. While they still do not critique or evaluate a work, they do more than describe it. A good informative abstract acts as a surrogate for the work itself. That is, the researcher presents and explains all the main arguments and the important results and evidence in the paper. An informative abstract includes the information that can be found in a descriptive abstract [purpose, methods, scope] but it also includes the results and conclusions of the research and the recommendations of the author. The length varies according to discipline, but an informative abstract is usually no more than 300 words in length.

Descriptive Abstract A descriptive abstract indicates the type of information found in the work. It makes no judgements about the work, nor does it provide results or conclusions of the research. It does incorporate key words found in the text and may include the purpose, methods, and scope of the research. Essentially, the descriptive abstract only describes the work being summarised. Some researchers consider it an outline of the work, rather than a summary. Descriptive abstracts are usually very short, 100 words or less.

Adapted from Andrade C. How to write a good abstract for a scientific paper or conference presentation. Indian J Psychiatry. 2011 Apr;53(2):172-5. doi: 10.4103/0019-5545.82558. PMID: 21772657; PMCID: PMC3136027 .

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What is a research abstract?

An abstract is a concise summary of a larger research project. It should address all the major points of the project, providing an overview of the research topic, question, methods, results, and significance. The abstract is a snapshot that captures a reader's attention and--although it can stand alone as a representation of the project--invites readers to learn more by viewing your poster or attending your presentation.

What should a research abstract include?

You will likely want to include:

• Background, context, and purpose (the "big picture" in which your research fits)
• Your question, hypothesis, or goal
• The methods and research design you employed/are employing
• Results, products, outcomes (achieved or anticipated)
• Implications and significance: for your field, for future work, for your viewers

What is the format of a research abstract?

The length and format of research abstracts can vary depending on the requirements of a particular conference or journal.

For the UChicago Undergraduate Research Symposium, the requirements are :

• Include a short, descriptive title, capitalized in title case
• Make it only one paragraph
• Have no section breaks, footnotes, or illustrations
• Adhere to a limit of 300 words.
• Pitch your abstract to an educated non-specialist audience (minimize jargon, spell out acronyms)

Should I show my abstract to my mentor?

YES! It is very important that your faculty mentor review and approve your abstract. Your abstract will be publicly available, so you and your mentor should work together to ensure that the abstract presents your work appropriately and does not raise any intellectual-property concerns. Your mentor will need to approve your abstract in our application system before you can be accepted to present at the Undergraduate Research Symposium.

Will you host abstract writing workshops?

Yes! Abstract workshops are now concluded. View the slides and a recorded workshop in our Resource Library .

Where can I find examples of research abstracts?

You can review abstracts from major conferences or journals in your field to ascertain the conventions of your discipline. You can also review the abstracts from prior Undergraduate Research Symposia to see what your peers have written.

Where do I submit my abstract for the upcoming Undergraduate Research Symposium?

Access the online submission form here .

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How to Write an Abstract for Research Proposal

by  Antony W

December 13, 2021

An abstract in a research proposal summarizes the main aspect of the assignment in a given sequence in 300 words or less. It highlights the purpose of the study, the research problem, design of the study, findings, summary of your interpretations and conclusions.

For what it’s worth, the abstract of your research proposal should give a clear and concise elaboration of the major aspects of an issue you’ve investigated.

In this guide, you’ll learn how to write an abstract for any research proposal. We’ll look at why an abstract is important, the types of abstracts, writing style, and what to avoid when it comes to writing an abstract for your research proposal.

Types of Abstracts for a Research Proposal

There are four types of abstracts that you can write for a research proposal:

• Critical abstract
• Descriptive abstract
• Informative abstract
• Highlight abstract

1. Critical abstract

A critical abstract in a research proposal describes the primary findings and gives a solid judgment on the validity, completeness, and reliability of the study. It’s your responsibility as a researcher to evaluate your work and then compare it with already existing work on the same subject.

Because a critical abstract includes an additional commentary, it tends to longer. Often, the length falls between 400 and 500 words. However, do keep in mind that this type of an abstract is very are, which means your instructor may never ask you to write a critical abstract for your research proposal.

2. Highlight Abstract

A highlight abstract is a piece of writing that can’t stand independent of its associated document. It uses incomplete and leading remarks, with the primary goal of grabbing the attention of the reader to the study.

Professors have made it clear that a highlight abstract is not by itself a true abstract to use in a research proposal. Since it cannot stand on its away separate from the associated article, it’s unlikely that your teacher will ask you to use it in academic writing.

3. Descriptive abstract

A descriptive abstract gives a short description of the research proposal. It may include purpose, method, and the scope of the research, and it’s often 100 words or less in length. Some people consider it to be an outline of the research proposal rather than an actual abstract for the document.

While a descriptive abstract describes the type of information a reader will find in a research proposal, it neither critics the work nor provides results and conclusion of the study.

4. Informative Abstract

Many abstracts in academic writing are informative. They don’t analyze the study or investigation that you propose, but they explain a research project in a way that they can stand independently. In other words, an informative abstract gives an explanation for the main arguments, evidence, and significant results.

In addition to featuring purpose, method, and scope, an informative abstract also include the results, conclusion, as well as the recommendation of the author. As for the length, an informative abstract should not be more than 300 words.

How to Write an Abstract for a Research Proposal

Of the four type of abstracts that we’ve discussed above, an informative abstract is what you’ll need to write in your research proposal. Writing an abstract for a research proposal isn’t difficult at all. You only need to know what to write and how to write it, and you’re good to get started.

1. Write in Active Voice

First, use active voice when writing an abstract for your research proposal. However, this doesn’t mean you should avoid passive voice in entirety. If you find that some sentences can’t make sense unless with passive sentence construction, feel free to bend this rule somewhat.

Second, make sure your sentences are concise and complete. Refrain from using ambiguous words. Keep the language simple instead.

Lastly, never use present or future tense to write an abstract for a research proposal. You’re reporting a study that you’ve already conducted and therefore writing in past sense makes the most sense.

Your abstract should come immediately after the title page. Write in block format without paragraph indentations. The abstract should not be more than 300 words long and the page should not have a number. The word “Abstract” in your research proposal should be center aligned in the page, unless otherwise stated.

In addition to these formatting rules, the last sentence of your abstract should summarize the application to practice or the conclusions of your study. In the case where it seems appropriate, you might want follow this by statement that suggests a need for additional research.

3. Time to Write the Abstract

There are no hard rules on when to write an abstract for a research proposal. Some students choose to write the section first while others choose to write it last. We strongly recommend that you write the abstract last because it’s a summary of the whole paper. You can also write it in the beginning if you’ve already outlined your draft and know what you want to talk about even before you start writing.

Your informative abstract is subject to frequent changes as you work on your paper, and that holds whether you write the section first or last. Be flexible and tweak this part of the assignment as necessary. Also, make sure you report statistical findings in parentheses.

Read abstract to be sure the summary of the study agrees with what you’ve written in your proposal. As we mentioned earlier, this section is subject to change depending on the direction your research takes. So make sure you identify and correct any anomalies if any.

Mistakes to Avoid When Writing an Abstract for Research Proposal

To wind up this guide, here are some of the most common mistakes that you should avoid when writing an abstract for your research proposal:

• Avoid giving a lengthy background
• Don’t include citations to other people’s work
• An abstract shouldn’t include a table, figure, image, or any kind of illustration
• Don’t include terms that are difficult to understand

About the author 

Antony W is a professional writer and coach at Help for Assessment. He spends countless hours every day researching and writing great content filled with expert advice on how to write engaging essays, research papers, and assignments.

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Introduction

The Creating a Research Space [C.A.R.S.] Model was developed by John Swales based upon his analysis of journal articles representing a variety of discipline-based writing practices. His model attempts to explain and describe the organizational pattern of writing the introduction to scholarly research studies. Following the C.A.R.S. Model can be useful approach because it can help you to: 1) begin the writing process [getting started is often the most difficult task]; 2) understand the way in which an introduction sets the stage for the rest of your paper; and, 3) assess how the introduction fits within the larger scope of your study. The model assumes that writers follow a general organizational pattern in response to two types of challenges [“competitions”] relating to establishing a presence within a particular domain of research: 1) the competition to create a rhetorical space and, 2) the competition to attract readers into that space. The model proposes three actions [Swales calls them “moves”], accompanied by specific steps, that reflect the development of an effective introduction for a research paper. These “moves” and steps can be used as a template for writing the introduction to your own social sciences research papers.

"Introductions." The Writing Lab and The OWL. Purdue University; Coffin, Caroline and Rupert Wegerif. “How to Write a Standard Research Article.” Inspiring Academic Practice at the University of Exeter; Kayfetz, Janet. "Academic Writing Workshop." University of California, Santa Barbara, Fall 2009; Pennington, Ken. "The Introduction Section: Creating a Research Space CARS Model." Language Centre, Helsinki University of Technology, 2005; Swales, John and Christine B. Feak. Academic Writing for Graduate Students: Essential Skills and Tasks. 2nd edition. Ann Arbor, MI: University of Michigan Press, 2004.

Creating a Research Space Move 1: Establishing a Territory [the situation] This is generally accomplished in two ways: by demonstrating that a general area of research is important, critical, interesting, problematic, relevant, or otherwise worthy of investigation and by introducing and reviewing key sources of prior research in that area to show where gaps exist or where prior research has been inadequate in addressing the research problem. The steps taken to achieve this would be:

• Step 1 -- Claiming importance of, and/or  [writing action = describing the research problem and providing evidence to support why the topic is important to study]
• Step 2 -- Making topic generalizations, and/or  [writing action = providing statements about the current state of knowledge, consensus, practice or description of phenomena]
• Step 3 -- Reviewing items of previous research  [writing action = synthesize prior research that further supports the need to study the research problem; this is not a literature review but more a reflection of key studies that have touched upon but perhaps not fully addressed the topic]

Move 2: Establishing a Niche [the problem] This action refers to making a clear and cogent argument that your particular piece of research is important and possesses value. This can be done by indicating a specific gap in previous research, by challenging a broadly accepted assumption, by raising a question, a hypothesis, or need, or by extending previous knowledge in some way. The steps taken to achieve this would be:

• Step 1a -- Counter-claiming, or  [writing action = introduce an opposing viewpoint or perspective or identify a gap in prior research that you believe has weakened or undermined the prevailing argument]
• Step 1b -- Indicating a gap, or  [writing action = develop the research problem around a gap or understudied area of the literature]
• Step 1c -- Question-raising, or  [writing action = similar to gap identification, this involves presenting key questions about the consequences of gaps in prior research that will be addressed by your study. For example, one could state, “Despite prior observations of voter behavior in local elections in urban Detroit, it remains unclear why do some single mothers choose to avoid....”]
• Step 1d -- Continuing a tradition  [writing action = extend prior research to expand upon or clarify a research problem. This is often signaled with logical connecting terminology, such as, “hence,” “therefore,” “consequently,” “thus” or language that indicates a need. For example, one could state, “Consequently, these factors need to examined in more detail....” or “Evidence suggests an interesting correlation, therefore, it is desirable to survey different respondents....”]

Move 3: Occupying the Niche [the solution] The final "move" is to announce the means by which your study will contribute new knowledge or new understanding in contrast to prior research on the topic. This is also where you describe the remaining organizational structure of the paper. The steps taken to achieve this would be:

• Step 1a -- Outlining purposes, or  [writing action = answering the “So What?” question. Explain in clear language the objectives of your study]
• Step 1b -- Announcing present research [writing action = describe the purpose of your study in terms of what the research is going to do or accomplish. In the social sciences, the “So What?” question still needs to addressed]
• Step 2 -- Announcing principle findings  [writing action = present a brief, general summary of key findings written, such as, “The findings indicate a need for...,” or “The research suggests four approaches to....”]
• Step 3 -- Indicating article structure  [writing action = state how the remainder of your paper is organized]

"Introductions." The Writing Lab and The OWL. Purdue University; Atai, Mahmood Reza. “Exploring Subdisciplinary Variations and Generic Structure of Applied Linguistics Research Article Introductions Using CARS Model.” The Journal of Applied Linguistics 2 (Fall 2009): 26-51; Chanel, Dana. "Research Article Introductions in Cultural Studies: A Genre Analysis Explorationn of Rhetorical Structure." The Journal of Teaching English for Specific and Academic Purposes 2 (2014): 1-20; Coffin, Caroline and Rupert Wegerif. “How to Write a Standard Research Article.” Inspiring Academic Practice at the University of Exeter; Kayfetz, Janet. "Academic Writing Workshop." University of California, Santa Barbara, Fall 2009; Pennington, Ken. "The Introduction Section: Creating a Research Space CARS Model." Language Centre, Helsinki University of Technology, 2005; Swales, John and Christine B. Feak. Academic Writing for Graduate Students: Essential Skills and Tasks . 2nd edition. Ann Arbor, MI: University of Michigan Press, 2004; Swales, John M. Genre Analysis: English in Academic and Research Settings . New York: Cambridge University Press, 1990; Chapter 5: Beginning Work. In Writing for Peer Reviewed Journals: Strategies for Getting Published . Pat Thomson and Barbara Kamler. (New York: Routledge, 2013), pp. 93-96.

Writing Tip

Swales showed that establishing a research niche [move 2] is often signaled by specific terminology that expresses a contrasting viewpoint, a critical evaluation of gaps in the literature, or a perceived weakness in prior research. The purpose of using these words is to draw a clear distinction between perceived deficiencies in previous studies and the research you are presenting that is intended to help resolve these deficiencies. Below is a table of common words used by authors.

NOTE : You may prefer not to adopt a negative stance in your writing when placing it within the context of prior research. In such cases, an alternative approach is to utilize a neutral, contrastive statement that expresses a new perspective without giving the appearance of trying to diminish the validity of other people's research. Examples of how to take a more neutral contrasting stance can be achieved in the following ways, with A representing the findings of prior research, B representing your research problem, and X representing one or more variables that have been investigated.

• Prior research has focused primarily on A , rather than on B ...
• Prior research into A can be beneficial but to rectify X , it is important to examine B ...
• These studies have placed an emphasis in the areas of A as opposed to describing B ...
• While prior studies have examined A , it may be preferable to contemplate the impact of B ...
• After consideration of A , it is important to also distinguish B ...
• The study of A has been thorough, but changing circumstances related to X support a need for examining [or revisiting] B ...
• Although research has been devoted to A , less attention has been paid to B ...
• Earlier research offers insights into the need for A , though consideration of B would be particularly helpful to...

In each of these example statements, what follows the ellipsis is the justification for designing a study that approaches the problem in the way that contrasts with prior research but which does not devalue its ongoing contributions to current knowledge and understanding.

Dretske, Fred I. “Contrastive Statements.” The Philosophical Review 81 (October 1972): 411-437; Kayfetz, Janet. "Academic Writing Workshop." University of California, Santa Barbara, Fall 2009; Pennington, Ken. "The Introduction Section: Creating a Research Space CARS Model." Language Centre, Helsinki University of Technology, 2005; Swales, John M. Genre Analysis: English in Academic and Research Settings . New York: Cambridge University Press, 1990

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A modern way to teach and practice manual therapy

Affiliations.

• 1 School of Health Sciences, Queens Medical Centre, University of Nottingham, Nottingham, NG7 2HA, UK.
• 2 Allied Health Research Unit, University of Central Lancashire, Preston, PR1 2HE, UK. [email protected].
• 3 Centre of Precision Rehabilitation for Spinal Pain, School of Sport, Exercise and Rehabilitation Sciences, University of Birmingham, Edgbaston, Birmingham, B15 2TT, UK.
• 4 Nottingham CityCare Partnership, Bennerley Rd, Nottingham, NG6 8WR, UK.
• 5 School of Medicine, University of Nottingham, Queens Medical Centre, Nottingham, NG7 2HA, UK.
• 6 Department of Orthopaedics, West Herts Hospitals Trust, Watford, WD18 0HB, UK.
• 7 School of Physiotherapy, Manchester Metropolitan University, Manchester, M15 6GX, UK.
• 8 Department of Orthopaedics, Duke University, 200 Morris Street, Durham, NC, 27701, USA.
• 9 School of Sport and Health Sciences, University of Brighton, Darley Rd, Eastbourne, BN20 7UR, UK.
• 10 Clinical Neuroscience, Trafford Building, Brighton and Sussex Medical School, University of Sussex, Brighton, BN1 9PX, UK.
• 11 University College of Osteopathy, 275 Borough High St, London, SE1 1JE, UK.
• 12 Department of Clinical Sciences, Obstetrics and Gynecology, Umeå University, S-90187, Umeå, Sweden.
• 13 The School of Soft Tissue Therapy, Exmouth, Devon, EX8 1DQ, UK.
• 14 Department of health, LUNEX, Differdange, 4671, Luxembourg.
• 15 Luxembourg Health & Sport Sciences Research Institute A.s.b.l., 50, Avenue du Parc des Sports, Differdange, 4671, Luxembourg.
• 16 Department of Occupation and Health, School of Organization and Development, HAN University of Applied Sciences, Nijmegen, the Netherlands.
• PMID: 38773515
• DOI: 10.1186/s12998-024-00537-0

Background: Musculoskeletal conditions are the leading contributor to global disability and health burden. Manual therapy (MT) interventions are commonly recommended in clinical guidelines and used in the management of musculoskeletal conditions. Traditional systems of manual therapy (TMT), including physiotherapy, osteopathy, chiropractic, and soft tissue therapy have been built on principles such as clinician-centred assessment, patho-anatomical reasoning, and technique specificity. These historical principles are not supported by current evidence. However, data from clinical trials support the clinical and cost effectiveness of manual therapy as an intervention for musculoskeletal conditions, when used as part of a package of care.

Purpose: The purpose of this paper is to propose a modern evidence-guided framework for the teaching and practice of MT which avoids reference to and reliance on the outdated principles of TMT. This framework is based on three fundamental humanistic dimensions common in all aspects of healthcare: safety, comfort, and efficiency. These practical elements are contextualised by positive communication, a collaborative context, and person-centred care. The framework facilitates best-practice, reasoning, and communication and is exemplified here with two case studies.

Methods: A literature review stimulated by a new method of teaching manual therapy, reflecting contemporary evidence, being trialled at a United Kingdom education institute. A group of experienced, internationally-based academics, clinicians, and researchers from across the spectrum of manual therapy was convened. Perspectives were elicited through reviews of contemporary literature and discussions in an iterative process. Public presentations were made to multidisciplinary groups and feedback was incorporated. Consensus was achieved through repeated discussion of relevant elements.

Conclusions: Manual therapy interventions should include both passive and active, person-empowering interventions such as exercise, education, and lifestyle adaptations. These should be delivered in a contextualised healing environment with a well-developed person-practitioner therapeutic alliance. Teaching manual therapy should follow this model.

Keywords: Chiropractic; Evidence-based healthcare; Manual Therapy; Osteopathy; Person-centred healthcare; Physiotherapy; Soft-tissue therapy.

© 2024. The Author(s).

Publication types

• Musculoskeletal Diseases / therapy
• Musculoskeletal Manipulations* / education
• Musculoskeletal Manipulations* / methods

• Open access
• Published: 14 May 2024

Enhancing pathological complete response prediction in breast cancer: the role of dynamic characterization of DCE-MRI and its association with tumor heterogeneity

• Xinyu Zhang 1 ,
• Xinzhi Teng 1 ,
• Jiang Zhang 1 ,
• Qingpei Lai 1 &
• Jing Cai 1 , 2  

Breast Cancer Research volume  26 , Article number:  77 ( 2024 ) Cite this article

205 Accesses

Metrics details

Early prediction of pathological complete response (pCR) is important for deciding appropriate treatment strategies for patients. In this study, we aimed to quantify the dynamic characteristics of dynamic contrast-enhanced magnetic resonance images (DCE-MRI) and investigate its value to improve pCR prediction as well as its association with tumor heterogeneity in breast cancer patients.

The DCE-MRI, clinicopathologic record, and full transcriptomic data of 785 breast cancer patients receiving neoadjuvant chemotherapy were retrospectively included from a public dataset. Dynamic features of DCE-MRI were computed from extracted phase-varying radiomic feature series using 22 CAnonical Time-sereis CHaracteristics. Dynamic model and radiomic model were developed by logistic regression using dynamic features and traditional radiomic features respectively. Various combined models with clinical factors were also developed to find the optimal combination and the significance of each components was evaluated. All the models were evaluated in independent test set in terms of area under receiver operating characteristic curve (AUC). To explore the potential underlying biological mechanisms, radiogenomic analysis was implemented on patient subgroups stratified by dynamic model to identify differentially expressed genes (DEGs) and enriched pathways.

A 10-feature dynamic model and a 4-feature radiomic model were developed (AUC = 0.688, 95%CI: 0.635–0.741 and AUC = 0.650, 95%CI: 0.595–0.705) and tested (AUC = 0.686, 95%CI: 0.594–0.778 and AUC = 0.626, 95%CI: 0.529–0.722), with the dynamic model showing slightly higher AUC (train p  = 0.181, test p  = 0.222). The combined model of clinical, radiomic, and dynamic achieved the highest AUC in pCR prediction (train: 0.769, 95%CI: 0.722–0.816 and test: 0.762, 95%CI: 0.679–0.845). Compared with clinical-radiomic combined model (train AUC = 0.716, 95%CI: 0.665–0.767 and test AUC = 0.695, 95%CI: 0.656–0.714), adding the dynamic component brought significant improvement in model performance (train p  < 0.001 and test p  = 0.005). Radiogenomic analysis identified 297 DEGs, including CXCL9, CCL18, and HLA-DPB1 which are known to be associated with breast cancer prognosis or angiogenesis. Gene set enrichment analysis further revealed enrichment of gene ontology terms and pathways related to immune system.

Dynamic characteristics of DCE-MRI were quantified and used to develop dynamic model for improving pCR prediction in breast cancer patients. The dynamic model was associated with tumor heterogeniety in prognostic-related gene expression and immune-related pathways.

Introduction

Breast cancer is one of the most common malignant in women. In 2020, there were around 2.3 million women newly diagnosed with and over 600,000 women died of breast cancer worldwide [ 1 ]. Recently, neoadjuvant chemotherapy (NAC) has become increasingly used in breast cancer systemic treatment. NAC was initially used in inoperable breast cancer to enable surgical resection, and expanded to other types of breast cancer for increasing the chance of breast conservation owing to its remarkable efficacy [ 2 ]. Current NAC treatment schemes are determined by hormone receptor (HR) status and human epidermal growth factor receptor 2 (HER2) status as recommended by American Society of Clinical Oncology (ASCO) [ 3 ]. Pathological complete response (pCR), defined as no residual disease in breast and axillary region after NAC, is a validated prognostic factor to assess treatment response and associated with long-term outcome [ 4 ]. However, only 10-50% patients achieved pCR, varying according to their receptor subtypes [ 5 ]. Moreover, the assessment of pCR status is performed at surgery after completion of NAC, prior to which non-responders have suffered from the toxicity and side effects caused by NAC. Therefore, it is essential to identify patients who are likely to achieve pCR before NAC to avoid unnecessary complications and maximize potential benefits.

Dynamic contrast-enhanced MRI (DCE-MRI) is the clinical routine for breast cancer assessment. It has high sensitivity in diagnosis and treatment monitoring [ 6 , 7 ]. Through acquisition of sequential images before, during, and after the administration of contrast agent, DCE-MRI provides valuable information about tissue perfusion and contrast agent enhancement dynamics associated with tumor angiogenesis [ 8 ]. Radiomics extracts high-dimentional image features that are imperceptible to human eyes to non-invasively quantify tumor characteristics [ 9 ]. Radiomic analysis of breast DCE-MRI has been used for pCR prediction in many previous studies, most of which only used radiomic features from one or several phases while ignoring the dynamic information [ 10 , 11 ]. Recently, attempts have been made to leverage the dynamic information embedded in DCE-MRI for pCR prediction by combining radiomic features extracted from different DCE-MRI phases. For instance, Peng et al. calculated delta-features between two different phases for pCR prediction [ 12 ]; Li et al. employed simple statistical patterns of radiomic features extracted from different phases for pCR prediction and achieved better performance compared to single-phase features, demonstrating the value of multi-phase information [ 13 ]. In BMMR2 challenge, radiomic features from kinetic maps, such as peak enhancement maps and signal enhancement ratio maps, were used to predict pCR [ 14 ]. However, the entire time series of radiomic features has not been fully explored and may contain additional information for tumor characterization. On the other hand, feature-based representation of time series data like 22 CAnonical Time-series CHaracteristics (Catch22) can capture the dynamic properties of time series data and was used in various tasks [ 15 , 16 ]. Accordingly, there developed an assumption that the dynamics of radiomic feature series extracted by Catch22 can characterize the dynamic information in DCE-MRI and improve pCR prediction of breast cancer patients.

In this study, we aimed to systematically extract dynamic properties of radiomic feature series from DCE-MRI to improve treatment response prediction of breast cancer patients. To achieve this, a large number of dynamic features were extracted by Catch22 from DCE-MRI feature series, and a dynamic model was then built for pCR prediction. Various combinations of dynamic models and existing radiomic and clinical models were developed to find the optimal one as the final model. In addition, radiogenomic analysis of binarized dynamic model predictions was conducted to explore its association with tumor heterogeneity and biological process. Figure  1 shows the overall workflow of this study.

Workflow of the study. Firstly, the collected DCE-MR images were preprocessed by normalization and discretization. Radiomic features were extracted from multiple phases of DCE-MRI, while dynamic features were extracted from radiomic feature series. Feature selection, model development, and model validation were then conducted separately for radiomic model and dynamic model. Subsequently, combined models were developed by integrating radiomic, dynamic, and clinical information and their performance were evaluated. In addition, radiogenomic analysis was performed on dynamic model to investigate potential biological mechanisms

Materials and methods

Patient data.

A total of 985 stage II/III locally advanced breast cancer patients enrolled in the multi-center I-SPY2 trial (clinical trial number: NCT01042379) during 2010 to 2016 were collected from the publicly available dataset on The Cancer Image Archive [ 17 , 18 , 19 ]. Institutional review board approval was waived due to the use of public data. The detailed descriptions of I-SPY2 trial have been reported by previous paper [ 20 ]. All the patients underwent MR examination and percutaneous biopsy before receiving NAC. After the completion of NAC, patients underwent surgical resection to assess residual disease. The exclusion criteria included: (1) incomplete image or clinicopathologic data; (2) deviations from the prescribed scanning protocol; (3) insufficient image quality.

Clinicopathologic data

Clinicopathologic data including HR, HER2, MammaPrint status (MP), pCR, and other patient characteristics was provided by the dataset. HR and HER2 were deternmined by immunohistochemical (IHC) staining or fluorescence in-situ hybridization (FISH) of tissues obtained during pre-treatment biopsy. HR was determined as positive when ≥ 5% tumor staining for ER and/or PgR was seen. HER2 was determined as positive by IHC 3 + or FISH overexpression [ 21 ]. The surrogate of treatment response pCR was defined as no residual disease in breast and axillary lymph nodes after NAC and obtained by post-treatment surgery [ 22 ].

Imaging data and tumor segmentation

The scanning process of DCE-MRI can be found on TCIA website [ 17 , 18 ]. DCE-MRI scanning protocol details are provided in Supplementary Material Table S1 . The pre-contrast phase and five post-contrast phases were used for radiomic feature extraction and subsequent analysis.

The region of interest was segmented by functional tumor volume (FTV) included in the dataset. The calculation of FTV involved background filtering, estimating signal enhancement ratio, and applying a peak enhancement threshold in a manual-defined 3D bounding box [ 23 ].

Image preprocessing and feature extraction

Image normalization was performed across different DCE-MRI phases of the same patient to preserve the dynamic information. All the images were isotropically resampled to 1*1*1mm 3 , and discretized by a fixed bin width of 5. More details of image preprocessing can be found in Supplementary Material Figure S1 . Radiomic features were extracted from each phase of DCE-MRI using PyRadiomics package version 3.0.1 following the standardization and definitions in the image biomarker standadization initiative [ 24 , 25 ]. The extracted features included morphological features ( n  = 14), first-order features ( n  = 17), and texture features ( n  = 79). The repeatability of radiomic features was evaluated by perturbation which involved random translation, rotation, and contour randomization of original masks [ 26 , 27 , 28 ]. Features with high-repeatabliity (intraclass correlation coefficient, ICC ≥ 0.9 [ 29 ]) were retained for better model repeatability. The fluctuation of radiomic features was measured by performing a single-sample t test on the variations between features from different phases. Radiomic feature series were constructed by concatenating the high-repeatable and phase-varying first-order and texture features. Dynamic features were extracted from radiomic feature series using the 22 CAnonical Time-series Characteristics (catch22) feature set, specifically designed for capturing the dynamic properties of time series data, such as distributions and outliers, linear and non-linear autocorrelation, and so on [ 30 ].

Model development and evaluation

The development of radiomic model and dynamic model followed the same process including feature selection and model building. The features with low variances were removed first to retain those providing more information. Then, features with significant correlations with pCR were identified by MannWhitney U test, where a p value smaller than 0.05 was defined as significant. LASSO was subsequently used to select the independently discriminative features. Finally, features were ranked by minimum redundancy and maximum relevance (mRMR) algorithm considering the relevance to pCR and redundancy at the same time [ 31 ]. Clinical factors that are commonly used in clinical decision making and have significant associations with pCR were identified and used in developing clinical model. Combined models were constructed using logistic regression with clinical factors, prediction score of the dynamic model, and prediction score of radiomic model as variables. Different combination strategies were adopted, including combining two of the three variables respectively, as well as the combination of all three together. The independence of the components in the combined models were examined by their coefficients and p values. All the models were developed using Logistic Regression with 10-fold cross-validation in training set and tested in independent testing set.

The pCR prediction performance of the candidate models was assessed by various metrics, including area under receiver operating characteristic curve (AUC), accuracy, sensitivity, and specificity. AUCs were calculated by continuous prediction (the probability) and the other metrics were calculated by binary prediction (pCR or non-pCR) dichotomized by Youden index. An AUC typically ranges from 0 to 1 while AUC equal to one means a perfect descrimination ability. The optimal model was determined by the highest internal validation AUC in the training set. Heatmap was employed to visualize the relationships between different models and their association with clinical factors. SHapley Additive Explanations (SHAP), a method to interpret and explain the output of machine learning models, was employed to evaluate the importance of each component in the model with the highest AUC [ 32 ]. In our case, where the model output is the probability of achieving pCR, the SHAP values for each parameter ranges from − 1 to 1 and a larger absolute value means a higher importance for model output. Calibration curves and Brier scores were used to further evaluate the alignment between model-predicted probabilities and actual probabilities. Brier score measures the accuracy of probabilistic predictions and takes the value from 0 to 1, for which 0 means a perfect prediction. Decision curve analysis was performed to evaluate the clinical benefit obtained by the optimal model [ 33 ]. Besides, to further demonstrate the generalizability of the optimal model, its association with pCR in various pre-defined molecular subtypes, namely HR + HER2-, HR + HER2+, HR-HER2-, and HR-HER2+, and patients receiving different treatments were evaluated.

Radiogenomic analysis

To examine whether the dynamic model can reflect tumor heterogeneity and its association with gene expression, we collected paired total mRNA expression data from National Center for Biotechnology Information (NCBI) [ 34 ]. Patients were divided into DYN + and DYN- groups according to the binary prediction of dynamic model. Student t test was performed to identify differentially expressed genes (DEGs) between the two groups. An absolute log-2 fold change larger than 0.25 and a p value smaller than 0.05 were used as cutoff. Enriched Gene Ontology (GO) terms and Kyoto Encyclopedia of Genes and Genomes (KEGG) pathways were identified by gene set enrichment analysis (GSEA) of DEGs [ 35 , 36 , 37 , 38 , 39 ]. A p value smaller than 0.05 and false discovery rate (FDR) smaller than 0.25 were considered statistically significant.

Statistical analysis and software

For statistical analysis, Chi-Square test or Fisher’s exact test was used for categorical variables and MannWhitney U test was used for continuous variables. A two-tailed p-value smaller than 0.05 was considered statistically significant. The 95% CIs for AUCs were calculated according to DeLong’s methods [ 40 ]. DeLong test was used to compare the AUCs of two independent models and likelihood ratio test was used to compare the model fit of nested models to demonstrate the improvements conferred by the additional factors in complex models. The statistical analysis was carried out on R4.2.2 [ 41 ] and Python3.7 [ 42 ]. Logistic regression was carried out by package scikit-learn 1.0.2 [ 43 ]. Radiogenomic analysis was conducted using packages scanpy 1.9.3 [ 44 ] and gseapy 1.1.0 [ 45 ].

Patient characteristics

A total of 785 patients with complete imaging data and clinicopathological record constituted the entire patient cohort in this study and were divided into training set and testing set with a ratio of 3:1 (Fig.  2 ). As shown in Table  1 , there is no significant difference in all of the patient characteristics between training set and testing set. The characteristics of pCR and non-pCR patients were tabulated in Supplementary Material Table S2 . Significant association with pCR was observed in treatment, HR, HER2, and MP, while the other characteristics were independent of pCR.

Patient cohort and train-test split

Feature repeatability and feature change

The summarized results of feature repeatability and feature variation are shown in Supplementary Material Figure S2 and Figure S3 . After removing the duplicate shape features and features with low repeatability, there were 480 radiomic features retained for each patient. For dynamic feature extraction, features repeatable in all the DCE-MRI phases and changing across different phases were retained. A total of 1232 dynamic features were extracted from 56 selected radiomic feature series for each patient and used in further analysis. An example of the dynamic feature is shown in Supplementary Material Table S3 .

Different models in pCR prediction

A 10-feature dynamic model and a 4-feature radiomic model were developed separately (Supplementary Material Table S4 ). Dynamic model achieved higher AUC than radiomic model in both training set (0.688 vs. 0.650) and testing set (0.686 vs. 0.626) (Fig.  3 (a)(b)), but the difference was not statistically significant (p value = 0.181 and 0.222). Dynamic model also had better performance in terms of accuracy and specificity, while the sensitivity was the same as radiomic model (Table  2 ). The significance of each feature in dynamic model and radiomic model was evaluated by the odds ratio and tabulated in Supplementary Material Table S5 and S6 .

Among the clinicopathological variables provided in the dataset, treatment, HR, HER2, and MP were significantly associated with pCR (Supplementary Material Table S2 ). Since we intended to study biomarkers and MP requires expensive genomic test, only HR and HER2 were retained for further analysis. Table  3 summarized the metrics for pCR prediction performance of clinical model and combined models. Clinical-radiomic-dynamic (CRD) model achieved the highest training and testing AUC (Fig.  3 (c)(d)), accuracy, and specificity, while clinical model had the highest sensitivity among all the models. The clinical factors, the dynamic model, and the radiomic model demonstrated independent value in CRD model as indicated by their coefficients and p values (Supplementary Material Table S7 ). Compared with clinical-radiomic (CR) model, CRD model shown significant improvement in both training and testing performance, indicating the additive value of dynamic model. Figure  3 (e) shows the heatmap of the predicted probability by different models. Models containing dynamic features were clustered as similar models, showing the distinctive characteristic of dynamic features. The dynamic model was not associated with HR and HER2, demonstrating the independent value of dynamic model.

Reciever operating characteristic (ROC) curve analysis of dynamic model and radiomic model in ( a ) training set and ( b ) testing set. ROC analysis of clinical model, radiomic-dynamic (RD) model, clinical-radiomic (CR) model, clinical-dynamic (CD) model, and clinical-radiomic-dynamic (CRD) model in ( c ) training set and ( d ) testing set. ( e ) Heatmap of predicted probability by different models

Evaluation of the optimal model

Overall, CRD model has the best performance in pCR prediction. The calibration curves of CRD model had Brier score of 0.174 and 0.180 in training and testing set respectively (Fig.  4 (a)), indicating well-alignment between predicted probablities and actual probabilities. The decision curve analysis of CRD model demonstrated its clinical usefulness by higher net benefit gain compared to clinical model and the other combined models (Fig.  4 (b)).

Calibration curve and decision curve analysis

The SHAP value analysis of CRD model shown high importance of dynamic model, which was comparable to HR. The importance of radiomic model and HER2 was a little bit lower, but still had significant effect on the model output (Fig.  5 (a)). The CRD model was also used in stratifying pCR and non-pCR patients under different pre-defined molecular subtypes. It shown a significant stratification ability in all the four molecular subtypes with odds ratio (OR) of 2.88–8.42. (Fig.  5 (b)). In the analysis of patients receiving different drugs, except for the marginally significant performance in Pertuzumab arm, CRD model shown significant association with pCR with OR of 2.88–10.93 in the other treatment arms (Fig.  5 (c)).

( a ) SHAP analysis for interpretable component importance of CRD model. The beaswarm plot shows how each variable influence model output on single data where one dot represents one patient (left). The mean absolute SHAP value reflects the global effect of each variable on model output (right). ( b ) Box plots showing the predictive ability of CRD model in patient subgroups of various molecular subtypes. The molecular subtypes were defined by the status of HR and HER2, namely HR + HER2-, HR + HER2+, HR-HER2+, and HR-HER2-. The box plots indicate that the CRD model yields significantly distinct prediction probabilities for patients with pCR and non-pCR in all the four molecular subtypes. ( c ) Box plots showing the predictive ability of CRD model in patients receiving various treatments. Patients received standard care (control) or standard care plus one trial agent (ABT888, AMG386, Ganetespib, Ganitumab, MK2206, Neratinib, Pembrolizumab, Pertuzumab, T-DM1) in the trial. The box plots suggest that CRD model demonstrates the capability to differentiate pCR and non-pCR patients across various treatment drugs in this trial, with the exception of a marginal significance observed in Pertuzumab. All the p values were obtained by student t test. OR: odds ratio

DEGs and enriched pathways

In DEG analysis, a total of 196 up-regulated genes and 101 down-regulated genes in DYN + group were identified. As compared with HR- group and HER2 + group, which also associate with better pCR outcome in ISPY2 trial, there are 7 common up-regulated genes and 22 common down-regulated genes (Fig.  6 (a)). In GSEA by GO terms, there are 36 biological processes, 3 cellular components, 2 molecular functions enriched in DYN+ (Fig.  6 (b)), many of which are associated with immune system. There are 4 enriched pathways in GSEA by KEGG, in which 3 pathways are related to viral disease and 1 pathway is related to immune disease (Fig.  6 (c)).

( a ) Up-regulated (left) and down-regulated (right) DEGs in DYN+, HR-, and HER2 + group. ( b ) Enriched GO terms in DYN + group. ( c ) Enriched KEGG pathways in DYN + group

While the dynamic information in DCE-MRI has shown potential in various clinical applications, the exploration of DCE-MRI-derived radiomic feature series has remained limited. This study systematically extracted dynamic features from DCE-MRI-derived radiomic feature series using feature-based time series analysis method and built dynamic model for pCR prediction. Adding dynamic model to exisitng clinical and radiomic model can improve pCR prediction. Radiogenomic analysis revealed correlations of dynamic model with some breast cancer prognosis-related genes and pathways, providing the potential biological explanations for the additive value.

The change in DCE-MR image appearances caused by the flow of contrast agent may contain valuable information for pCR prediction. Previous studies have employed delta features and statistical distributions to characterize the relevant dynamic information [ 12 , 13 ]. However, the former method may provide limited information by utilizing only two of multiple DCE-MR phases, while the latter method disregards the temporal information that is crucial for reflecting the directional flow of contrast agent. A recently published paper implemented several classical time series analysis algorithms in DCE-MRI-derived radiomic feature series and achieved an accuracy of 0.852 in breast cancer diagnosis, demonstrating the significance of serial information as well as the feasibility and efficacy of time series analysis [ 46 ]. In our study, we used radiomic features to comprehensively describe DCE-MR image appearance and adopted Catch22 to systematically analyze the dynamics of radiomic feature series. The Catch22 feature set takes into account both the temporal order and relative magnitude of series values. It has been successfully implemented in many time series analysis applications, such as breath signal and heart rate. To the best of our knowledge, it is the first study to apply a systematic feature-based time series analysis method to DCE-MRI for pCR prediction. Our results demonstrated the utility of the extracted dynamic features by showing a modestly higher AUC of dynamic model in comparison to the conventional radiomic model. Furthermore, the dynamic features provided additive value to the existing methods, as evidenced by a significantly improved model performance compared with both clinical model and CR model. Overall, we have demonstrated the feasibility and efficacy of extracting dynamic information through feature-based time series analysis and the potential of dynamic features in facilitating pCR prediction. Besides, our method offers the advantage of interpretability as Catch22 provides clear definition for each dynamic feature. And it is adaptable to different time series length which is frequently encountered in real-world clinical practice due to the variations of machines and scan settings. Our method demonstrates the potential to be implemented in real clinical practice, although further validation is required to confirm its performance in diverse settings.

Both single-modal and multi-modal models were developed in this study. While the imaging-based model and clinical model appeared to have similar performance, the combined models shown better performance than individual models. The CRD model achieved the highest AUC, which is significantly better than RD model and clinical model alone, indicating that imaging features and clinical factors may provide distinct and complementary information for pCR prediction. Subgroup analysis of the CRD model was conducted to further explore the effectiveness of CRD model under various conditions. Breast cancer is a highly heterogeneous disease characterized by various HR and HER2 status, resulting in four molecular subtypes. Our results on molecular subtype analysis resulted in varying effect size by OR ranging from 2.88 to 8.42, where a larger OR indicates a stronger predictive ability. While CRD model is significantly associated with pCR in all the molecular subtypes, our results suggested that CRD model has stronger predictive ability for patients of HR + HER2-. The CRD model was also evaluated by its effect for patients receiving different drugs, resulting in the largest OR in Ganetespib and marginally significant OR in Pertuzumab. This indicates the various predictive value of CRD model for various treatment drugs and assists the clinicians to decide applicable scenarios. In general, CRD model shown generalizability acorss various molecular subtypes and various treatment drugs. However, due to the nature of trial data, the patient numbers are small in each subgroups and further validation on larger cohort is required to confirm the results.

It is believed that radiomics is able to detect the underlying biological processes in the human body by analyzing image textures that are imperceptible to human eyes. Moreover, pre-treatment radiomics mostly reflect the baseline tumor characteristics, which is the result of various biological processes and associated with treatment response. Previous studies indicated the representativeness of image phenotypes for the biological characteristics by demonstrating their similar predictive ability to pCR [ 47 ]. However, few radiomics study has linked the image phenotype to biological processes through radiogenomic analysis [ 48 ]. In this study, we conducted a radiogenomic analysis to associate our dynamic model to the genomic profiles of breast tumors, providing insight into the underlying biological mechanisms of radiomics. Some DEGs in our DYN + subgroup is associated with better prognosis of breast cancer patients. For example, the DYN + subgroup has higher expression of CXCL9 which was demonstrated to associate with higher pCR rate in breast cancer patients receiving NAC in previous study [ 49 ]; HLA-DPB1 was up-regulated in DYN + subgroup and was also assocaited with more tumor infiltrating lymphcytes and thereby better prognosis [ 50 ]. On the other hand, DEGs such as CCL18 is associated with angiogenesis in breast cancer, demonstrating the potential of DYN to represent the dynamics in DCE-MRI [ 51 ].

Our study has several limitations. Due to the retrospective nature of the study, it is possible that our results suffer from spectrum bias and information bias, which may compromise the overall strength of evidence of our study. Besides, our study included a medium sample size ( n  = 785) without external validation, which may not be representative enough for the large population of breast cancer patients. Therefore, further study is needed to externally validate our methods and conclusions in a prospective manner. Also, our study only employed DCE-MRI, while multi-parametric MR images could be available in clinics. Further exploration on incorporating other MR images is warranted.

Conclusions

In conclusion, this study quantified the dynamic characteristics of DCE-MRI by calculating dynamic properties of radiomic feature series and developed a dynamic model. The dynamic model can aid in improving pCR prediction of breast cancer patients receiving NAC. The potential biological underpinnings of the dynamic model was explored by demonstrating its association with tumor heterogeneity in gene expression. Further investigations on more biological associations and assisting treatment selection are warranted.

Data availability

The dataset used in this study is a public dataset available at The Cancer Image Archive with accession code 70230072. Dynamic and radiomics features that support the findings of this study can be found here: https://github.com/Xinyu-Z000/DCE-MRI-dynamics.

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This research was partly supported by research grants of Mainland-Hong Kong Joint Funding Scheme (MHKJFS) (MHP/005/20), Shenzhen Basic Research Program (JCYJ20210324130209023), Project of Strategic Importance Fund (P0035421), Projects of RISA (P0043001) and Projects of RI-IWEAR (P0038684) from The Hong Kong Polytechnic University, Innovation and Technology Fund (ITS/047/22), Health and Medical Research Fund (HMRF 09200576), the Health Bureau, The Government of the Hong Kong Special Administrative Region.

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Xinyu Zhang, Xinzhi Teng, Jiang Zhang, Qingpei Lai & Jing Cai

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Contributions

XY.Z. and J.C. contributed to the conceptualization and all the authors were involved in study design. Data collection and preprocessing were performed by XZ.T. and J.Z. Data analysis and model development were performed by XY.Z. The draft of the manuscript was written by XY.Z. XZ.T., J.Z., QP.L., and J.C. commented and revised on previous versions of the manuscript. All the authors read and approve the final version of the manuscript.

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Correspondence to Jing Cai .

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Zhang, X., Teng, X., Zhang, J. et al. Enhancing pathological complete response prediction in breast cancer: the role of dynamic characterization of DCE-MRI and its association with tumor heterogeneity. Breast Cancer Res 26 , 77 (2024). https://doi.org/10.1186/s13058-024-01836-3

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Robust Spectral π Pairing in the Random-Field Floquet Quantum Ising Model

Harald schmid, alexander-georg penner, kang yang, leonid glazman, and felix von oppen, phys. rev. lett. 132 , 210401 – published 20 may 2024.

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Motivated by an experiment on a superconducting quantum processor [X. Mi et al. , Science 378 , 785 (2022) .], we study level pairings in the many-body spectrum of the random-field Floquet quantum Ising model. The pairings derive from Majorana zero and π modes when writing the spin model in Jordan-Wigner fermions. Both splittings have log-normal distributions with random transverse fields. In contrast, random longitudinal fields affect the zero and π splittings in drastically different ways. While zero pairings are rapidly lifted, the π pairings are remarkably robust, or even strengthened, up to vastly larger disorder strengths. We explain our results within a self-consistent Floquet perturbation theory and study implications for boundary spin correlations. The robustness of π pairings against longitudinal disorder may be useful for quantum information processing.

• Received 16 January 2024
• Revised 7 April 2024
• Accepted 30 April 2024

DOI: https://doi.org/10.1103/PhysRevLett.132.210401

© 2024 American Physical Society

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• Physical Systems

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• 1 Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany
• 2 Department of Physics, Yale University, New Haven, Connecticut 06520, USA

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Vol. 132, Iss. 21 — 24 May 2024

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Clean quantum Ising chain. (a) Single-particle Floquet spectrum of a periodic chain vs wave vector k for various transverse fields g . (b) Phase diagram with phases labeled by the Majorana modes present in the corresponding Kitaev chain. (c) Hybridization splitting δ 0 , π vs g of Majorana modes in finite chains of various lengths N ( J = 0.5 ), showing the symmetry between MZM and MPM phases. (d) Sketch of the pairing of many-body eigenphases in the MZM and MPM phases. Both pairings coexist in the MZM & MPM phase. (e),(f) Spin-spin correlation function G ( t ) for (e) long [note the factor ( − 1 ) t for the MPM phase] and (f) short times. For long times, G ( t ) oscillates with period 2 π / δ 0 , π , superimposed on rapid period-two oscillations in the MPM phase. Parameters: (a)  J = 0.5 , (e),(f) N = 8 , ( g , J ) = ( 0.2 , 0.5 ) (MZM), ( g , J ) = ( 0.8 , 0.5 ) (MPM).

(a),(b) Random transverse fields: (a) Average and (b) variance of ln δ 0 , π vs chain length N for both MZMs ( g < 1 / 2 ; triangles) and MPMs ( g > 1 / 2 ; dots). Numerical results (symbols) are in excellent agreement with analytical expressions (full lines) [ 19 ]. (c)–(e) Random longitudinal fields: Splitting distributions for various disorder strengths in (c) MZM and (d),(e) MPM phase. In (c), numerical results (full lines) are well reproduced by an analytical two-level approximation (dashed lines). In (d),(e), numerical results (full lines) can be interpreted in terms of second-order Floquet perturbation theory (dashed lines). (f) “Phase diagram” of the splitting distribution (MPM phase) in the N – g plane for fixed d h . Parameters: J = 0.5 , (a),(b) d g = 0.02 , N = 10 4 realizations, (c)  δ 0 = 5 × 10 − 10 , (d)  δ π = 5 × 10 − 10 , (e)  δ π = 2 × 10 − 6 , (c)–(e)  N = 12 , N = 10 3 .

Boundary spin-spin correlation function G ( t ) and its Fourier transform G ( ω ) with random longitudinal fields (see legends for strength). (a),(b) MZM phase: The random field suppresses the oscillations induced by the finite splitting δ 0 and generates a constant ( ω = 0 ) contribution. (c) MPM phase at g = 0.9 : The random field suppresses the oscillations induced by δ π in ( − 1 ) t G ( t ) . The decay is Gaussian for large disorder and becomes slower with increasing d h . The correlation function (markers) is well reproduced when restricting the summation in Eq. ( 6 ) to π -paired states n and m , and (d)  G ( ω ) approximately tracks the δ π ′ distribution, cf. Fig.  2 . (e),(f) MPM phase at g = 0.8 : ( − 1 ) t G ( t ) now decays exponentially reflecting the Lorentzian δ π ′ distribution. Parameters: J = 0.5 , N = 12 , N = 10 , (a)–(d)  δ 0 = δ π = 5 × 10 − 10 , (e),(f) δ π = 2 × 10 − 6 .

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