Revolutionizing Breast Cancer Diagnosis! It's Not Just AI, Mathematics is Advancing Breast Cancer Diagnosis

The tissue collected during a breast cancer examination is closely examined under a microscope by a pathologist.

It's not just about confirming the presence of cancer cells. The pathologist checks how much the cell shapes have changed from normal tissue, whether the original structure of the mammary gland remains, and whether the cells are arranged regularly or have lost order and spread. By integrating various characteristics, pathologists determine the type and malignancy of the cancer.

In determining the treatment plan for breast cancer, a multitude of information is used, including the presence of hormone receptors that respond to female hormones, a protein called HER2, the cell proliferation ability, tumor size, and lymph node metastasis.

However, accurately predicting how the cancer will progress in each patient and which treatment will be most effective is not easy.

To address these challenges, a research team from Columbia University and others have announced a new evaluation method using "topology," a branch of mathematics.

The research team aimed to express the "orderliness" or "disorderliness" of tumor tissue, which pathologists have visually assessed, as continuous numerical values. By converting the structure of the tissue into computable data, there is a possibility of more accurately predicting patient survival and treatment response.

Normal and cancerous tissues differ in their "arrangement"

In a normal mammary gland, cells maintain specific roles and arrangements to form structures such as ducts and lobules.

However, as cells become cancerous, this order gradually deteriorates. The size and shape of the cells become irregular, and the shape of the nuclei becomes irregular as well. The glandular structures that should be present collapse, and the boundaries of cell clusters become blurred.

Generally, tumors that maintain a structure close to normal tissue may progress relatively slowly. On the other hand, tumors that have significantly lost their tissue order may be more active in proliferation and invasion of surrounding areas.

Pathologists have long observed these changes in tissue.

However, it is difficult to fully quantify complex morphologies with the human eye alone. Although there are clear criteria for pathological diagnosis, there are subtle differences that cannot be expressed in a few grades.

Even among patients classified in the same grade, responses to treatment and risk of recurrence are not necessarily the same. The research team sought to mathematically extract the subtle differences that were buried within traditional classifications.

Analysis of 555 breast cancer tissues

In the study, tissue data from 555 breast cancer patients with diverse backgrounds, primarily from North Carolina, USA, were analyzed.

The research team used a technique called multiplex immunofluorescence staining to identify multiple cells and molecules within the tumor tissue.

The subjects included not only cancer cells but also immune cells like CD8-positive T cells, cells related to macrophages, stromal cells surrounding the tumor, and the expression of PD-L1, which is involved in mechanisms that suppress immune responses, was also examined.

The research team did not simply count the number of cells.

They recorded the coordinates of where each cell was located within the tissue and analyzed how cancer cells clustered, how close immune cells were to cancer cells, and what kind of spaces existed between cell groups.

In other words, they examined not just "how many cells are there," but "where each cell is located and what kind of relationships they form with each other."

"Persistent Homology" for Measuring Tissue Shape

The mathematical method used to quantify the complex arrangement of cells is called "persistent homology."

This is a method for examining shapes, connections, and structures like holes within data from different scales.

It is easier to understand if you think of each cell as a point marked on a map.

A small circle is drawn around each point, and the circle is gradually enlarged. When the circles are small, the cells exist as independent points. As the circles grow larger, nearby cells connect, forming multiple groups.

Further expanding the circles leads to the merging of previously separate groups. During this process, spaces or holes surrounded by cell groups appear and eventually disappear.

Persistent homology calculates at what scale each group or space appears and how long they persist.

Structures that disappear quickly may be due to random variation or noise in the image. On the other hand, structures that persist across different scales likely reflect essential characteristics of the tissue.

The research team converted this information into numbers that could be handled by statistical analysis and machine learning. They then created a score indicating the order of tumor tissue by combining factors such as intercellular distance, cell density, group shape, and PD-L1 intensity.

A high score indicates a relatively cohesive tissue structure. A low score indicates a significant disruption in cell arrangement and an increase in tissue disorder.

Patients with higher tissue order have better outcomes

The study found that the topology-based score was associated with the survival period of breast cancer patients.

Patients with high scores, indicating relatively organized tissue structure, tended to have longer survival periods and better outcomes. In contrast, tumors with lost tissue order and low scores were linked to more aggressive characteristics.

Even when analyzing only the structure of tumor cells, there was a certain predictive power, and adding information about immune cells and PD-L1 could enhance the model's performance.

The research paper reported that the topology-based indicators showed higher prognostic prediction accuracy than some traditional genetic and protein markers.

However, this does not mean that traditional tests will become unnecessary.

The prognosis of breast cancer is influenced by numerous factors, including tumor size, stage, molecular type, treatment content, and the patient's age and health condition. The new score is expected to be additional information rather than a replacement for existing tests.

Potential for smaller prediction differences by race or ethnicity

In this study, it was also noted that the predictive power of the topology indicator was relatively stable between non-Hispanic Black patients and non-Hispanic White patients.

Medical prediction models can sometimes have reduced accuracy in specific populations depending on the composition of the data used for development.

It has been reported that some traditional biomarkers show differences in predictive performance based on race or ethnicity. Compared to those, the topology indicator showed a tendency for less performance variation among patient groups.

Technology that can maintain stable accuracy across diverse patients is important in preventing the expansion of medical disparities.

However, this result alone does not prove fairness. Race and ethnicity are not simple biological classifications but are also related to multiple social factors, such as access to healthcare, living environment, income, and time to treatment initiation.

To actually use it in different countries and regions, further validation targeting a broader patient population will be necessary.

Predicting treatment response by combining with genetic information

The research team also combined the topology score obtained from tissue images with gene expression data.

As a result, gene groups linked to the characteristics of tissue structure were identified, and a "topology-derived gene signature" was created.

When this gene signature was applied to another breast cancer clinical trial data, the possibility of predicting the response to preoperative drug therapy was suggested.

In breast cancer, treatments may be administered to shrink the tumor by giving anticancer drugs or molecular targeted drugs before surgery.

A state where invasive cancer is not confirmed in the surgical specimen after treatment is called "pathological complete response" and is an important indicator for considering subsequent progress.

In the future, if tissue shape, genes, proteins, and clinical information of patients can be integrated, it may be possible to make more individualized judgments about "which treatment is effective for this patient."

However, at this stage, the topology score cannot be used to select treatment drugs. What was shown this time is the possibility that information about treatment response is also contained in tissue structure, and additional validation is essential for clinical use.

Tissue disorder is also related to metabolism and immunity

The study suggested that tissue structure disorder is not merely a visual change but may also be linked to metabolism and immune activity within the tumor.

A low topology score was associated with gene pathways related to cell movement, invasion, immune suppression, and a phenomenon called epithelial-mesenchymal transition.

The research team particularly focused on a metabolic enzyme called IL4I1 and a mechanism connected to a receptor called AHR.

This pathway may be related to cancer cell proliferation, movement, and immune response suppression. The study found that tumors with strong activity in this metabolic pathway tended to have lost tissue order.

However, it is not known which is the cause and which is the result.

Whether changes in metabolism and immunity cause tissue structure to collapse, or whether the collapse of tissue results in changes in the metabolic and immune environment, or whether both influence each other, requires separate experiments to confirm causality.

Not a "breast cancer early detection technology"

There is a particular point to be careful about in understanding this study.

This method is not a screening technology like mammography or ultrasound that finds breast cancer that has not yet been discovered.

It is a method for thoroughly analyzing tumor tissue already collected from patients to evaluate the nature of the cancer, prognosis, and response to treatment.

Although it is sometimes described in news headlines as a "method to improve diagnosis," it should be more accurately considered as a technology to assist pathological diagnosis and prognosis prediction.

Moreover, the multiplex immunofluorescence staining used in this study is not a test used routinely in all medical institutions.

The research team aims to develop a method that can be analyzed with more widely used tests like H&E staining in general pathology and apply it to routine pathological diagnosis.

If it becomes usable with standard pathology slides, there is potential to expand advanced image analysis not only to large university hospitals but also to regional medical institutions and areas with limited medical resources.

Expectations for personalized medicine on social media

The research findings were also introduced on the social media accounts of Columbia University's medical department, cancer center, and pathology department.

On Columbia University's official X, it was presented as research evaluating breast cancer tissue patterns in a new way to connect to patient outcome predictions. The cancer center's post also emphasized the conversion of tissue structure into topology-based biomarkers.

On Instagram, the research was introduced as "big news" when it was featured in general media, highlighting it as research intersecting mathematics, pathology, and digital image analysis.

Medical Xpress also introduced the research on X and Facebook, highlighting the aspect of "measuring the structure of breast cancer tissue as a continuous score." It was shared by accounts that disseminate medical information, spreading as a new example of digital pathology and personalized medicine.

The main reactions that can be read from public posts are centered on expectations such as the following:

Could it be possible to objectively measure information that has relied on the experience of pathologists? Could treatment choices for each patient be made more precisely? Could advanced diagnostic technology be expanded beyond well-equipped large hospitals?

On the other hand, as of August 4, 2026, the public posts that can be confirmed are mainly introductions by research institutions and medical media. Large-scale discussions, clear pros and cons, and accumulated actual usage experiences by patients and clinicians are not at the stage yet.

Based solely on the number of introductions and favorable expressions on social media, it cannot be judged that "evaluation in the medical world has been confirmed" or "it can be used in clinical practice immediately."

With new medical technology, it is necessary to consider not only the accuracy of research results but also the possibility of misjudgment, explanation to patients, introduction costs, examination time, management of personal information, and differences in image quality among medical institutions.

Not a replacement for pathologists

In medical research using image analysis and AI, there are sometimes extreme explanations such as "computers surpass doctors" or "specialists become unnecessary."

However, this technology does not replace pathologists.

Pathologists diagnose by integrating not only the shape of the tissue but also the condition of the specimen, type of tumor, presence of invasion, resection margins, lymph node metastasis, and expression of various proteins.

Experts are needed to interpret the numbers shown by the image analysis system in light of the patient's clinical information.

The value of this technology lies not in eliminating the human eye but in adding information that was difficult to measure with the human eye alone.

Pathologists interpret the meaning of the tissue, and computers calculate complex positional relationships with the same criteria. Combining both aims for more reproducible diagnoses and prognostic predictions.

Challenges remaining before practical application

The results of this study are promising, but there are several challenges before clinical application.

First, external validation with different patient populations is necessary. It must be examined whether the same accuracy can be maintained even if the country, region, age, molecular type of breast cancer, treatment method, and specimen processing method differ.

Next, a mechanism that can produce stable results even if the imaging equipment or staining method changes is needed.

Being able to predict prognosis and actually improving patient treatment outcomes are not the same. It is necessary to confirm through prospective clinical trials whether changing treatment policies using new indicators truly improves survival periods and quality of life.

Explaining to patients is also a challenge.

Simply conveying that "the score indicating tissue order is low" may increase anxiety. It must be explained clearly how much uncertainty there is in the numbers, how they combine with existing test results, and how much they influence treatment choices.

The research team also states that additional validation and clinical research are necessary for introduction into routine clinical practice.

Microscope images become "