Applications of Topological Data Analysis in Oncology

Advancing Precision Medicine: Algebraic Topology and Differential Geometry in Radiology and Computational Pathology

Precision medicine aims to provide personalized care based on individual patient characteristics, rather than guideline-directed therapies for groups of diseases or patient demographics. Images-both radiology- and pathology-derived-are a major source of information on presence, type, and status of disease. Exploring the mathematical relationship of pixels in medical imaging ("radiomics") and cellular-scale structures in digital pathology slides ("pathomics") offers powerful tools for extracting both qualitative and, increasingly, quantitative data. These analytical approaches, however, may be significantly enhanced by applying additional methods arising from fields of mathematics such as differential geometry and algebraic topology that remain underexplored in this context. Geometry's strength lies in its ability to provide precise local measurements, such as curvature, that can be crucial for identifying abnormalities at multiple spatial levels. These measurements can augment the quantitative features extracted in conventional radiomics, leading to more nuanced diagnostics. By contrast, topology serves as a robust shape descriptor, capturing essential features such as connected components and holes. The field of topological data analysis was initially founded to explore the shape of data, with functional network connectivity in the brain being a prominent example. Increasingly, its tools are now being used to explore organizational patterns of physical structures in medical images and digitized pathology slides. By leveraging tools from both differential geometry and algebraic topology, researchers and clinicians may be able to obtain a more comprehensive, multi-layered understanding of medical images and contribute to precision medicine's armamentarium.

Transcriptome analysis reveals the genes involved in spermatogenesis in white feather broilers

Semen volume is an important economic trait of broilers and one of the important indices for continuous breeding. The objective of this study was to identify genes related to semen volume through transcriptome analysis of the testis tissue of white feather broilers. The testis samples with the highest semen volume (H group, n = 5) and lowest semen volume (L group, n = 5) were selected from 400-day-old roosters for transcriptome analysis by RNA sequencing. During the screening of differentially expressed genes (DEGs) between the H and L groups, a total of 386 DEGs were identified, among which 348 were upregulated and 38 were downregulated. Gene ontology (GO) enrichment analysis and Kyoto Encyclopedia of Genes and Genomes (KEGG) analysis revealed that the immune response, leukocyte differentiation, cell adhesion molecules and collagen binding played vital roles in spermatogenesis. The results showed that 4 genes related to spermatogenesis, namely, COL1A1, CD74, ARPC1B and APOA1, were significantly expressed in Group H, which was consistent with the phenotype results. Our findings may provide a basis for further research on the genetic mechanism of semen volume in white feather broilers.

Topological Data Analysis and Use of Mapper for Cerebral Aneurysm Rupture Status Discrimination Based on 3-Dimensional Shape Analysis

BACKGROUND AND OBJECTIVES

Topological data analysis (TDA), which identifies patterns in data through simplified topological signatures, has yet to be applied to aneurysm research. We investigate TDA Mapper graphs (Mapper) for aneurysm rupture discrimination.

METHODS

Two hundred sixteen bifurcation aneurysms (90 ruptured) from 3-dimensional rotational angiography were segmented from vasculature and evaluated for 12 size/shape and 18 enhanced radiomics features. Using Mapper, uniformly dense aneurysm models were represented as graph structures and described by graph shape metrics. Mapper dissimilarity scores (MDS) were computed between pairs of aneurysms based on shape metrics. Lower MDS described similar shapes, whereas high MDS represented shapes that do not share common characteristics. Ruptured/unruptured average MDS scores (how "far" an aneurysm is shape-wise to ruptured/unruptured data sets, respectively) were evaluated for each aneurysm. Rupture status discrimination univariate and multivariate statistics were reported for all features.

RESULTS

The average MDS for pairs of ruptured aneurysms were significantly larger compared with unruptured pairs (0.055 ± 0.027 vs 0.039 ± 0.015, P < .0001). Low MDS suggest that, in contrast to ruptured aneurysms, unruptured aneurysms have similar shape characteristics. An MDS threshold value of 0.0417 (area under the curve [AUC] = 0.73, 80% specificity, 60% sensitivity) was identified for rupture status classification. Under this predictive model, MDS scores <0.0417 would identify unruptured status. MDS statistical performance in discriminating rupture status was similar to that of nonsphericity and radiomics Flatness (AUC = 0.73), outperforming other features. Ruptured aneurysms were more elongated ( P < .0001), flatter ( P < .0001), and showed higher nonsphericity ( P < .0001) compared with unruptured. Including MDS in multivariate analysis resulted in AUC = 0.82, outperforming multivariate analysis on size/shape (AUC = 0.76) and enhanced radiomics (AUC = 0.78) alone.

CONCLUSION

A novel application of Mapper TDA was proposed for aneurysm evaluation, with promising results for rupture status classification. Multivariate analysis incorporating Mapper resulted in high accuracy, which is particularly important given that bifurcation aneurysms are challenging to classify morphologically. This proof-of-concept study warrants future investigation into optimizing Mapper functionality for aneurysm research.

The shape of cancer relapse: Topological data analysis predicts recurrence in paediatric acute lymphoblastic leukaemia

Although children and adolescents with acute lymphoblastic leukaemia (ALL) have high survival rates, approximately 15-20% of patients relapse. Risk of relapse is routinely estimated at diagnosis by biological factors, including flow cytometry data. This high-dimensional data is typically manually assessed by projecting it onto a subset of biomarkers. Cell density and "empty spaces" in 2D projections of the data, i.e. regions devoid of cells, are then used for qualitative assessment. Here, we use topological data analysis (TDA), which quantifies shapes, including empty spaces, in data, to analyse pre-treatment ALL datasets with known patient outcomes. We combine these fully unsupervised analyses with Machine Learning (ML) to identify significant shape characteristics and demonstrate that they accurately predict risk of relapse, particularly for patients previously classified as 'low risk'. We independently confirm the predictive power of CD10, CD20, CD38, and CD45 as biomarkers for ALL diagnosis. Based on our analyses, we propose three increasingly detailed prognostic pipelines for analysing flow cytometry data from ALL patients depending on technical and technological availability: 1. Visual inspection of specific biological features in biparametric projections of the data; 2. Computation of quantitative topological descriptors of such projections; 3. A combined analysis, using TDA and ML, in the four-parameter space defined by CD10, CD20, CD38 and CD45. Our analyses readily extend to other haematological malignancies.

Supervised topological data analysis for MALDI mass spectrometry imaging applications

BACKGROUND

Matrix-assisted laser desorption/ionization mass spectrometry imaging (MALDI MSI) displays significant potential for applications in cancer research, especially in tumor typing and subtyping. Lung cancer is the primary cause of tumor-related deaths, where the most lethal entities are adenocarcinoma (ADC) and squamous cell carcinoma (SqCC). Distinguishing between these two common subtypes is crucial for therapy decisions and successful patient management.

RESULTS

We propose a new algebraic topological framework, which obtains intrinsic information from MALDI data and transforms it to reflect topological persistence. Our framework offers two main advantages. Firstly, topological persistence aids in distinguishing the signal from noise. Secondly, it compresses the MALDI data, saving storage space and optimizes computational time for subsequent classification tasks. We present an algorithm that efficiently implements our topological framework, relying on a single tuning parameter. Afterwards, logistic regression and random forest classifiers are employed on the extracted persistence features, thereby accomplishing an automated tumor (sub-)typing process. To demonstrate the competitiveness of our proposed framework, we conduct experiments on a real-world MALDI dataset using cross-validation. Furthermore, we showcase the effectiveness of the single denoising parameter by evaluating its performance on synthetic MALDI images with varying levels of noise.

CONCLUSION

Our empirical experiments demonstrate that the proposed algebraic topological framework successfully captures and leverages the intrinsic spectral information from MALDI data, leading to competitive results in classifying lung cancer subtypes. Moreover, the framework's ability to be fine-tuned for denoising highlights its versatility and potential for enhancing data analysis in MALDI applications.

Spatiochemical Characterization of the Pancreas Using Mass Spectrometry Imaging and Topological Data Analysis

Mass Spectrometry Imaging (MSI) is a technique used to identify the spatial distribution of molecules in tissues. An MSI experiment results in large amounts of high dimensional data, so efficient computational methods are needed to analyze the output. Topological Data Analysis (TDA) has proven to be effective in all kinds of applications. TDA focuses on the topology of the data in high dimensional space. Looking at the shape in a high dimensional data set can lead to new or different insights. In this work, we investigate the use of Mapper, a form of TDA, applied on MSI data. Mapper is used to find data clusters inside two healthy mouse pancreas data sets. The results are compared to previous work using UMAP for MSI data analysis on the same data sets. This work finds that the proposed technique discovers the same clusters in the data as UMAP and is also able to uncover new clusters, such as an additional ring structure inside the pancreatic islets and a better defined cluster containing blood vessels. The technique can be used for a large variety of data types and sizes and can be optimized for specific applications. It is also computationally similar to UMAP for clustering. Mapper is a very interesting method, especially its use in biomedical applications.

Effect of prior treatments on post-CDK 4/6 inhibitor survival in hormone receptor-positive breast cancer

PURPOSE

Multiple treatment options exist for patients with metastatic breast cancer (MBC). However, limited information is available on the impact of prior treatment duration and class on survival outcome for novel therapies, such as cyclin-dependent kinase 4/6 inhibitors (CDK4/6i) for patients with hormone receptor-positive, human epidermal growth factor receptor 2-negative (HR+ HER2-) MBC.

METHODS

This study used a nationwide, de-identified electronic health record-derived database to identify women with HR+ HER2- MBC who received at least one CDK 4/6i between 2011 and 2020. Hazard ratios (HR) and 95% confidence intervals (CI) were estimated for the association between prior duration and class of cancer treatment (both early-stage and metastatic) and prior CDK 4/6i survival as well as for those with multiple CDK 4/6i.

RESULTS

Of 5363 patients, the median survival from first CDK 4/6 inhibitor administration was 3.3 years. When compared to patients with no prior treatments, patients with < 1 year of prior treatment duration had a 30% increased hazard of death (HR, 1.30; 95% CI 1.15-1.46), those with 1 to < 3 years a 68% increased hazard of death (HR 1.68; 95% CI 1.49-1.88), and those with 3 or more years a 55% increased hazard of death (HR 1.55; 95% CI 1.36, 1.76). Patients who received prior therapy (endocrine or chemotherapy) before their CDK 4/6i had worse outcomes than those who received no prior therapy. Similar results were seen when comparing patients in the metastatic setting alone. Finally, patients who received a different CDK 4/6i after their first saw a lower hazard of death compared to patients who received subsequent endocrine or chemotherapy after their first CDK 4/6i.

CONCLUSION

Prior treatment duration and class are associated with a decreased overall survival after CDK 4/6 inhibitor administration. This highlights the importance for clinicians to consider prior treatment and duration in treatment decision-making and for trialists to stratify by these factors when randomizing patients or reporting results of future studies.

Characterizing emerging features in cell dynamics using topological data analysis methods

Filament-motor interactions inside cells play essential roles in many developmental as well as other biological processes. For instance, actin-myosin interactions drive the emergence or closure of ring channel structures during wound healing or dorsal closure. These dynamic protein interactions and the resulting protein organization lead to rich time-series data generated by using fluorescence imaging experiments or by simulating realistic stochastic models. We propose methods based on topological data analysis to track topological features through time in cell biology data consisting of point clouds or binary images. The framework proposed here is based on computing the persistent homology of the data at each time point and on connecting topological features through time using established distance metrics between topological summaries. The methods retain aspects of monomer identity when analyzing significant features in filamentous structure data, and capture the overall closure dynamics when assessing the organization of multiple ring structures through time. Using applications of these techniques to experimental data, we show that the proposed methods can describe features of the emergent dynamics and quantitatively distinguish between control and perturbation experiments.

Multiscale topology characterizes dynamic tumor vascular networks

Advances in imaging techniques enable high-resolution three-dimensional (3D) visualization of vascular networks over time and reveal abnormal structural features such as twists and loops, and their quantification is an active area of research. Here, we showcase how topological data analysis, the mathematical field that studies the "shape" of data, can characterize the geometric, spatial, and temporal organization of vascular networks. We propose two topological lenses to study vasculature, which capture inherent multiscale features and vessel connectivity, and surpass the single-scale analysis of existing methods. We analyze images collected using intravital and ultramicroscopy modalities and quantify spatiotemporal variation of twists, loops, and avascular regions (voids) in 3D vascular networks. This topological approach validates and quantifies known qualitative trends such as dynamic changes in tortuosity and loops in response to antibodies that modulate vessel sprouting; furthermore, it quantifies the effect of radiotherapy on vessel architecture.

Multiscale topology characterizes dynamic tumor vascular networks

Advances in imaging techniques enable high-resolution three-dimensional (3D) visualization of vascular networks over time and reveal abnormal structural features such as twists and loops, and their quantification is an active area of research. Here, we showcase how topological data analysis, the mathematical field that studies the "shape" of data, can characterize the geometric, spatial, and temporal organization of vascular networks. We propose two topological lenses to study vasculature, which capture inherent multiscale features and vessel connectivity, and surpass the single-scale analysis of existing methods. We analyze images collected using intravital and ultramicroscopy modalities and quantify spatiotemporal variation of twists, loops, and avascular regions (voids) in 3D vascular networks. This topological approach validates and quantifies known qualitative trends such as dynamic changes in tortuosity and loops in response to antibodies that modulate vessel sprouting; furthermore, it quantifies the effect of radiotherapy on vessel architecture.

Topological data analysis in biomedicine: A review

Significant technological advances made in recent years have shepherded a dramatic increase in utilization of digital technologies for biomedicine- everything from the widespread use of electronic health records to improved medical imaging capabilities and the rising ubiquity of genomic sequencing contribute to a "digitization" of biomedical research and clinical care. With this shift toward computerized tools comes a dramatic increase in the amount of available data, and current tools for data analysis capable of extracting meaningful knowledge from this wealth of information have yet to catch up. This article seeks to provide an overview of emerging mathematical methods with the potential to improve the abilities of clinicians and researchers to analyze biomedical data, but may be hindered from doing so by a lack of conceptual accessibility and awareness in the life sciences research community. In particular, we focus on topological data analysis (TDA), a set of methods grounded in the mathematical field of algebraic topology that seeks to describe and harness features related to the "shape" of data. We aim to make such techniques more approachable to non-mathematicians by providing a conceptual discussion of their theoretical foundations followed by a survey of their published applications to scientific research. Finally, we discuss the limitations of these methods and suggest potential avenues for future work integrating mathematical tools into clinical care and biomedical informatics.

Repairing the human with artificial intelligence in oncology

Artificial intelligence is a groundbreaking tool to learn and analyse higher features extracted from any dataset at large scale. This ability makes it ideal to facing any complex problem that may generally arise in the biomedical domain or oncology in particular. In this work, we envisage to provide a global vision of this mathematical discipline outgrowth by linking some other related subdomains such as transfer, reinforcement or federated learning. Complementary, we also introduce the recently popular method of topological data analysis that improves the performance of learning models.