Topological Data Analysis for the Quantification of Prostate Cancer Heterogeneity
PI: Justin D Silverman (IST, ICDS, Statistics, College of Medicine)
Tuition will be covered by the PI.
Level of Effort Effort:
50 Percent Weekly Allocation: 20 hours
• Research: 10 hrs/week
• ICDS Service: 8 hrs/week
• ICDS Engagement: 2 hrs/week
Project Description
Overview of Objectives: Computational tools for quantitative grading of human prostate cancer
This project will develop computational tools to quantify the 3D morphology of prostate cancer glands, supplementing and potentially improving upon traditional tumor grading systems. Prostate cancer is diagnosed and staged primarily by visual assessment of glandular morphology in 2D histopathology slides. However, this approach is sensitive to sectioning angle and subject to high inter-observer variability, as the Gleason score—a qualitative assessment of gland patterns—can change based on slide orientation. Recent advances in 3D virtual histology using propagation-based phase-contrast micro-CT (PBCT) now enable full-biopsy, high-resolution imaging without the need for staining. This new imaging modality resolves cellular structures in three dimensions, revealing tumor architecture with unprecedented fidelity. Despite these advances, there remains a critical gap: no rigorous tools exist for quantifying tumor grade or heterogeneity directly in 3D.
Approach: Quantifying tumor architecture of prostate cancer with topological data analysis (TDA)
This project will analyze 3D renderings of needle-core prostate biopsies collected via PBCT. The dataset includes biopsies across the spectrum from benign to Gleason pattern 5 disease, and nuclei have been presegmented using deep-learning approaches (e.g., 3D U-Net + StarDist). We will subdivide these volumes into hundreds of thousands of labeled sub-regions using synthetic augmentation techniques. Within each sub-image, point clouds will be extracted from nuclear centroids.
Under the mentorship of Dr. Silverman, a graduate student will apply tools from computational persistent homology—particularly the Smooth Euler Characteristic Transform (SECT)—to extract topological summaries that encode higher-order morphological structure. These summaries will be represented as smooth functions and decomposed via spline basis functions. Feature selection using penalized regression and other variable selection methods will yield a low-dimensional representation (¡5D) that maximally separates healthy and cancerous tissue. These features will be used to generate continuous phenotype maps over entire biopsies, and to quantify intra- and inter-biopsy morphological heterogeneity using mixed-effects models with spatial variance components.
Expected outcomes: Measurement of tumor heterogeneity within and between whole biopsies
This project provides an opportunity for a graduate student to train at the intersection of applied mathematics (TDA), functional data analysis, and biomedical imaging. The work will result in a novel, quantitative, and biologically grounded set of features that characterize prostate cancer morphology in 3D. These features can serve as covariates in downstream prognostic models, or be used independently to map heterogeneity within and across patients. We anticipate that this project will produce at least one first-author manuscript and a conference presentation. Ultimately, the proposed work will bridge a critical methodological gap by introducing scalable, rigorous computational tools for quantifying morphology in 3D prostate histology, with broad applications in cancer grading, biomarker development, and treatment stratification.
Expertise Sought
• Proficiency in Python and/or R for data analysis and scientific computing
• Background in machine learning and multivariate statistical modeling
• Experience working with image data, including segmentation and 3D reconstruction
• Strong mathematical foundation, with interest or expertise in topological data analysis (TDA) and functional data analysis (FDA)
• Familiarity with cancer biology or histopathology is highly desirable
Requirements & Expectations
• Should be a post-comprehensive exam graduate student in Bioinformatics and Genomics, Statistics, IST, or a related program
• Should be proficiency in Python and/or R for data analysis and scientific computing
• Should have experience working with image data
• Will be expected to meet weekly with Dr. Silverman and to present project progress quarterly at lab meetings and/or departmental seminars
Objectives for Supported Work
• Develop a rigorous, repeatable, morphology-based approach to 3D whole-biopsy images
• Adapt this approach to compare morphological features within and between biopsies
• Scale the custom method to the full dataset using available high-performance computing resources
• Assess concordance between morphology-derived features and Gleason grades assigned to matched histology sections
Medium to Long-Term Goal
Medium-term goals:
• Submit TDA pipeline and biological interpretation for publication in a journal with a broad audience
• Present work at statistics, machine learning, or computing conference to lay foundation for future collaboration with larger / higher dimensional datasets
Long-term goals:
• Develop methodology for 3D, whole-tumor image analysis to provide robust quantification of heterogenous tumor phenotypes.
• Build framework for an NIH RO1 application to leverage applied TDA and functional data analysis for translational cancer research and quantitative evaluation of treatment response.
Connection to ICDS Mission
This project directly supports the ICDS mission by fostering interdisciplinary research at the intersection of Statistics and Anatomic Pathology to advance computational approaches for biomedical research. It integrates state-of-the-art techniques in image segmentation, topological data analysis, and functional data analysis to tackle a scientifically and clinically significant challenge: the quantitative grading of prostate cancer using 3D virtual histology. The resources, expertise, and collaborative environment provided by ICDS are uniquely suited to accelerate progress in this emerging area, enabling rigorous, data-driven innovation in cancer diagnostics.
Team Engagement with ICDS
The proposed project will actively engage with ICDS resources, particularly the RISE team, to accelerate discovery and maximize the impact of 3D histological imaging data. The Junior Researcher will collaborate with RISE scientists to optimize large-scale image processing pipelines, develop scalable data workflows for extracting 3D morphological features, and build interactive visualizations for pathologists and translational collaborators. These efforts will ensure reproducibility, computational efficiency, and effective communication of results across disciplinary boundaries. Engagement with RISE will be ongoing throughout the project and integral to both method development and dissemination.
Project Timeline
• Months 1–3: Data Preparation and Topological Feature Construction
– Finalize selection of PBCT prostate biopsy scans for analysis (data already acquired)
– Refine and validate our existing prototype segmentation workflow which we have already started developing for this task
– Subdivide 3D volumes and generate synthetic sub-images
– Construct point clouds from nuclear centroids in each sub-region
– Compute topological summaries (e.g., SECT) and represent as smooth functions
– Develop pipeline for feature extraction using spline basis decomposition
• Months 4–6: Model Development and Large-Scale Implementation
– Begin variable selection and initial classifier development– Scale full pipeline to entire dataset using HPC resources (e.g., ROAR)
– Evaluate concordance with Gleason grades across matched histology
• Months 7–8: Interpretation and Statistical Modeling
– Meet with pathologists and collaborators to interpret morphological features
– Quantify intra- and inter-biopsy heterogeneity using mixed-effects models
• Months 9–12: Dissemination, Visualization, and Reporting
– Prepare manuscript for submission to a computational pathology or ML journal
– Develop interactive visualizations and share with collaborators
– Present results at a relevant scientific conference
– Submit final project report and materials to ICDS