Computational Topological Modelling of Breast Tubule Structures Using Persistent Homology

Lu, Meng Nam (2026) Computational Topological Modelling of Breast Tubule Structures Using Persistent Homology. Final Year Project (Bachelor), Tunku Abdul Rahman University of Management and Technology.

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Abstract

Breast cancer remains one of the leading causes of cancer-related deaths among women, and accurate tumour grading is essential for improving diagnosis and treatment outcomes. A critical feature in the Nottingham Histological Grading system is the presence and organization of tubules, yet manual grading is subjective and time-consuming while existing automated methods often lack robustness and interpretability. This study addresses this gap by applying persistent homology, a topological data analysis method to breast cancer histopathology images in order to provide an objective and reproducible framework for tubule detection. Thirty haematoxylin and eosin-stained slides were collected from Hospital Tuanku Fauziah, Malaysia and analysed using a computational pipeline. The workflow integrated preprocessing, fuzzy C-means segmentation, nuclei mask refinement and centroid detection in MATLAB followed by persistent homology analysis in Python with the GUDHI library. Through this approach, nuclei distributions were transformed into point-cloud data which enables the identification of connected components and loops that correspond to lumen-like structures. The results showed that persistent homology successfully detected well-formed tubules in most cases with long-lived topological features corresponding to true lumen structures and short-lived features reflecting non-true lumen structure. Although limitations occurred in irregular samples where false lumen detections appeared, the findings demonstrate that persistent homology can complement conventional pathology by providing consistent, quantitative, and biologically meaningful insights into tissue architecture