Topological Methods for Characterising Spatial Networks: A Case Study in Tumour Vasculature

TL;DR

This paper explores how topological data analysis (TDA) can be applied to characterize the complex spatial structure of tumour blood vessel networks, potentially aiding in cancer diagnosis and treatment.

Contribution

It introduces the application of TDA to analyze tumour vasculature, demonstrating its potential to uncover structural features relevant to disease progression.

Findings

TDA can identify global structures in vessel networks

Preliminary results show TDA distinguishes healthy and tumour vasculature

TDA reveals multi-scale features of blood vessel networks

Abstract

Understanding how the spatial structure of blood vessel networks relates to their function in healthy and abnormal biological tissues could improve diagnosis and treatment for diseases such as cancer. New imaging techniques can generate multiple, high-resolution images of the same tissue region, and show how vessel networks evolve during disease onset and treatment. Such experimental advances have created an exciting opportunity for discovering new links between vessel structure and disease through the development of mathematical tools that can analyse these rich datasets. Here we explain how topological data analysis (TDA) can be used to study vessel network structures. TDA is a growing field in the mathematical and computational sciences, that consists of algorithmic methods for identifying global and multi-scale structures in high-dimensional data sets that may be noisy and incomplete. TDA has identified the effect of ageing on vessel networks in the brain and more recently proposed to study blood flow and stenosis. Here we present preliminary work which shows how TDA of spatial network structure can be used to characterise tumour vasculature.