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Understanding how the spatial structure of blood vessel networks relates totheir function in healthy and abnormal biological tissues could improvediagnosis and treatment for diseases such as cancer. New imaging techniques cangenerate multiple, high-resolution images of the same tissue region, and showhow vessel networks evolve during disease onset and treatment. Suchexperimental advances have created an exciting opportunity for discovering newlinks between vessel structure and disease through the development ofmathematical tools that can analyse these rich datasets. Here we explain howtopological data analysis (TDA) can be used to study vessel network structures.TDA is a growing field in the mathematical and computational sciences, thatconsists of algorithmic methods for identifying global and multi-scalestructures in high-dimensional data sets that may be noisy and incomplete. TDAhas identified the effect of ageing on vessel networks in the brain and morerecently proposed to study blood flow and stenosis. Here we present preliminarywork which shows how TDA of spatial network structure can be used tocharacterise tumour vasculature.

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