Relational Persistent Homology for Multispecies Data with Application to the Tumor Microenvironment

by Bernadette J. Stolz, Jagdeep Dhesi, Joshua A. Bull, Heather A. Harrington, Helen M. Byrne, Iris H. R. Yoon

State-of-the-art data is exquisite in detail, often containing information on multiple species, e.g. cell types in imaging data. However, there are very few techniques equipped to analyse and quantify relations in such data. The paper by Stolz, Dhesi et al. proposes two topological approaches for multispecies data that can encode relations in spatial data. The authors showcase the methods on synthetic data of the tumour microenvironment which models the behaviour and interactions between tumour cells, macrophage subtypes, necrotic cells, and blood vessels. They demonstrate that relational topological features can extract biological insight, including dominant immune cell phenotype and parameter regimes of the data-generating model.

Relational persistent homology encodes spatial relations in multispecies data. We use synthetic images of the tumour microenvironment generated by an agent-based model as input to two different topological methods for encoding relations: Dowker persistent homology (top row) and multispecies witness persistent homology (bottom row). The topological features that we extract can classify the synthetic images according to dominant immune cell type and cluster qualitative behaviours of the model.