Topology across Scales on Heterogeneous Cell Data

TL;DR

This paper introduces new visualization and vectorization techniques for persistent homology to analyze complex spatial biological data, demonstrated on COVID-19 lung tissue and lupus mouse spleen datasets.

Contribution

It presents a novel visualization method for persistence homology and explores different weightings for persistence images, enhancing biological interpretation of spatial cell data.

Findings

New visualization of persistence homology developed

Different weightings for persistence images explored

Applied methods to COVID-19 and lupus datasets

Abstract

Multiplexed imaging allows multiple cell types to be simultaneously visualised in a single tissue sample, generating unprecedented amounts of spatially-resolved, biological data. In topological data analysis, persistent homology provides multiscale descriptors of ``shape" suitable for the analysis of such spatial data. Here we propose a novel visualisation of persistence homology (PH) and fine-tune vectorisations thereof (exploring the effect of different weightings for persistence images, a prominent vectorisation of PH). These approaches offer new biological interpretations and promising avenues for improving the analysis of complex spatial biological data especially in multiple cell type data. To illustrate our methods, we apply them to a lung data set from fatal cases of COVID-19 and a data set from lupus murine spleen.