Topological Approximate Bayesian Computation for Parameter Inference of an Angiogenesis Model

TL;DR

This paper introduces a novel method combining topological data analysis with Approximate Bayesian Computation to improve parameter inference in a spatial angiogenesis model, outperforming traditional spatial feature-based methods.

Contribution

It presents the first integration of topological data analysis with ABC for spatial biological models, enhancing inference accuracy.

Findings

Topological approach outperforms simpler spatial statistics in parameter inference.

The method is demonstrated on the Anderson-Chaplain angiogenesis model.

Code for the method is publicly available as a Snakemake workflow.

Abstract

Inferring the parameters of models describing biological systems is an important problem in the reverse engineering of the mechanisms underlying these systems. Much work has focused on parameter inference of stochastic and ordinary differential equation models using Approximate Bayesian Computation (ABC). While there is some recent work on inference in spatial models, this remains an open problem. Simultaneously, advances in topological data analysis (TDA), a field of computational mathematics, have enabled spatial patterns in data to be characterised. Here we focus on recent work using topological data analysis to study different regimes of parameter space for a well-studied model of angiogenesis. We propose a method for combining TDA with ABC to infer parameters in the Anderson-Chaplain model of angiogenesis. We demonstrate that this topological approach outperforms ABC approaches that use simpler statistics based on spatial features of the data. This is a first step towards a general framework of spatial parameter inference for biological systems, for which there may be a variety of filtrations, vectorisations, and summary statistics to be considered. All code used to produce our results is available as a Snakemake workflow.