Bayesian parameter identification in Cahn-Hilliard models for biological growth

TL;DR

This paper develops a Bayesian framework for estimating key parameters in a complex tumor growth model, demonstrating well-posedness and applying sequential Monte Carlo methods to infer parameters from synthetic data.

Contribution

It introduces a Bayesian approach to inverse problems in a Cahn-Hilliard tumor model, improving analytical results and providing a numerical methodology for parameter estimation.

Findings

Posterior measure is well-posed for both full and partial tumor observations.

Sequential Monte Carlo effectively approximates the posterior in synthetic data scenarios.

Analytical results are enhanced compared to previous studies.

Abstract

We consider the inverse problem of parameter estimation in a diffuse interface model for tumour growth. The model consists of a fourth-order Cahn-Hilliard system and contains three phenomenological parameters: the tumour proliferation rate, the nutrient consumption rate, and the chemotactic sensitivity. We study the inverse problem within the Bayesian framework and construct the likelihood and noise for two typical observation settings. One setting involves an infinite-dimensional data space where we observe the full tumour. In the second setting we observe only the tumour volume, hence the data space is finite-dimensional. We show the well-posedness of the posterior measure for both settings, building upon and improving the analytical results in [C. Kahle and K.F. Lam, Appl. Math. Optim. (2018)]. A numerical example involving synthetic data is presented in which the posterior measure is numerically approximated by the sequential Monte Carlo approach with tempering.