Markov chain Monte Carlo for Bayesian inference of the non-conducting region in intra-atrial reentrant tachycardia

TL;DR

This paper introduces an efficient Bayesian method using an adapted Metropolis-Hastings algorithm to estimate the boundary of non-conducting regions in cardiac tissue, accounting for measurement and discretization uncertainties.

Contribution

It develops a compressed likelihood and an adaptive MH algorithm that reduces sampling effort while robustly handling discretization errors in cardiac electrophysiology models.

Findings

The method accurately estimates the geometrical boundary with quantified uncertainty.

It significantly decreases the number of samples needed for posterior approximation.

The approach remains robust under different levels of measurement noise.

Abstract

We present a Bayesian approach to estimate the parameters of mathematical models of cardiac electrophysiology with quantified uncertainty. Such models capture the dynamics of the electrical signal that coordinates the muscle cell contraction in the heart wall and can support cardiac arrhythmia treatment. We consider an illustrative case motivated by a cardiac arrhythmia, namely, by intra-atrial reentrant tachycardia. We estimate a low-dimensional geometrical parameter that describes the boundary of an electrically non-conducting region in the heart tissue from synthetic electrical measurements outside of the tissue. Instead of relying on a deterministic fit for this region, we estimate a posterior distribution on the geometrical parameter using Bayesian inference that captures the uncertainty due to measurement errors. We propose a likelihood based on a set of quantities that characterize the data for improved accuracy. To efficiently approximate the posterior distribution, we propose a compressed likelihood function and an adapted Metropolis-Hastings (MH) algorithm. We obtain an algorithm that strongly decreases the number of samples by using an adaptive proposal strategy. Our algorithm also gives attention to the impact of discretization errors on inference outcomes, as these introduce artificial discontinuities in the posterior if not properly addressed. We account for discretization errors in the likelihood and in the accept-reject step of our adapted MH algorithm to improve the robustness of our estimates and to further increase the sampling efficiency. All of these elements combined give us a method that efficiently estimates the non-conducting parameters with uncertainty. We perform several experiments with different amounts of measurement noise and illustrate how this translates into the posterior distributions.