Quantifying the Uncertainty in Model Parameters Using Gaussian Process-Based Markov Chain Monte Carlo: An Application to Cardiac Electrophysiological Models

TL;DR

This paper introduces a Gaussian process-based Markov Chain Monte Carlo method that efficiently quantifies uncertainty in patient-specific cardiac model parameters, balancing computational speed with sampling accuracy.

Contribution

It integrates surrogate modeling into MCMC to improve acceptance rates and computational efficiency while maintaining accuracy in posterior estimation.

Findings

Significant reduction in computational time for parameter estimation.

Accurate uncertainty quantification of tissue properties.

Enhanced insights into tissue heterogeneity and non-identifiability.

Abstract

Estimation of patient-specific model parameters is important for personalized modeling, although sparse and noisy clinical data can introduce significant uncertainty in the estimated parameter values. This importance source of uncertainty, if left unquantified, will lead to unknown variability in model outputs that hinder their reliable adoptions. Probabilistic estimation model parameters, however, remains an unresolved challenge because standard Markov Chain Monte Carlo sampling requires repeated model simulations that are computationally infeasible. A common solution is to replace the simulation model with a computationally-efficient surrogate for a faster sampling. However, by sampling from an approximation of the exact posterior probability density function (pdf) of the parameters, the efficiency is gained at the expense of sampling accuracy. In this paper, we address this issue by integrating surrogate modeling into Metropolis Hasting (MH) sampling of the exact posterior pdfs to improve its acceptance rate. It is done by first quickly constructing a Gaussian process (GP) surrogate of the exact posterior pdfs using deterministic optimization. This efficient surrogate is then used to modify commonly-used proposal distributions in MH sampling such that only proposals accepted by the surrogate will be tested by the exact posterior pdf for acceptance/rejection, reducing unnecessary model simulations at unlikely candidates. Synthetic and real-data experiments using the presented method show a significant gain in computational efficiency without compromising the accuracy. In addition, insights into the non-identifiability and heterogeneity of tissue properties can be gained from the obtained posterior distributions.