Fast Posterior Estimation of Cardiac Electrophysiological Model Parameters via Bayesian Active Learning

Abstract

Probabilistic estimation of cardiac electrophysiological model parameters serves an important step toward model personalization and uncertain quantification. The expensive computation associated with these model simulations, however, makes direct Markov Chain Monte Carlo (MCMC) sampling of the posterior probability density function (pdf) of model parameters computationally intensive. Approximated posterior pdfs resulting from replacing the simulation model with a computationally efficient surrogate, on the other hand, have seen limited accuracy. In this study, we present a Bayesian active learning method to directly approximate the posterior pdf function of cardiac model parameters, in which we intelligently select training points to query the simulation model in order to learn the posterior pdf using a small number of samples. We integrate a generative model into Bayesian active learning to allow approximating posterior pdf of high-dimensional model parameters at the resolution of the cardiac mesh. We further introduce new acquisition functions to focus the selection of training points on better approximating the shape rather than the modes of the posterior pdf of interest. We evaluated the presented method in estimating tissue excitability in a 3D cardiac electrophysiological model in a range of synthetic and real-data experiments. We demonstrated its improved accuracy in approximating the posterior pdf compared to Bayesian active learning using regular acquisition functions, and substantially reduced computational cost in comparison to existing standard or accelerated MCMC sampling.

Global Sensitivity Analysis of Four Chamber Heart Hemodynamics Using Surrogate Models

“…We test the ability of machine learning-based GPEs, which approximate the model and estimate the uncertainty in the approximation, to provide a low-cost surrogate for the full physics-based model. While surrogate modeling of certain cardiac function models has gathered some traction in the context of physics-informed neural networks (PINNs) [27] – [29] this work is, to the best of the authors knowledge, the first attempt at developing a GPE based surrogate model in the context of four-chamber hemodynamics. As such it lays ground work for future studies including Bayesian history matching and inverse problems for inferring key hemodynamic biomarkers (such as atrial preload) in a non-invasive way.…”

Neural stochastic differential equations network as uncertainty quantification method for EEG source localization

“…Deep Bayesian UQ methods may generate a weaker performance than SDE-Net since they have difficulty determining their prior. It is primarily seen on MCD because higher dropout rates result in high predictive variance regardless of inherent noise in the data [4,39,73]. As we increased the dropout rate, not only do our mean predictions start to produce low image quality, but the variance (ECE) may also get more significant.…”

“…Several studies, especially for high-dimensional datasets, also utilized the Bayesian Active Learning (BAL) as an uncertainty quantification technique that approximates posterior using acquisition function [7,18,73]. It adopts a network trained on a small amount of data (as an initial training set) where the acquisition function repeatedly guides the selection of data points outside the training set.…”

Multiscale and Multiphysics Modeling of Anisotropic Cardiac RFCA: Experimental-Based Model Calibration via Multi-Point Temperature Measurements

“…However, additional volumetric sources (accounting for blood perfusion, metabolism, to name a few) and multi-field coupling phenomena should be included when modeling in-vivo cardiac ablation. In addition state-of-the-art machine learning algorithms and data assimilation procedures ( Barone et al, 2020a , b ; Zaman et al, 2021 ) are also foreseen in view of a patient-specific optimization applications ( Lopez-Perez et al, 2019 ; Aronis et al, 2021 ).…”