Bayesian inference of cardiac models emulated with a time series Gaussian process

Abstract

The objective of this research is to estimate the specific biophysical parameters of a cardiac mechanics model using a time series of variables that can be acquired in the clinic. This method is driven by the need to infer the passive stiffness of the myocardium to diagnose cardiophysiological diseases, which requires the measurement of the volume of the left ventricle (LV) of the heart at different time points. Although there have been many advancements in cardiac models, their computation is complex and costly. To overcome this challenge, we propose a method that utilizes a Gaussian process to construct a statistical model for emulation. Since the LV volumes are acquired in a time series, we employ the Kronecker product to compute two covariance matrices separately for time and biophysical parameters. Once we construct an accurate emulator to represent the passive filling process of the cardiac mechanics model during diastole, we can estimate the biophysical parameters inversely. We also aim to evaluate the impact of increasing the number of time points on reducing the uncertainty of the inverse estimation in this study.