Abstract

We present a new, computationally efficient framework to perform both forward and inverse uncertainty quantification (UQ) in cardiac electrophysiology. We consider the monodomain model to describe the electrical activity in a subject-specific left ventricle geometry, coupled with the Aliev-Panfilov model to characterize the ionic activity through the cell membrane. We take into account relevant inputs related to both models, such as electrical conductivities, pacing times, and coefficients affecting the ionic models. We address a complete UQ pipeline, including: (i) a variance-based sensitivity analysis for the selection of the most relevant input parameters; (ii) forward UQ to investigate the impact of intra-subject variability on clinically relevant outputs related to the cardiac action potential, and (iii) inverse UQ for the sake of parameter and state estimation within a Bayesian framework. All these stages exploit stochastic (Monte Carlo) sampling techniques, thus implying overwhelming computational costs because of the huge amount of queries to the high-fidelity, full-order coupled PDE -ODEs model. To mitigate this computational burden, we replace the high-fidelity model with computationally inexpensive projection-based reduced-order models aimed at reducing the state-space dimensionality. ROM approximation errors on the outputs of interest are finally taken into account by means of statistical error models built through Gaussian process regression, enhancing the accuracy of the whole UQ pipeline.