Employing Gaussian process priors for studying spatial variation in the parameters of a cardiac action potential model

Abstract: Cardiac cells exhibit variability in the shape and duration of their action potentials in space within a single individual. To create a mathematical model of cardiac action potentials (AP) which captures this spatial variability and also allows for rigorous uncertainty quantification regarding within-tissue spatial correlation structure, we developed a novel hierarchical Bayesian model making use of a latent Gaussian process prior on the parameters of a simplified cardiac AP model which is used to map forcing behavior to observed voltage signals. This model allows for prediction of cardiac electrophysiological dynamics at new points in space and also allows for reconstruction of surface electrical dynamics with a relatively small number of spatial observation points. Furthermore, we make use of Markov chain Monte Carlo methods via the Stan modeling framework for parameter estimation. We employ a synthetic data case study oriented around the reconstruction of a sparsely-observed spatial parameter surface to highlight how this approach can be used for spatial or spatiotemporal analyses of cardiac electrophysiology.