  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.
