Cardiac cells exhibit variability in the shape and duration of their action potentials, among individuals, and in space and time within a single individual. At short pacing periods, cardiac cells can exhibit a bifurcation that leads them to produce action potentials that alternate in duration, a phenomenon called alternans. Finding parameters for a cardiac action potentials model to reproduce specific alternans dynamics quantitatively is challenging because of the nonlinear dependence on pacing period and the number of parameters involved. We apply a Bayesian approach to find the probability distributions of the parameters of the Mitchel-Schaeffer (MS) cardiac action potential model fitted to action potentials from synthetic data represented on a grid that simulates measurements from optical mapping. We define a hierarchical model on the parameters of MS and simulate correlated values on a grid for one of the parameters. Using a latent Gaussian process as a prior for the grid parameter, we do inference in a subset of sampled locations used as training points to predict the values on the non-sampled locations. We apply a Markov Chain Monte Carlo technique, the Hamiltonian Monte Carlo algorithm implemented in Stan through the Not-U-Turn Sampler.
Joint work with Christopher Krapu, Elizabeth Cherry and Flavio Fenton.
Alejandro Nieto Ramos is a PhD student at the School of Mathematical Sciences, Rochester Institute of Technology.