Bayesian inference for fitting cardiac models to experiments: estimating parameter distributions using Hamiltonian Monte Carlo and approximate Bayesian computation.

Customization of cardiac action potential models has become increasingly important with the recognition of patient-specific models and virtual patient cohorts as valuable predictive tools. Nevertheless, developing customized models by fitting parameters to data poses technical and methodological challenges: despite noise and variability associated with real-world datasets, traditional optimization methods produce a single "best-fit" set of parameter values. Bayesian estimation methods seek distributions of parameter values given the data by obtaining samples from the target distribution, but in practice widely known Bayesian algorithms like Markov chain Monte Carlo tend to be computationally inefficient and scale poorly with the dimensionality of parameter space. In this paper, we consider two computationally efficient Bayesian approaches: the Hamiltonian Monte Carlo (HMC) algorithm and the approximate Bayesian computation sequential Monte Carlo (ABC-SMC) algorithm. We find that both methods successfully identify distributions of model parameters for two cardiac action potential models using model-derived synthetic data and an experimental dataset from a zebrafish heart. Although both methods appear to converge to the same distribution family and are computationally efficient, HMC generally finds narrower marginal distributions, while ABC-SMC is less sensitive to the algorithmic settings including the prior distribution.