Quantifying Distributions of Parameters for Cardiac Action Potential Models Using the Hamiltonian Monte Carlo Method

Area of Science:

• Computational Biology
• Biophysics
• Physiology

Background:

• Cardiac action potential (AP) models traditionally use single parameter values, neglecting individual variability and experimental condition differences.
• Bayesian approaches offer an alternative to single-value fitting, enabling the exploration of parameter distributions.

Purpose of the Study:

• To apply the Hamiltonian Monte Carlo (HMC) algorithm for determining distributions of physiological parameters in cardiac AP models.
• To assess HMC's accuracy with synthetic and experimental cardiac data across various cycle lengths (CLs).

Main Methods:

• HMC was applied to synthetic APs from Mitchell-Shaeffer (MS) and Fenton-Karma (FK) models with added noise.
• HMC was used with micro-electrode recordings of zebrafish APs to derive parameter distributions.
• Model performance was evaluated by voltage trace errors.

Main Results:

• HMC generated unimodal, quasi-symmetric parameter distributions for MS and FK models.
• Cardiac AP models using HMC-derived parameters showed low voltage trace errors (<5.0% for MS, <0.6% for FK) with synthetic data.
• A minimal zebrafish AP model using HMC parameters achieved voltage trace errors below 4.8% (MS) and 3.4% (FK).

Conclusions:

• HMC successfully identifies viable parameter distributions for cardiac AP models using both synthetic and experimental data.
• HMC facilitates population-based modeling by generating parameter sets that account for variability and uncertainty.
• This method offers quantitative insights into spatial/individual variability in cardiac electrophysiology.