Reproducing Cardiac Ionic Model Properties Using a Discrete-Time Model

Typical differential equations-based models of cardiac action potentials (APs) may be inefficient for studying processes that occur over long time scales, such as heart rate variability and electrophysiological remodeling due to atrial fibrillation or heart failure. A discrete-time model of cardiac APs and intracellular calcium cycling may offer advantages in such settings, but correlations between continuous- and discrete-time models so far have not been developed. We used particle swarm optimization to fit the parameters of the Qu et al. discrete-time model to AP duration (APD) values over a wide range of periods for the ten Tusscher et al. (2006), Beeler-Reuter, and Fox et al. models. We found that the discrete model is capable of reproducing the APD dynamics of each model over a wide range of pacing periods including the alternans regions. Unlike the detailed ionic models, the discrete model requires only a single update step for each APD value and retains information about calcium dynamics, such as peak intracellular calcium and sarcoplasmic reticulum calcium load during the AP. Using these fittings, the discrete model may offer advantages for studying aspects of cardiac APs or calcium dynamics normally investigated through detailed ionic models at a fraction of the computational cost.