Introduction and Aims: Typical differential-equations-based models of cardiac action potentials 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 action potentials and intracellular calcium cycling may offer advantages in such settings, but correlations between continuous- and discrete-time models so far have not been developed.
Methods: We fit the Qu et al. discrete-time model to action potential duration (APD) values over a wide range of periods for the Fox et al., Beeler-Reuter, and ten Tusscher et al. (2006) models. Each model was paced down in intervals of 10 ms using 150 beats per period, and the APD90 values from the last 4 beats were recorded for fitting. As the discrete model has a large number of parameters with complex nonlinear effects, we used particle swarm optimization to find parameter values that reproduced these APD dynamics for each model. Results: As shown in the figure, the discrete model is capable of reproducing the APD dynamics of each model over a wide range of pacing periods, including the alternans regions for the ten Tusscher et al. and Fox et al. models. Unlike the ionic models, the discrete model only requires a single update step for each APD value, and retains information about calcium dynamics such as peak intracellular calcium and SR calcium load during the action potential. Conclusion: We produced fittings of the Qu et al. discrete-time model to three ionic models. Using these fittings, the discrete model may offer advantages for studying aspects of cardiac action potential or calcium dynamics normally investigated through detailed ionic models at a fraction of the computational cost.