A Resonant Model of the Action Potential in Cardiac Cells

Abstract

Mathematical models of the bioelectric activity in the cardiac conduction system can be used to study the impact of drugs, conduct hypothetical experiments, and for closed-loop validation of cardiac devices. These applications demand real-time performance. To meet the goal of real-time simulations, we have developed a high-fidelity mathematical model of cardiac cells. These models, called as Resonant Model (RM), are based on truncated Fourier Series and are adaptable for parallel execution. In this paper, the RM is developed for human atrial myocyte, human inferior nodal extension, and human atrioventricular node. The RMs of these cardiac cells are validated with the experimental data and data obtained from detailed electrophysiology cell models. The RM cells were accurately able to generate the nonlinear AP morphologies with Pearson correlation coefficient above 0.99 between generated and simulated AP morphologies of the detailed cardiac cell models.

Flexible Cell Modeling Using Frequency Modulation

“…A similar methodology as the RM model [2] incorporating the electrophysiology of ionic current perturbation is done. This study focuses on the simulation of the Fabbri model [11] of the human SAN cell by varying the maximum funny current block, I f , from 0 to 1.…”

“…By extracting the fit-type equations for frequency ω and 29 coefficients of Δ w (t) A1, A2, …, A29, we calculate the coefficient of determination ( R 2 ) and the Root Mean Square Error (RMSE) for the reconstructed Δ w plots, which corresponds to I f blockade values varying from 0 to 1 in increments of 0.1. For the frequency parameter ω , the suitable type used was similar to that of Sehgal et al [2]. Most coefficients were successfully fitted using the PL4 fit type (refer to Table.5).…”

“…PL4 and PL5 utilize 4 and 5 linear segments for linear piecewise fitting. We use optimization method [19] frequency parameter ω, the suitable type used was similar to that of Sehgal et al [2]. Most coefficients were successfully fitted using the PL4 fit type (refer to Table.5).…”

“…To overcome this issue, Sehgal et.al. [1] [2] formulated the Resonant Model (RM), which utilizes the Fourier Series (FS) to reconstruct various detailed models like Kurata et al [14], Fabbri [11], Fenton Karma [9], O’Hara [29], Courtemanche et al [12] and Dobrzynski et al [13] models. The optimization of the Fourier Series coefficients was done by using the Levenberg-Marquardt algorithm [16].…”