Organ level simulation of bioelectric behavior in the body benefits from flexible and efficient models of cellular membrane potential. These computational organ and cell models can be used to study the impact of pharmaceutical drugs, test hypotheses, assess risk and for closed-loop validation of medical devices. To move closer to the real-time requirements of this modeling a new flexible Fourier based general membrane potential model, called as a Resonant model, is developed that is computationally inexpensive. The new model accurately reproduces non-linear potential morphologies for a variety of cell types. Specifically, the method is used to model human and rabbit sinoatrial node, human ventricular myocyte and squid giant axon electrophysiology. The Resonant models are validated with experimental data and with other published models. Dynamic changes in biological conditions are modeled with changing model coefficients and this approach enables ionic channel alterations to be captured. The Resonant model is used to simulate entrainment between competing sinoatrial node cells. These models can be easily implemented in low-cost digital hardware and an alternative, resource-efficient implementations of sine and cosine functions are presented and it is shown that a Fourier term is produced with two additions and a binary shift.

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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.

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