Discovering Cardiac Action Potential Model Equations Using Sparse Identification of Nonlinear Dynamics

Many models of cardiac action potentials (APs) have been developed, but identifying appropriate equations and parameter values to match particular datasets remains a challenge. To reproduce cardiac AP data, we consider the use of a data-driven approach, Sparse Identification of Nonlinear Dynamics (SINDy). SINDy is a sparse regression method that uses a set of chosen candidate functions to produce a differential-equations model that fits the provided data. Terms with small coefficients are iteratively discarded to reduce model complexity while maintaining an accurate fit. We analyzed SINDy's effectiveness in fitting synthetic AP data from two-variable models with polynomial terms, including the FitzHugh-Nagumo model (FHN), its cardiac variant that avoids hyperpolarization, and two additional cardiac-modified FHN models that can display complex dynamics. We found that SINDy could effectively reproduce the equations for each model, with the cardiac variants displaying greater sensitivity to parameter and optimizer choice than the baseline FHN model. Finally, we tested the ability of SINDy to handle the introduction of time-dependent stimulus currents, including identification during alternans dynamics. Overall, SINDy shows promise as an approach for identifying differential equations models to match cardiac AP data while balancing model complexity and accuracy.