Introduction and Aims: Many models of cardiac action potentials (APs) have been developed, but identifying appropriate equations and parameter values to match particular datasets remains challenging. To reproduce cardiac AP data, we consider the use of a data-driven approach, Sparse Identification of Nonlinear Dynamics (SINDy).
Methods: SINDy is a sparse regression method that uses a set of selected candidate functions to produce a differential-equations model that fits the provided data. Terms with small coefficients are iteratively discarded to produce a model with few terms that fits the data well.
Results: We analyzed SINDY's effectiveness in fitting synthetic AP data from two-variable models written with polynomial terms, including the FitzHugh-Nagumo model (FHN), its cardiac variant that avoids hyperpolarization (FHN-c), and a modified FHN model that can display alternans (Velasco-Fenton, VF-FHN). We found that SINDy could effectively reproduce the equations for each model, with FHN-c and VF-FHN requiring narrower parameter spaces than FHN to acquire the correct results. The best results for each model were obtained using the Stepwise Sparse Regression optimizer with the threshold parameter set to $10^{-5}$ and a function library restricted to two-variable polynomials up to degree 3 (Poly3). The dynamics also affected SINDy's performance; high excitability typical of cardiac APs required certain optimizers to obtain good agreement, whereas less excitable systems were recovered more easily without significant fine-tuning. In addition, we found that the inclusion of non-autonomous terms representing external stimuli made SINDy identification difficult, with spurious terms appearing in all cases where a stimulus was added, suggesting modifications may be necessary to handle stepwise, non-smooth functions.
Conclusion: As a data-driven approach, SINDy shows promise for finding appropriate differential equations models to match cardiac AP data when the proper parameters, optimizers, and modifications are used.