Contains code for investigating the applicability of Sparse Identification of Nonlinear Dynamics (SINDy) to creating PDE models that describe the voltage (and possibly calcium) dynamics of cardiac cells.
Cardiac voltage dynamics are known to be highly nonlinear; nevertheless, important properties can be captured with the relatively simple FitzHugh-Nagumo model, which consists of two coupled differential equations, one representing voltage and the other refractoriness. A cubic term in the voltage equation is the main source of nonlinearity (although an additional nonlinear term can produce voltage dynamics that avoid the hyperpolarization characteristic of neural voltage dynamics). Previous work using SINDy-type methods has shown that the FitzHugh-Nagumo model equations can be recovered from data.
In this project, we aim to extend this work to investigate whether more complex cardiac electrical dynamics, such as alternans, higher-order periodic behavior, and chaos, can be recovered using SINDy approaches. In particular, we are interested in whether the behavior of other simple cardiac models can be expressed using polynomial-type terms, or whether a different set of nonlinear terms, such as exponentials (which are more common in biological models), may be more appropriate. As time permits, we will work to develop a model that can describe complex data from cardiac experiments, including voltage alternans, higher-order rhythms commonly observed during overdrive pacing in frog hearts, and voltage-calcium coupling during alternans.