Abstract
The dynamics of the action potential in cardiac cells is a well-studied field. Many mathematical models of these and other excitable cells have been developed, allowing us to study them in silico. Such models typically consist of a series of nonlinear ordinary differential equations. Nevertheless, it is still a challenging task to calibrate the model parameters in order to recreate the signal of a measured data set. Many classical optimisation methods, such as gradient descent, struggle in this manner. This is largely due to the ubiquity of local minima in the cost functions caused by the non-linearity of the models. In this thesis, we propose the idea of using physics-informed neural networks (PINNs) to fit excitable cell models. This is a technique where a deep learning framework is constrained using a physical law, which has shown success in fitting various models of biological systems. We tested the viability of using PINNs to infer the dynamics of excitable cells by trying to fit the FitzHugh–Nagumo model to synthetic data. This is a simple two-state model that can be used to study excitable systems such as neurons and cardiac cells. We found that PINNs were able to fit the model very closely, even when using limited or noisy data. A lot of fine-tuning of hyperparameters was necessary before we achieved a quality fit. Furthermore, we found that analysing the structural identifiability of the model was an important step in understanding whether the model parameters can be determined from the data. Practical identifiability analysis was also performed, where we used the Fisher information matrix to estimate a lower boundary of the standard deviation of the inferred parameters. These tended to be very small relative to the nominal value of the parameters. Here, we have shown that PINNs are a viable method for fitting excitable cell models to data, especially when combined with identifiability analysis.