Latent Dynamics Neural Network models of cardiac electrophysiology in a patient-specific left atrium

Simulating left atrial electrophysiology is crucial for advancing the diagnosis and treatment of heart diseases. The traditional modeling and simulation approach involves coupling a monodomain equation, which describes the propagation of the transmembrane potential throughout the left atrium, with the Courtemanche-Ramirez-Nattel model, which characterizes atrial electrophysiology at the cellular scale. High-fidelity discretizations, utilizing methods such as the Galerkin Finite Element method and a Backward Difference Formula scheme, demand substantial computational resources, particularly when multiple solutions are needed for varying key parameters of the problem. This makes the full-order model not applicable to clinical scenarios that require real-time and multiple simulations. To reach an efficient solution of the parametric problem, this thesis employs a data-driven approach, called Latent Dynamics Network (LDNet). By leveraging a neural ODE, the system’s evolution is mapped into a low-dimensional space using a few latent variables. Then, through a second neural network, the transmembrane potential is predicted at query points in the left atrium. LDNets are trained and evaluated using in-silico data, divided into training, validation, and test datasets. In particular, the loss with respect to the validation dataset is used to analyze the generalization ability of the model, enabling the determination of whether feature augmentation is required to enhance the performance of the architecture. We conduct a numerical investigation of the Latent Dynamics model’s performance in predicting left atrial electrophysiology under both physiological and pathological conditions. In the first case, we consider different localizations of the impulse that triggers the cardiac chamber proximal to the Coronary Sinus Musculature (CSM) limbs. In the pathological case, we train the LDNet to predict the formation and self-sustainment of localized reentries, which are characteristic of atrial fibrillation. This is achieved by numerically simulating different scenarios triggered by a train of impulses with varying time intervals applied at a fixed point on the CSM limbs, thereby replicating clinical protocols commonly used in the ablation room. Our numerical results show that the proposed models provide a significant improvement in computational efficiency, with only a minor reduction in solution accuracy compared to the full-order model.