The aim of the project is to model, characterize, and numerically approximate depolarization wave patterns in the human heart. This includes the mathematical modeling of cardiac arrhythmias and their simulation with accurate and efficient numerical methods.

Cardiac depolarization waves are characterized by a very thin wavefront due to the steep upstroke of the action potential. Resolving this fine spatio-temporal structure is numerically challenging. Commonly used methods to simulate healthy as well as pathological pattern formation of cardiac depolarization waves at tissue level are based on the bidomain or monodomain equations. Those methods require a very fine resolution in space and time which makes them computationally expensive as well as time demanding. A model that combines the monodomain and eikonal equations to formulate cardiac electrophysiology with the goal of simulating chaotic reentrant waves in low-resolution meshes has been proposed by our group. This Diffusion-Reaction-Eikonal Alternant Model (DREAM) is inspired by the reaction-eikonal model and the multi-frontal fast marching method. DREAM combines the strengths of these two approaches and overcomes their key limitations for simulations of fibrillatory waves. So far, DREAM is able to show successful reentry in simple configurations. This project focuses on the numerical characterization of this reaction eikonal scheme for the precise computation of activation times. The numerical investigation will address the convergence, stability and accuracy of the model by comparison with simulations performed with the full model. Also, the simulation scenarios considered will be expanded step by step to more and more realistic settings.

One clinically relevant application for these electrophysiology simulations is the construction of patient-individual models, called digital twins. However, the estimation of decisive model parameters in an individual patient remains challenging. Physics-informed neural networks (PINNs) offer a promising approach to solve such inverse parameter identification problems. Therefore, we will work on the identification of the spatial distribution of clinically relevant cardiac tissue parameters through PINNs. The developed methods could then be applied in an optimal control problem to pave the way for the clinical adoption of painless overdrive pacing against atrial fibrillation.