The bidomain model and the finite element method are an established standard to mathematically describe cardiac electrophysiology, but are both suboptimal choices for fast and large-scale simulations due to high computational costs. We investigate to what extent simplified approaches for propagation models (monodomain, reaction-Eikonal and Eikonal) and forward calculation (boundary element and infinite volume conductor) deliver markedly accelerated, yet physiologically accurate simulation results in atrial electrophysiology. Methods: We compared action potential durations, local activation times (LATs), and electrocardiograms (ECGs) for sinus rhythm simulations on healthy and fibrotically infiltrated atrial models. Results: All simplified model solutions yielded LATs and P waves in accurate accordance with the bidomain results. Only for the Eikonal model with pre-computed action potential templates shifted in time to derive transmembrane voltages, repolarization behavior notably deviated from the bidomain results. ECGs calculated with the boundary element method were characterized by correlation coefficients >0.9 compared to the finite element method. The infinite volume conductor method led to lower correlation coefficients caused predominantly by systematic overestimations of P wave amplitudes in the precordial leads. Conclusion: Our results demonstrate that the Eikonal model yields accurate LATs and combined with the boundary element method precise ECGs compared to markedly more expensive full bidomain simulations. However, for an accurate representation of atrial repolarization dynamics, diffusion terms must be accounted for in simplified models. Significance: Simulations of atrial LATs and ECGs can be notably accelerated to clinically feasible time frames at high accuracy by resorting to the Eikonal and boundary element methods.

Objective: The bidomain model and the finite element method are an established standard to mathematically describe cardiac electrophysiology, but are both suboptimal choices for fast and large-scale simulations due to high computational costs. We investigate to what extent simplified approaches for propagation models (monodomain, reaction-eikonal and eikonal) and forward calculation (boundary element and infinite volume conductor) deliver markedly accelerated, yet physiologically accurate simulation results in atrial electrophysiology. Methods: We compared action potential durations, local activation times (LATs), and electrocardiograms (ECGs) for sinus rhythm simulations on healthy and fibrotically infiltrated atrial models. Results: All simplified model solutions yielded LATs and P waves in accurate accordance with the bidomain results. Only for the eikonal model with precomputed action potential templates shifted in time to derive transmembrane voltages, repolarization behavior notably deviated from the bidomain results. ECGs calculated with the boundary element method were characterized by correlation coefficients >0.9 compared to the finite element method. The infinite volume conductor method led to lower correlation coefficients caused predominantly by systematic overestimations of P wave amplitudes in the precordial leads. Conclusion: Our results demonstrate that the eikonal model yields accurate LATs and combined with the boundary element method precise ECGs compared to markedly more expensive full bidomain simulations. However, for an accurate representation of atrial repolarization dynamics, diffusion terms must be accounted for in simplified models. Significance: Simulations of atrial LATs and ECGs can be notably accelerated to clinically feasible time frames at high accuracy by resorting to the eikonal and boundary element methods.

No abstract

Atrial fibrillation is responsible for a significant and steadily rising burden. Simultaneously, the treatment options for atrial fibrillation are far from optimal. Personalized simulations of cardiac electrophysiology could assist clinicians in the risk stratification and therapy planning for atrial fibrillation. However, the use of personalized simulations in clinics is currently not possible due to either too high computational costs or non-sufficient accuracy. Eikonal simulations come with low computational costs but cannot replicate the influence of cardiac tissue geometry on the conduction velocity of the wave propagation. Consequently, they currently lack the required accuracy to be applied in clinics. Biophysically detailed simulations on the other hand are accurate but associated with too high computational costs. To tackle this issue, a regression model is created based on biophysically detailed bidomain simulation data. This regression formula calculates the conduction velocity dependent on the thickness and curvature of the heart wall. Afterwards the formula was implemented into the eikonal model with the goal to increase the accuracy of the eikonal model without losing its advantage of computational efficiency. The results of the modified eikonal simulations demonstrate that (i) the local activation times become significantly closer to those of the biophysically detailed bidomain simulations, (ii) the advantage of the eikonal model of a low sensitivity to the resolution of the mesh was reduced further, and (iii) the unrealistic occurrence of endo-epicardial dissociation in simulations was remedied. The results suggest that the accuracy of the eikonal model was significantly increased. At the same time, the additional computational costs caused by the implementation of the regression formula are neglectable. In conclusion, a successful step towards a more accurate and fast computational model of cardiac electrophysiology was achieved.