[Paper Review] Comparison of propagation models and forward calculation methods on cellular, tissue and organ scale atrial electrophysiology

Claudia Nagel, Cristian Barrios Espinosa+6 more|arXiv (Cornell University)|Mar 15, 2022

Cardiac electrophysiology and arrhythmias4 citations

TL;DR

This study evaluates simplified electrophysiological models—eikonal, reaction-eikonal, and monodomain—combined with fast forward calculation methods (boundary element method, infinite volume conductor) for atrial simulations. It demonstrates that the eikonal model with boundary element method achieves LATs and ECGs within 0.9 correlation coefficient of bidomain/FEM results, enabling up to 1,000x speedup while preserving physiological accuracy, except for repolarization dynamics which require diffusion terms.

ABSTRACT

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 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.

Motivation & Objective

• To assess the accuracy of simplified propagation models (eikonal, reaction-eikonal, monodomain) versus the bidomain model in simulating atrial electrophysiology.
• To evaluate forward calculation methods (boundary element method, infinite volume conductor) for ECG generation in comparison to the finite element method.
• To determine whether simplified models can achieve clinically feasible simulation times without sacrificing physiological fidelity in LATs and ECGs.
• To quantify errors in action potential duration, local activation times, and P wave morphology across cellular, tissue, and organ scales.
• To identify conditions under which diffusion terms are essential for accurate repolarization dynamics in simplified models.

Proposed method

• Simulations were performed on patient-specific bi-atrial geometry with 523 µm average mesh resolution, including fibrotic tissue as passive barriers.
• The bidomain model with finite element method served as the gold standard for both activation propagation and ECG computation.
• Simplified models included monodomain, reaction-eikonal, and eikonal formulations, with the eikonal model using pre-computed action potential templates shifted in time.
• Forward calculation used boundary element method (BEM) and infinite volume conductor method to compute body surface ECGs from cardiac sources.
• Conductivities were tuned via tuneCV to match conduction velocities from the bidomain model, with mesh resolution tested at 523 µm and 265 µm for error assessment.
• Metrics included action potential duration (APD90), local activation times (LATs), and ECG correlation (Pearson r) between simplified and gold standard methods.

Experimental results

Research questions

• RQ1 How accurately do eikonal, reaction-eikonal, and monodomain models reproduce local activation times (LATs) and P waves compared to the bidomain model in healthy and fibrotic atria?
• RQ2 To what extent do boundary element method (BEM) and infinite volume conductor method accurately reproduce ECGs compared to the finite element method?
• RQ3 What is the impact of excluding diffusion terms in simplified models on the accuracy of repolarization dynamics (APD90)?
• RQ4 How do mesh resolution and tissue heterogeneity (fibrosis, ion channel remodeling) affect numerical errors in LATs and ECGs?
• RQ5 Can simplified models reduce simulation time by orders of magnitude while maintaining physiological fidelity in LATs and ECGs?

Key findings

• The eikonal model produced LATs and P waves that closely matched the bidomain model, with correlation coefficients >0.99 for activation sequences.
• ECGs computed with the boundary element method showed correlation coefficients >0.9 compared to the finite element method, indicating high accuracy.
• The infinite volume conductor method systematically overestimated P wave amplitudes, especially in precordial leads, leading to lower correlation coefficients.
• Only the eikonal model with time-shifted action potential templates showed notable deviations in repolarization behavior (APD90), indicating loss of fidelity without diffusion terms.
• The monodomain model showed minimal error in LATs (≤1.2 ms) and APD90 (≤0.05 mV RMS error) on a 523 µm mesh, with 2% error in total activation time due to mesh resolution.
• A 2% numerical error (≈2 ms) in LATs was attributed to mesh resolution, with no significant additional discretization error in APD90.