Abstract:

Background: Computer models for simulating cardiac electrophysiology are valuable tools for research and clinical applications. Traditional reaction-diffusion (RD) models used for these purposes are computationally expensive. While eikonal models offer a faster alternative, they are not well-suited to study cardiac arrhythmias driven by reentrant activity. The present work extends the diffusion-reaction eikonal alternant model (DREAM), incorporating conduction velocity (CV) restitution for simulating complex cardiac arrhythmias. Methods: The DREAM modifies the fast iterative method to model cyclical behavior, dynamic boundary conditions, and frequency-dependent anisotropic CV. Additionally, the model alternates with an approximated RD model, using a detailed ionic model for the reaction term and a triple-Gaussian to approximate the diffusion term. The DREAM and monodomain models were compared, simulating reentries in 2D manifolds with different resolutions. Results: The DREAM produced similar results across all resolutions, while experiments with the monodomain model failed at lower resolutions. CV restitution curves obtained using the DREAM closely approximated those produced by the monodomain simulations. Reentry in 2D slabs yielded similar results in vulnerable window and mean reentry duration for low CV in both models. In the left atrium, most inducing points identified by the DREAM were also present in the high-resolution monodomain model. DREAM's reentry simulations on meshes with an average edge length of 1600$\mu$m were 40x faster than monodomain simulations at 200$\mu$m. Conclusion: This work establishes the mathematical foundation for using the accelerated DREAM simulation method for cardiac electrophysiology. Cardiac research applications are enabled by a publicly available implementation in the openCARP simulator.

Abstract:

Cardiac arrhythmias are a leading cause of morbidity and mortality, with atrial fibrillation (AF) being the most prevalent sustained arrhythmia, significantly impacting global public health. Despite its importance, AF treatment strategies remain insufficient due to an incom- plete understanding of the underlying mechanisms. Computational models are valuable tools for advancing research in cardiac electrophysiology and enhancing patient diagnostics and treatment. While reaction diffusion (RD) models are widely used, they are computationally intensive. In contrast, the eikonal model is computationally less demanding, making it attractive for large-scale simulations and clinical scenarios where faster computation times are critical. However, several limitations hinder its application in realistic settings. This work aims to explore how the eikonal model can be better understood and expanded to improve research, diagnosis, and treatment of atrial arrhythmias.To investigate the standard eikonal model, it was first compared to RD models by simulating single beats under sinus rhythm, both with and without fibrosis. Then, the standard eikonal model was modified to provide additional outputs, including conduction velocity (CV) magnitude and wavefront propagation direction under anisotropic conditions, alongside activation times. These outputs served as ground truth to evaluate the radial basis function method, which estimates CV based on activation times while ignoring anisotropy.The eikonal model was then extended by combining it with the RD model, forming the diffusion-reaction eikonal alternant model (DREAM). A new cyclical fast iterative method (cycFIM) was introduced to solve the anisotropic eikonal equation while enabling reactivations, a complex challenge for iterative methods.To address the eikonal model’s limitations, particularly its inability to account for source- sink mismatch, regression models were developed. Bidomain simulations examined the effects of wall thickness and tissue curvature on CV. Moreover, monodomain simulations investigated pacing frequency and source-sink mismatch effects on diffusion current (DC) amplitude. These findings were integrated into regression models for the eikonal model. To facilitate the regression, a new method was introduced to quantify source-sink mismatch based solely on activation times and node coordinates.Comparison with RD models showed that the eikonal model reasonably simulates sinus rhythm in non-fibrotic atrial geometry but significantly declines in performance with fibrosis due to its inability to capture source-sink mismatches. Additionally, when assessing the radial basis function it was found that neglecting anisotropic propagation when estimating CV can lead to significant errors up to 700 mm/s. DREAM simulations maintained low computational costs while effectively simulating action potentials, node reactivations, and reentries. Investigating CV restitution revealed that the steepness of restitution curves can modulate the dynamics of the vulnerable window and the average duration of reentry. Regression models based on RD simulations successfully predicted key factors in cardiac electrophysiology, such as CV and DC amplitude, using data available during eikonal simulations, including activation times and geometric factors like wall thickness and tissue curvature.This research highlights the eikonal model’s potential in advancing the understanding and clinical management of cardiac arrhythmias. As a computationally efficient alternative to more complex models, it provides valuable insights into arrhythmia mechanisms, diagnosis, and treatment, making it ideal for large-scale simulations and clinical settings with limited computing resources. The DREAM was applied to explore the role of personalized CV restitution curves in reentry dynamics. This study paves the way for broader applications of eikonal-based models in cardiac electrophysiology, ultimately improving patient outcomes. Additionally, the new cycFIM, embedded in the DREAM, could be used to simulate cyclical wave propagation in other fields beyond medical applications.