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:

Background and Objective: Planning the optimal ablation strategy for the treatment of complex atrial tachycardia (CAT) is a time consuming task and is error-prone. Recently, directed network mapping, a technology based on graph theory, proved to efficiently identify CAT based solely on data of clinical interventions. Briefly, a directed network was used to model the atrial electrical propagation and reentrant activities were identified by looking for closed-loop paths in the network. In this study, we propose a recommender system, built as an optimization problem, able to suggest the optimal ablation strategy for the treatment of CAT.Methods: The optimization problem modeled the optimal ablation strategy as that one interrupting all reentrant mechanisms while minimizing the ablated atrial surface. The problem was designed on top of directed network mapping. Considering the exponential complexity of finding the optimal solution of the problem, we introduced a heuristic algorithm with polynomial complexity. The proposed algorithm was applied to the data of i) 6 simulated scenarios including both left and right atrial flutter; and ii) 10 subjects that underwent a clinical routine.Results: The recommender system suggested the optimal strategy in 4 out of 6 simulated scenarios. On clinical data, the recommended ablation lines were found satisfactory on 67% of the cases according to the clinician’s opinion, while they were correctly located in 89%. The algorithm made use of only data collected during mapping and was able to process them nearly real-time.Conclusions: The first recommender system for the identification of the optimal ablation lines for CAT, based solely on the data collected during the intervention, is presented. The study may open up interesting scenarios for the application of graph theory for the treatment of CAT.

Abstract:

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. <i>Methods:</i> We compared action potential durations, local activation times (LATs), and electrocardiograms (ECGs) for sinus rhythm simulations on healthy and fibrotically infiltrated atrial models. <i>Results:</i> All simplified model solutions yielded LATs and P&#x00A0;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 <inline-formula><tex-math notation="LaTeX">$&gt;$</tex-math></inline-formula>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&#x00A0;wave amplitudes in the precordial leads. <i>Conclusion:</i> 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. <i>Significance:</i> 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.

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.

Abstract:

We present in silico experiments investigating the potential relationship between atrial arrhythmias in patients with systemic lupus erythematosus (SLE) and the combined effects of structural and electrical remodeling due to chronic inflammation. The study utilized a computational model to simulate the structural and electrical changes in atrial tissue caused by chronic inflammation, with the ultimate goal of shedding light on the mechanisms underlying the development of atrial arrhythmias in SLE patients. The experiment results indicate that electrical remodeling associated with SLE can alter the depolarization pattern and facilitate the emergence of reentry patterns that could initiate arrhythmias. Mild inflammation was found to be insufficient to trigger arrhythmias, while severe inflammation could induce arrhythmias that were not sustained but exhibited a repetitive pattern. This pattern exhibited a 2:1 block of the left atria. These findings provide important insights into the mechanisms underlying the development of atrial arrhythmias in SLE patients and suggest that inflammation-induced structural and electrical remodeling may contribute to this condition. The study offers a valuable starting point for further investigating the complex relationship between SLE, chronic inflammation, and atrial arrhythmias. Furthermore, in the future, this could contribute to the development of new therapeutic strategies for this condition.

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.