A finite element formulation for atrial tissue monolayer.

Area of Science:

• Computational biology
• Cardiac electrophysiology
• Biomedical engineering

Background:

• Studying complex atrial arrhythmias like atrial fibrillation requires computationally intensive simulations.
• Approximating thin atrial walls as curved monolayers is a common method to reduce computational workload.
• The finite element method (FEM) is a standard technique for solving the governing partial differential equations.

Purpose of the Study:

• To present a generalized 2D FEM for simulating wave propagation in arbitrarily shaped monolayers (ML).
• To enable the use of existing FEM software with minimal modifications for cardiac modeling.
• To reduce the computational demand of studying atrial arrhythmias.

Main Methods:

• Developed a generalized 2D FEM to compute stiffness and coupling matrices for monolayers.
• Incorporated a single additional coordinate transformation compared to standard 2D FEM.
• Validated the algorithm using benchmark geometries and a detailed atrial anatomy model.

Main Results:

• The ML model successfully simulated electric activation in curved, anisotropic cardiac tissue.
• Simulations in branching tissue showed slight deviations from volumetric models.
• Activation times in the atrial anatomy model correlated strongly (0.88) with clinical data across five pacing protocols.

Conclusions:

• The presented 2D FEM offers an effective and straightforward method for modeling wave propagation in monolayers.
• This approach has minor limitations compared to full volumetric models.
• The method facilitates more efficient computational studies of atrial arrhythmias.