A finite element formulation for atrial tissue monolayer

Using computer models for the study of complex atrial arrhythmias such as atrial fibrillation is computationally demanding as long observation periods in the order of tens of seconds are required. A well established approach for reducing computational workload is to approximate the thin atrial walls by curved monolayers. On the other hand, the finite element method (FEM) is a well established approach to solve the underlying partial differential equations.

A generalized 2D finite element method (FEM) is presented which computes the corresponding stiffness and coupling matrix for arbitrarily shaped monolayers (ML). Compared to standard 2D FEM, only one additional coordinate transformation is required. This allows the use of existing FEM software with minor modifications. The algorithm was tested to simulate wave propagation in benchmark geometries and in a model of atrial anatomy.

The ML model was able to simulate electric activation in curved tissue with anisotropic conductivity. Simulations in branching tissue yielded slightly different patterns when compared to a volumetric model with finite thickness. In the model of atrial anatomy the computed activation times for five different pacing protocols displayed a correlation of 0.88 compared to clinical data.

The presented method provides a useful and easily implemented approach to model wave propagation in MLs with a few restrictions to volumetric models.