Efficient time splitting schemes for the monodomain equation in cardiac electrophysiology. (2nd January 2023)

• Record Type: Journal Article
• Authors: Lindner, Laura P.; Gerach, Tobias; Jahnke, Tobias; Loewe, Axel; Weiss, Daniel; Wieners, Christian
• Is Part Of: International journal for numerical methods in biomedical engineering. Volume 39:Number 2(2023)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2023-01-02
• Subjects: Beeler–Reuter cell model -- cardiac electrophysiology -- monodomain equation -- splitting methods -- time integration; Biomedical engineering -- Periodicals; Imaging systems in medicine -- Periodicals; Numerical analysis -- Periodicals; Engineering mathematics -- Periodicals; 610.28
• DOI: 10.1002/cnm.3666
• Languages: English
• ISSNs: 2040-7939

Abstract

Abstract: Approximating the fast dynamics of depolarization waves in the human heart described by the monodomain model is numerically challenging. Splitting methods for the PDE‐ODE coupling enable the computation with very fine space and time discretizations. Here, we compare different splitting approaches regarding convergence, accuracy, and efficiency. Simulations were performed for a benchmark problem with the Beeler–Reuter cell model on a truncated ellipsoid approximating the left ventricle including a localized stimulation. For this configuration, we provide a reference solution for the transmembrane potential. We found a semi‐implicit approach with state variable interpolation to be the most efficient scheme. The results are transferred to a more physiological setup using a bi‐ventricular domain with a complex external stimulation pattern to evaluate the accuracy of the activation time for different resolutions in space and time.