title: High-order finite element methods for cardiac monodomain simulations.
abstract: Computational modeling of tissue-scale cardiac electrophysiology requires numerically converged solutions to avoid spurious artifacts. The steep gradients inherent to cardiac action potential propagation necessitate fine spatial scales and therefore a substantial computational burden. The use of high-order interpolation methods has previously been proposed for these simulations due to their theoretical convergence advantage. In this study, we compare the convergence behavior of linear Lagrange, cubic Hermite, and the newly proposed cubic Hermite-style serendipity interpolation methods for finite element simulations of the cardiac monodomain equation. The high-order methods reach converged solutions with fewer degrees of freedom and longer element edge lengths than traditional linear elements. Additionally, we propose a dimensionless number, the cell Thiele modulus, as a more useful metric for determining solution convergence than element size alone. Finally, we use the cell Thiele modulus to examine convergence criteria for obtaining clinically useful activation patterns for applications such as patient-specific modeling where the total activation time is known a priori.
authors: Department of Bioengineering, University of California San Diego La Jolla, CA, USA.
authors: Kevin P
authors: KP
authors: Vincent
authors: Department of Bioengineering, University of California San Diego La Jolla, CA, USA.
authors: Matthew J
authors: MJ
authors: Gonzales
authors: Department of Mathematics, University of Arizona Tucson, AZ, USA.
authors: Andrew K
authors: AK
authors: Gillette
authors: Department of Bioengineering, University of California San Diego La Jolla, CA, USA.
authors: Christopher T
authors: CT
authors: Villongco
authors: Dipartimento di Matematica, Politecnico di Milano Milano, Italy ; Center for Computational Medicine in Cardiology, Institute of Computational Science, Università della Svizzera italiana Lugano, Switzerland.
authors: Simone
authors: S
authors: Pezzuto
authors: Department of Bioengineering, University of California San Diego La Jolla, CA, USA ; Department of Medicine, University of California San Diego La Jolla, CA, USA.
authors: Jeffrey H
authors: JH
authors: Omens
authors: Department of Mathematics, University of California San Diego La Jolla, CA, USA.
authors: Michael J
authors: MJ
authors: Holst
authors: Department of Bioengineering, University of California San Diego La Jolla, CA, USA ; Department of Medicine, University of California San Diego La Jolla, CA, USA.
authors: Andrew D
authors: AD
authors: McCulloch
keywords: cardiac activation pattern; cell Thiele modulus; finite element analysis; monodomain model; serendipity methods