TY - JOUR
T1 - High-order finite element methods for cardiac monodomain simulations
AU - Vincent, Kevin P.
AU - Gonzales, Matthew J.
AU - Gillette, Andrew K.
AU - Villongco, Christopher T.
AU - Pezzuto, Simone
AU - Omens, Jeffrey H.
AU - Holst, Michael J.
AU - McCulloch, Andrew D.
N1 - Publisher Copyright:
© 2015 Vincent, Gonzales, Gillette, Villongco, Pezzuto, Omens, Holst and McCulloch.
PY - 2015
Y1 - 2015
N2 - 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.
AB - 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.
KW - Cardiac activation pattern
KW - Cell Thiele modulus
KW - Finite element analysis
KW - Monodomain model
KW - Serendipity methods
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U2 - 10.3389/fphys.2015.00217
DO - 10.3389/fphys.2015.00217
M3 - Article
AN - SCOPUS:84941004424
SN - 1664-042X
VL - 6
JO - Frontiers in Physiology
JF - Frontiers in Physiology
IS - Aug
M1 - 217
ER -