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High-order finite element methods for cardiac monodomain simulations.

Vincent KP, Gonzales MJ, Gillette AK, Villongco CT, Pezzuto S, Omens JH, Holst MJ, McCulloch AD - Front Physiol (2015)

Bottom Line: 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.

View Article: PubMed Central - PubMed

Affiliation: Department of Bioengineering, University of California San Diego La Jolla, CA, USA.

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.

No MeSH data available.


Cubic Hermite-style serendipity elements (red) converge better per degree of freedom than conventional cubic Hermite (black) or linear Lagrange (blue) elements.
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Figure 2: Cubic Hermite-style serendipity elements (red) converge better per degree of freedom than conventional cubic Hermite (black) or linear Lagrange (blue) elements.

Mentions: Next, the convergence behavior of the three basis types was examined in more detail using the second test problem with planar wavefront propagation. Here, the serendipity Hermite solutions converged with fewer total degrees of freedom than the cubic and linear solutions (Figure 2). Solutions using the same number of cubic Hermite and serendipity Hermite elements were almost identical for this test problem.


High-order finite element methods for cardiac monodomain simulations.

Vincent KP, Gonzales MJ, Gillette AK, Villongco CT, Pezzuto S, Omens JH, Holst MJ, McCulloch AD - Front Physiol (2015)

Cubic Hermite-style serendipity elements (red) converge better per degree of freedom than conventional cubic Hermite (black) or linear Lagrange (blue) elements.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4525671&req=5

Figure 2: Cubic Hermite-style serendipity elements (red) converge better per degree of freedom than conventional cubic Hermite (black) or linear Lagrange (blue) elements.
Mentions: Next, the convergence behavior of the three basis types was examined in more detail using the second test problem with planar wavefront propagation. Here, the serendipity Hermite solutions converged with fewer total degrees of freedom than the cubic and linear solutions (Figure 2). Solutions using the same number of cubic Hermite and serendipity Hermite elements were almost identical for this test problem.

Bottom Line: 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.

View Article: PubMed Central - PubMed

Affiliation: Department of Bioengineering, University of California San Diego La Jolla, CA, USA.

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.

No MeSH data available.