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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.


The relationship between cell Thiele modulus and conduction velocity error is nearly constant for each basis function type. Symbol color indicates interpolation type:cubic Hermite (black), cubic Hermite serendipity (red), and linear Lagrange (blue). Filled symbols represent solutions using the ten Tusscher (ten Tusscher and Panfilov, 2006) cellular ionic model and open symbols represent solutions using the Beeler-Reuter cellular ionic model (Beeler and Reuter, 1977). Diffusivity is represent by symbol shape: D = 0.0126 mm2/ms (boxes), D = 0.0953 mm2/ms (circles), D = 0.953 mm2/ms (triangles). Element lengths ranged from 0.05 to 4.0 mm.
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Figure 3: The relationship between cell Thiele modulus and conduction velocity error is nearly constant for each basis function type. Symbol color indicates interpolation type:cubic Hermite (black), cubic Hermite serendipity (red), and linear Lagrange (blue). Filled symbols represent solutions using the ten Tusscher (ten Tusscher and Panfilov, 2006) cellular ionic model and open symbols represent solutions using the Beeler-Reuter cellular ionic model (Beeler and Reuter, 1977). Diffusivity is represent by symbol shape: D = 0.0126 mm2/ms (boxes), D = 0.0953 mm2/ms (circles), D = 0.953 mm2/ms (triangles). Element lengths ranged from 0.05 to 4.0 mm.

Mentions: Since numerical solutions of the monodomain model depend on membrane kinetics and monodomain conductivity as well as spatial discretization, we compared solutions to the second test problem using eight element sizes, three diffusivities (D = 0.0126, 0.0953, and 0.953 mm2/ms), two ionic models with different membrane kinetics (the ten Tusscher and Panfilov, 2006 human ventricular myocyte model with a normalized dV/dtmax of 2.47 ms−1 and the Beeler and Reuter (1977) ventricular myocyte model with a normalized dV/dtmax of 1.38 ms−1). Figure 3 demonstrates that the convergence error for these simulations is an almost unique function of cell Thiele modulus for each element type. A cell Thiele Modulus of 1.0 resulted in an error in the conduction velocity of approximately 0.1% with Hermite basis functions compared with 4% with linear Lagrange basis functions.


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)

The relationship between cell Thiele modulus and conduction velocity error is nearly constant for each basis function type. Symbol color indicates interpolation type:cubic Hermite (black), cubic Hermite serendipity (red), and linear Lagrange (blue). Filled symbols represent solutions using the ten Tusscher (ten Tusscher and Panfilov, 2006) cellular ionic model and open symbols represent solutions using the Beeler-Reuter cellular ionic model (Beeler and Reuter, 1977). Diffusivity is represent by symbol shape: D = 0.0126 mm2/ms (boxes), D = 0.0953 mm2/ms (circles), D = 0.953 mm2/ms (triangles). Element lengths ranged from 0.05 to 4.0 mm.
© Copyright Policy
Related In: Results  -  Collection

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

Figure 3: The relationship between cell Thiele modulus and conduction velocity error is nearly constant for each basis function type. Symbol color indicates interpolation type:cubic Hermite (black), cubic Hermite serendipity (red), and linear Lagrange (blue). Filled symbols represent solutions using the ten Tusscher (ten Tusscher and Panfilov, 2006) cellular ionic model and open symbols represent solutions using the Beeler-Reuter cellular ionic model (Beeler and Reuter, 1977). Diffusivity is represent by symbol shape: D = 0.0126 mm2/ms (boxes), D = 0.0953 mm2/ms (circles), D = 0.953 mm2/ms (triangles). Element lengths ranged from 0.05 to 4.0 mm.
Mentions: Since numerical solutions of the monodomain model depend on membrane kinetics and monodomain conductivity as well as spatial discretization, we compared solutions to the second test problem using eight element sizes, three diffusivities (D = 0.0126, 0.0953, and 0.953 mm2/ms), two ionic models with different membrane kinetics (the ten Tusscher and Panfilov, 2006 human ventricular myocyte model with a normalized dV/dtmax of 2.47 ms−1 and the Beeler and Reuter (1977) ventricular myocyte model with a normalized dV/dtmax of 1.38 ms−1). Figure 3 demonstrates that the convergence error for these simulations is an almost unique function of cell Thiele modulus for each element type. A cell Thiele Modulus of 1.0 resulted in an error in the conduction velocity of approximately 0.1% with Hermite basis functions compared with 4% with linear Lagrange basis functions.

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.