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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.


(A) Non-physiological oscillations were seen in unconverged solutions. Here t = 0 ms is set to the activation time of the fully converged (ϕc = 1.0) solution. (B) The amplitude of these oscillations is a function of the cell Thiele modulus. Symbol color indicates element type: cubic Hermite (black), cubic Hermite-style 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 4: (A) Non-physiological oscillations were seen in unconverged solutions. Here t = 0 ms is set to the activation time of the fully converged (ϕc = 1.0) solution. (B) The amplitude of these oscillations is a function of the cell Thiele modulus. Symbol color indicates element type: cubic Hermite (black), cubic Hermite-style 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: Non-physiological oscillations were observed in unconverged solutions (Figure 4A). The amplitude of these oscillations, measured as the maximum negative deviation from resting membrane potential before the action potential upstroke, was a function of the cell Thiele modulus (Figure 4B). However, this relationship was much more non-linear than the relationship between conduction velocity error and cell Thiele modulus. The oscillation amplitude decreased sharply to zero around ϕc = 4.0 for the cubic Hermite and serendipity Hermite basis functions and were completely eliminated at ϕc ≲ 1.0.


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)

(A) Non-physiological oscillations were seen in unconverged solutions. Here t = 0 ms is set to the activation time of the fully converged (ϕc = 1.0) solution. (B) The amplitude of these oscillations is a function of the cell Thiele modulus. Symbol color indicates element type: cubic Hermite (black), cubic Hermite-style 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
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getmorefigures.php?uid=PMC4525671&req=5

Figure 4: (A) Non-physiological oscillations were seen in unconverged solutions. Here t = 0 ms is set to the activation time of the fully converged (ϕc = 1.0) solution. (B) The amplitude of these oscillations is a function of the cell Thiele modulus. Symbol color indicates element type: cubic Hermite (black), cubic Hermite-style 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: Non-physiological oscillations were observed in unconverged solutions (Figure 4A). The amplitude of these oscillations, measured as the maximum negative deviation from resting membrane potential before the action potential upstroke, was a function of the cell Thiele modulus (Figure 4B). However, this relationship was much more non-linear than the relationship between conduction velocity error and cell Thiele modulus. The oscillation amplitude decreased sharply to zero around ϕc = 4.0 for the cubic Hermite and serendipity Hermite basis functions and were completely eliminated at ϕc ≲ 1.0.

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.