High-order finite element methods for cardiac monodomain simulations.
High-order finite element methods for cardiac monodomain simulations.
复制标题
DOI：
10.3389/fphys.2015.00217
复制
发表时间：
2015
影响因子：
4
通讯作者：
McCulloch AD
中科院分区：
文献类型：
--
作者：
Vincent KP;Gonzales MJ;Gillette AK;Villongco CT;Pezzuto S;Omens JH;Holst MJ;McCulloch AD
组织尺度心脏电生理的计算建模需要数值收敛的解决方案，以避免虚假的伪影。心脏动作电位传播固有的陡峭梯度需要精细的空间尺度，因此需要大量的计算负担。由于高阶插值方法在理论上具有收敛优势，因此在这些模拟中已经提出了高阶插值方法。在本研究中，我们比较了线性Lagrange、三次Hermite和新提出的三次Hermite式偶然性插值方法在心脏单域方程有限元模拟中的收敛性。与传统的线性单元相比，高阶方法以更少的自由度和更长的单元边缘长度获得收敛解。此外，我们提出了一个无量纲数，即单元Thiele模量，作为确定解收敛性的更有用的度量，而不是单独的单元大小。最后，我们使用细胞Thiele模量来检查收敛标准，以获得临床有用的激活模式，如患者特异性建模，其中总激活时间是已知的先验。
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.