A Cell-Based Framework for Numerical Modeling of Electrical Conduction in Cardiac Tissue
A Cell-Based Framework for Numerical Modeling of Electrical Conduction in Cardiac Tissue
复制标题
心脏组织导电数值模拟的基于细胞的框架
作者：
A. Tveito;K. H. Jæger;M. Kuchta;K. Mardal;M. Rognes
在本文中，我们研究了一个数学模型的基础上明确表示的单个细胞的心脏组织。在该EMI模型中，细胞外（E）空间、细胞膜（M）和细胞内（I）空间被表示为单独的几何域。该表示引入了详细表示心脏细胞（包括其膜）的特性所需的建模灵活性。特别是，我们将表明，该模型允许离子通道沿沿着细胞膜非均匀分布。这样的功能是很难包括在经典的均质化模型，如单域和双域模型经常用于心脏电生理学的计算分析。使用有限差分法（FDM）和有限元法（FEM）的两个变体来求解EMI模型。我们比较这三个计划的数字，报告CPU的努力和收敛速度。最后，我们通过模拟离子通道沿着细胞膜非均匀分布的心肌细胞单层，说明了EMI模型与经典模型相比的独特功能。由于每个单元的详细表示，使用EMI模型产生的计算问题比经典的均匀化模型大得多，因此代表了计算挑战。然而，我们的数值模拟表明，FDM方案是最佳的，在这个意义上说，计算复杂度成比例地增加模型中的心脏细胞的数量。此外，我们提出了模拟，涉及~ 1.17亿个未知数，代表高达~ 16000细胞的方程系统的基础上。我们的结论是心脏细胞的集合可以使用EMI模型进行模拟，并且EMI模型比经典的单域和双域模型具有更大的建模灵活性。
In this paper, we study a mathematical model of cardiac tissue based on explicit representation of individual cells. In this EMI model, the extracellular (E) space, the cell membrane (M) and the intracellular (I) space are represented as separate geometrical domains. This representation introduces modelling flexibility needed for detailed representation of the properties of cardiac cells including their membrane. In particular, we will show that the model allows ion channels to be non-uniformly distributed along the membrane of the cell. Such features are difficult to include in classical homogenized models like the monodomain and bidomain models frequently used in computational analyses of cardiac electrophysiology. The EMI model is solved using a finite difference method (FDM) and two variants of the finite element method (FEM). We compare the three schemes numerically, reporting on CPU-efforts and convergence rates. Finally, we illustrate the distinctive capabilities of the EMI model compared to classical models by simulating monolayers of cardiac cells with heterogeneous distributions of ionic channels along the cell membrane. Because of the detailed representation of every cell, the computational problems that result from using the EMI model are much larger than for the classical homogenized models, and thus represent a computational challenge. However, our numerical simulations indicate that the FDM scheme is optimal in the sense that the computational complexity increases proportionally to the number of cardiac cells in the model. Moreover, we present simulations, based on systems of equations involving ~ 117 million unknowns, representing up to ~ 16000 cells. We conclude that collections of cardiac cells can be simulated using the EMI model, and that the EMI model enable greater modeling flexibility than the classical monodomain and bidomain models.
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影响因子：
20.1
作者：
LUO, CH;RUDY, Y
通讯作者：
RUDY, Y
DOI：
10.1152/ajpheart.00760.2013
发表时间：
2014-03
期刊：
American journal of physiology. Heart and circulatory physiology
影响因子：
--
作者：
R. Veeraraghavan;R. Gourdie;S. Poelzing
通讯作者：
R. Veeraraghavan;R. Gourdie;S. Poelzing
影响因子：
20.1
作者：
Trayanova NA
通讯作者：
Trayanova NA
DOI：
10.1016/j.physrep.2014.05.002
发表时间：
2014-10-10
期刊：
Physics reports
影响因子：
--
作者：
Qu Z;Hu G;Garfinkel A;Weiss JN
通讯作者：
Weiss JN
影响因子：
3.4
作者：
Xie, Yuanfang;Sato, Daisuke;Weiss, James N.
通讯作者：
Weiss, James N.