A parallel solver for reaction-diffusion systems in computational electrocardiology
A parallel solver for reaction-diffusion systems in computational electrocardiology
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DOI：
10.1142/s0218202504003489
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发表时间：
2004-06-01
影响因子：
3.5
通讯作者：
Pavarino, LF
中科院分区：
文献类型：
--
作者：
Colli-Franzone, P;Pavarino, LF
在这项工作中，一个并行的三维求解器的数值模拟在计算心电学的介绍和研究。求解器是基于各向异性Bidomain心脏模型，由两个退化的抛物线反应扩散方程描述的心肌组织的细胞内和细胞外电位的系统。该模型包括壁内纤维旋转和各向异性的传导系数，可以是完全正交各向异性或轴对称的纤维方向。求解器还包括更简单的各向异性单域模型，仅由一个反应扩散方程组成。这些心脏模型与用于离子电流的膜模型耦合，该膜模型由可以从简单的FitzHugh-Nagumo（FHN）模型变化到更复杂的I相Luo-Rudy模型（LR 1）的常微分方程系统组成。求解器在空间上采用结构化等参Q（1）有限元，在时间上采用半隐式自适应方法。并行化和可移植性基于PETSc并行库。在并行计算机上进行了大规模的计算，未知数高达O（10（7）），模拟了三维域中的激发和复极化现象。
In this work, a parallel three-dimensional solver for numerical simulations in computational electrocardiology is introduced and studied. The solver is based on the anisotropic Bidomain cardiac model, consisting of a system of two degenerate parabolic reaction-diffusion equations describing the intra and extracellular potentials of the myocardial tissue. This model includes intramural fiber rotation and anisotropic conductivity coefficients that can be fully orthotropic or axially symmetric around the fiber direction. The solver also includes the simpler anisotropic Monodomain model, consisting of only one reaction-diffusion equation. These cardiac models are coupled with a membrane model for the ionic currents, consisting of a system of ordinary differential equations that can vary from the simple FitzHugh-Nagumo (FHN) model to the more complex phase-I Luo-Rudy model (LR1). The solver employs structured isoparametric Q(1) finite elements in space and a semi-implicit adaptive method in time. Parallelization and portability are based on the PETSc parallel library. Large-scale computations with up to O(10(7)) unknowns have been run on parallel computers, simulating excitation and repolarization phenomena in three-dimensional domains.