Trayanova N
Department of Biomedical Engineering, Tulane University, New Orleans, LA 70118, USA.
IEEE Trans Biomed Eng. 1996 Dec;43(12):1129-40. doi: 10.1109/10.544337.
This paper presents a model describing the steady-state response of a two-dimensional (2-D) slice of myocardium to extracellular current injection. The model incorporates a continuous representation of the multicellular, syncytial cardiac tissue based on the bidomain model. The classical bidomain model is modified by introducing periodic conductivities to better represent the electrical properties of the intracellular space. Thus, junctional discontinuity between abutting myocytes is reflected in the macroscopic representation of cardiac tissue behavior. Since a solution to the resulting coupled differential equations governing the intracellular and extracellular potentials in the tissue preparation is not computationally tractable when traditional numerical approaches, such as finite element or finite difference methods are used, spectral techniques are employed to reduce the problem to the solution of a set of algebraic equations for the transform of the bidomain potentials. Further, the solution to the "periodic" bidomain problem in the Fourier space is decomposed into two separate solutions: One for the classical-bidomain potentials where it is assumed that the intracellular conductivity values along and across cells incorporate the average contribution from cytoplasm and junction, and another for the junctional potential component. The decomposition of the total solution allows to approximately solve for the junctional component thus achieving high overall computational efficiency. The results of simulation are presented in an accompanying paper.
本文提出了一个模型，用于描述心肌二维切片对细胞外电流注入的稳态响应。该模型基于双域模型，对多细胞合胞体心脏组织进行了连续表示。通过引入周期性电导率对经典双域模型进行了修正，以更好地表示细胞内空间的电学特性。因此，相邻心肌细胞之间的连接不连续性反映在心脏组织行为的宏观表示中。由于当使用传统数值方法（如有限元或有限差分法）时，求解组织制备中控制细胞内和细胞外电位的耦合微分方程的解在计算上难以处理，因此采用谱技术将问题简化为一组用于双域电位变换的代数方程的解。此外，傅里叶空间中“周期性”双域问题的解被分解为两个单独的解：一个用于经典双域电位，假设沿细胞和跨细胞的细胞内电导率值包含细胞质和连接的平均贡献；另一个用于连接电位分量。总解的分解允许近似求解连接分量，从而实现较高的整体计算效率。模拟结果在随附的论文中给出。
