Plonsey R, Barr R C
Biophys J. 1984 Mar;45(3):557-71. doi: 10.1016/S0006-3495(84)84193-4.
Cardiac tissue has been shown to function as an electrical syncytium in both intracellular and extracellular (interstitial) domains. Available experimental evidence and qualitative intuition about the complex anatomical structure support the viewpoint that different (average) conductivities are characteristic of the direction along the fiber axis, as compared with the cross-fiber direction, in intracellular as well as extracellular space. This report analyzes two-dimensional anisotropic cardiac tissue and achieves integral equations for finding intracellular and extracellular potentials, longitudinal currents, and membrane currents directly from a given description of the transmembrane voltage. These mathematical results are used as a basis for a numerical model of realistic (though idealized) two-dimensional cardiac tissue. A computer simulation based on the numerical model was executed for conductivity patterns including nominally normal ventricular muscle conductivities and a pattern having the intra- or extracellular conductivity ratio along x, the reciprocal of that along y. The computed results are based on assuming a simple spatial distribution for Vm, usually a circular isochrone, to isolate the effects on currents and potentials of variations in conductivities without confounding propagation differences. The results are in contrast to the many reports that explicity or implicitly assume isotropic conductivity or equal conductivity ratios along x and y. Specifically, with reciprocal conductivities, most current flows in large loops encompassing several millimeters, but only in the resting (polarized) region of the tissue; further, a given current flow path often includes four or more rather than two transmembrane excursions. The nominally normal results showed local currents predominantly with only two transmembrane passages; however, a substantial part of the current flow patterns in two-dimensional anisotropic bisyncytia may have qualitative as well as quantitative properties entirely different from those of one-dimensional strands.
心脏组织在细胞内和细胞外（间质）区域均表现为电合体。关于复杂解剖结构的现有实验证据和定性直觉支持这样一种观点：在细胞内和细胞外空间中，与纤维轴垂直方向相比，沿纤维轴方向具有不同的（平均）电导率。本报告分析二维各向异性心脏组织，并直接从给定的跨膜电压描述中得出用于求解细胞内和细胞外电位、纵向电流以及膜电流的积分方程。这些数学结果被用作真实（尽管理想化）二维心脏组织数值模型的基础。基于该数值模型对包括名义上正常心室肌电导率以及沿x方向的细胞内或细胞外电导率与沿y方向的电导率之比为倒数的电导率模式进行了计算机模拟。计算结果基于假设Vm具有简单的空间分布，通常为圆形等时线，以分离电导率变化对电流和电位的影响，而不混淆传播差异。这些结果与许多明确或隐含假设各向同性电导率或沿x和y方向电导率相等的报告形成对比。具体而言，对于倒数电导率，大多数电流在包含几毫米的大环中流动，但仅在组织的静息（极化）区域；此外，给定的电流流动路径通常包括四个或更多而非两个跨膜偏移。名义上正常的结果显示局部电流主要只有两个跨膜通道；然而，二维各向异性双合体中电流流动模式的很大一部分在定性和定量性质上可能与一维链完全不同。
