Roth B J
Biomedical Engineering and Instrumentation Program, National Center for Research Resources, National Institutes of Health, Bethesda, MD 20892.
J Math Biol. 1992;30(6):633-46.
The bidomain model, which describes the behavior of many electrically active tissues, is equivalent to a multi-dimensional cable model and can be represented by a network of resistors and capacitors. For a two-dimensional sheet of tissue, the intracellular and extracellular conductivity tensors can be visualized as two ellipses. For any pair of conductivity tensors, a coordinate transformation can be found that reduces the extracellular ellipse to a circle and aligns the intracellular ellipse with the coordinate axes. The eccentricity of the intracellular ellipse in this new coordinate system is an important parameter. It can have two special values: zero (in which case the tissue has equal anisotropy ratios) or one (in which case the tissue is comprised of one-dimensional fibers coupled through the two-dimensional extracellular space). Thus the bidomain model provides a unifying framework within which the electrical behavior of a wide variety of nerve and muscle tissues can be studied. When the anisotropy ratios in the intracellular and extracellular domains are not equal, stimulation with an anode always causes depolarization of some region of tissue. An analogous effect occurs in models that describe one-dimensional fibers, in which an "activating function" determines the site of stimulation. Experiments indicate that cardiac muscle does not have equal anisotropy ratios. Therefore, models developed to describe stimulation of axons may also help in understanding stimulation of two- or three-dimensional cardiac tissue, and may explain the concept of anodal stimulation of cardiac tissue through a "virtual cathode".
双域模型描述了许多电活性组织的行为，等同于多维电缆模型，可用电阻器和电容器网络表示。对于二维组织片，细胞内和细胞外电导率张量可可视化为两个椭圆。对于任何一对电导率张量，可找到一种坐标变换，将细胞外椭圆简化为圆形，并使细胞内椭圆与坐标轴对齐。在这个新坐标系中，细胞内椭圆的偏心率是一个重要参数。它可以有两个特殊值：零（在这种情况下，组织具有相等的各向异性比率）或一（在这种情况下，组织由通过二维细胞外空间耦合的一维纤维组成）。因此，双域模型提供了一个统一的框架，在其中可以研究各种神经和肌肉组织的电行为。当细胞内和细胞外区域的各向异性比率不相等时，用阳极刺激总会导致组织某些区域的去极化。在描述一维纤维的模型中也会出现类似的效应，其中“激活函数”决定刺激部位。实验表明，心肌不具有相等的各向异性比率。因此，开发用于描述轴突刺激的模型也可能有助于理解二维或三维心脏组织的刺激，并可能通过“虚拟阴极”解释心脏组织阳极刺激的概念。
