Henriquez C S, Plonsey R
Department of Biomedical Engineering, Duke University, Durham, NC 27706.
IEEE Trans Biomed Eng. 1990 Sep;37(9):850-60. doi: 10.1109/10.58596.
This paper presents a mathematical description based on a three-dimensional model for studying propagation in cardiac muscle. The model makes use of the bidomain concept to construct a representation of a cylindrical, multicellular bundle lying in an extensive volume conductor. The equations for the cylindrical bidomain are derived here for different combinations of boundary conditions and simplifying assumptions. The analysis shows that an analytic model for propagation can be set up if one assumes that the ratio of the intracellular and interstitial bidomain conductivities in the radial and axial direction are the same (i.e., equal anisotropy) and the intracellular radial current density vanishes at the surface. The simulation of this model will be discussed in a subsequent paper. As a point of reference, the classical one-dimensional cable model is also examined and the expressions governing propagation are reformulated to account for the extracellular medium, a factor ignored in most simulation studies.
本文提出了一种基于三维模型的数学描述，用于研究心肌中的电传播。该模型利用双域概念构建了一个位于广阔容积导体中的圆柱形多细胞束的表示。本文针对不同的边界条件组合和简化假设，推导了圆柱形双域的方程。分析表明，如果假设细胞内和细胞间质双域电导率在径向和轴向的比值相同（即各向异性相等），且细胞内径向电流密度在表面消失，则可以建立一个传播分析模型。该模型的模拟将在后续论文中讨论。作为参考，还研究了经典的一维电缆模型，并重新推导了控制传播的表达式，以考虑细胞外介质，这是大多数模拟研究中忽略的一个因素。
