Mathias R T, Eisenberg R S, Valdiosera R
Biophys J. 1977 Jan;17(1):57-93. doi: 10.1016/S0006-3495(77)85627-0.
This paper presents the construction, derivation, and test of a mesh model for the electrical properties of the transverse tubular system (T-system) in skeletal muscle. We model the irregular system of tubules as a random network of miniature transmission lines, using differential equations to describe the potential between the nodes and difference equations to describe the potential at the nodes. The solution to the equations can be accurately represented in several approximate forms with simple physical and graphical interpretations. All the parameters of the solution are specified by impedance and morphometric measurements. The effect of wide circumferential spacing between T-system openings is analyzed and the resulting restricted mesh model is shown to be approximated by a mesh with an access resistance. The continuous limit of the mesh model is shown to have the same form as the disk model of the T-system, but with a different expression for the tortuosity factor. The physical meaning of the tortuosity factor is examined, and a short derivation of the disk model is presented that gives results identical to the continuous limit of the mesh model. Both the mesh and restricted mesh models are compared with experimental data on the impedance of muscle fibers of the frog sartorius. The derived value for the resistivity of the lumen of the tubules is not too different from that of the bathing solution, the difference probably arising from the sensitivity of this value to errors in the morphometric measurements.
本文介绍了一种用于骨骼肌横管系统（T 系统）电特性的网格模型的构建、推导和测试。我们将不规则的小管系统建模为微型传输线的随机网络，使用微分方程描述节点间的电位，用差分方程描述节点处的电位。方程的解可以用几种近似形式精确表示，且具有简单的物理和图形解释。解的所有参数由阻抗和形态测量确定。分析了 T 系统开口间宽周向间距的影响，并表明所得的受限网格模型可由具有接入电阻的网格近似。网格模型的连续极限被证明与 T 系统的圆盘模型具有相同的形式，但曲折因子的表达式不同。研究了曲折因子的物理意义，并给出了圆盘模型的简短推导，其结果与网格模型的连续极限相同。将网格模型和受限网格模型都与青蛙缝匠肌纤维阻抗的实验数据进行了比较。推导得到的小管管腔电阻率值与浴液的电阻率值相差不大，这种差异可能源于该值对形态测量误差的敏感性。
