A modified technique of the finite-difference method calculations to mimic the four-terminal method measurements of electrical impedance and admittance of skeletal muscles
A modified technique of the finite-difference method calculations to mimic the four-terminal method measurements of electrical impedance and admittance of skeletal muscles
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DOI：
10.1088/1361-6463/abaa6d
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发表时间：
2020-09
期刊：
影响因子：
--
通讯作者：
K. Sekine
中科院分区：
文献类型：
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作者：
K. Sekine
提出了一种改进的有限差分法计算技术，以模拟四端法测量骨骼肌的阻抗Z和导纳Y。这项技术中的元素包含成束的多个肾小管肌细胞。横向电流基于二维悬浮理论，纵向电流基于离散化的索线理论。利用电流关系，建立了胞间介质中的电势和单元中心处的胞内电位的同时线性关系。利用表面膜的等效复电导率考虑了T管和表面膜折叠的影响。电流供应电极被表征为固定电位区。在每个电位拾取电极上，使电流之和为零。Z和Y由进入电流供应电极的电流和在电位拾取电极上的电位差得到。修正方法的计算结果与传统方法的计算结果吻合较好，证明了改进方法的有效性。FDM计算表明，肌萎缩侧索硬化症小鼠腓肠肌Z值的变化是由于肌细胞直径的减小，而生长的变化是由于肌细胞的直径和整个肌肉的大小增加。在解剖的肌肉样本中观察到的α松弛可以用外部电场方向与理想的纵向和横向的偏差来解释。
A modified technique of the finite-difference method (FDM) calculations was developed to mimic the measurements of the electrical impedance, Z, and admittance, Y, of skeletal muscles using the four-terminal method. The elements in this technique contained bundled plural tubular muscle cells. The electrical currents in the transversal direction were formulated based on a theory for two-dimensional suspensions, and those in the longitudinal direction were formulated based on the discretized cable-line theory. Using the relations for the currents, simultaneous linear relations with respect to electrical potentials in the intercellular medium and cell interior at the center of the elements were constructed. The effects of the T-tubules and surface membrane folding were included using the equivalent complex conductivity for the surface membrane. The current-supply electrodes were characterized as regions of fixed potentials. At each potential-pickup electrode, the summation of the electrical current was made to be null. Z and Y were obtained from the current into the current-supply electrodes and the difference between the potentials at the potential-pickup electrodes. The validity of the modified technique was demonstrated by the good agreement between the results of the calculations using the modified and conventional techniques. The FDM calculations revealed that changes reported in the Z value of the gastrocnemius muscle of mice due to amyotrophic lateral sclerosis were attributable to the decrease in the diameter of the muscle cells, and those due to growth were attributable to the increase in the diameter of the muscle cells and size of the whole muscle. The α-relaxation observed in the dissected samples of the muscles could be explained by the deviation of the direction of the external electrical fields from the ideal longitudinal and transversal directions.