A modified technique of the finite-difference method calculations to mimic the four-terminal method measurements of electrical impedance and admittance of skeletal muscles

Abstract

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.