Determination of diffusion and permeability coefficients in muscle

A theory is presented for the study of diffusion in heterogeneous tissue-like structures. It is applicable to a common type of measurement in which the change of the amount of substance remaining in the tissue is determined as the substance diffuses from the tissue into an adjacent medium, for instance, Ringer's solution. The main objective of this paper is to obtain a method for the calculation of the diffusion coefficient in the intercellular space and of the permeability coefficients between this space and the cells, based on the type of measurement mentioned above. Although the fundamental ideas upon which the theory is based are applicable to any type of tissue, the formulae derived are limited to the case in which the cells form a flat bundle of parallel fibers. The theory is applied to the experimental results of E. J. Harris and G. P. Burn on diffusion of sodium in the sartorius muscle of the frog. We find that if we know the ratio of the cellular and intercellular volumes of the muscle the ratio of the equilibrium concentrations of sodium outside and inside the cells can be determined. A very simple mathematical analysis of the experimental relation between the amount of substance diffusing out of the muscle and the time of diffusion gives us this ratio. The ratio of the equilibrium sodium concentrations in the case of the sartorius frog muscle is between about 10 and 30, depending on the muscle used. The same mathematical analysis makes it possible to obtain the permeability coefficients of muscle fibers through simple calculations, if their sizes are known. The permeability coefficients for the experimental work mentioned above using sodium are 1.25 to 11.5×10⁻⁸ cm/sec for the flow into the fibers and 3.2 to 16×10⁻⁷ cm/sec for the flow in the opposite direction. The determination of the diffusion coefficient in the intercellular space is more laborious and yields only an order of magnitude: 10⁻⁶ cm²/sec.