An approximation method for the determination of diffusion and permeability coefficients in nerve trunks

A recently introduced approximation method is applied in order to obtain an expression for the amount of a substance remaining within a nerve at any time, the nerve having been soaked for a long time in a solution containing the substance until the time zero when it is bathed in the same solution but without the substance. The case of a uniform nerve without a sheath leads to substantially the same results as previously obtained by A. V. Hill (1928) for this case. A solution is given for the case of a nerve without sheath but having fibers which are permeable. In this case it is shown how an effective diffusion coefficient for the interstitial fluid can be obtained, as well as the effective inward and outward fiber permeabilities. A solution is given for the case of a nerve with a sheath in which the substance considered does not penetrate the fibers, and it is shown how the effective diffusion coefficients of the sheath and the interstitial fluid can be obtained.