The distribution of membrane current in nerve with longitudinal linearly increasing applied current

The distribution of membrane current in three models of nerve, when a longitudinal, linearly increasing current is applied, is derived. For the simple core conductor model it is shown that, if the region over which such a current is applied is large compared to the space constant of the model, the membrane current in the mid-portion of the region is a constant, independent of the distance, the time following the application of the current, and the impedance of the membrane. The effect of nonlinear membrane electrical properties is discussed. It is further shown that these conclusions apply equally to the case in which the simple model is surrounded by another concentric sheath (the double cable model). In this case the impedance of the sheath does not influence the membrane current in the mid-polar region. Finally, it is shown that the form of the solution for the saltatory model, for this type of applied current, is identical with that for the simple model.