Evaluation of the cable model for electrical stimulation of unmyelinated nerve fibers

The cable model, used to calculate the membrane potential of an unmyelinated nerve fiber due to electrical stimulation, is reexamined under passive steady-state conditions. The validity of two of the assumptions of the cable model are evaluated, namely that the membrane potential be a function of the axial coordinate only and that the extracellular potential due to the presence of the nerve fiber be negligible. The membrane potential calculated from the passive steady-state cable model is compared with the membrane potential obtained from an analytical three-dimensional (3-D) volume conductor model of a nerve fiber. It is shown that for very small electrode-fiber distances (of only a few fiber radii), both assumptions are violated and the two models give quite different results. Over a wide range of the electrode-fiber distance (about 0.1 mm to 1 cm), both assumptions are fulfilled and the two models give approximately the same results. For very large distances (more than 10 cm, independent of fiber diameter) only the second assumption is satisfied, but a modification of the activating function of the cable model allows to calculate the membrane potential in agreement with the 3-D model.