Electrical interaction of parallel non-myelinated nerve fibres-I. Change in excitability of the adjacent fibre

We consider the passage of nerve impulses along the fibres located in the direct proximity of each other and bathed by a restricted volume of conducting fluid. A set of equations is derived for the differences in membrane potentials and its solution found. For each fibre we have obtained two steady solutions corresponding to impulses spreading at different speeds. One of these impulses is stable and the other unstable. We have analysed in detail the case in which the pulse of nervous excitation spreads only over one of the fibres and the second remains passive. In this period the wave of change in the membrane potential spreads over the second fibre so that at first the fibre is hyperpolarized, then depolarized and finally, again hyperpolarized. Thus, the threshold of excitability of the second fibre at first increases, then falls and finally, again rises. Such a change in excitability has been experimentally observed by Katz and a number of other authors. The conditions in the second region when the threshold of excitability is lowered are analysed. If it falls to zero, than spontaneous excitation of this fibre occurs. Analysis has shown that such excitation in normal conditions is practically impossible; it may only occur when the threshold of excitability of the second fibre is artificially reduced, for example, as a result of damage or treatment with special chemical substances.