Some Physico-Mathematical Aspects of Nerve Conduction

Abstract

It has been shown previously by the author that, from the physical point of view, the process of propagation of the nerve impulse is essentially different from the propagation of other kinds of disturbances usually studied in physics. Instead of being described by a differential equation, this type of propagation leads to a simple integral equation. In the domain of the inorganic similar types of propagation are met in the spread of activation on the surface of passive metals. In the present paper the problem of such types of propagation is treated mathematically for two different cases. In the first case it is assumed, that the nerve is electrically uniform all along its length. In this case the final formula for the velocity of propagation reduces to a rather simple expression which applied to the ischiadicus of the frog, leads to a value of 15 meters per second for the velocity of propagation. In the second case the nerve sheath is assumed to be completely insulating, except at the Ranvier nodes, where its continuity is broken, so that the electrical properties of the nerve vary periodically along its length. For the second case a more complicated formula is obtained, which reduces to the first one, when the distance between the nodes tends to zero. Effects of possible distributed capacity are briefly discussed.