Mathematics of Nerve Signals

Abstract

Mathematical models describing the signals propagating in nerve fibres are described. The emphasis is on the mathematical structures of governing equations while the extremely rich physiological aspects are here not analysed. Based on models of single waves, a joint coupled model is presented which is able to describe the action potential and the accompanying mechanical effects togehter with temperature changes within one system of partial differential equations. The whole signal is an ensemble which includes primary and secondary components. The primary components of a signal are the action potential itself and longitudinal mechanical waves in axoplasm and surrounding biomembrane. These components are characterized by corresponding velocities. The secondary components of a signal are derived from primary components and include transverse displacement of a biomembrane and the temperature change. These secondary components have no independent velocities in the presented model.