Hyperbolic equations for neuronal membrane deformation waves accompanying an action potential

Experiments show that the propagation of an action potential along an axon is accompanied by mechanical deformations. We describe the mechanisms of the effect using fluid dynamic equations, Laplace's and Hook's laws for surface tension, and Lippmann's law, which relates membrane tension to membrane potential. We derived a minimal, 1-D model, which is a hyperbolic system of equations. Our model qualitatively reproduces the membrane's mechanical deformation evoked by either the propagation of an action potential or the stepwise change of membrane potential. The understanding of the relationship between electrical activity and mechanical deformation provides guidance toward non-invasive imaging of neuronal activity.