Shock and Detonation Waves at an Interface and the Collision of Action Potentials

Abstract

Action potentials in neurons are known to annihilate each other upon collision, while there are cases where they might penetrate each other. Compression waves that travel within the plasma membrane of a neuron have previously been proposed as a thermodynamic basis for the propagation of action potentials. In this context, it was recently shown that two dimensional compressive shock waves in the model system of lipid monolayers can nearly annihilate each other upon head on collision when excited close to a phase transition. However, weaker shock waves showed penetration. In general, once the approximation of small perturbation is not valid, compression waves do not interact linearly anymore. While experiments in lipid monolayers demonstrated this principle, a mechanism remained unclear. In this article, we summarise the fundamentals of shock physics as applied to an interface and how it previously explained the observation of threshold and saturation of shockwaves in the lipid monolayer (all or none). While the theory has the same fundamental premise as the soliton model, i.e. the conservation laws and thermodynamics, we elaborate on how the two approaches make different predictions with regards to collisions and the detailed structure of the wave-front. As a case study and a new result, we show that previously unexplained annihilation of shock waves in the lipid monolayer is a direct consequence of the nature of state changes, i.e. jump conditions, within these shockwaves, and elaborate on the consequence of these results for the general understanding of the excitation waves in a thermo-fluids framework.