Periodic pressure waves and transmembrane wavefronts in an electromechanical nerve model

We show that axoplasmic pressure waves governed by the improved Heimburg–Jackson hydrodynamic equation evolve as periodic soliton pulses, in which the membrane capacitance effectively ensures the coupling between transmembrane voltage (modeled by the modified Hodgkin–Huxley cable equation) and the pressure waves. Time independent wavefronts that serve as steady state solutions of the transmembrane voltage are analytically obtained, with it threshold values vital in determining wavefronts propagation in the entire nerve fiber. An increase in numerical value of the membrane coupling coefficient generally decrease the amplitude and speed of the propagating electromechanical wavefronts, thereby leading to the effective control of neuronal information and other mechanosensory processes. This work finds application in the field of anesthetics because the amplitude and speed of propagating wavefronts which transmit pain, can be controlled by varying the parameters of the system.