Euler-Lagrange equations and Noether’s theorem of multi-scale mechano-electrophysiological coupling model of neuron membrane dynamics

Noether’s theorem is applied into a multi-scale mechano-electrophysiological coupling model of neuron membrane dynamics. The Euler-Lagrange equations in generalized coordinates of this model are deduced by the nonconservative Hamilton principle. The Noether symmetry criterion and conserved quantities based on the Lie point transformation group are given. The influence of external non-potential forces and material parameters on the forms of Noether conserved quantities is detailed discussed, which indicates that the conserved quantities are very depending on the loading rate and mechanical parameters of the membrane.