Nerve signal modelling

Bachelor thesis exploring the governing equations of nerve signals

Most of the thesis was about theoretical background for nerve signal propagation in a nerve axon. So I explained the derivation of Hodgkin-Huxley model from the first principles. Since measurements show accompaning effects to the electrical pulse, they need to be studied as well. The main effect I studied was longitudinal wave in a myelinated axon. For this I used the improved Heimbur-Jackson equation \[ \begin{aligned} u_{tt} &= [(c_{0}^{2} + pu + qu^{2})u_{x}]_x - h_{1}u_{xxxx} + h_{2}u_{xxtt} + a_1 \phi_x \\ \phi_{tt} &= c_1^2 \phi_{xx} - \eta^2 \phi - a_2 u_x. \end{aligned} \] The idea was to study the behaviour of this system of equations. The code that solves and plots graphs for comparisons can be found from .