Comparison of Hodgkin Huxley model and Poisson Nernst Planck equations

• Main Authors: Bo-Yun Chen, 陳博允
• Other Authors: 林太家
• Format: Others
• Language: en_US
• Published: 2019
• Online Access: http://ndltd.ncl.edu.tw/handle/sw4uru

碩士 === 國立臺灣大學 === 應用數學科學研究所 === 107 === This thesis presents a dynamic simulation of intracellular and extracellular ionic concentrations and electric potential, then create an action potential, which is generated by a difference of the electrochemical potential between two sides of a cell membrane. Ion species including Sodium, Potassium and Chlorine. This simulation would involve Poisson-Nernst-Planck (PNP) system and Hodgkin–Huxley (HH) model. The former gives a standard model for describing behaviors of ionic diffusion and electrophoresis. The latter gives a transformation between mechanism of ion channels and a circuit. We want to combine and compare the results of these two models, then try to verify that the PNP equations can reduce to the HH model. In this study, methodologies are based on finite volume method and pseudospectral method for space discretization. After changing the semi-discrete scheme to a system of ODE by method of lines(MOL), we use ode15s solver on MATLAB to handle for time integration.