Deriving Behaviour of Hodgkin Huxley model with fever dynamics: A computational study

Abstract

A single neuron can be modeled by the set of differential equations. Hodgkin-Huxley (HH) model, the one of the most famous neuron model, can be considered as a dynamical system with four independent variables. Here we studied to reduce the number of differential equation required for conductance based HH model under strong inhibitory noise. Exponential Integrate and Fire (EIF) model, one independent variable, is used as a reduced model of HH model by using current-voltage (I-V) curve of the original model. The required reduction parameters are determined from this curve. The behaviour of HH model and its reduced EIF (rEIF) model are in good agreement in sub-threshold level. Above-threshold behaviour of reduced EIF model and original model compared in terms of threshold voltage under strong inhibitory noise. Our numerical simulations clearly show that sub-threshold behaviour of HH model perfectly reduced to rEIF model