Modelling and sensitivity analysis of neuronal signal transmission under mechanical loading

Purpose: The study of the neuronal structure of the nervous system is difficult due to the complexity and the occurrence of interactions between structures at different levels of hierarchy. The aim of the present research was to develop a mathematical model of signal transmission by a neuron, taking into account the structure of neurons, and to analyse the sensitivity of model parameters in the scope of interaction of mechanical, biochemical and electrochemical phenomena in the context of disturbances of nerve signals caused by overloads.

Methods: To modelling of the potential action then Hodgkin and Huxley (HH) model was used. The model consists of four coupled differential equations: one partial differential equation, which describes the temporal and spatial variation of the membrane potential, and three ordinary differential equations, which represent the dynamics of voltage-gated ion channels. The HH model consists of four coupled differential equations: one partial differential equation, which describes the temporal and spatial variation of the membrane potential, and three ordinary differential equations, which represent the dynamics of voltage-gated ion channels. This model was solved numerically by the finite difference method.

Results: The results indicate on change of the action potential for a nerve cell activated by a continuous electrical stimulus, assuming high conductivity of the Na₊ and K₊ channels. According to the presented model the ion channels respond to pressure, what modulate the permeability of the neuronal membrane for ions.

Conclusions: The results of the analyses suggest that pressure above 1.4 kPa can disrupt the normal functioning of nerve cells, leading to serious health consequences. In addition, a load of nerve cells, less than 1%, can cause disorders in the functioning of the nervous system. As a result, this mechanism leads to damage to nerve cells, disorders in the conduction of nerve impulses and affects the functioning of synapses.