Mathematic modelling of the enteric nervous network. 5. Excitation propagation in a planar neural network.

A mathematical model of the enteric nervous system (Auerbach's plexus) as a planar neural network has been developed, based on the actual morphological data of its organization. The network is composed of excitatory (cholinergic) and inhibitory (adrenergic) neurones interconnected by polysynaptic channels, formed of the geometrically non-uniform unmyelinated nerve axons. The synaptic zones are modelled as a three-compartment open pharmacokinetics system, i.e., presynaptic terminal, synaptic cleft and postsynaptic membrane where the pharmacokinetic mechanisms of electrochemical coupling are considered. All the chemical reactions of transformation of acetylcholine and adrenaline within them are described by first order Michaelis-Menten kinetics. The propagation of the electrical impulse along the pathways and in the vicinity of the nerve terminal is described by the modified Hodgkin-Huxley equations. The results of numerical simulation of the propagation of excitation within the neuronal chain, inhibitory feedback circuit, and a planar neuronal network under normal physiological conditions and after treatment with cholinergic/adrenergic agonists and antagonists are presented. The model predicts the dose-dependent influence of pharmacological agents on the neural network function.