Revista de Matemáticas Aplicadas y Computacionales

Spectral Element Simulation of Reaction-Diffusion System in the Neuromuscular Junction

Abstract

Don Liu, Yifan Wang and Mark A DeCoster

Studying the synaptic signal transmission in the neuromuscular junction (NMJ) is central to the understanding of neuromuscular disorders such as myasthenia gravis disease. Investigating the dynamics of acetylcholine and acetylcholine receptors in an NMJ under the conditions of activated enzyme is an important step towards this mission. In this article, we developed a numerical model of high order accuracy for complex geometry to simulate the complex processes in an NMJ cleft. This model has a full description of three-dimensional reaction and diffusion processes with nonlinear reaction source terms and is capable of predicting the concentration rates of acetylcholine with receptors and enzymes. Simulation results agree with experimental measurement of the reported maximum number of open receptors during the course of a normal action potential. The time variation of populations of open receptor as well as concentration rates are investigated and discussed. This model has the potential to further the in depth investigation of dynamics within an NMJ.