alexa Spectral Element Simulation of Reaction-Diffusion System in the Neuromuscular Junction | OMICS International | Abstract
ISSN: 2168-9679

Journal of Applied & Computational Mathematics
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Research Article

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

Don Liu1*, Yifan Wang1 and Mark A DeCoster2

1Mathematics and Statistics, Louisiana Tech University, Ruston, LA 71272, USA

2Biomedical Engineering, Louisiana Tech University, Ruston, LA 71272, USA

*Corresponding Author:
Don Liu
Mathematics and Statistics, Louisiana Tech University
Ruston, LA 71272, USA
Tel: 318 257 4670
E-mail: [email protected]

Received date: August 18, 2013; Accepted date: September 12, 2013; Published date: September 18, 2013

Citation: Liu D, Wang Y, DeCoster MA (2013) Spectral Element Simulation of Reaction-Diffusion System in the Neuromuscular Junction. J Appl Computat Math 2: 136. doi: 10.4172/2168-9679.1000136

Copyright: © 2013 Liu D, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Abstract

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.

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