Water, Energy, Food and Environment
Journal license

Journal

Water, Energy, Food and Environment


Volume
& Issue

Volume 1, Issue 2


Published
on

May 1, 2020


Pages

47-69


DOI

Article

Reactions / Diffusion Mathematical Models for Exploring the Complex Behavior of the Brain

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Authors

Ibrahim Mustafa Affiliation:
Department of Chemical Engineering, Waterloo University, Ontario, Canada. N2L3G1; Biomedical Engineering Dept, Faculty of Engineering, Helwan University, Cairo, Egypt.
, Asmaa Awad Affiliation:
Department of Chemical Engineering, Waterloo University, Ontario, Canada. N2L3G1
, A. Elkamel Affiliation:
Department of Chemical Engineering, Waterloo University, Ontario, Canada. N2L3G1
and Said Elnashaie* Affiliation:
Chemical and Biological Engineering Department, University of British Columbia (UBC), Vancouver, Canada.


Abstract

Enzymes-Reactions Model is used to study: dynamics, bifurcation, and chaos of the acetylcholine neurocycle (ACNC). The effects of feed choline concentrations, Acetylcholinesterase (AChE) activity as bifurcation parameters are studied. It was found that feed choline concentrations are important and have direct effect on ACNC through certain important range of parameters. Detailed bifurcation analysis is carried out in order to uncover important features of the system, such as static/dynamic bifurcation and chaos. These findings are related to the real phenomena occurring in the neurons, like periodic stimulation of neural cells and non-regular functioning of acetylcholine receptors. Results are compared to the results of physiological experiments and other published models. As there is strong evidence that cholinergic brain diseases like Alzheimer's disease (AD) and Parkinson's disease (PD) are related to the concentration of acetylcholine, the present findings are useful for uncovering some of the characteristics of this illnesses/remediation.


Keywords

Acetylcholinesterase, Acetylcholine, Choline, Acetate, Parkinson's disease (PD), Alzheimer's disease (AD), Dynamic behavior, Bifurcation, Chaos


Citation

Mustafa, I., Awad, A., Elkamel, A., & Elnashaie, S. (2020). Reactions / diffusion mathematical models for exploring the complex behavior of the brain. Water, Energy, Food and Environment, 1(2), 47–69. https://doi.org/10.18576/wefej/010205

Published by: Engineering Journals

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