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Mathematical Biosciences and Engineering (MBE)
 

Development of a computational model of glucose toxicity in the progression of diabetes mellitus

Pages: 1043 - 1058, Volume 13, Issue 5, October 2016      doi:10.3934/mbe.2016029

 
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Danilo T. Pérez-Rivera - Department of Chemistry, University of Puerto Rico at Cayey, Cayey, PR 00736-9997, United States (email)
Verónica L. Torres-Torres - Department of Natural Sciences, University of Puerto Rico at Cayey, Cayey, PR 00736-9997, United States (email)
Abraham E. Torres-Colón - Department of Natural Sciences, University of Puerto Rico at Cayey, Cayey, PR 00736-9997, United States (email)
Mayteé Cruz-Aponte - Department of Mathematics - Physics, University of Puerto Rico at Cayey, Cayey, PR 00736-9997, United States (email)

Abstract: Diabetes mellitus is a disease characterized by a range of metabolic complications involving an individual's blood glucose levels, and its main regulator, insulin. These complications can vary largely from person to person depending on their current biophysical state. Biomedical research day-by-day makes strides to impact the lives of patients of a variety of diseases, including diabetes. One large stride that is being made is the generation of techniques to assist physicians to ``personalize medicine''. From available physiological data, biological understanding of the system, and dimensional analysis, a differential equation-based mathematical model was built in a sequential matter, to be able to elucidate clearly how each parameter correlates to the patient's current physiological state. We developed a simple mathematical model that accurately simulates the dynamics between glucose, insulin, and pancreatic $\beta$-cells throughout disease progression with constraints to maintain biological relevance. The current framework is clearly capable of tracking the patient's current progress through the disease, dependent on factors such as latent insulin resistance or an attrite $\beta$-cell population. Further interests would be to develop tools that allow the direct and feasible testing of how effective a given plan of treatment would be at returning the patient to a desirable biophysical state.

Keywords:  $\beta$-cells, diabetes mellitus, computational model, glucose toxicity, dynamical systems, mathematical modeling, mathematical biology.
Mathematics Subject Classification:  Primary: 92B05; Secondary: 92C50.

Received: October 2015;      Accepted: April 2016;      Available Online: July 2016.

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