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My βIG Fat Math Model: β-Cell Compensation and Type 2 Diabetes

In this work we mathematically explore the biological consequences of the effect of overnutrition, fat accumulation, and β-cell function in a model of the progression of Type 2 diabetes (T2D). More specifically, we focus on the effects of fat mass in the liver and the mechanism underlying the initiation and progression of β-cell failure. This mathematical model is based on a previous model that considers glucose-insulin and β-cell mass dynamics. We incorporated fat (assumed to grow linearly), the direct effect of insulin sensitivity, and the effect of β-cell sensitivity in our model. We assumed that β-cell sensitivity embodies a logistic response by initially increasing as fat accumulates due to the compensatory response triggered by increased glucose levels. As fat continues to accumulate, β-cell sensitivity decreases due to β-cell failure and eventually β-cells begin to die. The threshold at which β-cell compensation fails marks the clinical onset of T2D, which with time can progress to the stage where it is no longer reversible due to severe loss of β-cell mass. Using the theory of dynamical systems we analyze the various stages of T2D, investigate whether weight loss in the pre-diabetic and diabetic stages would reverse T2D, and study when this treatment strategy is no longer effective.

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Javier Baez- Arizona State University
Tracy Gonzalez- St. Mary’s University
Anarina Murillo- Arizona State University
Danielle Toupo- University of Delaware
Rosalıa Zarate- University of California Santa Barbara
Erika T. Camacho- Arizona State University, West