My BIG Fat Model: Beta Cell Compensation in Type 2 Diabetes

In this work we mathematically explore the biological consequences of the effect of over-nutrition, fat accumulation, and beta-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 beta-cell failure. This mathematical model is based on a previous model that considers glucose-insulin and beta-cell mass dynamics. We incorporated fat (assumed to grow linearly), the direct effect of insulin sensitivity, and the effect of beta-cell sensitivity in our model.  More specifically, we modeled liver fat as having an inverse effect on insulin sensitivity and beta-cell sensitivity with a logistic term.  We assumed that betad-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, beta-cell sensitivity decreases due to beta-cell failure and eventually beta-cells begin to die. The threshold at which beta-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 beta-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.