Progression to Diabetes Determined by a Slow Manifold

This is supplementary material for a paper in review at SIAM J. Life Sci.Mathematical models support the concept that glucose homeostasis depends on a balance between insulin sensitivity and the ability of pancreatic beta cells to secrete an appropriate amount of insulin (beta-cell function). When beta-cell function is inadequate, type 2 diabetes (T2D) may eventually develop. The product of insulin sensitivity and beta-cell function, known as the disposition index (DI) is a clinically validated measure of diabetes risk or progression. Level sets in the plane of beta-cell function vs insulin sensitivity are curves of constant glucose. Here we show that this DI plane is a phase plane of the slow variables in the model of Topp et al (PMID: 11013117). The stable manifold of the saddle point in this plane defines the threshold for progression to T2D. In contrast, clinical diagnostic cut points defined in terms of glucose (because insulin resistance and beta-cell function are not easily measured) are not true thresholds. Matlab codes for Figures 2 - 9 are contained in the posted zip file.