Applied Mathematics Seminar-The Mathematical Structure of Diabetes on a Slow Manifold

Title: The Mathematical Structure of Diabetes on a Slow Manifold 
Speaker: Dr. Joon Ha
Affiliation: NIH and GWU
Date and Time:Monday, March 4, 4:00pm-5:00pm
Place: Rome 730

Abstract: Type 2 diabetes (T2D) is a chronic disorder in glucose homeostasis, caused by both genetic and environmental factors. A common form of pathophysiology of the disease is the failure of insulin-secreting pancreatic β-cells to increase levels of insulin, demanded mainly by obesity and aging. Such increased insulin levels are utilized to maintain a normal range of blood glucose concentration. Blood glucose sharply rises at the onset of the disease, as clinically observed, suggesting that there exists a threshold in glucose homeostasis. Using a model of T2D pathogenesis, we found that the threshold is not solely determined by glucose concentration, but corresponds to the crossing of a separatrix in the plane of insulin sensitivity and beta-cell mass, which is the phase plane of the slow subsystem of the model. The product of sensitivity and mass corresponds to the disposition index (DI), which is frequently used in clinical trials to quantify diabetes risk. This finding highlights that a dynamic interaction of insulin secretion and sensitivity plays a major role in progression to diabetes. Furthermore, the threshold formed in the DI plane addresses well how both genetic and environmental factors contribute to developing diabetes. These insights will aid in applying the mathematical model of progression to diabetes to clinical studies of personalized medicine.