Seminar in PSA 102

ABSTRACT

Title: Modeling Pathways to Diabetes through Dynamical and Statistical Approaches 

 By:    Clint Mason, Department for Mathematics and Statistics

The dynamical modeling of glucose and insulin has attempted to explain rising glucose levels in those with diabetes. These models have recently been modified to account for changes in insulin production due to Beta cell dynamics. The current Beta-I-G model (Topp, 2000) provides for the possibility of rich dynamics in the glucose system. While the previous theoretical models have been used to approximate gradual transitions to diabetes over a long time scale, this may not be the true pathogenetic scenario. Distinctly linear transitions to a diabetic state are relatively unobserved by widespread glucose measurements (OGTT & FPG) in biennial data. Population studies estimate the "average" linear transition rate between different glucose levels. However, these averages ignore possible nonlinear transition processes, and may grossly underestimate the actual "jumping time" to a diabetic state. The Beta-I-G model may permit such a "rapid jump" scenario, and data collected by NIH and the Gila River Health Care Corporation on the Pima Indian population may support this hypothesis.