Deterministic and Stochastic Modeling of Insulin Sensitivity

Diabetes mellitus is a common disease where a person has high blood glucose levels. The disease has two main causes. The first one is inability of the pancreas to produce enough insulin. The second one is the inability of cells to respond to the insulin produced by the pancreas. In type 2 diabetes patients, the body fails to respond to insulin which results in low insulin sensitivity". In this thesis, measurements from Intra Venous Glucose Tolerance Test (IVGTT) for both healthy subjects and type 2 diabetes patients were used together with Bergman's deterministic minimal model (ODE) to estimate the insulin sensitivity based on a nonlinear mixed effect model. In addition to the IVGTT data some basic covariates were included and tested for significance. Type 2 diabetes patients are shown to be less sensitive to insulin than healthy subjects and thus need larger amount of insulin to lower blood glucose level. A linear regression model from the covariates was used for estimating insulin sensitivity but did not give conclusive results. The covariates were included in the nonlinear mixed effect model to achieve better parameter estimates. By incorporating the covariates the estimated standard deviation for insulin sensitivity decreased substantially. An attempt was made to extend the deterministic minimal model to a stochastic differential equation (SDE) model to improve the performance and to get better parameter estimates