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Title Stochastic Models and Methods to characterize the Glucose/Insulin System
Author Møller, Jonas Bech
Supervisor Madsen, Henrik (Mathematical Statistics, Department of Informatics and Mathematical Modeling, Technical University of Denmark, DTU, DK-2800 Kgs. Lyngby, Denmark)
Institution Technical University of Denmark, DTU, DK-2800 Kgs. Lyngby, Denmark
Thesis level Master's thesis
Year 2008
Abstract Background: This thesis deals with mathematical models for the glucose/insulin feedback system. These models are based on restructered versions of published models and data obtained from an oral glucose tolerance test (OGTT). This concept, identified as Grey-box modelling is applied to models using C-peptide, and insulin measurements obtained from 174 Caucasian subjects. Parameters are estimated according to a population scheme, which enables a simultaneous estimation for all subjects. As a way to extend proposed models, stochastic differential equations (SDEs) are introduced as identifiers for unmodelled dynamics. Results: Population parameters in different OGTT models based on C-peptide and insulin measurements were succesfully estimated using the commercial software NONMEM VI. A likelihood-ratio test (LRT) showed significant interindividual variability (IIV) for all estimated parameters. Related to this, the estimated noise parameters obtained from the SDE implementation indicate that proposed OGTT models are too simple and should preferably be revised. A special SDE version where residual error is described by an Ornstein-Uhlenbeck (OU) process seem to have good modelling performance based on the autocorrelation function (ACF) of prediction residuals. A beta-cell index derived from an insulin based OGTT model turned out to be significantly correlated with acute insulin response (AIR0−8) measured from the intravenous glucose tolerance test (IVGTT)(r 0.6). Conclusion: Based on obtained results, it is concluded that non-linear mixedeffects (NLME) population OGTT models based on C-peptide and insulin measurements can be succesfully implemented. Extension of insulin models to use SDEs caused better model predictions, lower objective function values, and exact quantification of dynamic system noise. Based on the ACF all models are falsified although the SDEs caused the residuals to be significantly less correlated. It is thus concluded that SDEs seem to be a very promising tool in PK modelling of the glucose/insulin system. Prediction of AIR0−8 following an IVGTT using direct parameters obtained from OGTT models is concluded to have limited precision.
Series IMM-M.Sc.-2008-59
Original PDF ep08_59_net.pdf (5.49 MB)
Admin Creation date: 2008-07-02    Update date: 2008-07-15    Source: dtu    ID: 221238    Original MXD