"Mathematical modeling and identification of the glucose - insulin metabolism"
Mathematical modeling and identification of the glucose - insulin metabolism
Sprache des Titels:
This diploma thesis is concerned with mathematical modeling and identification of the glucose – insulin metabolism of human beings.
The first part of this work gives a short overview over physiological models for the glucose – insulin metabolism found in literature. These physiological models are the Bergman’s minimal model , the model of Sorensen  and the model of C. Dalla Man, R. A. Rizza and C. Cobelli . Furthermore the first part describes some possible extensions to the model  such that physical exercise and insulin injection can be considered in the model . The extensions are based on  and . Simulation results for the original model  and for the model  with the extensions are shown and critically discussed.
The second part of this work is dedicated to the identification of the model  with the extension for the subcutaneous insulin injections. For the identification the extensions for physical exercise are not considered. The identification is done both with simulated data and also with real measured data. The data were collected for an EU project . The most important data are the concentration of glucose in the blood, concentration of insulin in the blood, ingested amount of glucose and injected dose of insulin. The second part of this work also shows comparisons between the real measured data and the signals, which are simulated with the identified model.