Diabetes Mellitus Modelling Based on Blood Glucose Measurements

Insulin Dependant Diabetes Mellitus(IDDM) is a chronic disease characterized by the inability of the pancreas to produce sufficient amounts of insulin. To cover the deficiency 4-6 insulin injections have to be taken daily. The aim of this insulin therapy is to maintain normoglycemia, blood glucose level between 4-7 mmol/L. To determine the amount and timing of these injections different approaches are used. Mostly qualitative and semiquantitative models and reasoning are used to design such a therapy. In this Master Thesis an attempt is made to show how system identification and automatic control perspectives may be used to estimate quantitative models. Such models can then be used to design optimal insulin regimens. The system was divided into three subsystems, the insulin subsystem, the glucose subsystem and the insulin/glucose interaction. The insulin subsystem aims to describe the absorption of injected insulin from the subcutaneous depots and the glucose subsystem the absorption of glucose from the gut following a meal. These subsystems were modelled using compartment models and proposed models found in the literature. Several black box models and grey-box models describing the insulin/glucose interaction have been developed and analysed. These models have been fitted to real data monitored by a IDDM patient. Many difficulties were encountered, typical of biomedical systems. Non-uniform and scarce sampling, time-varying dynamics and severe non-linearities were some of the difficulties encountered during the modelling. None of the proposed models were able to describe the system accurately. However, all the linear models shared some dynamics, and there is ground to suspect that these dynamics are essential parts of the true system. More research has to be undertaken, primarily to investigate the non-linear nature of the system and to see whether other variables than glucose flux and insulin absorption are important for the dynamics of the system