Resumen de Uncertainty in Postprandial Model Identification in type 1 Diabetes
Individual patient characterization is key in the creation of a closed loop system for glucose homeostasis. Usage of mathematical models for patient individualization and prediction is not yet performed out of the research environment due to lack of reliable models, and especially because of the low repeatability of the glycaemic response of diabetic patients. This thesis is devoted to the study and application of methods that focus on improving the quality of diabetic patient¿s identi_cation. Data acquisition in diabetes is very restricted due to safety concerns in the diabetic population. It is of great relevance to obtain glucose pro_les that enhance the individualization of the patients and at the same time avoid dangerous drops or increments in the glucose levels. In this work, optimal experiment design was applied to the case of a patients monitoring in several days, using boundaries in the optimization as safety limits for the patient. The outcomes of the experiment design con_rm the importance of separation between meal ingestion and insulin treatment. The use of Continuous Glucose Monitor (CGM) models for both simulation and analysis is a crucial step for the design of robust controllers. In this thesis, two commercial CGM devices where modeled regarding at four signal properties of the error committed in the glucose estimation: 1) An exponential distribution was _tted to the delay, 2) Stationarity of the mean and standard deviation was analyzed and compensated, 3) Auto-correlation was modeled using AR models, 4) Several probability distributions were _tted to the data, resulting the best _t on the normal distribution for both monitors. Uncertainty in the postprandial glucose pro_le, and especially that due to intrapatient variability is the great problem to overcome in experimental identi_cation for diabetes. Patients response drastically change from day to day even when the circumstances are the same in the patient¿s life. In this thesis, this problem was assessed by allocating the uncertainty of the data into interval model¿s parameters. Representative predictions of each patient were achieved in a cross validation experiment for 12 diabetic patients. Finally, one speci_c combination of monitoring periods, corresponding to the real variability displayed by each patient, was found to be optimal for predicting the patient¿s behavior perfectly.
