Parametric Identification of Sorensen model for glucose-insulin-carbohydrates dynamics using evolutive algorithms

Diabetes mellitus (DM) is a disease affecting millions of people worldwide, and its medical care brings an economic wear to patients and public health systems. Many efforts have been made to deal with DM, one of them is the full-automation of insulin delivery. This idea consists in design a closed-loop control system to maintain blood glucose levels (BGL) within normal ranges. Dynamic models of glucose-insulin-carbohydrates play an important role in synthesis of control algorithms, but also in other aspects of DM care, such as testing glucose sensors, or as support systems for health care decisions. Therefore, there are several mathematical models reproducing glycemic dynamics of DM, most of them validated with nominal parameters of standardized patients. Nevertheless, individual patient-oriented models could open the possibility of having closed-loop personalized therapies. This problem can be addressed through the information provided by open-loop therapy based on continuous glucose monitoring and subcutaneous insulin infusion. This paper considers the problem of identifying particular parameters of a compartmental model of glucose-insulin dynamics in DM; the goal is fitting the model response to historical data of a diabetic patient collected during a time period of her/his daily life. At this time, Sorensen model is one of the most complete compartmental models representing the complex dynamics of the glucose-insulin metabolism. This is a system of 19 ordinary differential equations (ODEs), thus the identification of its parameters is a non-easy task. In this contribution, parameter identification was performed via three evolutionary algorithms: differential evolution, ant colony optimization and particle swarm optimization. The obtained results show that evolutionary algorithms are powerful tools to solve problems of parametric identification. Also, a comparative analysis of the three algorithms was realized throw a wilcoxon sign-rank test, in which colony optimization had the better performance. The model obtained with the estimated parameters could be used to in type 1 diabetes mellitus (T1DM) care, such as in the design of full-automation of insulin infusion.