Physiological analysis on oscillatory behavior of glucose-insulin regulation by model with delays

In artificial pancreas, glucose level measurement and insulin infusion are often implemented in the subcutaneous tissues. Understanding the dynamics of glucose and insulin in the subcutaneous tissues is important in the regulation of blood glucose level. We propose a new two-compartmental model of glucose-insulin interaction with two explicit delays that can study the interaction of glucose in different organs and the oscillatory behavior of the glucose-insulin system. The glucose and insulin space are split into plasma compartment and interstitial fluids compartment, respectively. The four m parameters of insulin dynamics and the two delays are analyzed for their influence on the glucose-insulin regulatory system. The ranges of the six parameters are estimated for sustaining the oscillation of glucose and insulin, and ranges for different subjects are discussed based on simulation results. The effect of these parameters on the oscillatory system is related to diseases and irregular blood glucose level. The lag between glucose and insulin in the two compartments has provided an insight on the distribution and metabolism of glucose and insulin in quick- and slow-equilibrating organs and tissues. We have reported in this paper, a model that can effectively deal with concentration of glucose and insulin in the interstitial compartment. This is important for the development of artificial pancreas.