A simple two-compartment model for analysis of feedback control of glucose regulation

Abstract

The minimal model (MM) is widely used for analyzing glucose-insulin interactions under healthy and diabetic conditions. The MM departs from a two-compartment scheme and involves three states for the concentration of glucose and insulin, and the action of insulin is the remote compartment. Although the derivation of the MM model is tacitly based on plasma and interstitial fluid compartments, the interpretation of the three variables and the underlying parameters is not straightforward. For instance, it is not clear if the glucose concentration corresponds to either the plasma or interstitial fluid compartment. The issue is important given the recent developments in the monitoring of glucose dynamics via interstitial fluid measurements. Specifically, a proper model should include glucose states in both plasma and interstitial fluid compartments to dispose of a suitable framework for, e.g., monitoring and designing feedback control strategies for dealing with diabetes disorders. The present work aims to develop a two-compartment mathematical model for glucose and insulin interactions. The approach is based on mass balances of glucose and insulin in plasma and interstitial compartments. It is shown that the model is reduced to the three-states MM via very restrictive assumptions and the four-states Padova model. Numerical simulations were used to illustrate several typical dynamics linked to glucose-insulin interaction failures. The model allows the analysis of feedback control strategies systematically. For instance, the performance of feedback control strategies involving measurements in both compartments at different sampling frequencies (e.g., cascade control) is analyzed.