A New General Glucose Homeostatic Model using a Proportional-Integral-Derivative Controller

Abstract

The glucose-insulin system is a challenging process to model due to the feedback mechanisms present, hence the implementation of a model-based approach to the system is an on-going and challenging research area. A new approach is proposed here which provides an effective way of characterising glycaemic regulation. The resulting model is built on the premise that there are three phases of insulin secretion, similar to those seen in a proportional-integral-derivative (PID) type controller used in engineering control problems. The model relates these three phases to a biological understanding of the system, as well as the logical premise that the homeostatic mechanisms will maintain very tight control of the system. It includes compartments for insulin, glucose, insulin action and a compartment to simulate an integral function of glucose.Structural identifiability analysis was performed on the model to determine whether a unique set of parameter values could be obtained from the available observations, which would allow meaningful conclusions to be drawn from parameter estimation. Although two parameters - glucose production rate and the proportional control coefficient - were found to be unidentifiable, the former is not a concern as this is known to be impossible to measure without a tracer experiment, and the latter can be easily estimated from other means. Subsequent parameter estimation and the model simulations have shown good agreement with respect to real data.