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 states for insulin, glucose, insulin action and a state 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 identidied from the available observations, which should permit 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 ex- * Principle corresponding author * * Corresponding author

Wherefore Art Thou, Homeo(stasis)? Functional Diversity in Homeostatic Synaptic Plasticity

“…Although such engineering models have been conceptually applied to homeostatic behavior of physiological systems [13–15] including neural ones [16, 17], in this paper we will systematically examine the literature via the lens of closed-loop control to explicate the abundant body of existing data. In a closed-loop control system, a sensor monitors system output and feeds the information back to a controller which adjusts one or more control parameters to maintain output at a desired level.…”

Characterisation of linear predictability and non-stationarity of subcutaneous glucose profiles

“…9 The trend was derived as a level connecting local minima and by taking into account the fact that there is no food intake during night time. Prandial events can be considered as responses to glucose intake and a number of mathematical models exist [25,26] [25]. Matlab function nlinfit, which performs nonlinear square regression, was used for fitting.…”

The Artificial Pancreas

“…Although P/PD controllers may appear empirical, they do have a basis in physiology, as illustrated by the fitting of intravenous glucose tolerance and hyperglycemic clamp data using proportional-integral-derivative control for insulin secretion (8). An integral control function has thus been added:This control component provides the second-phase response to glucose excursions, such as those following meals.…”