ANALYSIS OF GLUCOSE REGULATION USING FUZZY CLUSTERING BASED PIECEWISE AFFINE APPROXIMATION APPROACH

Abstract

This paper deals with the analysis of the nonlinear glucose regulation system from its Piecewise Affine (PWA) equivalent Piecewise Affine (PWA) equivalent model. The use of PWA model was motivated by the fact that it has developed as an attractive tool for nonlinear system analysis in recent years, since it allows the use of well developed concepts in the field of linear systems and control theory. The analysis mainly involves the behavioral study of the system at steady state for different types of input and different sets of physiological parameters. The number of affine systems required to represent a nonlinear system is an important consideration in PWA modeling. In this paper, the optimal number of piecewise affine systems is obtained by a technique based on a fuzzy clustering. From the PWA representation, it is possible to determine the equilibrium point (basal condition) of the glucose regulation system quite easily without solving a complex transcendental equation. The presence of a compensating mechanism between insulin sensitivity and insulin secretion is utilized by the PWA model to determine a particular profile (characteristics) for insulin sensitivity for a modified insulin secretion characteristics that would maintain a normal basal glucose level. A condition for the existence of a stable limit cycle of plasma glucose concentration as a function of delay in hepatic glucose production is determined from the model. This allowed determining the point of hopf bifurcation without carrying out extensive simulations, as is done with the existing models. The response obtained from the numerical simulation of the model, is in line with the experimental results.