Investigating a Novel Model of Human Blood Glucose System at Molecular Levels from Control Theory Point of View

According to the data provided by the World Health Organization (WHO) diabetes has become an endemic of these days. There are several nonlinear models describing the dynamic of glucose-insulin of diabetes mellitus, like the simplest one with only three state variables, also known as the model of Bergman, and the most complex with 19 state variables, the model of Sorensen. Their common characteristic is that they describe type 1 diabetes physiologically. A recently published theoretical model [1] is capable of describing human blood glucose system at molecular levels. This paper is based on its analysis from a control theory point of view with multiple purposes: nonlinear analysis, rank reduction possibilities with physiological explanations, defining physiological working points for further polytopic modeling, analyzing control properties of the linear systems in the defined working points.

[1]  R. Hovorka,et al.  Partitioning glucose distribution/transport, disposal, and endogenous production during IVGTT. , 2002, American journal of physiology. Endocrinology and metabolism.

[2]  M. Morari,et al.  Closed-Loop Control of Blood Glucose , 2007 .

[3]  A. Sherman,et al.  A mathematical model of metabolic insulin signaling pathways. , 2002, American journal of physiology. Endocrinology and metabolism.

[4]  R N Bergman,et al.  Assessment of insulin sensitivity in vivo. , 1985, Endocrine reviews.

[5]  T D Hockaday,et al.  Insulin deficiency and insulin resistance interaction in diabetes: estimation of their relative contribution by feedback analysis from basal plasma insulin and glucose concentrations. , 1979, Metabolism: clinical and experimental.

[6]  A. Isidori.  Nonlinear Control Systems , 1985 .

[7]  L. Mandarino,et al.  Dose-response characteristics for effects of insulin on production and utilization of glucose in man. , 1981, The American journal of physiology.

[8]  J. Peraire,et al.  Balanced Model Reduction via the Proper Orthogonal Decomposition , 2002 .

[9]  Fusheng Tang,et al.  Modeling a simplified regulatory system of blood glucose at molecular levels. , 2008, Journal of theoretical biology.

[10]  S. Wild,et al.  Global prevalence of diabetes: estimates for the year 2000 and projections for 2030. , 2004, Diabetes care.

[11]  R. Bergman,et al.  Physiologic evaluation of factors controlling glucose tolerance in man: measurement of insulin sensitivity and beta-cell glucose sensitivity from the response to intravenous glucose. , 1981, The Journal of clinical investigation.

[12]  E. Mosekilde,et al.  Computer model for mechanisms underlying ultradian oscillations of insulin and glucose. , 1991, The American journal of physiology.

[13]  Hubert Roth,et al.  Glucose appearance in the peripheral circulation and liver glucose output in men after a large 13C starch meal. , 2004, The American journal of clinical nutrition.

[14]  John Thomas Sorensen,et al.  A physiologic model of glucose metabolism in man and its use to design and assess improved insulin therapies for diabetes , 1985 .

[15]  Y. Z. Ider,et al.  Quantitative estimation of insulin sensitivity. , 1979, The American journal of physiology.

[16]  Francis J. Doyle,et al.  Robust H∞ glucose control in diabetes using a physiological model , 2000 .

[17]  R. Gleason,et al.  A Model of Glucose-insulin Homeostasis in Man that Incorporates the Heterogeneous Fast Pool Theory of Pancreatic Insulin Release , 1978, Diabetes.