Complex Systems

A Complex System Model of Glucose Regulatory Metabolism Download PDF

Perambur S. Neelakanta
Electronic mail address: neelakan@fau.edu

Meta Leesirikul

Zvi Roth

Salvatore Morgera
Department of Electrical Engineering,
Florida Atlantic University,
Boca Raton, Florida 33431

Abstract

Consistent with inherent characteristics of a complex system made of a large number of interacting units having deterministic as well as spatiotemporal attributes, a model is developed to represent the human glucose regulatory metabolism within a complex system framework. Essentially, the mass-flow relations pertinent to sugar transport (in the form of glucose), and sugar regulatory hormones (namely, insulin and glucagon) across various participant parts of the body are depicted as nonlinear (logistic) functions; and hence, the temporal growth of blood plasma glucose concentration as well as the rate of change of such concentration levels are derived and expressed in terms of a Bernoulli-Langevin expression, (which functionally depicts the associated nonlinearity whose spatial order is implicitly dictated by the underlying complexity of the processes involved). Simulated results based on theoretical formulations derived are validated with respect to available clinical data due to Cobelli and Mari [1, 2], whose deterministic model of mass-balance relation pertinent to glucose regulatory metabolism is modified and adapted into complex system considerations. The results illustrate the statistical spread with upper and lower bounds associated with the temporal excursions of glucose concentration and its rate of appearance in blood plasma. The outcome of this study, for example, can find applications in refining predictive control algorithms adopted in closed-loop glucose control regimens (via insulin infusion pumping) prescribed to maintain normoglycemia in Type I diabetic patients.