A model for the hepatic glucose metabolism based on Hill and step functions

Marcello D'Abbicco ^[1] ; Nicoletta Del Buono ^[1] ; Patrizia Gena ^[1] ; Marco Berardi ^[2] ; Giuseppe Calamita ^[1] ; Luciano Lopez ^[1]
1. [1] University of Bari Aldo Moro
  
  University of Bari Aldo Moro
  
  Bari, Italia
2. [2] Water Research Institute
  
  Water Research Institute
  
  Bari, Italia
Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 292, Nº 1 (15 January 2016), 2016, págs. 746-759
Idioma: inglés
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Resumen
- We propose a system of first-order ordinary differential equations to describe and understand the physiological mechanisms of the interplay between plasma glucose and insulin and their behaviors in diabetes. The proposed model is based on Hill and step functions which are used to simulate the switch-like behavior that occurs in metabolic regulatory variables when some of the threshold parameters are approached. A simplified piecewise-linear system is also proposed to study the possible equilibria and solutions and used to introduce simple theoretical control mechanisms representing the action of an artificial pancreas and regulating exogenous insulin.