In vivo measurement of the rate constant of liver handling of glucose and glucose uptake by insulin-dependent tissues, using a mathematical model for glucose homeostasis in diabetic rats

J Theor Biol. 2018 Feb 14;439:205-215. doi: 10.1016/j.jtbi.2017.12.001. Epub 2017 Dec 5.


Diabetes mellitus is a disease that affects glucose homeostasis. The World Health Organization informs that there are over 347 million people in the world with diabetes. The diagnosis and characterization of glucose homeostasis in different metabolic conditions are subjects of great importance with high clinical impact. There are many mathematical models that describe the glucoregulatory system in detail. However, the use of these models is limited because they have a large number of mathematical equations and parameters and they require complex methodologies to estimate of them. This forced to work with average values that decrease the validity of results and the applicability of the models. In this study two mathematical models for rats with diabetes mellitus were developed. The difference between these models and others lies in the possibility of obtaining all parameters for each animal from simple measurements (glucose and insulin plasma levels). Moreover, the models allow to measure in vivo the different physiological processes involved in glucose homeostasis in animals: insulin secretion and its plasma clearance, absorption of insulin from a subcutaneous injection, the liver handling of glucose, intestine absorption of glucose, glucose uptake rate of insulin-independent tissues, glucose uptake rate of insulin-dependent tissues, and renal glucose excretion.

Keywords: Diabetes mellitus; Glucose; Parameter estimation; Simulation.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Animals
  • Biological Transport
  • Blood Glucose / metabolism
  • Computer Simulation
  • Diabetes Mellitus, Type 1 / metabolism*
  • Glucose / metabolism*
  • Homeostasis*
  • Insulin / blood
  • Insulin / metabolism*
  • Liver / metabolism*
  • Models, Theoretical*
  • Rats


  • Blood Glucose
  • Insulin
  • Glucose