Mathematical modeling and qualitative analysis of insulin therapies

Math Biosci. 2007 Nov;210(1):17-33. doi: 10.1016/j.mbs.2007.05.008. Epub 2007 May 29.

Abstract

Several insulin therapies are widely in clinical use with the basic strategy that mimics insulin secretion in a normal glucose-insulin endocrine metabolic regulatory system. In this paper, we model the insulin therapies using a delay differential equation model. We study the dynamics of the model both qualitatively and quantitatively. The analytical results show the existence and uniqueness of a stable periodic solution that corresponds to ultradian insulin secretion oscillations. Numerically we simulate the insulin administration based on our model. The numerical simulation results are in agreement with findings of clinical studies.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Activity Cycles
  • Blood Glucose / metabolism
  • Diabetes Mellitus, Type 1 / blood
  • Diabetes Mellitus, Type 1 / drug therapy
  • Diabetes Mellitus, Type 1 / physiopathology
  • Humans
  • Insulin / administration & dosage*
  • Insulin / metabolism
  • Insulin Infusion Systems / statistics & numerical data*
  • Insulin Secretion
  • Mathematics
  • Models, Biological

Substances

  • Blood Glucose
  • Insulin