ScienceAsia 34 (2008): 077-086 |doi: 10.2306/scienceasia1513-1874.2008.34.077

Modelling Glucose-Insulin Feedback Signal Interchanges Involving β-Cells with Delays

Warunee Sarika^a, Yongwimon Lenbury^a*, Kanchana Kumnungkit^b and Wannapa Kunphasuruang^c

 
ABSTRACT:    In this paper, we studied a mathematical model system of delay-differential equations which describe the dynamic behavior of the glucose-insulin feedback system which involved β-cells, incorporating two time delays, one being the glucose triggered insulin production delay τg, and the other being the hepatic glucose delay τ i. This secretory mechanism was governed by nonlinear and time-delayed feedforward and feedback signal interchanges. Moreover, delayed responses to the changes in β-cell density were incorporated. The model system was analyzed to investigate the effect of delays on the dynamic behavior of the system and the possibility of periodic solution which simulate sustained oscillations frequently observed in the experiments.

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a Department of Mathematics, Faculty of Science, Mahidol University, Bangkok, 10400, Thailand.
b Department of Mathematics, Faculty of Science, King Mongkut’s Institute of Technology Ladkrabang, Bangkok, 10520, Thailand.
c Department of Mathematics, Faculty of Science, Silpakorn University, Nakhon Pathom, 73000, Thailand.

* Corresponding author, E-mail: scylb@mahidol.ac.th

Received 4 Jun 2007, Accepted 19 Oct 2007