Quantitative and Stability Analysis of Three Time Delays in Glucose and Insulin Oscillations Profile using Artificial Pancreas

Abstract

In the present paper, we extend our attempt of modeling the closed loop control of glucose concentration level by considering three time delays for the proper functioning of artificial pancreas. Several time delays exist in the glucose - insulin regulatory system, the time delays which we are considering in the present study are delay in insulin secretion, delay in inhibition in hepatic glucose production stimulated by insulin and delay in time taken by insulin to reach interstitial compartment to lower glucose level (i.e. glucose utilization delay or insulin action delay). None of the time delay is negligible. Our analytical and numerical results shows that periodic and sustained oscillations of glucose and insulin concentration exists for type 1 diabetic people and delay in insulin secretion may be one of the major possible reason behind the occurrence of ultradian oscillations. Range of all three time delays have been quantified from the simulation of present model, which may be proved very useful in better designing and improved functioning of artificial pancreas.