Modelling the glucose-insulin regulatory system and ultradian insulin secretory oscillations
Catherine
Lloyd
Auckland Bioengineering Institute, The University of Auckland
Model Status
This CellML model runs in both COR and OpenCell however it does not recreate the published results. Glucose and insulin concentrations do not oscillate over time. This is most likely to be due to the lack of time delays in the CellML model (which are currently impossible to represent in CellML, but are required for equation 1 in the paper). The units are consistent. Parameter values have been taken from table 1 and di=0.06 and Gin=0.54 - as in figure 4.
Model Structure
ABSTRACT: In the glucose-insulin regulatory system, ultradian insulin secretory oscillations are observed to have a period of 50-150 min. After pioneering work traced back to the 1960s, several mathematical models have been proposed during the last decade to model these ultradian oscillations as well as the metabolic system producing them. These currently existing models still lack some of the key physiological aspects of the glucose-insulin system. Applying the mass conservation law, we introduce two explicit time delays and propose a more robust alternative model for better understanding the glucose-insulin endocrine metabolic regulatory system and the ultradian insulin secretory oscillations for the cases of continuous enteral nutrition and constant glucose infusion. We compare the simulation profiles obtained from this two time delay model with those from the other existing models. As a result, we notice many unique features of this two delay model. Based on our intensive simulations, we suspect that one of the possibly many causes of ultradian insulin secretion oscillations is the time delay of the insulin secretion stimulated by the elevated glucose concentration.
model diagram
Schematic diagram of the glucose-insulin regulatory system model. The dotted lines indicate that elevated glucose concentration stimulates insulin synthesis and secretion by the pancreatic beta-cells, and also insulin promotes glucose utilisation in muscle, fat and other tissues.
The original paper reference is cited below:
Modeling the glucose-insulin regulatory system and ultradian insulin secretory oscillations with two explicit time delays, Jiaxu Li, Yang Kuang, and Clinton C. Mason, 2006, Journal of Theoretical Biology, 242, 722-735. PubMed ID: 16712872
G
glucose
$\frac{d G}{d \mathrm{time}}=\mathrm{Gin}+1.0\mathrm{f5\_I}+-(1.0\mathrm{f2\_G}+\mathrm{f3\_G}\mathrm{f4\_I})\mathrm{f2\_G}=\mathrm{Ub}(1.0-e^{1.0\frac{-G}{\mathrm{C2}\mathrm{Vg}}})\mathrm{f3\_G}=\frac{G}{\mathrm{C3}\mathrm{Vg}}\mathrm{f4\_I}=\mathrm{U0}+\frac{\mathrm{Um}-\mathrm{U0}}{1.0+e^{-\mathrm{beta}\ln (1.0\frac{I}{\mathrm{C4}(\frac{1.0}{\mathrm{Vi}}+\frac{1.0}{E\mathrm{ti}})})}}\mathrm{f5\_I}=\frac{\mathrm{Rg}}{1.0+e^{\mathrm{alpha}\frac{I}{1.0\mathrm{Vp}-1.0\mathrm{C5}}}}$
I
insulin
$\frac{d I}{d \mathrm{time}}=1.0\mathrm{f1\_G}-\mathrm{di}I\mathrm{f1\_G}=\frac{\mathrm{Rm}}{1.0+e^{\frac{\frac{\mathrm{C1}-G}{1.0\mathrm{Vg}}}{\mathrm{a1}}}}$
pancreas
insulin
glucose
beta cell
ultradian oscillations
keyword
Li et al.'s 2006 mathematical model of the glucose-insulin regulatory system and ultradian insulin secretory oscillations with two explicit time delays
pancreas
The University of Auckland, Auckland Bioengineering Institute
Modeling the glucose-insulin regulatory system and ultradian insulin secretory oscillations with two explicit time delays
242
722
735
c.lloyd@auckland.ac.nz
The University of Auckland
Auckland Bioengineering Institute
Catherine Lloyd
Clinton
Mason
C
Journal of Theoretical Biology
Jiaxu
Li
2007-06-21
16712872
2006-10-07
This is the CellML description of Li et al.'s 2006 mathematical model of the glucose-insulin regulatory system and ultradian insulin secretory oscillations. Note that the two time delays - tau1 and tau2 - included in the original published model have not been included in the current CellML description of the model. At present, there is no way for the CellML to handle these delays.
Yang
Kuang
Catherine
Lloyd
May