Bio-medical Ontologies Maintenance and Change Management

The Minimal Model of Glucose Disappearance in Type I Diabetes 297
Fig. 1. Schematic diagram of the integrated model
insulin self-administration during the window, those windows were excluded from
the analysis . The 300 min time frame was chosen, since this time seems appropriate
for an oral glucose tolerance test (OGTT) to reach its steady state.
3 Background
The integrated mathematical model used in this research has been represented in
Fig. 1, where glucose dynamics is described by the well known minimal model
of glucose disappearance [3]. This model consists of two compartments that involve
plasma glucose concentration y1 and the action of insulin x, and is detailed in
Section 3.1.
Since in Type I diabetes there is very little insulin production, plasma insulin is
obtained through the external administration of insulin (fast acting or monomeric)
in the insterstitium. Infused insulin stored in the insterstitial compartment is represented
by qx, qy in the insulin absorption model and qz accounts for the subcutaneous
distribution pool. The dynamics of subcutaneous insulin absorption is being
modelled as detailed later on in Section 3.4, which in turn hands out plasma insulin
concentration y2(t), regarded as an input to the glucose dynamics model. The insulin
infusion rate IR, as recorded in the patient’s log of events, is supplied through
the interstitial compartment.
The integrated model also includes the rate of appearance of absorbed glucose
Ra(t) as an external input following the glucose loads recorded by the patients. This
rate of absorption is obtained through a modelling function subsequently described
in Section 3.3 and represented as input u1(t) in the glucose model.
There are two versions of the minimal model that have been used by the authors
in order to see if both models perform in a similar way for the data under study.
They are the nonlinear classic minimal model developed by Bergman et al. [3] and