Bio-medical Ontologies Maintenance and Change Management

y 2 (μU/ml)
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The Minimal Model of Glucose Disappearance in Type I Diabetes 303
2
0 50 100 150 200 250 300 350
Time (mins)
(a) Injection of 0.12 (U/kg) at t = 0
y 2 (μU/ml)
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20
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0 50 100 150 200 250 300 350
Time (mins)
(b) Injection of 0.12 (U/kg) at t = 0 and
basal rate of 0.0212 (U/min)
Fig. 5. Simulation results for plasma insulin concentration y2(t), according to the model by
Wilinska et al.
affected by the amount of insulin supplied in the previous window. Therefore, an
initial zero level in the insulin compartments is regarded as an approximation. The
simulation results can be observed in Fig. 4 for a bolus injection of 0.12 U/kg at
t = 0 and for the same bolus injection plus a basal rate of 0.0212 U/min.
Regarding the validity of this model, a recent publication [19] shows a model
like Shichiri’s model underestimates the post meal peak of plasma insulin, whilst
improvement in the model fit has been enhanced when two absorption channels were
included in a model formulated by Willinska and coworkers [19]. For this reason,
this latter model is being used in the present study in substitution to Shichiri’s model.
This model has plasma insulin represented by a single compartment. Insulin in
the interstitial compartment is decomposed into 2 compartments to describe the
delay in insulin absorption and maintaining two pathways for absorption. The degradation
of insulin is assumed saturable and is modelled by a Michaelis-Menten
functional type. Following the original nomenclature, the model equations can be
formulated as follows:
dQ1a
dt = ku − ka1Q1a − LDa (9)
dQ1b
dt =(1−k)u − ka2Q1b − LDb (10)
dQ2
dt = ka1Q1a − ka1Q2 (11)
dQ3
dt = ka1Q2 + ka2Q1b − keQ3 (12)
LDa = VMAX,LDQ1a/(KM,LD + Q1a) (13)
LDb = VMAX,LDQ1b/(KM,LD + Q1b). (14)
where Q1a and Q1b are in mU and stand for mass of insulin administered through
continuous infusion and bolus injection respectively, Q3 represents insulin mass in
plasma expressed in mU, u is the insulin input in mU/min and LDa and LDb are