Bio-medical Ontologies Maintenance and Change Management

298 M. Fernandez, M. Villasana, and D. Streja
the linear approximation proposed by Fernandez et al. [15]. Their equations are
described in the next sections.
3.1 The Classic Minimal Model
The interaction between glucose and insulin has been modelled using the minimal
model (MM) of Bergman et al. [3]. This model includes two compartments and its
uniquely identifiable parameterisation is described by:
˙y1 = −SGy1 − xy1 + p0 + u1(t), y1(0)=y10 (1)
˙x = −p2 [x − SI (y2(t) − y20)], x(0)=0 (2)
where y1 (mg/dL) is glucose concentration in plasma, x (1/min) is insulin action,
y2(t) (μU/ml) is insulin plasma concentration, y10 is basal glucose concentration, y20
is basal insulin concentration, u1(t) (mg/dL per min) is external glucose, p2 (1/min)
describes insulin action, p0 (mg/dL per min) is the extrapolated hepatic glucose production
at zero glucose concentration and SG (1/min) and SI (1/min per μU/ml) are
parameters of glucose effectiveness and insulin sensitivity respectively.
The model has been written so that the constants SG and SI are physiologically
meaningful. In this case, SG measures the effect of glucose on its own disappearance,
while SI measures the effect that insulin has on the disposal of glucose.
Model output is given by the concentration of glucose in blood y1. Inputs to this
model include the extrapolated hepatic production of glucose given by p0 = SGy10
from steady state constraints and two external inputs which in the present study are
represented by:
1. The plasma insulin y2(t) present at time t, due to the injection of monomeric
insulin analogues subcutaneously, where y2(t) is obtained from the model of
absorption formulated by Willinska and coworkers [19] and described in
Section 3.4.
2. The rate at which the external (ingested) glucose is absorbed u1(t)=Ra(t)/V1 ×
10 2 ,whereV1 (ml) is 20% of the patient’s body weight [6]. The rate of absorption
Ra(t) is estimated from the model of glucose absorption proposed by
Lehmann and Deutsch [16] as presented in Section 3.3.
Initial values for parameters SG and SI of the MM were taken from [5] for the
normal man after an OGTT/MGTT. The initial value of p2, the insulin action parameter,
was taken as reported for the IVGTT in the normal man [8].
3.2 The Linear Minimal Model
This model is formally equivalent to the nonlinear minimal model presented by
Bergman et al. in 1979 [3] and has been successfully validated in previous studies,
including Type I [10, 14, 9] and Type II [15, 12] diabetic patients. It has the advantage
of its linear structure which makes it simpler and a good candidate for the
closed loop control of glucose.