Bio-medical Ontologies Maintenance and Change Management

302 M. Fernandez, M. Villasana, and D. Streja
consists of 3 compartments representing the subcutaneously infused insulin pool,
the subcutaneous insulin distribution pool and the plasma insulin space.
In this model, the equations that govern the dynamics for the subcutaneous insulin
absorption are given by:
qx ˙ = IR(t) − k12qx, qx(0)=0 (5)
qy ˙ = k12qx − (k20 + k23)qy, qy(0)=0 (6)
qz ˙ = k23qy − k30qz, qz(0)=0 (7)
y2(t) =qz/V (8)
where IR(t) is the insulin infusion rate expressed in μU/min; qx and qy represent the
insulin quantities in the subcutaneously infused insulin pool and in the subcutaneous
insulin distribution pool, respectively, and are given in μU; qz is the plasma insulin
quantity in μU; k12, k20, k23, k30 are rate constants in min −1 ; y2(t) is the plasma
insulin concentration in μU/ml and V is the plasma insulin volume expressed in ml.
In [18] the constants of this model were estimated by using a nonlinear least
squares method to fit the data obtained in ten Type I diabetic subjects treated with
Pro(B29) human insulin (Insulin Lispro , U-40, Eli Lilly Co., Indianapolis, IN,
U.S.A.), which is a fast acting insulin. To calculate each constant, 0.12 U/kg of
Lispro insulin diluted to the concentration of 4 U/ml with saline was subcutaneously
injected into the abdominal walls of the patients. This experiment resulted in:
k12 = 0.017
k30 = 0.133
k20 = 0.0029
k23 = 0.048
and V was estimated as V = 0.08 ml per body weight in g.
The initial values for this model have been assumed to be qx(0)=qy(0)=qz(0)=
0 in our simulations. However, the patients’ initial condition in each window is
y 2 (μU/ml)
60
50
40
30
20
10
0
0 50 100 150 200 250 300 350
Time (mins)
(a) Injection of 0.12 (U/kg) at t = 0
y 2 (μU/ml)
60
50
40
30
20
10
0
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. 4. Simulation results for plasma insulin concentration y2(t), according to the model by
Shichiri et al.