Slides - Automatica - Università degli Studi di Padova
Slides - Automatica - Università degli Studi di Padova
Slides - Automatica - Università degli Studi di Padova
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Analisi (4/4): Modelli Biologici Compartimentali<br />
3.6. DRUG ADMINISTRATION 87<br />
u<br />
V1<br />
b0<br />
k0<br />
k1<br />
k2<br />
V2<br />
(a) Two compartment model<br />
Modelli per sistemi biologici<br />
Proprietà fondamentali<br />
dc1<br />
V1<br />
V2<br />
k03<br />
V3<br />
k31<br />
k13<br />
u1<br />
V1<br />
k64 k54<br />
k06<br />
k05<br />
V6<br />
V4<br />
V5<br />
k46 k45<br />
88 C<br />
b4<br />
u4<br />
b1<br />
k21<br />
k12<br />
(b) Thyroid hormone model<br />
Figure 3.18: Schematic <strong>di</strong>agrams of compartment models. (a) A simple two-compartment<br />
model. Each compartment is labeled by its volume, and arrows in<strong>di</strong>cate the flowGlucose of chemical Pancreas<br />
into, out of and between compartments. (b) A system with six compartments used to study<br />
Insulin<br />
the metabolism of thyroid hormone [God83]. The notation kij denotes the transport from<br />
compartment j to compartment i.<br />
Liver<br />
Stomach<br />
Stomach Tissue<br />
Pancreas<br />
Glucose<br />
in blood<br />
Large<br />
Small<br />
volumes of the compartments. The mass intestine balances for the compartments intestine Liver are Tissue<br />
dt = q(c2 − c1) − q0c1 + c0u, c1 ≥ 0,<br />
dc2<br />
dt = q(c1<br />
0<br />
0<br />
− c2), (a) c2Relevant ≥ 0, body organs<br />
(3.26)<br />
(b) Schematic <strong>di</strong>agram (c) In<br />
Figure 3.19: Insulin–glucose dynamics. (a) Sketch of body parts invol<br />
V2<br />
k02<br />
Glucose [mg/dl]<br />
Insulin [µU/ml]<br />
400<br />
200<br />
0<br />
0<br />
100<br />
50
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