Biomedical Engineering Reference
In-Depth Information
1
1
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0
0
0
20
40
60
80
0
50
100
150
(a)
Time
(b)
Time
FIGURE 7.31
q
4
for the open unilateral system shown in Figure 7.27 for (a) 40 and
(b) 80 compartments. The model is identical to the one shown in Figure 7.29, except
Plots of the response for
K
40
ΒΌ
0.2.
7.8.4 General Multicompartment Model
Although the previous models presented in this section are important, many systems are
more complex and follow the form of a general multicompartment model. Some systems
are composed of subsystems, described in Sections 7.8.1-7.8.3, which are linked together
with transference among subunits. For example, a model
13
that describes thyroid hormone
distribution and metabolism using two mammillary three-compartment models linked
together is shown in Figure 7.32. Mammillary compartments 1-3 describe T3, and mammil-
lary compartments 4-6 describe T4; compartments 1 and 4 are the same space, as are 2 and
5, and 3 and 6. The plasma is represented by compartments 2 and 5, compartments 1 and 4
represent the
fast
tissue (liver, kidneys, lung, heart, and gut), and compartments 3 and 6
represent the
slow
tissue (muscle, skin, and brain).
Fast
and
slow
indicate how quickly the
hormones are synthesized via transfer rates
K
i
0
. Transfer rates
K
41
and
K
63
are used to
f
2
(t)
K
10
K
12
K
23
K
30
q
1
q
3
q
2
K
21
K
32
K
41
K
63
K
40
K
45
K
56
K
60
q
6
q
4
q
5
K
54
K
65
f
5
(t)
FIGURE 7.32
Six-compartment model that describes thyroid hormone distribution and metabolism.
13
See DiStefano and Mori, 1977, in references for original problem development.
