Biomedical Engineering Reference
In-Depth Information
Illustrated in Figure 7.23 is a plot of the quantity in each compartment. While it is difficult to
see the oscillations, the first peak is evident by the overshoot or undershoot. To determine the time
at peak undershoot for
q
3
, we use the technique of Section 2.9.2 by finding the time that satisfies
@
q
3
@
t
¼
0, which gives
T
p
3
¼
1
:
21
:
Similarly,
T
p
¼
1
:
81 for both
q
1
and
q
2
.
6
5
4
q
3
3
2
q
1
q
2
1
0
0
0.5
1
1.5
2
2.5
3
Time
FIGURE 7.23
Illustration of the quantity in each compartment in Example Problem 7.14.
7.7.3 Source Compartment
In Section 7.5.1, a source compartment in a two-compartment model was described as
one that only has output to other compartments, without any inputs from other compart-
ments. A source compartment also appears in three-compartment models, whose output
is solved independent of the other compartments as before.
The following example involves a three-compartment mammillary model with a source
compartment, as illustrated in Figure 7.24. The body is now divided into the digestive sys-
tem, plasma, and the tissues to more accurately depict their behavior.
f
1
(t)
K
12
K
32
q
1
q
2
q
3
K
23
K
20
FIGURE 7.24
Illustration for Example Problem 7.15. Compartment 1 is the digestive system, compartment 2 is
the plasma, and compartment 3 is the tissues.
