Biomedical Engineering Reference
In-Depth Information
2
2
1.5
1.5
1
1
0.5
0.5
0
0
0
5
10
15
20
0
10
20
30
40
(a)
Time
(b)
Time
2
2
1.5
1.5
1
1
0.5
0.5
0
0
0
10
20
30
40
0
50
100
150
(c)
Time
(d)
Time
FIGURE 7.30
Plots of the response for
q
4
for the closed unilateral system shown in Figure 7.28 for (a) 10, (b) 20,
(c) 40, and (d) 80 compartments. A bolus input of 5 to compartment 3 is the only input.
Figure 7.28 (with zero initial conditions and equal transfer rates,
K
¼
2) with input
f
3
(
t
)
¼
5d(
). The response for a model of 10, 20, 40, and 80 compartments is shown in
Figure 7.30 (note the time scale changes for each model). As shown, the number of oscilla-
tions increases as the number of compartments increases, and the steady-state value
decreases. The time it takes for the solute to move through the system also increases as
the number of compartments increases. For 20 compartments and higher, there is essen-
tially no solute left in the compartment after the initial oscillation until the solute flows
through the system.
If the system is open and solute is allowed to move into the environment, the oscillatory
behavior is reduced. Consider the model used in Figure 7.28, with the exception that solute
output to the environment is allowed in compartment 4, with a transfer rate of
t
0.2 (10
percent of the transfer rate among the compartments). Shown in Figure 7.31 is the response
for
K
40
¼
q
4
with 40 and 80 compartments. An oscillatory response is still noted with fewer prom-
inent oscillations as compared with no output to the environment. Also note that the peak
oscillation for the first is much smaller than before. Finally, observe that the steady-state
value is now zero.
