Biomedical Engineering Reference
In-Depth Information
7.6.1 Source Compartment
A compartment that only outputs to other compartments, without any inputs from other
compartments, is called a source compartment. A source compartment has an input
).
This type of compartment is simply a one-compartment model that can be solved indepen-
dently of the other compartments in the system. The output of the source compartment is
an exponential decay, as described in Section 7.5. While in many situations, the source com-
partment does not send the solute to the environment, it is perfectly fine for a source
compartment to do so.
Using the model shown in Figure 7.15, a source compartment exists if either
f
(
t
K
21
is
zero. For repeated roots in a two-compartment model, a source compartment must be one
of the compartments and (
K
12
or
K
10
þ
K
12
).
In Example Problem 7.8, the digestive system is introduced as a source compartment. By
including a digestive system component, the solute is not instantaneously delivered into the
plasma but is slowly released from the digestive system into the plasma through a bolus
input.
K
20
þ
K
21
) must equal (
EXAMPLE PROBLEM 7.8
Consider the two-compartment model shown in Figure 7.17 with the ingestion of a bolus solute
in the digestive system and removal of the solute via metabolism and excretion in urine. Solve for
the plasma concentration.
Solution
This model has a source compartment. Rather than solving the problem with a bolus input,
the initial condition is changed to
q
2
(0) with no input. The conservation of mass for each compart-
ment is
q
1
¼
K
21
q
2
K
1
M
þ
K
1
U
ð
Þ
q
1
ð
7
:
53
Þ
q
2
¼
K
21
q
2
ð
7
:
54
Þ
Digestive
System
q
2
K
21
K
1M
K
1U
q
1
Metabolized
Urine
Plasma
FIGURE 7.17
A two-compartment model with realistic ingestion of solute and removal from the plasma by
metabolism and excretion in urine. It normally takes about 30 minutes to pass through the digestive system.
