Biomedical Engineering Reference
In-Depth Information
(c) Exhaled vapor is in equilibrium with the body fluids.
Hence, by Henry's law (Chapter 2),
P
B
=
k
B
X
B
, which can convert gas
P
B
to liquid
content.
One compartment model is often used to predict the basic parameters such
as clearance rate and apparent volume of distribution. However, the assumption
is that there is immediate distribution and equilibrium of the therapeutic agent
throughout the body, which may not be possible in many scenarios. If distribution
is minimal, the one compartment can be an adequate approximation. If not, the
model is altered to either better fit the data or to a more physiological condition.
For example, when a positron emitting tracer is injected for a PET scan, under-
standing the concentration changes with the tissue is important to assess the utility
of the tracer. In these scenarios, the human body could be treated as a plasma com-
partment (also referred as central compartment) and a tissue compartment (also
referred as peripheral compartment). Although these compartments do not neces-
sarily have a physiological significance, commonly plasma compartment includes
blood and well-perfused organs such as liver and kidney; tissue compartment in-
cludes poorly perfused tissues such as muscle, lean tissue, and fat.
For a bolus intravenous injection directly into the plasma (Figure 10.4), con-
servation of mass principle can be used to arrive at the differential equation for the
system as
dC
()
t
(
)
(10.19)
P
V
=
k V
C
−
k
−
k
V
C
DP
T
DT
T
P
E
DP
P
dt
dC
()
t
()
(10.20)
T
V
=
k
V C
−
k V
C
DT
p
D
p
T
DT
T
dt
where
V
DP
is the apparent volume of distribution in the plasma compartment,
V
DT
is the apparent volume of distribution in the tissue compartment,
C
p
is the con-
centration of the tracer in the plasma,
C
T
is the concentration of the tracer in the
plasma,
k
P
,
k
T
, and
k
E
are rate constants as shown in Figure 10.5. The initial condi-
tions are
C
T
(0)
D
o
/V
p
. Typically, these set of differential equations
can be solved using numerical integration techniques. Nevertheless, solving the
above two differential equations (using the eigenvalue approach), the solutions are:
=
0, and
C
p
(0)
=
C
(
)
(
)
(10.21)
P
0
⎡
−
Bt
−
At
⎤
Ct
()
=
k
−
Be
−
k
−
Ae
⎣
⎦
P
T
T
AB
−
