Biomedical Engineering Reference
In-Depth Information
of assessment are necessary. In these cases, both numerator and denominator terms
in (10.9) are integrated with respect to time to obtain total clearance,
Q
Tcle
∞
∫
excretion rate in urine [mass/time]
dt
D
(10.27)
Q
[volume/time]
=
0
=
Tcle
∞
AUC
∫
∞
plasma concentration [mass/volume]
dt
0
where
D
is the intravenous dose given and AUC
is the total area under the curve in
the
C
p
versus
t
profile. This may not be true for other routes of delivery. Neverthe-
less, knowing all the parameters is not relevant in many applications as the main
focus is to obtain information on the distribution and elimination of a therapeutic
agent to facilitate the formulation of optimum dosing guidelines. Hence, a general
form of (10.21) or (10.22) is used
∞
−
At
−
Bt
Ct
()
=
α
e
+
β
e
(10.28)
where
are lumped constants. Equation (10.28) is used to fit the data and
understand few parameters such as apparent volume of distribution, volume of
distribution within the tissue, and clearance rate. Depending upon the magnitude
of
A
relative to
B
, when
t
becomes large and consequently the
e
−
At
in (10.28) be-
comes negligible [Figure 10.6(b)],
α
and
β
α
reduces progressively until it reaches zero. Then
(10.28) reduces to
−
Bt
Ct
()
=
β
e
(10.29)
One could assume that the drug concentration between the plasma and tissue
compartment have reached a pseudoequilibrium phase. Plot of
lnC
p
versus
time
will be a straight line and from the
y
-intercept, the
value can be determined.
Further on, the slope of the line is
B
. Using these values and (10.29), one can calcu-
late various
C
p
(
t
) values for different time points. The new
C
p
(
t
) is represented as
C
*
p
(
t
) to separate from original
C
P
(
t
) values. Then one can plot
ln
(
C
p
β
C
*
p
) with
−
various time points. One can determine the
value from the y-intercept of this line
and A from the slope of the line. This concept is the basis of “curve striping” (also
referred to as feathering or the method of residual), commonly used for the identifi-
cation of compartmental models. The same equation is also used in many scenarios
if a plot of
lnC
p
versus
time
appears similar to Figure 10.6(b).
α
10.3
Special Cases of Compartmental Modeling
10.3.1 Modeling Dialysis
Kidney function in patients with partial or complete kidney (renal) failure is in-
sufficient to adequately remove fluid (water) intake (resulting in the retention of
fluids that is characterized as edema) and adequately remove excess electrolytes
