Biomedical Engineering Reference
In-Depth Information
particularly important role in drug elimination kinetics, hence it garnered special
attention in liver clearance models that can be grouped into three main classes: (a)
well-stirred models, (b) parallel tube models, and (c) distributed tube models. We
briefly compare and contrast these three models and their outcomes based on an
earlier meta-analysis [
56
].
The Well-Stirred Model is the simplest model mathematically but it does not
correspond to liver anatomy. Here the kinetic equation for the drug concentration in
the liver,
C
(
t
)
,isgivenby
V
d
C
)
d
t
=
(
t
Q
(
C
in
−
C
)
−
fCL
int
C
,
(3)
where
Q
is the rate of blood flow,
CL
int
is the internal clearance rate and
C
in
is the
drug concentration at the entrance to the liver. At steady state we find that
QC
in
C
=
fCL
int
=
C
in
F
,
(4)
Q
+
where the coefficient
F
is termed bioavailability which is given by
1
1
F
=
=
X
,
(5)
1
+
fCL
int
Q
1
+
where
X
=
fCL
int
/
Q
. Total hepatic clearance is then defined as
QX
1
CL
H
=
Q
(
1
−
F
)=
X
.
(6)
+
In the Parallel Tube Model each tube (blood vessel) satisfies a plug flow equation
given by
S
d
C
Q
d
C
d
t
+
d
x
=
−
ρ
(
)
(
)
,
x
g
C
(7)
where
describes enzyme distribution and
g
is an enzyme kinetics Michaelis-
Menten term. The linear kinetics in this model simplifies to
ρ
(
x
)
Q
d
C
d
z
=
−
fCL
int
L
,
C
(8)
=
−
(
/
)
with the introduction of the moving variable
z
x
Q
S
t
, such that its solution is
governed by exponential decay
C
in
exp
−
zx
L
C
(
z
)=
.
(9)
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