Biomedical Engineering Reference
In-Depth Information
model
, imparting some finite value for the
D
N
number that yields asymmetric outflow
dilution curves.
32
,
33
The three models have been extended to include the sinusoidal
transmembrane barrier
34
−
38
for a description of the hepatic clearances of solutes.
Other hepatic clearance models include the enzyme-distributed model,
39
the series-
compartment model,
40
the zonal-compartment model,
14
and Goresky's model that
describes variable capillary transit times and barrier-limited transport.
41
Zonal het-
erogeneities of enzymes and transporters
13
,
42
,
43
are additional variables that need to
be considered in hepatic drug clearance model. This is particularly important for
highly extracted compounds in which cellular substrate concentration is maintained
low and enzymes and transporters compete for the substrate.
In the absence of a barrier and futile cycling, the important equations detailing the
steady-state extraction of the models are for the well-stirred model,
f
u
CL
int
f
u
CL
int
+
E
=
(1)
Q
for the parallel-tube model,
e
−
f
u
CL
int
/
Q
E
=
1
−
(2)
and for the dispersion model,
e
−
[
f
u
CL
int
/
Q
+
(
f
u
CL
int
/
Q
)
2
D
N
]
E
=
1
−
(3)
where
f
u
is the unbound fraction in the vasculature (plasma or blood with rapid
drug equilibration), CL
int
the total intrinsic clearance (sum of
V
max
/
K
m
or intrinsic
clearances for metabolism and excretion under first-order conditions),
Q
the blood
flow rate and
D
N
the dispersion number. The equations have been extended to include
transport barriers. For the well-stirred model,
f
u
CL
influx
CL
int
Q
CL
efflux
+
=
E
(4)
+
CL
int
(
Q
f
u
CL
influx
)
for the parallel tube model,
e
−
f
u
CL
int
CL
influx
/
[
Q
(CL
int
+
CL
efflux
)]
E
=
1
−
(5)
and for the dispersion model,
e
−
[(1
−
√
(1
+
4D
N
R
N
))
/
(2D
N
)]
E
=
1
−
(6)
where the efficiency number
R
N
contains terms pertaining to unbound fraction
f
u
, the
total intrinsic clearance CL
int
, and the influx and efflux clearance parameters CL
influx
and CL
efflux
, respectively:
f
u
CL
int
CL
influx
Q
(CL
efflux
+
R
N
=
CL
int
)
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