Page 114 - The Toxicology of Fishes

94 The Toxicology of Fishes

CL int, = CL int f u (3.15)
u
where
CL int = CL h ( − E) (3.16)
1
and
E = CL Q (3.17)
h
Given values for CL , f , and Q, questions can then be answered about how CL , E, and F (oral
h
int
u
bioavailability) will change if a change occurs in hepatic blood flow, plasma protein binding, or hepatic
metabolism activity. The useful working equations for this model are:
+
E = f CL int, u ( Q f CL ) = CL ( Q CL ) (3.18)
+
u
int
int,
u
int
u
CL h = Qf CL int, u ( Q f CL ) = QCL ( Q CL ) (3.19)
+
+
u
u
int
int
u
int,
The letter F is commonly used to represent the fraction of an oral dose that enters the systemic circulation
and has two contributing parts: F , which represents the fraction of the dose that is absorbed from the GIT
ab
into the blood, and F , which represents the fraction of the absorbed dose that escapes elimination by the
fp
liver. The overall bioavailability of an orally administered compound is the product of these two fractions:
F = F F (3.20)
ab fp
F can also be calculated from CL , f , and Q using the following relationship:
u
int
fp
(
Q Q f CL ) =
+
F fp =− E = ( + u int, u Q Q CL ) (3.21)
1
int
The independent variables in Equations 3.18, 3.19, and 3.21 are CL int,u , f , and Q. The dependent variables
u
are E, CL , and F . This is an extremely important concept and is reinforced by the diagram shown in
h
fp
Figure 3.19.
The appropriate value to use for Q depends on the reference region. If the reference region is whole
blood, then Q should be the whole blood flow to the liver; if plasma, then plasma flow should be used.
If the external water is the reference region, then plasma water flow to the liver should be used. In this
latter case, if no binding of toxicant occurred in the exposure water, then CL and CL int,u would have
int
the same value.
The relationships among CL int,u , f , and Q and the dependent variables E, CL , and F are simplified
u
fp
h
when the value of E is small (<0.25) or large (>0.75); for example, for larger E, CL >> Q, and Equation
int
3.19 becomes CL = Q. For some toxicants, the value of E lies between 0.25 and 0.75, and the full
h
CL h f u
Q CL int
E CL int,u
F fp
FIGURE 3.19 Relationships between independent physiological and biochemical determinants (Q, CL int,u , f u ), and depen-
dent pharmacokinetic parameters (CL h , E, F fp ) of the well-stirred hepatic clearance model: Q, hepatic blood flow; CL int,u ,
intrinsic unbound clearance; f u , fraction of toxicant unbound in blood; CL int , intrinsic hepatic clearance; CL h, hepatic
clearance; E, hepatic extraction ratio; F fp , fraction of an oral dose that escapes first-pass elimination. Dashed lines depict
an inverse relationship between variables; solid lines depict a direct relationship between variables.