Page 113 - The Toxicology of Fishes

Toxicokinetics in Fishes 93

Q
C a

C v

CL int
FIGURE 3.18 Well-stirred model of the liver. The liver is represented as a well-stirred volume supplied by a blood flow
of Q which contains chemical at a concentration of C a . The concentration of chemical inside the liver and in blood exiting
the liver is C v , and the activity of metabolizing enzymes is represented by CL int .

–dX/dt = QEC a (3.10)

Because (dX/dt)/C is equal to CL , it is apparent that CL = QE. Thus, CL is that part of the hepatic
a
h
h
h
blood flow that is totally cleared of toxicant.
With this model, the drug concentration in the liver is equal to C . Because the rate of elimination is
v
controlled by both Q and by the capacity of hepatic metabolizing enzymes, it is useful to separate these
two influences. This can be accomplished by defining the intrinsic hepatic clearance (CL ). The CL int
int
is the rate of toxicant elimination divided by the toxicant concentration in the liver; that is, the concen-
tration in contact with metabolizing enzymes:
–dX/dt = CL C = CL C v (3.11)
int
a
h
and
CL int = CL C C v = CL h ( − E) (3.12)
1
h
a
The rate of chemical elimination by the liver is therefore proportional via the hepatic clearance to the
toxicant concentration entering the liver or via the intrinsic hepatic clearance to the toxicant concentration
leaving the liver.
A more general model for hepatic clearance that accounts for the possibility of chemical binding to
plasma proteins may be written by defining a new reference concentration, the unbound toxicant
concentration in the liver (C ), and a new clearance parameter, the intrinsic unbound hepatic clearance
v,u
(CL int,u ). Accounting for plasma binding, the rate of elimination may be written as:
f C
–dX/dt = CL int,u C = CL int,u u v (3.13)
v,u
where f is the fraction of chemical unbound in plasma. CL represents the activity of the metabolizing
u int,u
enzyme toward the toxicant and can be expressed in terms of Michaelis–Menten kinetics as V max /(K +
m
C ). When C is low relative to K (< 10%), the relationship simplifies to V /K , and metabolism
v,u v,u m max m
becomes first order with respect to C :
v,u
/
−dX dt = (V max K m )C v u, (3.14)
Values for CL and CL can be calculated from CL , Q, and f as follows:
int,u int h u