Page 122 - The Toxicology of Fishes

102 The Toxicology of Fishes

Body Weight—A modification of the static exposure model is required when experiments are conducted
using individual fish of different sizes. Larger fish will deplete the exposure solution faster, but the
amount of toxicant absorbed per gram of body weight will be less than in smaller fish because the
absorbed toxicant distributes into a larger body size. In this case, Equations 3.32 and 3.51 must be
rewritten to explicitly consider fish body weight (W):
(
dX dt = ρ W C w − C p u, ) (3.53)
/
(
ρ
−dC dt = W C w − C p u, ) V w (3.54)
w
Integrating, one obtains equations analogous to those given previously:

X = VV C w  1 − e − ( ( WV w)+(1 V))ρ t  (3.55)
w
,0
WV w + V    
 V ( − ( ( V))ρ t 
C w = C w  − 1 − e WV w)+(1 ) (3.56)
,0 1
 WV w + V 
To fit Equation 3.55 and Equation 3.56 to experimental data, both time and fish weight are entered as
independent variables, along with measured values of C and X.
w
Oral Administration
A single oral dose may be administered to a fish that has been prepared with an indwelling vascular
catheter. If the absorption kinetics are first order and monoexponential, then the rate of appearance of
chemical in the fish is:
dX/dt = k X – CLC p (3.57)
ab
g
where k is the absorption rate constant, and X is the amount of toxicant remaining in the GIT. From
g
ab
this equation it is possible to derive the following relationship:
−
C p = k F dose e ( −( CL V t ) − e ) ( CL V ) ) (3.58)
⋅
k t
/
V k ab − (
ab
ab
where F is the fraction of the dose that reaches the systemic circulation of the fish (oral bioavailability;
see earlier section on hepatic clearance). The value of F may be estimated by comparison of the area
under the C ,t profile with the area determined after an intravascularly administered dose, where F is unity.
p
When the dietary exposure is continuous, the rate of change of the amount of chemical in the fish is:
dX/dt = FR – CLC (3.59)
in p
where R is the rate of chemical ingestion. In this case, the mass of chemical exponentially approaches
in
a constant or steady-state value:
X ss = ( FR V CL) − (1 e ) (3.60)
−
kt
el
in
Two-Compartment Model
A one-compartment model assumes that a chemical distributes instantaneously throughout all tissues of
the exposed animal. This assumption often fails because chemical distribution to each tissue is linked
to blood perfusion rate, and tissue-specific perfusion rates vary considerably. When the kinetics of internal
distribution affect the shape of the plasma concentration–time profile, a higher order compartment model
is required. Perhaps the most common example of this phenomenon occurs when log-transformed plasma
concentration data from an intravascular dosing study decrease in a biphasic manner (Figure 3.21). The