Page 121 - The Toxicology of Fishes

Toxicokinetics in Fishes 101

−
M = ρ CL C t (ρ + CL m) − CL X ss(1 − e ) (ρ + CL m) (3.45)
kt
el
m
m
w
The dependent parameters ρ, V, and CL , can be estimated by fitting Equations 3.42 and 3.45 to
m
measured values of X and M. Initial parameter estimates (required as inputs to the data-fitting software)
can be obtained from a graph of (X – X) vs. time on semilogarithmic coordinates. The slope of this
ss
plot is equal to k /–2.3. The value of ρ can then be estimated from the relationship:
el
(3.46)
ρ= kX C w
el
ss
Importantly, the presence of a metabolic elimination pathway cannot be deduced from the X,t profile
alone. The model-predicted M,t profile (Equation 3.45) indicates that M will increase linearly with time
after a transient period (T ) that is determined by the half-life of the parent toxicant:
lag
t 12/ = 0 693 V(ρ + CL m) = 0 693 k el (3.47)
.
.
By extrapolating the linear part of the M,t plot to the time axis, it is possible to obtain an estimate of
T , which can be shown to be equal to 1/k by solving Equation 3.45 when M = 0. Substituting, Equation
el
lag
3.45 may now be written as:
)
M = ρ CL C w (ρ + CL m)  t T lag( 1 − e − / tT lag   (3.48)
−

 
m
The BCF for this case is:
BCF = X C = ρ V (ρ + CL m) (3.49)
ss
w
Rather than being equivalent to V (as in the model without metabolism), the BCF is now a fraction of
V that is equal to the ratio ρ/(ρ + CL ) (Karara and Hayton, 1984).
m
Static Exposure—In a static exposure, the C may decline due to uptake of chemical by the exposed
w
organisms. Under these circumstances, Equation 3.37 may be integrated to give:
VV C w  V))ρ 
X = w ,0 1 − e − ( ( 1 V w)+(1 t (3.50)
V w + V    

where C is the initial concentration of chemical in the exposure water, and V is the volume of exposure
w
w,0
water. The water concentration would decline according to the relationship:
dt ρ (3.51)
−dC w = (C w − C p u, ) V w
Integrating, one obtains:
 V ( t 
C w = C w  − 1 − e − ( ( 1 V w)+(1 V))ρ ) (3.52)
,0 1
 V w + V 
An examination of Equation 3.50 suggests that the time to achieve steady state is influenced by the value
of V and that it is shorter than it would have been had C remained constant (as in a flow-through
w
w
exposure). This influence of V on the time to steady state can be exploited to shorten the time required
w
to characterize the X,t profile when the time to steady state would otherwise be very long. By making
V relatively small compared with V, the time to steady state is minimized.
w