Page 119 - The Toxicology of Fishes

Toxicokinetics in Fishes 99

C = C e –(CL/V)t (3.29)
p
0
where t is time and C is the plasma concentration at t = 0 (i.e., the dose/V). This equation predicts that
0
the plasma concentration will decline exponentially and a graph of log C vs. time should give a straight
p
line. From the slope of the line, the ratio CL/V may be obtained, which is commonly referred to as the
elimination rate constant (k ):
el
k = –2.3 · slope = CL/V (3.30)
el
The elimination half-life (t ) is calculated from k :
1/2 el
t 12/ = 0 693 k el = 0 693 V CL (3.31)
.
/
.
This relationship shows that a change in t may result from a change in CL or V. Barron et al. (1987b)
1/2
found that the t for di-2-ethylhexylphthalate (DEHP) in rainbow trout increased with acclimation
1/2
temperature and that this increase was primarily due to changes in V and not CL. The y-axis intercept
of the semilog plot gives an estimate of C that is used to calculate a value for V:
0
V = dose C 0 (3.32)
As a minimum, the number of plasma samples should be three times the number of parameters to be
estimated (in this case, six samples to estimate the two parameters CL and V). These samples should
be uniformly spaced and should be taken over a time span at least three times the t .
1/2
Infusion Dose—In some cases, it may be advantageous to administer the dose at a constant rate (R ).
0
This approach avoids the high transient plasma concentration associated with a bolus dose and provides
a larger volume of solvent to dissolve the toxicant. The plasma concentration will increase exponentially
during the infusion, followed by an exponential decline after the infusion is stopped. During the infusion,
the predicted plasma concentration is:
C p = ( R CL) − (1 e ) (3.33)
−
kt
el
0
After three to four half-lives, the exponential approaches a value of zero, and a steady-state condition
is achieved in which the rate of infusion equals the rate of elimination of the toxicant.
Plasma samples are generally obtained after the infusion has been stopped using the same cannula
employed to infuse the toxicant. The value of k is obtained from the slope of a semilog plot of the
el
post-infusion plasma data (Equation 3.30). If the infusion was sufficient to achieve a steady-state
condition, CL can be calculated from:
CL = R C ss0 (3.34)

where C is the steady-state plasma concentration, estimated from the y-axis intercept of a semilog plot
ss
of the post-infusion C ,t profile. The volume of distribution (V) can then be calculated as:
p
V = CL k el (3.35)

If the infusion was stopped prior to steady state, k may still be estimated from the slope of the semilog
el
plot, but estimation of CL and V is less straightforward because the amount of toxicant in the fish at
the end of the infusion is unknown. Equation 3.33 may be rearranged to give the following expression
for estimation of CL, which can then be used along with k to estimate V:
el
CL = ( R C end) − (1 e − kt inf ) (3.36)
el
0
where C is the concentration in plasma at the end of the infusion, estimated from the semilog plot,
end
and t is the duration of the infusion.
inf