Page 125 - The Toxicology of Fishes

Toxicokinetics in Fishes 105

The latter, when multiplied by C during the log-linear or β phase, gives the amount of toxicant in the
p
organism. V reflects only distribution, whereas V is, in addition, a function of the kinetics of distribution
β
ss
and elimination. V ≥ V because during the β phase there is a positive chemical gradient from
β
ss
compartment 2 to compartment 1. For a given plasma concentration, this results in more toxicant in the
organism during the β phase than during steady state. The t 1/2,α term is characteristic of the time required
for distribution, and t 1/2,β is the elimination half-life of the toxicant, which is similar to the half-life for
a one-compartment model.
The CL parameter represents the total body clearance and may reflect elimination by several pathways
(e.g., branchial elimination, renal excretion, and hepatic metabolism; see Equation 3.7). The amount of
chemical eliminated by each pathway is directly proportional to the magnitude of the clearance for the
pathway. To obtain a clearance value for each pathway, the amounts eliminated by each pathway must
be determined. The individual clearances may then be calculated as follows:
CL h = ( M ∞ X CL (3.80)
)
0
CL r = ( X r ∞, X CL (3.81)
)
0
CL b = ( X b ∞, X CL (3.82)
)
0
where M is the total amount of metabolite formed, and X and X are the amounts of chemical
∞
b,∞
r,∞
eliminated in urine and expired branchial water. Calculation of X requires the use of urinary duct
r,∞
catheters to quantitatively collect the urine (Kleinow, 1991).
Utility of Compartmental Models for Fish
Compartmental models have the advantage of requiring limited data relative to physiologically based
models and require only time-series data for the parent compound in a reference tissue, such as plasma,
to infer chemical dynamics in other tissues and the whole fish (Barron et al., 1990). Compartmental
modeling allows estimation of the key pharmacokinetic parameters characterizing chemical uptake from
water (CL ), distribution (V), and persistence (half-life). The modeled compartments generally do not
b
have any physiological or anatomical reality, but clearance-based constants do allow a degree of phys-
iological interpretation and realism. A common inference is that after intravascular administration of a
chemical, the lower limit on the size of V is the blood or plasma volume, and a larger V indicates that
the chemical is distributing outside of the vascular system. The magnitude of CL is directly interpretable
b
as a proportion of ventilation volume and cannot exceed ventilation volume unless biotransformation
occurs in the blood. Compartmental models are limited in their ability to extrapolate across species but
have been used to assess the effects of body size and environmental factors such as temperature on
toxicokinetics in fish and to discern presystemic biotransformation in the gill (Barron et al., 1987b, 1989;
Schultz and Hayton, 1994).

Physiologically Based Toxicokinetic Models
Physiologically based toxicokinetic (PBTK) models are founded on the premise that chemical uptake
and disposition can be described from anatomical, physiological, and biochemical attributes of the
exposed organism and physicochemical characteristics of the compound. The compartments in a phys-
iological model correspond to actual tissues and organs, and chemical transport within the animal is
defined by blood flow relationships. This mechanistic foundation provides for the possibility of extrap-
olating kinetic information among species and chemicals by making appropriate adjustments of biological
and chemical inputs.
Mass-balance differential equations that describe chemical kinetics in a tissue exchanging with blood
were developed in the 1930s (Teorell, 1937). The computing power required to simultaneously solve
equations for several tissues was not widely available, however, until the 1960s. Early use of the
physiological modeling approach consisted primarily of describing the kinetics of chemotherapeutic