Page 138 - The Toxicology of Fishes

118 The Toxicology of Fishes

The first step in modeling elimination is to specify the organs where it occurs and the chemical kinetics
(e.g., first-order, saturable) over the concentration range to which the tissue is exposed. Elimination may
then be modeled by incorporating a clearance expression (dA /dt) into the mass-balance equation for
cl
the eliminating compartment:
dA dt = ( C vi) − dA dt (3.110)
Q C art −
i
i
cl
Referenced to the chemical concentration in venous blood draining the tissue, the kinetics of first-order
clearance can be written as:
dA dt = k C V i (3.111)
cl
vi
fc
Saturable pathways can be described using a Michaelis–Menten type of equation where K and V max
m
are parameters that define an in vivo intrinsic clearance term:

CL int = V max ( K m + C vi) (3.112)

dt = V C vi ( K m + C vi) =
dA cl max CL C viint (3.113)
Although often localized to the liver as a matter of convenience, biotransformation can be incorporated
into any one or more of the individual tissue descriptions. Ascribing metabolism to the tissue where it
actually occurs may be critical to the modeling outcome when this activity limits chemical uptake across
the gills or gut (Barron et al., 1989; Van Veld, 1990). In some cases, a modeler may be more interested
in the kinetics of a metabolite than of the parent compound from which it was derived. Under these
circumstances, the disappearance of parent compound (including both the rate of metabolism and the
site where this metabolism occurs) is equated to the production of the metabolites) (Nichols, 1999).
Additional information, including equilibrium partitioning, plasma binding, chemical reactivity (e.g.,
covalent binding to tissue macromolecules), and subsequent elimination, is then required to develop a
description of metabolite kinetics.

Model Parameterization
Anatomical, physiological, and biochemical information required to develop PBTK models for fish is
given throughout this text. Additional information is provided in numerous texts and hundreds of scientific
papers. Although it is true that most of this information has been developed for a relatively few fish
species, allometric and temperature relationships permit the extrapolation of these data to other, untested
species. The goal of this section is to provide guidance on how existing data can be used in PBTK
modeling efforts. An emphasis is placed on chemical elimination pathways, as these pathways are often
found to be primarily responsible for differences in chemical disposition that exist among species.

Physiological Inputs
In the absence of measured values for a given fish species, it may be possible to estimate the values of
critical physiological inputs using allometric scaling relationships. A review of allometric scaling tech-
niques is given by Schmidt-Nielsen (1984). These principals have been applied to PBTK modeling efforts
by several authors (Dedrick, 1973; Mordenti, 1986; Rowland, 1985; Travis et al., 1990). In mammals,
physiological parameters linked to cellular metabolism (e.g., cardiac output, oxygen consumption rate)
often scale to the 3/4 power of body weight (exponent of 0.75). Renal clearance and the capacity for
hepatic metabolism (V max ) were reported by Travis et al. (1990) to scale to an exponent of 0.75. In a
more recent review, Hu and Hayton (2001) found that renal clearance scales to the 2/3 power of body
weight (exponent of 0.67). The Michaelis–Menten constant, K , which is a measure of the substrate
m
affinity of an enzyme, is thought to remain relatively constant across species.
In studies with fish, it has been difficult to make comparisons among species because of differences in
experimental design (e.g., temperature, light cycle) that affect metabolic rate. The strongest comparisons,