Page 139 - The Toxicology of Fishes

Toxicokinetics in Fishes 119

therefore, have been made using different sized individuals of a single species held under otherwise
identical conditions. Although highly variable among species, the average allometric exponent for oxygen
consumption rate is about 0.8, or slightly higher than the average value for mammals (Schmidt-Nielsen,
1984). Within a single species, gill surface area also tends to scale to an exponent of about 0.8 (Hughes,
1984), as does the absorptive surface area of the intestinal mucosa (Buddington and Diamond, 1987).
Skin surface area within a species scales to an exponent of about 0.67 in accordance with the surface
law (Schmidt-Nielsen, 1984). Data presented by Wood and Shelton (1980) suggest that cardiac output
in rainbow trout scales to an exponent of about 0.9. The dependence of cardiac output on acclimation
temperature also has been characterized for rainbow trout (Barron et al., 1987a). Cardiac output in trout
had a Q10 of 4.0 (i.e., a 10°C increase in temperature was associated with a fourfold increase in cardiac
output). Q10 values reported for oxygen consumption in fish and other poikilotherms generally average
around 2.0 (Ott et al., 1980).
Small fish present special challenges for PBTK modeling because direct measurements of many
anatomical and physiological parameters are difficult or impossible to make. Lien and McKim (1993)
addressed this problem in studies with Japanese medaka and fathead minnows by calculating effective
respiratory volume (Q ) and functional gill surface area as functions of oxygen consumption rate, which
w
can be easily measured even in larval fishes. Cardiac output for these small fish species was estimated
using a relationship given by Erickson and McKim (1990b) that accounts for the effect of both size and
temperature.

Chemical Partitioning
Mass-balance equations that describe chemical flux between blood and tissues include a term that defines
both the direction and magnitude of the concentration gradient. Generally, the blood is defined as the
reference state. The concentration gradient is then calculated as the difference between the chemical
concentration in blood and the concentration in the tissue, divided by an equilibrium tissue–blood
partition coefficient. In the context of this description, it is assumed that chemical associations with
blood and tissue constituents are low affinity. Operationally, this means that the kinetics of chemical
dissociation from binding sites in blood and tissues are fast relative to the residence time of blood in
tissues and do not, therefore, limit the overall kinetics of distribution. Partition coefficients are also
required to develop physiological descriptions of chemical flux at the gills, skin, and gut.
Chemical partition coefficients can be obtained directly from chemical concentrations in blood and
tissues of animals that have been exposed to near steady state, provided that metabolism or some other
route of elimination does not reduce tissue concentrations below those expected from simple partitioning.
The disadvantage of this approach is that it requires prior exposure of animals to generate model
simulations. A number of in vitro systems have also been developed to generate partition coefficients.
Gargas et al. (1989) used a vial headspace equilibration technique to determine partition coefficients for
a large number of volatile hydrocarbons. This method was subsequently adapted for use with fish tissues
(Hoffman et al., 1992). The vial equilibration method measures the depression in headspace concentration
that occurs as a result of chemical partitioning to the sample. Samples generally consist of tissue
homogenates diluted in saline, although the technique has also been adapted for use with intact samples
of skin (Mattie et al., 1993). Other in vitro partitioning methods have been developed for nonvolatile
compounds. Law et al. (1991) obtained partitioning estimates for pyrene in trout tissues using an
equilibrium dialysis technique. Jepson et al. (1994) used a filtration method to evaluate the partitioning
of lindane, parathion, paraoxon, perchloroethylene, and two haloacetic acids between rat tissues and
saline. Murphy et al. (1995) measured the partitioning of TCDD and estradiol between rat tissues and
propylene carbonate. Because this solvent is essentially immiscible with tissues, this method did not
require a filtration step.
To a first approximation, hydrophobic organic compounds partition between tissues and blood in
accordance with the lipid content of each phase (Van der Molen et al., 1996). n-Octanol is frequently
used as a surrogate for biological lipid. By assuming a correspondence between n-octanol–water
partitioning and lipid–water partitioning, Nichols et al. (1991) developed an algorithm to predict
blood–water partitioning in rainbow trout. A similar approach, expanded to include partitioning to
phospholipid, was used to predict tissue–blood partition coefficients in rats (Poulin and Krishnan, 1995).