Page 154 - The Toxicology of Fishes

134 The Toxicology of Fishes

noted by Thomann et al. (1992b) and others, equilibrium partitioning models can substantially under-
estimate the accumulation of PCBs, chlorinated pesticides, and other organochlorine compounds in upper
trophic level fishes because trophic transfer is not considered.

Fugacity-Based Models
Fugacity-based models were initially developed from engineering principles (models of gas transfer)
and have been applied extensively in environmental fate modeling to estimate chemical concentrations
in different environmental compartments (phases), including air, water, sediment, and biota. Using a
fugacity approach, the concentration of a contaminant is expressed in units of moles/volume (e.g.,
3
mol/m ) rather than mass/mass (e.g., mg/kg body weight) or mass/volume (e.g., mg/L water) and is
3
calculated as the product of chemical fugacity f (Pa) and the fugacity capacity Z (mol/Pa m ). The
fugacity of a compound is an expression of chemical activity that characterizes the escaping tendency
from a particular phase, while fugacity capacity can be viewed as a kind of solubility (Mackay and
Paterson, 1982). In general, fugacity-based models assume that a chemical achieves equilibrium between
all of the environmental phases, although transfer resistances (model terms that limit transfer from phase
to phase) can be incorporated to model retention of a chemical.
Fugacity-based models have been developed to describe chemical bioaccumulation in fish (Gobas et
al., 1989) and trophic transfer in aquatic food webs (Campfens and Mackay, 1997). To illustrate this
approach we can consider the one-compartment model for chemical bioconcentration given earlier as
Equation 3.123:
dC dt = k C w − k C f2 (3.140)
f
1
When expressed in fugacity terms, this same equation takes the following form:
VZD dt = D f f w − D f f f (3.141)
f
3
where V is the volume of the fish (m ) and D is a fish-to-water transport parameter (mol/Pa/hr). Impor-
f
tantly, this equation implies that at steady state chemical fugacities in the water (f ) and fish (f ) are equal.
w f
Extending this approach further, steady-state bioaccumulation in fish exposed to contaminated food
and water may be calculated from the relationship:
D fw f + D a a f = ( D w + D e + D m + ) (3.142)
f f
D g
where D f is uptake from water, D f is uptake from food, and the transport parameters in the parentheses
a a
f w
account for elimination into water (D ; due to branchial efflux) and feces (D ), biotransformation (D ),
e
w
m
and growth dilution (D ). Using this approach, Campfens and Mackay (1997) concluded that fecal
g
egestion and growth dilution are the major loss processes for high log K compounds and that there is
ow
a net loss of chemical through the gills.
The principal advantage of a fugacity-based modeling approach is that thermodynamic relationships
among compartments can be assessed using a common (fugacity) metric. When used for fish bioaccu-
mulation modeling, the main disadvantage of this approach is that model parameters are not directly
interpretable in terms of physiological quantities such as clearance and water and blood flows.

References
Abbas, R. and Hayton, W.L. 1997. A physiologically based pharmacokinetic and pharmacodynamic model
for paraoxon in rainbow trout. Toxicol. Appl. Pharmacol., 145: 192–201.
Abbas, R., Schultz, I.R., Doddapaneni, S., and Hayton, W.L. 1996. Toxicokinetics of parathion and paraoxon in
rainbow trout after intravascular administration and water exposure. Toxicol. Appl. Pharmacol., 136: 194–199.