McKay, Donald. "Front matter" Multimedia Environmental Models ...

and Mackay (2000) describe the fate of PAHs from atmospheric sources to Lac Saint
Louis in the St. Lawrence River. Diamond et al. (1994) treat the fate of a variety of
organic chemicals and metals in a highly segmented model of the Bay of Quinte
which is connected to Lake Ontario.
8.9.1 Introduction
©2001 CRC Press LLC
8.9 A FISH BIOACCUMULATION MODEL
The fish bioaccumulation phenomenon is very important as a means by which
chemicals present at low concentration in water become concentrated by many orders
of magnitude, thus causing a potential hazard to the fish and other creatures, especially
to the birds and humans who consume these fish. For example, DDT may be
found in fish at concentrations a million times that of water. The primary cause of
this effect is simply the difference in Z values between water and fish lipids as
characterized by K OW, but there are other, more subtle effects at work. The kinetics
of uptake are also important, because a fish may never reach thermodynamic equilibrium.
There is also a fascinating biomagnification phenomenon that is not yet
fully understood in which concentrations increase progressively through food chains.
It is useful to define some terminology, although opinions differ on the correct
usage. Bioconcentration refers here to uptake from water by respiration from water,
usually under laboratory conditions when the fish are not fed. Bioaccumulation is
the total (water plus food) uptake process and can occur in the laboratory or field.
Biomagnification is a special case of bioaccumulation in which there is an increase
in concentration or fugacity from food to fish. This situation may occur for nonmetabolizing
chemicals of log K OW exceeding 5.
A comprehensive review of methods of estimating bioaccumulation is that of
Gobas and Morrison (2000). Other reviews are the texts by Connell (1990) and
Hamelink et al. (1994) and the paper by Mackay and Fraser (2000). The models
described here are based on those of Clark et al. (1990), Gobas (1993), and Campfens
and Mackay (1997). Figure 8.10 shows the processes of uptake and clearance.
The approach taken here is to set out the mass balance equations in conventional
rate constant form, then show that they are equivalent to the fugacity forms using
D values. The final model gives both rate constants and D values.
8.9.2 Equations in Rate Constant Format
Here, we treat the fish as one “box.” The conventional concentration expression
for uptake of chemical by fish from water, through the gills only under laboratory
conditions, was first written by Neely et al. (1974) as
dC F/dt = k 1C W – k 2C F
where C F and C W are concentrations in fish and water, k 1 is an uptake rate constant
and k 2 is the clearance rate constant. The fish is regarded as a single compartment.