Page 132 - The Toxicology of Fishes

112 The Toxicology of Fishes

to fluid flow) chemical transport in both blood and water, did not yield an analytical solution. An
approximate analytical solution was obtained, however, by segregating the lamellar unit into layers in
which only advective or diffusive transport predominates. This may be visualized as a diffusion barrier
consisting of the gill epithelium and stagnant boundary layers in the adjacent water and blood channels.
With these simplifications, branchial flux can be calculated as the product of the concentration gradient
between inspired water and venous blood and an exchange coefficient (k ):
x
F g = ( C P bw) (3.97)
k C w −
x
v
where
− kd kb − − kd kw
k x = e e
e − kd kb e − kd kw (3.98)
−
k w k b
The terms k , k , and k in the equation for k represent the capacity of respiratory water, blood flowing
w b d x
through the gills, and chemical diffusion across the gills, respectively, to support branchial flux:
k = Q (3.99)
w w
k = Q P (3.100)
b
c bw
k = DA/h (3.101)
d
where D, A, and h, respectively, refer to the chemical diffusivity in, the total area of, and the effective
thickness of the gill diffusion barrier. Importantly, this model assumes that chemical diffusion in the
aqueous phase of the gill epithelium limits flux. The model does not, therefore, incorporate the partition
coefficient (P ), which appears in the model given by Hayton and Barron (1990) (Equation 3.27). A
mw
simulation for rainbow trout generated using the complete model (approximate analytical solution) is
shown in Figure 3.25. This simulation accurately describes all of the observed trends in the data, including
the reduction in uptake of high log K compounds.
ow
The complete gill model has been used to describe branchial uptake of waterborne chemicals by
several fish species, requiring the collection of necessary physiological and gill morphometric information
(Figure 3.26) (Lien et al., 2001; Nichols et al., 1993). For many compounds, however, a good approx-
imation of branchial flux can be obtained using the simpler flow-limited model. Direct experimental
evidence for the predominant influence of flow limitations on branchial uptake has been obtained by
independently varying Q and Q for chemicals with different log K values (Schmieder and Weber,
ow
w
c
1992). Finally, it is important to understand that both the flow-limited and complete gill models separate
the blood circulation into arterial and venous sides. In a PBTK model, chemical taken up across the
gills (predicted by the gill description) is added to that already present in venous blood to provide a new
value for the arterial blood concentration. The arterial blood concentration is then used as an input to
each of the tissue descriptions (Figure 3.22).
Dermal Uptake
Dermal uptake represents a second possible route of exposure that may be important for small fish,
juveniles of larger species, and fish that live in intimate contact with contaminated sediments. The
structure and function of fish skin were addressed earlier in this chapter. Additional information is
provided in a recent review (McKim and Lien, 2001). The general architecture of fish skin (epidermis,
dermis, and hypodermis) is similar in most species, but the thickness of these layers varies widely.
Additional differences exist with respect to the presence or absence of scales and the number and location
of sensory organs, mucous glands, and other specialized structures.
A PBTK model for dermal uptake in small fish was developed by Lien and co-workers (Lien and
McKim, 1993; Lien et al., 1994) from the gill model given in Equation 3.97 by assuming that water
flow does not limit chemical transport across the skin. This model can be visualized as a parallel network