Page 116 - The Toxicology of Fishes

96 The Toxicology of Fishes

Chemical diffusivity in aqueous solution may be calculated from equations given in standard physical
chemistry texts and is expected to decline with increasing molecular volume.
If the permeability of the gill epithelium to a toxicant is sufficiently high, branchial uptake may be
limited by the rate of blood flow through the gill lamellae. Chemical binding to plasma proteins or to
cells in the blood would increase the capacity of blood to carry toxicant away from the gills. The uptake
clearance when blood flow is the rate-limiting factor may be expressed as:

CL = Q P (3.25)
c bw
b
where Q is the total cardiac output, and P is an equilibrium blood–water partition coefficient.
bw
c
Because the value of P can be very large, it is possible for water flow across the absorbing surface
bw
of the gills to control the rate of chemical uptake. In this case, the value of CL is equal to the effective
b
respiratory volume (Q ), which is the flow rate of inspired water that exchanges with blood:
w
CL = Q w (3.26)
b
To a first approximation, the potential rate limitations on branchial flux can treated as if they were
resistances in series in an electrical circuit (Hayton and Barron, 1990):
CL b = ( h DP A +1 Q P bw +1 Q w) −1 (3.27)
mw
c
A more complex model based on the counter-current structure of fish gills was developed by Erickson
and McKim (1990a,b) and is described below in the section on physiologically based toxicokinetic
models; however, in the case where one resistance is the principal determinant of chemical flux (by
virtue of being much greater than the other two), the two models reduce to a common description.

Compartmental Models for Fish
The use of compartmental models to characterize the kinetics of absorption, distribution, and elimination
of exogenous and endogenous substances by a variety of species is well established. The foundations
of this approach (Wagner, 1981) were developed by Haggard (1924), Widmark and Tandberg (1924),
Dominquez and Pomerene (1934), and Teorell (1937). In the decades since this early work was published,
there have been refinements in modeling concepts and in the techniques for data analysis. A number of
textbooks on this topic are available (Gibaldi and Perrier, 1982; Rowland and Tozer, 1995; Wagner,
1993; Welling, 1986). Riggs (1963) defined the term compartment as follows:
If a substance, S, is present in a biological system in several distinguishable forms or locations,
and if S passes from one form or location to another form or location at a measurable rate, then
each form or location constitutes a separate compartment for S.

In the context of toxicokinetics, a parent toxicant and its metabolites would be forms of substance S, and
a location would be one or more tissues in which the forms had similar kinetic behavior. As an example,
a tank of exposure water might be a compartment from which toxicant absorption occurs, the blood and
highly perfused tissues might constitute a second compartment, the poorly perfused tissues would be a
third compartment, and a metabolite might require specification of a fourth compartment (Figure 3.20A).
Compartments are assumed to behave like a tank that contains a well-stirred fluid; that is, toxicant
that enters a compartment is assumed to distribute instantaneously and linearly, such that the concen-
tration is everywhere proportional to the amount of chemical in the compartment. The number of
compartments is generally small (1 to 5) to maintain mathematical simplicity and the capability to fit
model-based equations to experimental data. Body compartments are usually arranged so chemical enters
and exits from only one of the compartments, the so-called central compartment. With multiple-com-
partment models, the added peripheral compartments are usually attached to the central compartment
so chemical exchanges between the central and each peripheral compartment; this configuration is termed
mammillary, as opposed to the catenary configuration, which refers to a chain-like series of compartments.