Page 130 - The Toxicology of Fishes

110 The Toxicology of Fishes

slow diffusion across biological membranes: large molecular volume, the existence of charged or highly
polar substituent groups, and extreme hydrophobic character. The specific rate (per gram of tissue) of
tissue blood perfusion may also be a factor. Low blood perfusion rates are associated with large inter-
capillary diffusion distances. Moreover, in a tissue with very low metabolic demand (e.g., the white muscle
of a resting fish), only a fraction of the total tissue mass may be perfused at any point in time. In mammals,
diffusion limitations have also been observed in highly perfused tissues, presumably because of reduced
blood residence times. In modeling efforts with fish conducted to date, diffusion limitations have been
employed to describe the uptake of pyrene into muscle tissue of rainbow trout (Law et al., 1991) and the
accumulation of TCDD in adipose tissue of brook trout (Nichols et al., 1998). In the brook trout model,
the PA product was calculated as a fraction of the estimated fat blood flow rate. The fitted value of the
PA was then interpreted as the effective rate of blood flow to fat.
As the kidney and liver of fish receive both arterial and portal blood, a simple description of these
organs can be developed by assuming that arterial and portal blood mix before exchanging with the
tissue. Under these circumstances, total blood flow (Q ) equals the sum of arterial (Q ) and portal inputs
mi
i
(Q ):
pi
Q = Q + Q pi (3.93)
mi
i
where Q is equal to all or a fraction of arterial flow to the upstream compartment. The chemical
pi
concentration in mixed blood (C ) can be calculated by summing the flow-weighted contributions of
mi
arterial and portal blood (C ):
pi
C mi = ( Q C art + Q C pi) Q mi (3.94)
i
pi
where C is equal to the concentration in venous blood exiting the upstream compartment. Assuming
pi
further that chemical uptake by the tissue is flow limited, a mass balance for the compartment may then
be written as:
dX dt = Q mi( C mi − C vi) (3.95)
i
When the kinetic descriptions for all tissues have been defined, the concentration of chemical in mixed
venous blood can be calculated from the flow-weighted contributions of venous blood draining each
tissue compartment. In a model with chemical uptake at the gills, this mixed venous concentration
provides one of the inputs to the branchial exchange description (see below). The complete model
consists of a system of simultaneous mass-balance differential equations. Numerical integration proce-
dures are then used to solve these equations at each time point.

Routes of Exposure
A critical part of any PBTK model is the route of exposure description. In experimental dosing studies,
the investigator generally controls the route and timing of the exposure. Natural exposures may be more
difficult to characterize and are more likely to be of a mixed type—that is, involving chemical flux at
more than one exchange surface; for example, a compound that is present in water may also be present
in prey items upon which a fish feeds. Environmental routes of uptake (branchial, dermal, dietary) can
also function as routes of elimination. Indeed, it is possible for one exchange surface to function as a
route of uptake (e.g., the gastrointestinal tract), while at the same time another operates as a route of
elimination (e.g., the gills). In contrast, some experimental routes of exposure, such as intravascular
infusion, function only as routes of uptake.

Branchial Uptake
The structure of fish gills reflects their primary function as a gas-exchange and osmoregulatory organ.
A large surface area for exchange is achieved by an elaboration of plate-like structures termed lamellae,
which form narrow channels above and below each gill filament. In most species, blood flows through