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

Paterson et al. (1991), and Hung and Mackay (1997). This topic is the focus of
considerable research, and improved models will no doubt be developed in the near
future.
©2001 CRC Press LLC
8.13 PHARMACOKINETIC MODELS
Physiologically based pharmacokinetic models (PBPK models) treat an animal
as a collection of connected boxes in which exchange occurs primarily in the blood,
which circulates between all the boxes. The model can include uptake from air and
food and possibly by dermal contact or injection. We then calculate the dynamics
of the circulation of the chemical in venous and arterial blood, to and from various
organs or tissue groups including adipose tissue, muscle, skin, brain, kidney, and
liver. There may be losses by exhalation and metabolism, and in urine, feces and,
sweat. In mammals, nursing mothers also lose chemical to their offspring in breast
milk, and they lose tissue when giving birth. Analogous processes occur during egglaying
in birds, amphibians, and reptiles. As in environmental models, partition
coefficients or Z values can be deduced to quantify chemical equilibrium between
air, blood, and various organs. Flows of blood to each organ can be expressed as D
values. Metabolic rates can be expressed using rate constants, usually invoking
Michaelis–Menten kinetics, as described in Chapter 6, and translated into D values.
Mass balance equations then can be assembled, describing the constant conditions
that develop following exposure to long-term constant concentrations or the dynamic
conditions that follow a pulse input. Experiments are done, often with rodents, to
follow the time course of chemical transport and transformation in the animal. The
resulting data can be compared with model assertions to achieve a measure of
validation.
Much of the pharmacokinetic literature is devoted to assessment of the time
course of the fate of therapeutic drugs within the human body. The aim is to supply
a sufficient, but not too large and thus toxic, dose of drug to the target organ. Closer
to environmental exposure conditions are PBPK models for occupational exposure
to toxicants such as solvent or fuel vapors, which may be intermittent or continuous
in nature. An example is the model of Ramsey and Andersen (1984), which was
translated into fugacity terms by Paterson and Mackay (1986, 1987). Accounts of
various aspects of pharmacokinetics and PBPK models and their contribution to
environmental science are the works of Welling (1986), Parke (1982), Reitz and
Gehring (1982), Tuey and Matthews (1980), Fisherova-Bergerova (1983), Menzel
(1987), Nichols et al. (1996, 1998), and Wen et al. (1999). A fugacity model has
been developed for whales by Hickie et al. (1999) and a rate constant model for
birds by Clark et al. (1987).
Figure 8.12, which is adapted from Paterson and Mackay (1987), illustrates the
fugacity approach to modeling the fate of a chemical in the human body. In principle,
it is possible to calculate steady- and unsteady-state fugacities, concentrations,
amounts, fluxes, and response times, thus linking external environmental concentrations
to internal tissue concentrations. Ultimately, from a human health viewpoint,
it is likely that it will be possible to undertake these calculations and compare levels