The third example is a fish bioconcentration model. The biological/ecological phe- nomenon of bioconcentration is one of crucial importance in aquatic systems, mainly for persistent organic chemicals, such as certain organochlorines (see Chapter 7). The potential for harm to humans and other biota resulting from the release of even small amounts of chemical into the environment is increased many times by the concentrations of the chemical that are attained in higher trophic levels. The ecological basis for this is explained in Chapter 7. The task of the mod- eller is to determine the steps in the bioaccumulation process that influence the concentration in the tissue and to make appropriate quantitative estimates of these. An understanding of the chemical structure of organic compounds and the way in which the structure is related to the behaviour of the chemical is central to this type of modelling.
The model illustrated in Figure 4.18 illustrates the various processes in which the chemical is involved and which are incorporated into this particular model. They include
a. Uptake from water via the gills; b. Uptake from food;
c. Loss via the gills; d. Loss by egestion; e. Loss by metabolism;
f. Dilution of tissue concentration through growth of the organism.
The expressions for input and output processes in Figure 4.18 are expressed in two alternative ways: as a rate constant (K) or in fugacity (D) form. The explanations of the terms and equations are provided in Mackay (1991). Fugacity (from fugare, to flee or escape) is a thermodynamic criterion of equilibrium of a substance in solution in two phases. It is closely related to chemical potential and can be regarded as an idealised partial pressure. When a substance such as benzene achieves equilibrium among phases such as air, water, and sediment, it has a common fugacity, in all these media, but differing concentrations. Fugacity plays the same role for distribution of mass in solution as temperature plays for dis- tribution of heat. D values are fugacity rate constants.
Such a model, because it quantifies the exposure routes for the fish, may eluci- date the primary route of exposure or correct a prior erroneous assumption about the major route of exposure.
EFFECTS MODELLING
Following the estimation of the accumulation of a chemical in an organism, further modelling, also based on chemical structure, assesses effects and may utilise the so-called quantitative structure-activity relationship (QSAR) approach (see Section 5.5). It is obvious that this approach not only provides a means of assessing the
behaviour and fate of chemicals already in the environment but also provides one way of assessing the risks of new chemicals. Increasingly, regulatory agencies are accepting model predictions and risk assessments for ranking the environmental significance of potentially toxic substances.
4.6.3 Some other models for use in environmental toxicology
In addition to the preceding examples, a number of different models that also address the fate of chemicals are available. In addition to the mass balance type, models include chemical transformation models such as Henrikson’s acidification model (Henrikson et al., 1988), which was used to calculate the permissible emis- sions of acid gases in the context of determining a target loading of acid for sen- sitive lakes. Table 4.14 lists just a few models in an attempt to illustrate the range of those that have application to environmental toxicology. Not all these models directly involve the living organism. For example, WHAM (Windermere Humic Acid Model) is a chemical equilibrium speciation model, which can predict the
loss include the following: K values are the rate constants: K1= the uptake
rate constant; K2= the depuration rate constant; KR= the degradation rate
constant; KA= the food uptake rate constant; KE= the egestion rate constant;
KD= the growth dilution rate constant. C values are concentrations: CW= the
dissolved concentration in fish; CF= the concentration in whole fish; CA= the
concentration in food. fW, fF, and fAare the fugacity transport rate constants
corresponding to the concentrations CW, CFand CA. D values (e.g., DV) are
fugacity rate constants corresponding to the rate constants such as K1. The
groups K1CWand DVfW, respectively, are essentially equivalent methods of
expressing the same process rate. Based on Mackay (1991).
Modelling 173
chemical forms of metals, with particular reference to the effect of natural organic substances (humic acids). Toxicologists know that organic substances have a major influence on the toxicity of metals, through their ability to affect the bioavailabil- ity. Thus, WHAM, although it deals exclusively with chemistry, has real value to the environmental toxicologist. Each of the models was designed with a specific purpose in mind, a point that should be emphasised when considering the advan- tages and disadvantages of modelling in environmental toxicology.
Comparisons have been made among different models that address the same or similar problems. Games (1983) compared three types of models for estimat- ing exposure to linear alkylbenzene sulphonate (LAS) and concluded that “each model is applicable at a particular stage in hazard assessment”. This appears to reinforce the maxim that in applying any method or approach in science, it is critically important to start with a clear understanding of the question that one is to address.
4.6.4 Advantages, limitations, and pitfalls in the modelling for
environmental toxicology
The advantages of the modelling approach were described in Section 4.6.3. Briefly, these advantages include the capacity of models to
a. Synthesise knowledge;
b. Analyse the properties of entire systems;
Table 4.14. Examples of mathematical modelling applied to
environmental toxicology
Perturbation/toxic Type of model/model Reference substance characteristics
Organic chemical in a Environmental fate: fugacity Mackay (1991) water body
LAS Environmental fate: exposure Burns et al. (1981) analysis modelling system
LAS Simplified lake/stream analysis DiToro et al. (1981) Metals in combination WHAM designed to calculate Tipping (1994)
with organic matter equilibrium chemical speciation of metals in surface and ground waters, sediments and soils
PAHs Environmental fate: transport, Bartell et al. (1984) degradation, and
bioaccumulation
Mercury Distribution among compartments Harris (1991) in a reservoir
Sulphuric acid (acidic Steady-state chemistry, prediction Henrikson et al. (1988) deposition) in fresh of critical loading with respect