## Info

kg body weight

The animal must eat one-tenth its body weight each day to maintain the stated body burden.

### 18.7.2 Steady-State Model and Bioaccumulation

The uptake and retention of contaminants in tissues in excess of concentrations in the source of the contaminant (such as food or water) is called bioaccumulation. In Figure 18.8, uptake is being held constant, but elimination increases as concentration increases. A situation is approached asymptotically where elimination balances uptake, and the system will be at steady state. The concentration at which this will occur can be determined in two equivalent ways, as mentioned above. One would be to take the limit of equation (18.22) as t !i. The other is to set equation (18.21) to zero and solve for C. Either way gives the same result for the steady-state concentration, Css. The ratio of Css to Cf is the bioaccumulation factor, KB (also designated BAF):

Cf ke

Bioaccumulation can occur with other routes of exposure. One would develop different models for KB if this were the case. In this case, since Css is expressed per unit body weight and Cf is per weight of food, KB will depend on the mass of food ingested per day per body weight. The caloric requirement of organisms is related to their surface area; therefore, smaller animals tend to have higher bioaccumulation by ingestion (although other routes of exposure may be more important). It can also depend on other things that influence metabolic rate, such as stress or temperature. If elimination occurs predominantly by interphase mass transfer, as is often the case with xenobiotic compounds, ke will be inversely related to the partition coefficient, making KB directly related. This accounts for the observation that bioaccumulation is strongly correlated with KOW, especially if the concentration in fatty tissues is used in place of whole body concentration.

Example 18.7 In Example 18.6, what is the bioaccumulation factor?

Answer Kb = 80mg/kg/(10mg/kg)= 8; also, Kb = aWf¡ke = (1.0) (0.102 day"1)/ 0.0128 day"1 = 8.

### 18.7.3 Equilibrium Model and Bioconcentration

Other mechanisms can give proportional bioaccumulation relationships. For example, consider a one-compartment model in which both uptake and elimination are by mass transfer between the environmental concentration, Cenv, and the concentration within the organism, Corg. For example, this might apply to the uptake of hydrocarbons from the air by terrestrial animals or from the water for aquatic animals. In such cases, uptake and elimination could be described by equation (18.12), with mass transfer coefficients ku and ke for the respective rates ru and re:

re ke(KPCenv Corg)

Assuming steady state, the mass balance leads to the relationship that the rate of uptake equals the rate of elimination:

The process in which bioaccumulation occurs by direct uptake from the environment is called bioconcentration. It is distinguished from bioaccumulation in that bioaccumulation includes all routes of exposure, whereas bioconcentration only considers uptake directly from the environmental medium in which the organism lives. The term bioconcentration is usually reserved for aquatic systems.

Equations (18.27) and (18.28) can be combined and solved for the ratio of organism concentration to environmental concentration, called the bioconcentration factor (KC, also designated BCF). In this case,

Thus, for this model the bioconcentration factor is equal to the partition coefficient. Again, it must be emphasized that both the bioaccumulation factor and the bioconcentration factor can be derived from different models using different assumptions. For example, if we assume simple first-order rate processes for uptake and elimination:

where in this case ku and ke are the uptake and elimination rate coefficients, respectively, then the bioconcentration factor would be written as

Thus, the bioconcentration and bioaccumulation factors are not defined uniquely in terms of a particular model. More generally, they are defined as the ratio of organism concentration to the concentration in the environment and/or the food supply.

Whatever the theoretical mechanisms are to explain the bioconcentration factor, experimental measurements have shown that it correlates with KOW. For example, measurements with 64 organics in fish have been used to develop the following empirical relationship:

Relationships such as this should be used cautiously, however. Although they are useful over a wide range of KOW, at a particular values the upper and lower 95% confidence levels can differ by a factor of 63. Furthermore, numerous correlations of this form have been developed for different groups of chemicals and different species. Some studies have correlated KC with aqueous solubility instead of KOW. Several of these physicochem-ical parameters are given in Table 18.5.

A more complete model would separately take into account the processes of environmental uptake, ingestion, biotransformation, and excretion:

Assuming steady state, rearranging, and substituting for KC and KB from equations (18.26) and (18.31) shows the contribution to body burden by environmental uptake and ingestion:

TABLE 18.5 Bioconcentration Factors and Physicochemical Parameters for Some Compounds That Bioaccumulate

Compound Log Kow Log10 KC CS (mg/L)

Chlordane