Risk Index for Multiple Substances That Cause Deterministic Responses

2 Risk Index for Multiple Substances That Cause Deterministic Responses. The risk index for mixtures of substances that cause deterministic responses should be expressed in terms of dose, rather than risk, because risk is not proportional to dose and the goal of risk management is to limit doses to less than the threshold in the dose-response relationship (see discussion of Equation 6.2 in Section 6.3). As noted previously, deterministic responses from exposure to radionuclides should not be of concern in classifying waste, in which case only the risk index for chemicals that induce deterministic responses needs to be considered. 

Formulation of the risk index for mixtures of substances that cause deterministic effects is considerably more complex than in the case of substances that cause stochastic effects discussed in the previous section. The added complexity arises from the threshold dose-response relationship for these substances and the need to keep track of the dose in each organ or tissue at risk in evaluating whether the dose in each organ is less than the allowable dose in that organ. For substances that cause deterministic responses, the index T can refer not only to a specific organ or tissue (e.g., the liver or skin) but also to a body system that may be affected by a particular chemical, such as the immune or central nervous system. 

In essence, the procedure for evaluating Equation 6.5 involves calculation of a separate risk index for each organ at risk and a comparison of the results. The various steps in the procedure are described as follows  

The order in which the summations over the responses (r) and substances (i) of concern are executed in the second and third steps above is arbitrary. However, these steps must be executed before the MAX and INTEGER functions are applied to the result. If the risk index for substances causing deterministic responses were based on calculations of health risk per se, rather than dose, the INTEGER function in Equation 6.5 would not be necessary, because the risk would be zero whenever a dose is below the threshold. Again, however, evaluation of the risk index for substances that cause deterministic responses based on dose is recommended when the dose-response relationship is assumed to have a threshold. The use of dose is supported by the observation that the dose-response relationship above the threshold generally is nonlinear. 

It must be emphasized that the sum-of-fractions rule for substances that cause stochastic responses (see Equation 6.4) generally does not apply in calculating the risk index for mixtures of substances that cause deterministic responses. That is, based on an assumption of a 

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