Risk assessment mathematical model

Environmental toxicology—Mathematical models. 2. Health risk assessment—Mathematical models. 3. Extrapolation. I. Solomon, Keith R. II. SETAC (Society)... 

The structure and mathematical expressions used in PBPK models significantly simplify the true complexities of biological systems. If the uptake and disposition of the chemical substance(s) is adequately described, however, this simplification is desirable because data are often unavailable for many biological processes. A simplified scheme reduces the magnitude of cumulative uncertainty. The adequacy of the model is, therefore, of great importance, and model validation is essential to the use of PBPK models in risk assessment. 

Mathematical Modeling Application to Environmental Risk Assessments... 

This gives an example of fate modeling in which the risks of an insect growth inhibitor, CGA-72662, in aquatic environments were assessed using a combination of the SWRRB and EXAMS mathematical models.. Runoff of CGA-72662 from agricultural watersheds was estimated using the SWRRB model. The runoff data were then used to estimate the loading of CGA-72662 into the EXAMS model for aquatic environments. EXAMS was used to estimate the maximum concentrations of CGA-72662 that would occur in various compartments of the defined ponds and lakes. The maximum expected environmental concentrations of CGA-72662 in water were then compared with acute and chronic toxicity data for CGA-72662 in fish and aquatic invertebrates in order to establish a safety factor for CGA-72662 in aquatic environments. 

The major objective of this presentation is to illustrate how an environmental risk assessment of a chemical can be made using mathematical models which are available at the present time. CGA-72662, a CIBA-GEIGY insect growth inhibitor, is used as an example to show how a risk assessment can be carried out using the SWRRB runoff model coupled to the EXAMS fate model. 

ECETOC (1994) HAZCHEM. A mathematical model for use in risk assessment of substances. Special report n. 8. European Centre for Ecotoxicology and Toxicology of Chemicals, Brussels... 

Other major early contributions of biochemical engineering have been in the development of the artificial kidney and physiologically based pharmacokinetic models. The artificial kidney has been literally a lifesaver. Pharmacokinetic models divide the body of an animal or human into various compartments that act as bioreactors. These mathematical models have been used very successfully in developing therapeutic strategies for the optimal delivery of chemotherapeutic drugs and in assessing risk from exposure to toxins. 

Typically extrapolations of many kinds are necessary to complete a risk assessment. The number and type of extrapolations will depend, as we have said, on the differences between condition A and condition B, and on how well these differences are understood. Once we have characterized these differences as well as we can, it becomes necessary to identify, if at all possible, a firm scientific basis for conducting each of the required extrapolations. Some, as just mentioned, might be susceptible to relatively simple statistical analysis, but in most cases we will find that statistical methods are inadequate. Often, we may find that all we can do is to apply an assumption of some sort, and then hope that most rational souls find the assumption likely to be close to the truth. Scientists like to be able to claim that the extrapolation can be described by some type of model. A model is usually a mathematical or verbal description of a natural process, which is developed through research, tested for accuracy with new and more refined research, adjusted as necessary to ensure agreement with the new research results, and then used to predict the behavior of future instances of the natural process. Models are refined as new knowledge is acquired. 

The most widely used of the many mathematical models proposed for extrapolation of carcinogenicity data from animal studies to low-dose human exposures (i.e., low-dose extrapolation) is the LMS model. This has, in effect, become the default approach for quantitative risk assessment and has been used by, e.g., the US-EPA for many years as well as by the WHO in relation to derivation of drinking-water guideline values for potential carcinogens (WHO 1996) (see Section 9.2.1.2 for drinking-water guideline values). 

In ecological risk assessment, we use mathematical models to determine which variables to measure, specify how they relate, and to estimate the values of variables we cannot measure directly. Model uncertainty is a serious challenge in ecological... 

A probabilistic risk assessment (PRA) deals with many types of uncertainties. In addition to the uncertainties associated with the model itself and model input, there is also the meta-uncertainty about whether the entire PRA process has been performed properly. Employment of sophisticated mathematical and statistical methods may easily convey the false impression of accuracy, especially when numerical results are presented with a high number of significant figures. But those who produce PR As, and those who evaluate them, should exert caution there are many possible pitfalls, traps, and potential swindles that can arise. Because of the potential for generating seemingly correct results that are far from the intended model of reality, it is imperative that the PRA practitioner carefully evaluates not only model input data but also the assumptions used in the PRA, the model itself, and the calculations inherent within the model. This chapter presents information on performing PRA in a manner that will minimize the introduction of errors associated with the PRA process. 

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