Concentration-duration relationships

After determining the health-effect endpoint to be used in deriving the value(s) for n, the next step is to evaluate the quality and the quantity of the data to be used in the derivation. Obviously, two data points will define the slope of a curve describing the exposure concentration-duration relationship. However, the validity and, hence, the values of n will depend on many factors, including the scientific soundness of the exposure concentration-duration data, the length of the empirical exposure duration(s) relative to the AEGL-specified exposure periods, and the known or perceived similarities in effects and mechanism of action of the chemical at the reported exposure concentrations and durations. Generally, three empirical data points will improve the scien... 

Once the health-effect endpoint and data points describing the exposure concentration-duration relationship have been selected, the values are plotted and fit to a mathematical equation from which the AEGL values are developed. There may be issues regarding the placement of the exponential function in the equation describing the concentration-duration relationship (e.g., C x t = k vs C X t = k2 vs X E = k3>. It is clear that the exposure concentration-duration relationship for a given chemical is directly related to its pharmacokinetic and pharmacodynamic properties. Hence, the use and proper placement of an exponent or exponents to describe these properties quantitatively is highly complex and not completely understood for all materials of concern. 

The quantitative description of actual empirical data of the concentration-duration relationship can be expressed by any of a number of linear regression equations. In the assessment of empirical data reported by ten Berge et al. (1986), these workers quantified the exposure concentration-duration relationship by varying the concentration to the n power. Since raising c or t or both to a power can be used to define quantitatively the same relationship or slope of the curve and to be consistent with data and information presented in the peer-reviewed scientific literature, the equation C x t = k is used for extrapolation. It must be emphasized that the relationship between C and t is an empirical fit of the log transformed data to a line. No conclusions about specific biologic mechanisms of action can be drawn from this relationship. 

When adequate data describing exposure concentration-duration relationships for a specific chemical and toxic endpoint of interest are not available, an alternative approach to estimating this relationship quantitatively must be followed. The approach used by the NAC/AEGL Committee involves the application of the equation C x t = k and the selection of a value or values of n that results in AEGL values that best fit the supporting data for the chemical and toxic endpoint in question. It is important to distinguish the difference between the derivation of values of n as described in the preceding section and the selection of values of n as described in this section. 

CD c/f CO nj 3 CD /I c 5. Description of the data from the surrogate chemical used to derive the exposure concentration-duration relationship. If a derived value of n is used, the equation should be included. 

Probit Equation The probit equation has been used in an attempt to quantitatively correlate hazardous material concentration, duration of exposure, and probability of effect/injury, for several types of exposures. The objective of such use is to transform the typical sigmoidal (S-shaped) relationship between cause and effect to a straight-line relationship (Mannan, Lees Loss Prevention in the Process Industries, 3d ed., p. 9/68, 2005). 

Insufficient data were available to establish a concentration-exposure duration relationship for a single end point. LC50 values for the rat at 15 min and 4 h were several hundred thousand parts per million (Table 3-3). 

Neurological Effects. The major public health concern regarding -hexane exposure is the potential for the development of neurotoxicity. Occupational studies have documented that human exposure to -hexane can result in a peripheral neuropathy that in severe cases can lead to paralysis (Altenkirch et al. 1977 Yamamura 1969 Wang et al. 1986). The dose-duration relationship has not been well characterized in humans, but concentrations of 500 ppm and above, and exposure for 2 months or more have been associated with human neurotoxicity. Brief exposure to extremely high concentrations of w-hexane may cause signs of narcosis in humans prostration and coma have been observed in animals exposed to a mixture of hexanes at concentrations of 70,000-80,000 ppm (Hine and Zuidema 1970). At these levels, however, explosion and fire would be the main concern. 

Doses selected for safety pharmacology studies are typically based on the criteria established in the ICH S7A guidance.25 Doses should exceed those projected for clinical efficacy and at the upper limit be bound by (1) adverse pharmacodynamic effects in the safety pharmacology study (2) moderately adverse effects in other non-clinical studies that follow a similar route and duration of dosing or (3) limit of solubility/toxicity. In the absence of adverse effects, the maximum administrable dose can be used. If nonreusable animals enter the study, then the maximum tolerated dose may be appropriate. Most importantly, the doses/concentrations should establish the dose/concentration-response relationship of the adverse effect. 

Some drugs exhibit unusual concentration/response relationships, which minimizes the utility of TDM. In these cases, clinical response correlates more with duration of dosing than the actual dose or resultant plasma concentrations. 

If appropriate toxicologic data for the exposure concentration-exposure duration relationship of a specific health-effect endpoint are available for the AEGL-specified exposure periods, use the empirical data directly. 

If toxicity data are available for aU four AEGL-specified exposure periods, there is no need to derive values of n, and the empirical data for each exposure period can be used directly. However, it is rare that toxicity data are sufficiently comprehensive to encompass all the AEGL-specified exposure periods from 10 min to 8 h. Further, there are instances in which empirical data are not available to estimate n and predict the exposure concentration-exposure duration relationship using C" x t = k. Therefore, the sequential approaches used by, or available to, the NAC/AEGL Committee to establish AEGL values for the specified exposure periods are discussed in the following sections. 

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