Concentration × time analyses of sensory irritants revisited: Weight of evidence or the toxic load approach. That is the question.

The toxic effects resulting from inhalation exposure depend on both the concentration (C) of the inhaled substance and the exposure duration (t), including the assumptions that the exposure-limiting toxic effect is linearly linked with the accumulated C × t (inhaled dose), and detoxification or compensatory responses diminishing this dose are negligible. This interrelationship applies for both constant and fluctuating concentrations and is usually expressed by the toxic load equation C ⁿ × t = constant effect (k). The toxic load exponent 'n' is derived from both C- and t-dependent exponents with C ^b2 ×t ^b3 = k with n = b ₂ /b ₃ . This model is taken as a fundamental basis for assessing the acute hazard posed by atmospheric releases of noxious substances, whether deliberate or accidental. Despite its universal use, especially for inhaled irritants, the toxicological significance of this mathematical construct is still discussed controversially. With n = 1 this equation is called Haber's rule. The underlying assumption is that the exposure-based calculated and the actually inhaled C ^b2 ×t ^b3 are identical. Unlike the calculated dose, the latter is dependent on the test species and its t-dependent change in respiratory minute volume (MV). The retention patterns of inhaled irritant vapors may differ in obligate nasal breathing rodents and oronasally breathing humans as well. Thus, due to the interdependence of n on both C, t and k, this mathematical construct generates a bioassay-specific 'n' which can hardly be considered as human-equivalent, especially following exposure to sensory irritants known to elicit reflex-related changes in MV. The C- and t-dependent impact on C ⁿ × t = k was analyzed with the sensory irritant n-butyl monoisocyanate and compared with t-dependent changes elicited by highly, moderately, and poorly water-soluble sensory irritants ammonia, toluene diisocyanate, and phosgene, respectively. This comparison reveals that n depends on several factors: In cases where MV is instantly and plateau-like depressed with onset of exposure, n appears to be most dependent on C ^b2 × MV whereas for a similar slower time-dependent response n becomes more dependent on MV × t ^b3 . For any ensuing risk characterization that focuses on acute non-lethal threshold C ^b2 × t ^b3 's, the sensory irritation-related depression in MV must be known to arrive at meaningful conclusions. In summary, both C ⁿ - and t-dependent dosimetry-related pitfalls may occur in acute bioassays on rodents following inhalation exposure to irritants. These must be identified and dealt with judiciously prior to translation to apparently similar human exposures. By default, extrapolations from one duration to another should start with that C ⁿ × t eliciting the least depression in MV with n = 1.
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