Does Haber's Law Apply to Human Sensory Irritation?

Irritation of the eyes, nose, and throat by airborne chemicals—also referred to as “sensory irritation”—is an important endpoint in both occupational and environmental toxicology. Modeling of human sensory irritation relies on knowledge of the physical chemistry of the compound(s) involved, as well as the exposure parameters (concentration and duration). A reciprocal relationship between these two exposure variables is postulated under Haber's law, implying that protracted, low-level exposures may be toxicologically equivalent to brief, high-level exposures. Although time is recognized as having an influence on sensory irritation, the quantitative predictions of Haber's Law have been addressed for only a handful of compounds in human experimental studies. We have conducted a systematic literature review that includes a semiquantitative comparison of psychophysical data extracted from controlled human exposure studies versus. the predictions of Haber's law. Studies containing relevant data involved exposures to ammonia (2), chlorine (2), formaldehyde (1), inorganic dusts such as calcium oxide (1), and the volatile organic compound 1-octene (1). With the exception of dust exposure, varying exposure concentration has a proportionally greater effect on sensory irritation than does changing exposure duration. For selected time windows, a more generalized power law model (cⁿ × t = k) rather than Haber's law per se (c × t = k) yields reasonably robust predictions. Complicating this picture, however, is the frequent observation of intensity–time “plateauing,” with time effects disappearing, or even reversing, after a relatively short period, depending on the test compound. The implications of these complex temporal dynamics for risk assessment and standard setting have been incompletely explored to date.