ABSTRACT
The concept that the product of the concentration (C) of a substance and the length of time (t) animals are exposed to it produces a xed level of effect for a given endpoint has been ascribed to Ferdinand Flury and Fritz Haber, who described the behavior of war gases (Witschi, 1999) in the early 1900s. While it was recognized that C × t = k was applicable only under certain conditions, many toxicologists have used this rule to analyze experimental data whether or not the respective chemicals, biological endpoints, bioassay, and exposure scenarios were suitable candidates for the rule. In the early days of toxicology, the mathematical solutions were straightforward using a log-log plot of C and t composed of two or more rectilinear segments, for when the log-log plot was curvilinear, and for when the slope of the dosage-mortality curve was a function of C. Experimental data from this relationship suggest that C and t are interchangeable within the short time limits given, but that under specic conditions, concentration becomes more important than time in predicting toxicity. Such dose-rate-dependent variables may come into play when the inhaled dose is not any longer proportional to C because the rate of intake is affected by time-related changes in ventilation. Likewise, intake does not necessarily mean uptake, which, for gases, is retention dependent. Retention changes with time due to the t-dependent saturation of the immediate compartment of uptake. Hence, with increasing exposure duration, the tissues of the respiratory tract become increasingly saturated, and inhaled gases, depending on the chemical reactivity and water solubility, may be exhaled without being retained. At steady state, the retention of an inhaled gas decreases toward a plateau, and ventilation becomes less important than perfusion. This picture might further be complicated by time-dependent changes in wash-in/wash-out equilibria. Accordingly, C × t relationships have to be analyzed and interpreted with caution and need to be distinguished for exposure durations representing the early yet non-steady-state condition and that occurring at steady state. When substituting the
6.1 Introduction .......................................................................................................................... 121 6.2 Background on Requirements for Time Scaling .................................................................. 122 6.3 Time Dependence of Toxicological Outcomes ..................................................................... 125 6.4 Haber’s Rule and the Toxic Load Exponent ......................................................................... 130
6.4.1 Haber’s Rule, Irritation, and Variables That Affect Dosimetry ............................... 131 6.4.2 Haber’s Rule, Exposure Regimen, and Species Differences .................................... 133
6.5 Implications for Hazard Identication and Risk Assessment ............................................... 133 6.6 Conclusion ............................................................................................................................ 134 Questions ........................................................................................................................................ 135 References ...................................................................................................................................... 135
toxic load exponent n = a/b in Ca × tb, this equation is simplied to Cn × t = constant effect outcome, which appears to embrace most of the variables affecting the dose rate of uptake.
