Validation of Haber's Rule (dose × time = constant) in rats and mice for monochloroacetic acid and 2,3,7,8-tetrachlorodibenzo-p-dioxin under conditions of kinetic steady state

Haber's Rule and associated time to coma after monochloroacetic acid (MCA) exposure in male Sprague-Dawley (SD) rats and time to death after 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD) exposure in female Sprague-Dawley rats and male A/J mice were investigated at isoeffective or nearly isoeffective doses. Animals exposed to MCA received either single bolus intravenous (iv) doses or a loading dose rate via the iv route followed by a maintenance dose rate through subcutaneously implanted osmotic mini pumps. For TCDD, rats received a loading dose rate via bolus oral gavage followed by maintenance dose rates through iv injection every fourth day until death. Mice received both loading and maintenance (once a week) dose rates via oral gavage. Different dosing regimens were employed to demonstrate that the key to Haber's Rule lies not in the route of administration but in conducting experiments under conditions of kinetic steady state. Single doses of MCA produced inconsistent time responses but a reasonably constant c × t product (7657 ± 391 mg/kg × min) which was not anticipated although it should have been expected because MCA's elimination half-life (2 h) is twice as long as its time to coma (∼1 h). Generation of kinetic steady state by infusion of MCA after iv injection of a loading dose rate resulted in a consistently decreasing time response with increasing dose which diminished the variability in the c × t (dose × time) = k relationship (8032 ± 136 mg/kg × min). Both acute and chronic toxicity of TCDD under conditions of kinetic steady state yielded consistent time responses with inverse proportionality between dose and time leading to robust c × t = k products in both rats (1060 ± 82 μg/kg × day) and mice (80 ± 2 mg/kg × day).