Vol. 296, Issue 3, 663-668, March 2001

The Role of Time as a Quantifiable Variable of Toxicity and the Experimental Conditions When Haber's c × t Product Can Be Observed: Implications for Therapeutics

Karl K. Rozman and John Doull

Department of Pharmacology, Toxicology and Therapeutics, University of Kansas Medical Center, Kansas City, Kansas (K.K.R, J.D.); Section of Environmental Toxicology, GSF-Institut für Toxikologie, Neuherberg, Germany (K.K.R.)

One hundred years ago, Warren established for the first time a quantitative link between dose and time while studying the toxicity of sodium chloride in Daphnia magna (Straus). During this century, many toxicologists in different contexts returned to this idea, which has become known as Haber's Rule of inhalation toxicology. Most attempts to explore this relationship ended in frustration because of the observed deviations from it, which were unfortunately called exceptions. Thus, toxicologists concentrated on the quantitative relationship between dose and effect under mostly isotemporal conditions, while time was assigned such arbitrary, semiquantitative designations as acute, subacute, subchronic, and chronic. Time itself as a quantifiable variable of toxicity was seldom studied and when it was examined, it was often not done under isodosic (steady-state) conditions. A recent analysis of time as a variable of toxicity indicated the existence of at least three independent time scales (toxicokinetic, toxicodynamic, exposure frequency/duration) in toxicological studies, which interact with dose and effect to yield the enormous complexity known to every toxicologist. Based on prototypical examples when toxicokinetic (dioxins, chloroacetic acid), toxicodynamic (nitrosamines, soman, sarin, tabun), exposure frequency (methylene chloride), or other experimental design-related conditions (HgCl₂, CdCl₂) represent the critical time scale, the general validity of the c × t = k concept will be discussed as a starting point for a theory of toxicology. As endpoints of toxicity, (delayed) acute toxicity, blood dyscrasias, and cancer will be used to illustrate the critical conditions needed to demonstrate the validity of this theory. The relevance of this theory to the pharmacologic action of chemicals and its implication for the therapeutic index are also discussed.