Quantitative definition of toxicity: a mathematical description of life and death with dose and time as variables

Abstract

This manuscript raises some fundamental issues about the role of time as a variable in toxicology, with implications for all biological sciences and also for disciplines dealing with inanimate systems. The dose-response has taken center stage ever since its formulation by Paracelsus. Time-responses have been considered in the past in various contexts such as time to tumor development or half-life of a compound in an organism. However, there has been, to my knowledge, no successful attempt to tie together dose and time in a generalizable theory. This paper describes toxicity by the minimum number of variables (dose and time) from a macroscopic point of view. Interestingly, these fundamental considerations of the dose- and time-dependence of toxicity led to a simple mathematical formulation, which consists of parts previously recognized as valid under specific conditions of experimentation (Haber's Law of Inhalation Toxicology, Druckrey's Law of Cancer Development).