ABSTRACT

The mathematical modeling of biological systems, restricted even to the field of toxicology, is an extremely large and vigorously growing area. Broadly speaking, modeling is the principal conceptual tool by which toxicology seeks to develop as a mechanistic science. In an iterative process, models are developed or proposed, tested by experiment, reformulated and so on in a continuous cycle. Such a cycle could also be described as two related types of modeling - explanatory (where the concept is formed) and correlative (where data are organized and relationships derived). The outcomes of the cycle are predictions (with cautious extrapolation beyond the range of existing data) and inferences (about analogous situations which are difficult or impossible to measure directly, such as risk of carcingogenesis at extremely low levels of exposure to a material). It is the special area of these last two (prediction and inference) that will be addressed here. An excellent introduction to the broader field of modeling of biological systems can be found in Gold (Gold, 1977).