Role of similarity principles in data extrapolation.

This paper addresses the problem of extrapolating from data set gathered on a particular system to problems of more general physiological interest. It asks: what are the limits of the extrapolability of data? Under what circumstances can data derived from a particular system be transformed into data about another, different system? Such questions address the general problem of similarity analysis. A mathematical exploration of the meaning and usefulness of the concept of similarity is presented, and the necessity for a "prototype" is introduced. The discussion shows what we mean by the relationship between natural systems and the purest form of model of such systems, the mathematical model. The value and limitations of Dimensional Analysis are considered. It is concluded that the principle of dimensional homogeneity which underlies Dimensional Analysis is not strong enough to cope effectively with situations involving many phases, as arise in biological studies. Therefore, a more general approach is used. It is shown that the problems associated with data extrapolation are very deep and lead to some of the deepest issues in all of science. The extrapolation of data from animal models to human beings has been a general characteristic of pharmacologic research and, for that matter, biomedical investigations generally. Attention to limitations and dangers of such extrapolations seems overdue. With proper understanding of the essential nature of the extrapolatory action, and modeling relations, models can be validated.