AJP - Regulatory, Integrative and Comparative Physiology, Vol 244, Issue 5 591-R599, Copyright © 1983 by American Physiological Society
Role of similarity principles in data extrapolation
R. Rosen
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.
