Perspectives on dimensional analysis in scaling studies

Scaling, as defined here, refers to the precise identification of those structural and functional aspects of selected systems that are size-independent, over some specified size-range. Small and large instances of such systems are said to be similar in respect to those aspects. Physicists and engineers have developed an elaborate methodology for identifying quantitative similarity criteria applicable to physical systems. These criteria are usually derived by dimensional analysis of physical laws pertinent to a given system. Knowledge of similarity criteria allows one to predict quantitatively the behavior of a large-scale prototype from measurements made on a small-scale model (e.g., in a wind tunnel). Numerous workers have sought to apply this elegant methodology to scale-up in biology. After briefly reviewing dimensional analysis, scaling, and modeling, as deployed in physics and engineering, this article discusses several well-known examples of their application to bioscaling problems (chiefly in mammals) and gives reasons for doubting their validity. It concludes that this methodology is unlikely to provide explanations applicable to scale-up in diverse species.