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THE ROLE OF MODELS IN THEORETICAL BIOLOGY 179

thirty to fifty numerical parameters, most of which are independent of size and many of which are dimensionless, and therefore are physical modeling criteria. Transparent plastic casts of the human bronchial trees were used for flow studies by Dekker (1961) and West and Hugh-Jones (1959). In both cases, there was nearly perfect geometrie similarity. Dyes allowed flow pattern visualization, with air or water as media. The Reynolds number was picked as the basie modeling invariant and also indicated tendency to turbulent flow.

An entirely different lung phenomena is modeled in a report by Birath (1959), who used an artificial model to study gas-mixing between the stagnant “dead” space of the bronchial trees and the alveolar lung volume which is active in gas exchange. Studies were madę of effects of residual lung volumes and flow rates on the mixing front depth. Pertinent similarity criteria for this situation include volume, velocity and flow ratios, the Euler and Reynolds numbers and others. Very similar types of model studies have been used in Chemical engineering (Johnstone and Thring, 1957) for analysis of entry of Chemicals through pipes into reactor vessels. A model of dead-space mixing phenomena is described by Wise and Defares (1959), but without explicit statement of physical similarity conditions.

An example of physiological modeling entirely comparable to what is normally encountered in engineering practice is presented in the work of Holladay and Bowen (1963) and Bowen and Holladay (1962) which deals with the use of rabbits to study blast effects from atomie weapons on humans. In this case the rabbit is a “natural model” of the human, but the authors also analyze eąuations for artificial physical analogs of the thoracic cage subjected to sudden pressure waves. Some of the Principal dimensionless parameters are volume and section ratios, pressure ratios (Thoma number), and the Euler number. Another engineering approach is exemplified in reports of Friedlander (1964) and Hursh (1962) on particulate deposition in the human lung. The object of these studies was to develop eąuations covering all sizes of animals, lungs, and particulates, and for various flow rates, which is a typical kind of engineering reąuirement.

C. Electrical Analog Models

A number of reports on electronanalog models of physical (not control) phenomena in the cardiovascular-respiratory systems are also available. For example, Defares et al. (1963), Newburg (1963), and De Pater and Van Den Berg (1964) all attempt to create complex analog simulators