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182 WALTER R. STAHL

titative greenhouse studies on the effects of water, light intensity, fertil-izer concentration, etc., on plant size and useful yield. Physical models have been madę of water spread, trapping, and leaching in soils (Cline, 1961). Civil engineers have, for many years, used models of water run-off, erosion, and various wind effects. Margalef (1962, 1963) constructed physical analogs of the energy distribution in a marinę ecosystem, with simulation of vertical mixing, sunlight penetration, plankton mass transfer, and other phenomena. Odum (1960) describes an electroanalog model of an ecosystem based on energy, biomass migration, and move-ment phenomena, while Olson (1963) uses an analog Computer model of radionuclide movement in ecosystems.

It is elear that a very wide variety of physical analogs of biological structures have been constructed, but in only a very few instances have all necessary conditions for quantitative modeling been satisfied. It is desirable that reports dealing with physical biological models state precisely which similarity criteria or dimensionless numbers are pertinent to the particular analog and under what conditions quantitative findings from the model can be extrapolated to the living prototype.

IV. Artificial Organs

Heart-lung machines and artificial kidneys are characterized by certain variables such as volumetric flow rates, oxygen uptake rates, membranę constants, active and passive volumes, certain linear flow rates (veloc-ities), etc., which are also applicable to the natural organs. These vari-ables may be combined into certain dimensionless numbers which characterize performance of the artificial organ. It is very significant that in most cases the pertinent design criteria are also appropriate to the natural organ system and have, in some cases, already been used for quantification of physiological performance. Artificial organs are in-complete but operative models of real ones, though usually much larger in size, completely dissimilar in appearance, madę of different materials, and lacking in many physiological mechanisms. Since they are only partial models, data obtained from artificial organs is certainly never expected to yield valid information about organs in situ.

A. Heart-Lung Machines

Numerous reports are available on heart-lung machines, which, in generał, contain equivalents to a heart pump, vasculature, lung volumes, lung membranę, capillary membranę, and oxygen-intake flow system.