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THE ROLE OF MOBELS IN THEORETICAL BIOLOGY 185

situ. This similarity can be demonstrated in an objective manner by reference to modeling criteria.

C. Miscellaneous Artificial Analogs of Biological Systems

Brief mention will be madę of a variety of qualitative simulators of biological Systems which have not previously been analyzed from the yiewpoint of physical similarity theory. Among such devices one may include artificial heart valves, arm prostheses, mannikins used for studies of car crashes or radiation effects, and many other physical artifacts.

Artificial cardiac valves have been brought to an advanced state and are now regularly implanted in humans. Flap-type valves with one to three leaflets have been madę artificially and function much Iike the natural ones, but entirely different valve arrangements, such as the ball-in-cage valve are also very successful. Model studies of these valves have been madę on the assumption of Reynolds number invariance, which makes possible study of flow pattern and local turbulence effects. Artificial aortas and other vessels madę of synthetic fabrics are widely used. Flow pattern models of such structures have been madę. These analogs share in common with their prototypes certain dimensional constants pertaining to elasticity, stress resistance, surface roughness, and geometry.

Mannikins or full-size structural models of humans are physical analogs based largely on geometrie similarity. They may be constructed of various specific materials whose dimensional constants reflect a partic-ular kind of simulation need. For example, mannikins have been much used for studies on injury in automobiles, airplanes, space vehicles, and during military combat. A very complete static structural model of the human body, which reproduces location of center of gravity to within a fraction of an inch, has been discussed by Hanayan (1964) in connection with astronautics. Physical models of yarious types have been used in design of space vehicles. In such cases the stress moduli of the mannikin usually relate to those of tissue.

Gelatin blocks have been used to study shock waves from bullets entering the body. Yarious mock-ups of the skuli and brain are useful for simulation of brain concussion. Rather different effects are simulated by so-called “radiation phantoms” designed to reveal radiation penetra-tion into the organism. These physical models are only partially similar geometrically, but madę of materials with precisely the same radiation absorption characteristics as tissue; they yield quantitative results for