Stahl67 bmp

178 WALTER R. STAHL

a dimensionless criterion associated with the Poiseuille flow law. Bugliarello and Hsiao (1964) madę models of blood flow and celi “skim-ming” phenomena at bifurcations of smali vessels, whereas Scharfstein and co-workers (1963) used a pbysical analog to study boundary layer shearing effects in blood vessels that may cause injury and eventually atherosclerosis. Charm et al. (1963) applied models to study the anomalous viscosity of blood in smali vessels.

The rather large majority of so-called compartment model studies are based on numerical kinetics, as discussed in Section III, B, but purely physical analogs of mixing and flow between Chemical reactor vessels are also known and already used in Chemical engineering. Gorton and Gunnells (1961) have described a glass tubing model of the aorta which is used to simulate mixing phenomena when a dye is injected into the circulation. Wendel (1961) uses a hydrodynamic model to study entry, absorption, and excretion of drugs into the circulation. A model of the circulation based on “random-walk” theory is described by Sheppard (1962). Although largely numerical in naturę, this work makes use of dimensionless physical variables relating diffusion time to circulation.

The above analogs should be distinguished from qualitative simulators of the cardiovascular system of mammals, such as the very complete one described by Rothe and Selkurt (1962). This tabletop system demon-strates a wide variety of phenomena pertaining to cardiac and peripheral relationships, but is not invariant for all of the basie similarity criteria which govern the natural cardiovascular system and therefore cannot yield real quantitative data about a natural prototype.

Although not part of the cardiovascular system proper, the spiral cochlea of the ear has been modeled using hydrodynamic principles. It has a diameter roughly proportional to overall animal length and is known to function in a physical analog manner, in the sense that travel-ing waves in the cochlea appear to form resonant points at certain particular locations. The natural modeling invariants for the cochlea are of interest and not known at present. An enlarged fluid model of the cochlea with simulated nerve sensors is described by Bekesy (1961); Tonndorf (1960) constructed a plastic model of the cochlea enlarged five times and studied fluid pulse wave and turbulence phenomena with the specific assumption of Reynolds number inyariance.

B. Respiratory Analogs

Similar work has been done on the respiratory system. Mammalian respiratory function can be analyzed objectively by the study of some