Stahl67 bmp

THE BOLE OF MODELS IN THEOKETICAL BIOLGJY 183

Examples of dimensionless numbers appropriate both to heart-lung machines and mammalian system are: air flow to blood flow ratio, oxygen flow to blood flow ratio, “dead” to active exchange volumes in oxygen-ators, linear blood flow velocity to membranę velocity constants, and the several dimensionless numbers characterizing pumps. Many of these criteria tum out to be independent of size in mammals. Peirce (1960) compares a multiple film oxygenator with the human lung in terms of gas pressure gradients, mean blood film thickness, blood or oxygen flow per unit area of exchange membranę, and mean machinę or film oxygen transit times. Ali of these parameters have counterparts in mammalian physiology.

Dimensional analysis as such is useful for engineering analysis of complex physical phenomena occurring in devices such as rotating disk or vertical falling film oxygenators. Characteristic performance parameters for such devices are described in reports of Jones (1959), L. C. Clark (1959), and Theye et al. (1962). In a discussion of falling film oxygenator efficiency, Leonard (1962) uses dimensionless numbers previously developed for study of falling films of condensate fluid in condensers and boilers. An interesting scaling problem arises in the design of heart-lung machines for children and infants (Ross, 1960) that are governed by certain dimensionless criteria similar to those suitable for analysis of the respiratory system in vivo.

Artificial hearts certainly function as pumps; a very well-defined set of dimensionless numbers, presented elsewhere (Stahl, 1967), is avail-able for characterizing pump performance. For example, Akutsu et al. (1960) describe a “roller pump” which approximately matches the real heart in regard to pressures, stroke volumes, rates, normal and maximal flows, and forward flow to back leakage ratios. Ali the criteria cited for pumps are applicable to this artificial model. There is, however, lack of detailed geometrie similarity and the dimensional constants characterizing various materials are not the same as in the heart. Clearly, measure-ments on artificial hearts are not expected to yield data for any real heart, but they are useful similators nonetheless.

In earlier publications (Stahl, 1963a,b) the author proposed that the design and function of artificial organs be analyzed systematically by use of dimensionless performance criteria. This approach would apply techniąues used by engineers for comparing motors, pumps, aireraft, bridges, etc. Performance analysis of artificial hearts has recently been discussed by Kantrowitz (1965) and implies yarious dimensionless entities.