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180 WALTER R. STAHL

of the entire cardiovascular system based on dozens of eąuations for the heart, aorta, and peripheral vasculature. McLeod and Defares (1963) discuss a detailed model of the myocardium, with representation of Starling’s Law of the heart (ejection force proportional to filling volume). A numerical Computer model of electrical wave propogation in the myocardium is offered by Reinboldt et al. (1963).

Quite similar studies have been done on the lung. An analog model of lung gas flow, as influenced by volumes, respiratory compliance, resist-ance, etc., is described by McWilliam and Adams (1963); it makes it possible to simulate various kinds of lung pathology. Osborn and asso-ciates (1963) use an analog Computer model to assess total respiratory work rates under various combinations of flow rates and expiratory pressures.

In all of these cases the specific defining conditions for similarity of the model and prototype were not stated. With the morę complex simulations of the whole vascular system the model implies many dozens of separate dimensionless variables and it is certain that all of them are not invariant for the prototype. Accordingly, these models must be classed as complex qualitative simulators, but they are nonetheless of considerable interest.

Analog models of natural biological (circadian) rhythms have been analyzed extensively by O. H. Schmitt (1962) and Klotter (1960). These are usualły based on simultaneous solution of sets of differential eąuations and may demonstrate effects of temperaturę on natural freąuency, synchronization with light, or feeding rhythms.

Although sometimes phenomenological in naturę, such models provide much insight into natural biological cycles and rhythms.

D. Chemical and Molecular Analogs

Chemical and molecular models constitute another class of physical analogs. These may pertain to the organismal, tissue, cellular, or molecular levels and cover such diverse phenomena as membranę action, muscle contraction, or drug distribution in body compartments.

In a report entitled “Models of Muscle,” Pringle (1960) describes both the mathematical eąuations and partial physical models which have been used to conceptualize the behavior of mammalian muscle. The complex mechanochemical action of muscles makes analytical formulation of thedr action rather difficult and models help to clarify the importance of internal yiscoelastic phenomena, time constants, etc. Actomyosin and