Stahl67$ bmp

188 WALTER R. STAHL

Reeve and Bailey (1962) developed a rather complex differential equa-tion representation of the distribution of radioactive iodinated albumin and foimd it to predict quantitative data for humans in a very satis-factory manner. Marshall (1964) described a model of alkaline earth metabolism, pertinent to problems of fallout accumulation in the body. He obtained good fits using power law functions for accumulation and excretion. It might be noted that these power laws involve T^x, with T equal to time.

The distribution and accumulation of drugs represents a special in-stance of a compartment model problem. In a book dealing with ap-plication of mathematical techniques to biology, Riggs (1963) discusses the many demanding conditions that must be met before an alleged drug or compartment model can provide quantitative information. These include obtaining precise data on all pertinent dimensional constants and coefficients, as well as statistical verification of equation parameters. Riggs notes the importance of dimensional consistency of constants in equations, but does not discuss similarity criteria as such, although a number of invariants are implied in his analysis.

Bellman et al. (1960) and Jacquez et al. (1960) describe complex models of drug distribution based on integrodifferential equations, whereas Jacquez (1962) stresses the importance of such simulations for effective cancer chemotherapy. Plackett (1963) uses biometric concepts to study the simultaneous action of two noninteracting drugs in a biometric model. Numerous other reports on drug kinetics could be cited, but are not concemed with models as such.

C. Enzyme and Cellular Kinetics Models

The modeling of cellular enzyme kinetics is another well-studied example of numerical simulation, frequently carried out on computers. Initial studies of the problem by Chance (1960) explored both analog and Computer modeling methods, but the former tend to become quite awkward when dealing with large systems. Reports by Garfinkel (1963) and Garfinkel et al. (1961) are devoted to design of special Computer simulation methods for accurate numerical representation of Michaelis-Menten enzyme kinetics. A model based on 89 reactions involving 65 Chemicals is described in Garfinkel and Hess (1964) and represents accurately a number of observable reactions of the system in vivo. Garfinkel (1962) has also used a Computer to simulate enzyme kinetics and compartment effects arising in the glutamate metabolism of the brain in rats. The specific similarity criteria for such models include