On the Statistical Nature of Mortality, with Especial Reference to Chronic Radiation Mortality

Abstract

Important problem in radiation biology today is that of estimating the consequences, in illness and mortality, for human populations exposed to ionizing radiations in arbitrary amount and temporal distribution. Since an experimental determination is precluded, we must rely principally on information obtained from animals. The problem then arises of making valid inferences about effects on man in terms of laboratory experience. 2 Such inference is possible in principle only in so far as there are common terms between the lower mammals and man, arising from their homologies with respect to physiologic constitution. It is presumed that homologous systems of different species are alike in mechanism, that they differ in the numerical values of their parameters, and that these parameters can be estimated for the species concerned. Projection from animals to man can then be carried out as indicated schematically in Figure 1. This diagram brings out the importance for interspecies prediction of the relation between physiologic effects and lethality within species. The present paper is devoted to establishing the nature of this relation. Equally important is the problem of understanding and quantitatively describing physiologic injury. This latter aspect will not be discussed here. Statistical Nature of the Death Process It is an intuitive judgment on the basis of clinical and laboratory experience that the occurrence or non-occurrence of death in a given interval cannot be predicted with certainty in the individual case, however precisely the conditions be known or controlled. This judgment has a counterpart in the fact that the future behavior of a directly observed physiologic process cannot be predicted with certainty, even with extensive information about its past behavior. Considerations such as these lead to the hypothesis that the unpredictability of mortality is a consequence of the uncertainty that is inherent in the dynamics of physiologic function. According to this hypothesis, the occurrence within an organism of a failure of function leading to death is the result of a fluctuation of the physiologic state of the organism, of such magnitude as to exceed the limits within which homeostatic regulation can occur. 3 The mathematical problem becomes one of determining how frequently such extreme fluctuations occur as a function of the homeostatic parameters of the organism or population. This is equivalent to finding a new kind of quantitative measure for the homeostatic capacities of organisms. As a starting point for the development of this theory, we shall examine the hypothetical case of a homogeneous population in which all members are indistinguishable one from another. Such a population is defined by the specification that the physiologic processes of all members have the same mean values and the same magnitudes and rates of fluctuation.