A commonly used experimental procedure for the study of granulocyte kinetics involves the labelling and subsequent tracing of granulocyte DNA. Following the introduction of a label into the system, observations are made periodically on the concentration of label in the DNA of granulocytes taken from the circulating blood. A mathematical model for the expected value of this concentration has been derived, studied, and related to experimental observations from studies using P32 as a label. Insofar as the derivation of the model (...) accurately incorporates the relevant aspects of granulocyte kinetics, the model will be useful in the interpretation of the experimental observations in terms of these kinetics.Among other things, study of the model indicates that the assumption of “flash” labelling made with respect to some labels is quite crucial and needs to be examined critically. It has also been necessary to make adjustments to allow for the observed emergence of labelled cells from the marrow soon after label introduction. In addition, despite a high degree of confounding of parameter effects it has been possible to suggest bounds on some of the parameters of the model for some species. The bounds will be refined as the model is improved and more data become available. Study and development of the model continues with particular interest in generalizations to include the diseased state chronic granulocytic leukemia. (shrink)

This note is viewing survival data of a natural cohort as being generated by a possibly nonlinear, nonhomogeneous death process. It proves that the usual conditional distributions of the number of survivors at a certain age are binomial if and only if the death process is linear. Thus the customary statistical methods for the analysis of life table data are, strictly speaking, invalid whenever the underlying death process is nonlinear. For example, if a contagious disease is the cause of some (...) or all of the deaths, the deaths will not be independent and the death process, not linear. One should then base the statistical analysis on a model for the spread of the disease rather than the routine binomial model. (shrink)

Because of the important role which the ‘autocatalytic’ or ‘logistic’ equation has played in determining the direction of a good deal of research both in demography and in the study of individual growth phenomena, a critical and comparative evaluation of those leading ideas inRobertson's book which pertain to this equation and of some of the criticisms levelled against it seemed to be of interest. The present paper shows that, contrary to common belief,Robertson did not really assume that the autocatalytic reactions (...) to which he compared growth processes, took place in closed systems . On the other hand, he does not seem to have found a satisfactory representation of how the growth phenomena of the individual cells in an organism might interact to yield the overall growth of the organism as a whole. Nor is the manner in which he made his equation account for the openness of the individual cells free from possible criticism. An alternative equation is here proposed, which will be discussed in another paper. The properties of the solutions of this equation are such that the autocatalytic theory might never have gained a foothold if this, more realistic, equation would have been the object of the initial studies. (shrink)