Mathematical Analysis of the Division Delay Produced by Ionizing Radiations

Recent advances in knowledge about the relation of divison delay to dose invalidate Lea's linear model of the recovery process. Since the present evidence is that delay is a straight-line function of dose, the first model considered is one postulating zero-order recovery kinetics. Although this yields a straight-line delay/dose relation, it is inconsistent in other respects. Lea's first-order model is reexamined and shown to lead to a logarithmic delay/dose relation which fails to fit the data for synchronized cell populations. A model is next considered in which the rate of recovery depends on the amount of uninjured biosynthetic substances remaining after irradiation. This model leads to second-order kinetics and a logistic recovery function. It is shown that this model yields a straight-line delay/dose relation and consistent estimates of the injury and recovery parameters. This second-order model is fitted to data for mammalian cells in culture and for vegetative division of Paramecium aurelia. The model does not fit data for cleavage of fertilized Arbacia eggs, but it is pointed out that marine eggs have great reserves of material, and hence are different from cells in a steady state of synthesis and division. It is concluded that the second-order model fits the data appreciably better than do the other models considered.