CARCINOGENESIS FROM INDEPENDENT EVENTS 1G3 



there is a logarithmic increase with age in mortality from natural cancer there 

 will be a similar logarithmic increase with age in radiation-induced cancer and 

 a given radiation exposure will produce more cases of cancer the older the 

 individuals at the time of exposure. 



This radiation-induced logarithmic increase above natural age-specific 

 cancer rates is to be expected if the probability of the first kind of event but 

 not the second kmd is appreciably increased by radiation. In the experimental 

 situation where the induced cancer rate is very much higher than the spon- 

 taneous rate, as in the experimental induction of bone cancer by bone- 

 seeking isotopes, it may be supposed that radiation can cause both kinds of 

 event with probabilities so much larger than the spontaneous probability 

 that control incidence and spontaneous probabilities may be neglected. In 

 this case whatever the relative probabilities of induction by radiation of the 

 first and second kinds of event, the incidence of bone tumours at any fixed 

 time after administration should depend on their combined jirobabilities. With 

 radioactive materials emitting a- or |8-particles there is no problem in deciding 

 what parameter of radiation dose to use because clearly it must be the 

 particles themselves which are responsible for the (hypothetical) ceUular 

 events. Thus the incidence of bone tumours at any fixed time should depend 

 on the square of the number of radioactive distintegrations since the admini- 

 stration of the isotope. Figure 1 gives the observed over-all tumour incidence 

 in a series of experiments in which mice were given a single injection of radio- 

 active material and a range of amounts of different bone-seeking isotopes were 

 used. If life-span is not shortened by the induction of other lesions then over- 

 all tumour incidence should depend on the square of the administered dose 

 and it can be seen that the data agree reasonably well with this expectation. 



The hypothesis also requires that the rate of development of tmnours with 

 time after the injection of an isotope should be proportional to the square of 

 the number of radioactive events in the time interval concerned. An experi- 

 ment in which the body burden of radioactivity is maintained at a constant 

 level by monthly injections should provide a test of this prediction but it 

 should be noted that what is scored in such an experiment is not the time of 

 origin of a tumour but the time when there is a gross bone-tumour, often a 

 tumour large enough to kill. When the data of Brues (1949) on ^^Sr were used 

 in Fig. 3, a fixed time ^ = 150 days was subtracted from the time at which the 

 bone tumour was recorded, this period of tune being considered to be the 

 average development time of a tumour, the time mterval from its start to the 

 moment when it was big enough to kill or be recorded. When this is done it 

 can be seen that there is a good fit of the observed data to the prediction that 

 the rate of tumour development, dNIdt, scored over successive fifty-day 

 periods, should be proportional to the square of the number of preceding 

 radioactive events. The abscissa is the square of time so that the rates of 



