In accord with the objective of our initial commentary (Edwards and Cox, 1999) we will restrict our response to Busby's letter to the biophysical aspects of the Second Event Theory.

First, he points out that the perfect packing of cells in tissue should not be expected. We agree, but the mathematical formula he used to calculate the overlap probability for ⁹⁰Sr and ⁹⁰Y decays (Busby, 1998) is based upon this assumption without reference to biological data. We simply pointed out the errors in calculation that he had made when formulating and deriving predictions from his own model. Perfect cellular packing means that each ⁹⁰Sr- ⁹⁰Y decay results in at least one cell receiving two electron tracks. As cell packing is decreased the mean number of cells hit twice per ⁹⁰Sr- ⁹⁰Y decay decreases below Busby's assumed minimum of 1 .0 because of the increasing probability of ⁹⁰Sr being bound extracellularly. As noted in our commentary, there is compelling evidence that the majority of ⁹⁰Sr intake is deposited in bone matrix and not in intracellular material. Therefore, under practical circumstances the number of potential target cells for double events is very low indeed. For these reasons we see no merit in the counter arguments that Busby has given in his letter. Busby also focuses attention on the energy deposited in rare cells experiencing a sequential ⁹⁰Sr-⁹⁰Y decay. In our view this adds nothing to the discussion since the calculation provided shows that there will be countless somatic cells per individual sustaining radiation doses more than twice the average background level due to chance coincidence of single events. Second, in order to avoid the gamma-ray quadratic dose-response that the Second Event Theory unambiguously predicts, Busby provides an additional theoretical element whereby cells at most risk of neoplastic initiation require only one hit in the critical window of the cell cycle from a low LET radiation track, i.e. from gamma-rays and, individually, from ⁹⁰Sr and ⁹⁰Y decay. Given the very low probability of correlated double events, this theoretical manoeuvre simply converts the Second Event Theory into a quasi-One Event Theory. This is equivalent to assuming that at low doses of internal and external radiations, risk is simply proportional to dose to target cells which, as noted in our Commentary, is the conventional view in radiological protection. On this biophysical point it seems that we can now agree.

The remaining novel component of Busby's theoretical work appears to be the proposal of a cell-cycle- specific window of exquisite radiosensitivity. In this context, Goodhead (1997) has commented upon the relatively modest variation in radiosensitivity through the cell cycle in comparison to the large radiosensitivity enhancement factor that Busby has sought to identify. However, given the calculations we have provided, cell-cycle radiosensitivity is of no consequence since it will apply equally to correlated and uncorrelated double events; according to Busby, it will also apply to single events generated in some cells by gamma-rays and ⁹⁰Sr- ⁹⁰Y decay. It follows that there can be no effect of cell-cycle radiosensitivity on the magnitude of the enhancement factor that he uses in his arguments. Indeed, we have been unable to identify any biological factors which when coupled with Busby's theories will provide for such enhancement of radiation response.

In conclusion, we remain firm in our view that the Second Event Theory and its variant forms do not lend support to the high cancer risks after low doses of ⁹⁰Sr and other internal emitters that Busby has claimed.

References

Busby, C. C., 1998a, Recalculating the Second Event Error. http://www.llrc.org/secevnew.htm

Edwards, A. A. and Cox, R., 1999, Commentary on the Second Event Theory of Busby, International Journal of Radiation Biology,76, 119-124

Goodhead, D. T. 1997. Transcript of oral presentation. In Bramhall, R. (ed.), 1997, The Health Effects of Low Level Radiation. (Aberystwyth: Green Audit Books) pp. 36-60.

A. A. Edwards and R. Cox*
National Radiological Protection Board
Chilton, Didcot, Oxon. OX11 0RQ UK

*author for correspondence