Second Event theory published

International Journal of Radiation Biology
IJRB 2000, Vol 76, No 1, 119-125
Commentary on the Second Event Theory of Busby
(*author for correspondence)

NRPB, Harwell, Didcot, Oxon. OX11 0RQ, UK)
(Received 23 March 1999; accepted 26 April 1999)

Biological plausibility is an increasingly important element in the interpretation of epidemiological data on cancer causation in human populations and it was included in the epidemiological criteria of Bradford-Hill (1971). Such supporting biological evidence can include data from animal studies, the existence of characterised cellular mechanisms and, in the case of radiation carcinogenesis, biophysical features of radiation action on cells and tissues.

The Second Event Theory of Busby is relevant to the last of these. Although yet to complete formal scientific peer review, the theory has been described and discussed in a published book (Busby 1995), in meeting proceedings (Bramhall 1997) and on an internet website (Busby 1998).

The principal thrust of the theory is that internally deposited radionuclides such as 90Sr, which undergo sequential decay, pose a hitherto unrecognised radiobiological hazard because of the increased probability per unit of dose that a single cell in surrounding tissue will be subject to two sequential traversals (a correlated double-event) from the resulting radiation tracks. Busby has provided biophysical calculations that seek to evaluate this double-event probability in the context of post-irradiation cell synchronisation and cell-cycle radiosensitivity. These calculations are then used to justify a special double- event carcinogenic mechanism for certain radionuclides which distinguishes them from gamma-rays for which, it is claimed, double-event probability is very much lower. On this basis it is proposed that current estimates of cancer risk for such internal emitters are seriously in error. Stated simply, the Second Event Theory is being used to seek biological plausibility for contentious epidemiological claims that cancer risk from internal emitters resulting from weapons fall-out and other sources has been grossly underestimated (Busby 1995, Bramhall 1997).

The theory has been discussed at a number of scientific meetings where it was pointed out by others (e.g. see Bramhall 1997) that the geometrical factors that govern double-event probabilities had not been accounted for adequately. The plausibility of the biological assumptions of the theory have been questioned and discussed by Goodhead (1997) and it is not our intention to reiterate these here. It is the biophysical arguments and computational problems that will be considered.

A revised version of the theory (Busby 1998) attempts to rectify some of these computational problems but, in our view, fails to do so adequately. In the appendix to this commentary we provide what we believe to be the correct form of the calculation with regard to the probabilities of double-events in single cells within range of sequential electron decay from 90Sr--90Y. This double-event probability is compared to that of gamma-rays in order to test for the risk enhancement that the theory claims to predict. These present calculations retain the questionable biological parameters of the theory and, in general form, do not differ substantially from those of Busby (1998). The data given in the appendix may be brought together in the following manner. Gamma-rays at natural background dose rates (1 mGy/y-1) will randomly produce double-events in single cells with a probability of 1.1 x l0-4 y-1 ((table 2)). At a dose of 1 mGy in one year, approximately the same double event probability may be ascribed to random hits from different 90Sr--90Y decays although, in practice, the probability is a little less because of differences in electron energies (e.g. figure 1). In addition, there is the probability that individual 90Sr--90Y decays will produce correlated double-events; this is given by the data of table 3 and the factor of 1. 1 generated by the formula given. Thus, for an annual dose of 1 mGy from 90Sr--90Y, the probability per cell of double-events overall is 1.1 x 10-4 + (2.8 x 10-5 x 1.1) = 1.4 x 10-4. Accordingly, by comparison to 1 mGy gamma-rays at natural background dose rates the enhancement factor for double-event production by an annual dose of 1 mGy 90Sr--90Y is 1.4 x 10-4 /1.1 x 10-4, that is, about 1.3. Busby (1998) suggests an enhancement factor of this form of around 30. The difference between this value and the factor of 1.3 provided here is due principally to an underestimate by an order of magnitude by Busby of the number of cells of 10 micron diameter contained in 1 g of tissue together with a failure to take account of the contribution from cells receiving three or more events as given in table 1. Other less important computational differences include assumptions on the number of events per cell per mGy and the statistical factor of 2 used in respect of the independent order of events.

Table 1. Calculation of the fraction of all cels gamma-irradiated at 1 mGy y-1 which receive a double event in one year.

No. of events in 1 year N Fraction of cells with N events Probability that two events will be separated by 100.5 hours Fraction of all cells with 2 events separated by 100.5 hours
0 0.3679 0 0
1 0.3679 0 0
2 1839 2.283 x 10-4 4.2 x 10-5
3 0.06131 6.849 x 10-4 4.2 x 10-5
4 0.01533 13.7 x 10-4 2.1 x 10-5
5 0.003066 22.83 x 10-4 0.7 x 10-5
6 0.000511 34.25 x 10-4 0.175 x 10-5
7 0.000073 47.95 x 10-4 0.035 x 10-5
8 0.0000091 63.93 x 10-4 0.006 x 10-5
9 0.0000010 82.19 x 10-4 0.001 x 10-5
Total - - 11.42 x 10-5

Thus, irrespective of its biological validity or interpretation, the Second Event theory does not predict the degree of double-event risk enhancement that has been claimed. Even using the conservative assumption that 90Sr resides within and around cells and not in the bone matrix, the additional probability per cell per year of such a double-event from correlated 90Sr--90Y decays at an annual dose of 1 mGy is very low (~ 3 x 10-5). The total probability of these double events (1.4 x 10-4) is comparable to that resulting from an annual dose from natural background gamma-rays (taken to include cosmic rays of 1 mGy (UNSCEAR 1993). Moreover, in practice, all human 90Sr exposures will be coincident with those from natural background gamma rays and, at the very least, the potential effects of this and other radiation sources on cancer risk need to be included in epidemiological reasoning.

In his commentaries on epidemiological data, Busby has expressed specific concern on the under-estimation of osteosarcomagenic and leukaemogenic risk in regions of the UK resulting from 90Sr in weapons fall- out, associating claims of high risks at low doses with his Second Event Theory (Busby 1995, Bramhall 1997). At its peak in 1963, the annual 90Sr dose to bone marrow in the UK population was around 0.3 mGy, approximately 25 - 30% that of natural background gamma-rays (NRPB 1995). However, using the reasoning and calculation method given in the annex, under these circumstances the Second Event Theory produces a probability of critical correlated double-events from 90Sr--90Y decay of 9.24 x 10-6 per cell, that is, only around 10% of that of biophysically identical random double events (1.1 x 10-4 per cell) arising in the same period from natural background gamma-rays. Thus in all practical circumstances of low dose (< 1 mGy) and low dose rate exposure, the probability of naturally arising random double-events should dominate over that which is associated in a correlated fashion with sequential radionuclide decay. In short, due to computational error, Busby's theory and his epidemiological claims have been incorrectly matched.

It is appreciated, however, that the calculations presented above relate to a specific set of biophysical assumptions which are open to question. Accordingly, the sensitivity of conclusions to the major assumptions made has been investigated (calculations nor shown). Varying the time interval between events (5 -20 h) and the associated cell-cycle window size (1 - 2 h) made no difference to the conclusions. Reducing the target cell diameter to 5 microns increased the probability of correlated decays by a factor 2 compared to uncorrelated decays; this ratio was not dependent upon whether a whole cell or a cell nucleus of a given size was considered to be the target. It is judged therefore that the conclusions reached are acceptably robust.

It is for others to comment upon the epidemiological data and methods with which Busby justifies his claims on radiation cancer risk; it is sufficient to say here that, since it fails to provide the quantitative predictions that were sought, his biophysical theory adds no substance to these claims. Indeed, independent of concerns on its biological validity, a paradoxical feature emerges from the application of the Second Event Theory in a broad radiological protection context as indicated below.

In reviewing animal carcinogenesis and other relevant data UNSCEAR (1993) suggest that the dose and dose- rate effectiveness factor (DDREF) used for estimating cancer risk at low doses and dose rates of radiation "should, on cautious grounds have a low value, probably no more than 3" (UNSCEAR 1993, p. 687). A similar position is adopted by ICRP (ICRP 1990) who recommend a DDREF in respect of cancer risk of 2 for use in radiological protection. In a general sense, these views on DDREF accord with conventional judgements that single event (linear) kinetics, are most appropriate for estimating low dose cancer risk (see Cox et al., 1995). By equating the dominant element of radiation cancer risk with the probability of double-events in single cells the Second Event Theory predicts that, in the case of the uncorrelated events from gamma-rays and other low LET radiations, the dose response for cancer risk would vary as a quadratic function of dose rate (table 2). This leads to a value of DDREF that is many orders of magnitude greater than those given by UNSCEAR (1993) and ICRP (1990) and would serve to depress estimates of low dose risk in respect of the random track component from any radiation source. In this way application of the Second Event Theory to, for example, internalised 137Cs at low doses and low dose rates would result in cancer risk estimates that were dramatically lower than those obtained by the procedures recommended by ICRP (ICRP 1990). By contrast, for 90Sr, the theory predicts that linear extrapolation should be used table 3 implying a low value for DDREF in agreement with current recommendations. These predictive features of the Second Event Theory appear to be at odds with Busby's general claims that cancer risk from low doses of internal radiations have been seriously underestimated.

In summary, irrespective of judgements on its biological plausibility, it is evident that the Second Event Theory does not predict high relative biological effectiveness for 90Sr. This conclusion accords with judgements made on the basis of animal carcinogenesis data (Moskalev and Strelt'sova 1973; Lloyd et al. 1994)


Calculations based upon the Second Event Theory

For the purposes of making calculations, the critical biological assumption of the Second Event Theory is that two events must occur in the same cell separated by an interval of 10 h within the cell-cycle with a one hour time window (Busby 1995, Bramhall 1997. Busby 1998, but see also Goodhead, 1997). This annex shows the calculation of the fraction of cells per year, subjected to various gamma-ray dose rates, that experience such a double-event. It also shows a similar calculation for a sequential 90Sr-- 90Y decay.


Figure 1 gives the average dose to a cell from a single electron track as it varies with photon energy and cell diameter. These are original calculations based on Monte Carlo generated electron tracks entering and created within a sphere of given diameter. It is reasonable to assume a diameter of 10 microns for a typical cell in agreement with Busby (1998). The electron spectra are created by monoenergetic photons of different energy. A typical photon energy of 300 keV delivers an average of about 1 mGy to a 10 micron diameter cell per event.

For a dose rate of 1 mGy y-1 every cell will receive 1 event on average each year. The fraction of cells with 0, 1, 2 events etc. is given by the Poisson distribution. The chance that any two events in a cell are separated by exactly 100.5 h is 2/365/24 = 2.28 x 10-4. The factor two arises because the order of the events is not relevant. If there are two events in a cell there is only one pairing, for three events there are three pairings, for four events there are six pairings etc. Thus to calculate the total probability table 1 can be constructed for a dose rate of 1 mGy y-1.

For a gamma ray dose of 1 mGy at a dose rate of 1 mGy y-1, approximately 1 cell in 10,000 will be subject to a double-event. Similar tables can be constructed for other dose rates to give results as shown in (table 2). Note from table 2 the square law increase of probability with dose rate. Note also that exactly the same probabilities would arise if the interval between events were 5 h or 20 h.

90Sr--90Y decays

The half life of 90Y is 64 h so the probability that the 90Y decay will occur between 9.5 and 10.5 h after the 90Sr decay is exp(-9.5/92.33) -exp (- 10.5/92.33) = 0.00972.

Each 90Sr--90Y decay produces 1.13 MeV (196 keV from 90Sr + 935 keV from 90Y) on average and, accordingly, for a dose of 1 mGy there are 5.52 x 106 disintegrations in 1 g. For a 10 micron diameter cell there are 1.91 x 109 cells per gram of tissue assuming perfect packing. In this way 2.89 x 10-3 cells per gram will have a 90Sr--90Y decay and 2.81 x 10-5 will have a double-event separated by 100.5 h. This leads to the values shown in table 3. Note from table 3 the linear increase of probability with dose, independent of dose-rate.

It is also necessary to take account of spatial factors associated with 90Sr--90Y decay when calculating double-event probabilities. Each90Sr--90Y decay produces two electrons, the maximum track ranges of which are: 90Sr decay, 2 mm exactly equivalent to 200 cell diameters: 90Y decay, 15 mm exactly equivalent to 1500 cell diameters. The solid angle property of these electron track paths means that the number of surrounding cells receiving double-events from a single 90Sr-- 90Y decay will be small. Constraining the decay process to occur within a single cell implies that, on average, a number of between one and two cells will be so affected. The equation given below, similar to that of Busby (1998) may be used to estimate a value for this number on the basis of the maximum of 200 cell diameters that limit the potential for double-event production from a single decay. The rationale for this formula is as follows. The central cell containing the single 90Sr--90Y decay always receives a double hit; in the 16 cells in the first shell surrounding the central cell the double hit probability is 1/ 16; in the 64 cells in the second shell the double hit probability is 1/64 and so on up to 200 such shells.

Cox and Edwards 
reuse Busby's excess probability of overlapping tracks. 
[expression at bottom is "n = 1"]

This calculation indicates that on average about 1.1 cells will receive a correlated double-event from single 90Sr--90Y decay. This value is sufficiently close to 1 .0 that approximations in the above formula are judged to be unimportant. It should be noted that, in practice, most of the Sr in the body is incorporated into mineral bone (ICRP 1993) and so does not reside in bone marrow cells or those on bone surfaces. Thus the factor 1.1 above leads to a large overestimate of the correlated double-event probability.


Bradford-Hill, A., 1971, Principles of Medical Statistics. 9th edn. (London: The Lancet Ltd.)

Bramhall, R. (ed.), 1997, The Health Effects of Low Level Radiation. (Aberystwyth: Green Audit Books).

Busby, C., 1995, Wings of Death: Nuclear Pollution and Human Health. (Aberystwyth: Green Audit Books).

Busby, C., 1998, Recalculating the second event error. http: / / secevnew.htm.

Cox, R., Muirhead, C. R., Stather, J. W. Edwards. A. A. and Little, M. P., 1995. Risk of radiation-induced cancer at low doses and low dose rates for radiation protection purposes. Documents of the NRPB Vol. 6, No. 1.

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.

ICRP, 1990, Recommendations of the International Commission on Radiological Protection. ICRP Publication 60. Annals of the ICRP, 21, Nos. 1-3.

ICRP Publication 67, 1993. Age dependent doses to members of the public from intake of radionuclides: Part 2: Ingestion dose coefficients. Annals of the ICRP, 23, Nos. 3-4.

Lloyd, R. D., Miller, S. C., Taylor, G. N., Bruenger. F. W., Jee, W. S. S. and Angus, W., 1994, Relative effectiveness of 239Pu and some other internal emitters for bone cancer induction in beagles. Health Physics, 67, 346-353.

Moskalev, Y. I. and Strelt'sova, V. N., 1973. Dependence of osteosarcaromagenic activity of radionuclides on their physical properties and physiological state of the animal. In Radionuclide Carcinogenesis, edited by C. L. Sanders. R. H. Busch, J. E. Ballou and D. D. Mahlum. (Washington: US Atomic Energy Commission) pp. 307- 311.

NRPB-R276 Risks of leukaemia and other cancers in Seascale from all sources of ionising radiation exposure. (London: HMSO)

UNSCEAR, 1993, Sources and effects of ionising radiation. 1993 Report to the General Assembly, with annexes. New York, United Nations.

Busby's reply is printed in the same issue of IJRB, and reproduced on this site

If you are seeing this page full screen (i.e. without a navigation bar on the left) you can't see how the rest of the site is organised.
This Home page link takes you to the index page, which has links to all the topics we discuss on the site [only use it if this page is full screen]
Use the Flaws in NRPB / ICRP science link to see what else we have to say on this topic.

Send email to: . with questions or comments about this web site.

This page was last updated May 2001