The Sigmoid No Threshold Radiation Dose Response Model Jack Devanney ThorCon USA, Inc Stevenson, WA This is a preliminary, incomplete draft for internal discussion only. Please send any comments to [email protected]. Copyright 2017 ThorCon USA, Inc This report makes use of data obtained from the Radiation Effects Research Foundation (RERF) in Hiroshima, Japan. RERF is a private foundation funded equally by the Japanese Ministry of Health, Labour, and Welfare and the U.S. Department of Energy through the U.S. National Academy of Sciences. The conclusions in this report are those of the authors and do not necessarily reflect the scientific judgement of RERF or its funding agencies.
Transcript
The Sigmoid No Threshold
Radiation Dose Response Model
Jack Devanney
ThorCon USA, Inc
Stevenson, WA
This is a preliminary, incomplete draft for internal discussion only.Please send any comments to [email protected].
This report makes use of data obtained from the Radiation Effects Research Foundation(RERF) in Hiroshima, Japan. RERF is a private foundation funded equally by the JapaneseMinistry of Health, Labour, and Welfare and the U.S. Department of Energy through the U.S.National Academy of Sciences. The conclusions in this report are those of the authors and donot necessarily reflect the scientific judgement of RERF or its funding agencies.
CONTENTS 1
Contents
1 Introduction 2
2 Fitting the Logistic Function to LSS data 3
3 Handling Chronic Dose 11
4 Implications of Sigmoid No Threshold 14
5 Linear No Threshold versus Sigmoid No Threshold 16
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1 Introduction
In order to reconcile the statistically significant increase in cancer that is observed for acute ra-diation doses of 100 mSv or more, with the fact that large populations living in high backgroundradiation areas for 70 years or more show no discernible increase in cancer, the dose responsecurve must be non-linear. But current radiation rules are based on the Linear No Thresholdhypothesis. Linear No Threshold (LNT) is inconsistent with what we know about cellular repairmechanisms; and epidemiological data shows that Linear No Threshold does a very poor job ofmodelling the health effects associated with radiation at the all important low dose rate end.
It is not the purpose of this paper to argue this point. This paper assumes that the readerhas already reached this conclusion. But, if Linear No Threshold is invalid at low dose, which iswhere the most important policy issues arise, with what should we replace it? The public needssimple guidelines. Regulators need an easily understood framework. Can we come up with asimple model which does a better job of estimating cancer incidence from ionizing radiationthan LNT, especially at the low end.
I suggest the answer is yes. I suggest we accept the fact that nature abhors discontinuousderivatives. This rule takes Linear No Threshold, Linear with Threshold, and quadratic (non-sense at the high end) off the table. It implies that the dose response curve should have zeroslope at both the zero dose end and the always fatal end. I propose that for the purposes ofregulation we assume cancer incidence is a monotonically increasing function of dose.
There is considerable evidence that low dose can stimulate protective responses. But it isequally clear that certain kinds of damage escape those responses. We are looking at a verycomplex battle between a wide range of damages and a wide range of responses to these damages.And we can be sure that the outcome of this battle varies from individual to individual. So tobe conservative, we go monotonic. From this point of view, up regulation of protective responsesis just another reason why the response is non-linear.
Under these rules, we need a sigmoid response function. The five parameter logistic functionis a family of such functions that allows us to model a wide range of dose responses meetingthese basic rules. This is neither radical nor original. It embodies the establishment position:no threshold, risk increases with dose. In fact, the logistic is standard practice throughoutmedicine except in radiation. There are a half dozen software packages on the market to helpyou fit logistic curves to dose response data.
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2 Fitting the Logistic Function to LSS data
As a poor example, let’s fit a logistic curve to the RERF Life Span Study (LSS) solid cancerdata for the Hiroshima and Nagasaki survivors. This sloppy fit is based on the grouped figuresshown in Figure 1. This is just the raw cancer incidence data binned. It has not been stratifiedby sex, age, or anything else. Moreover, there are all sorts of problems with the RERF data andI will compound those by blithely converting grays to sieverts on a 1 to 1 basis. This exercise isaimed at highlighting the qualitative differences between Linear No Threshold and Sigmoid NoThreshold from a policy point of view. It is not an attempt at quantitatively accurate fits to aparticular data set.
Source: RERF file lss14.csvDownloaded 2014-04-10 from www.rerf.or.jp/library/dl_e/index.html
Error bars based on binomial sampling,Non-informative beta prior, 2 sigma
Figure 1: RERF Solid Cancer Incidence, Grouped, Unstratified
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Figure 2 compares the a least squares linear fit with the best logistic fit I was able to comeup with.1 Figure 2 is the kind of big picture that the RERF likes to show us. From this broadperspective, there’s not that much difference between the two approaches. From this distance,just about any family of curves can be made to look like a fit. At the top end, the two curvesdiverge as the logistic fit slowly heads for the assumed top end of 1.0 while the Linear NT lineshoots up to where it will kill the same people over and over. But aside from having a modelthat does not do anything nonsensical, we are not really that interested in the high end. Whatcounts is the low end.
Figure 2: Linear versus Sigmoid NT for RERF Solid Cancers: 0 to 10,000 mSv Acute Dose
1 Actually we used least squares weighted by the number of samples in each group, but it turns out whetheror not you do this weighting does not make a great deal of difference in the overall fit.
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Figure 3 takes a closer look at the portion of the curves below 1000 mSv. Now we begin tosee some interesting differences between the two fits. The zero slope at zero dose requirementforces the logistics curve lower in the very low dose end and pushes it to a steeper slope in theintermediate dose range. Radiotherapists have been making good use of the latter phenomenonfor nearly a century. If the doctor can locate his dose so that the edge of the tumor is in thesteep part of the curve, he can do a lot more damage to the tumor than to the surroundinghealthy tissue. Here’s a quote from the Royal College of Radiologists,[8].
Dose-response relationships for tumour control are steep and a 4-5% dose increasemight lead to a 10% increase in probability of tumour control.
It is often claimed that LNT is conservative. But that is only true at the low end. In themid dose range, the logistic fit is higher. For this data, the cross over is slightly above 200 mSv.And it is hardly conservative to trade 1600 deterministic deaths for near zero stochastic deathsas we did at Fukushima.
The best logistic fit is highly asymmetric. The high end portion of the “S” is far larger thanthe low end. In fact, the low end hook is not even visible in Figure 2. There is no reason toexpect a symmetric curve. It would be quite surprising if the curve were symmetric. But thefact that the low end hook is small when viewed from the scale of Figure 2 is one of the reasonsthat has allowed Linear No Threshold to survive.
When we zoom in on the 0 to 150 mSv range, Figure 4, which is what we are really interestedin, we start to see how large the relative differences are.
Table 1 displays this relative difference. The last column is just the Linear NT fit excesscancer incidence ratioed to the Sigmoid NT fit excess cancer incidence. At 100 mSv, the differ-ence is a factor of two. As you move down in dose, this difference increases rapidly. At 25 mSv,the difference is a factor of 9. At 5 mSv, it is a factor of 60. Both fits ignore the reduced solidcancer incidence in the 20,000 person 5-20 mSv, and 20-40 mSv groups. But the logistic curveclearly does a less bad job of fitting the data in this range than the straight line. According tothe logistic fit and a very conservative mortality calculation, a 25 mSv acute dose is equivalentto a Lost Life Expectancy (LLE) of less than a day.2 This is far less than the risks we acceptwithout any thought in the normal course of living. According to Cohen, being a pedestrianhas an LLE of 36 days.[1] Bernie estimates automobile use costs us 207 days. He puts the LLEassociated with abandoning the 55 mph speed limit at 2.0 days. Relaxing the speed limit hadoverwhelming political support. The body politic judged that the benefits of relaxing the speedlimit far outweighed the costs. Airline travel is perceived to be extremely safe. Bernie puts theLLE of airline travel for the average American at 0.4 days.
In the case of nuclear power, we should make the same kind of comparison. Dockery andPope estimate that living in a mildly polluted city has an LLE of 292 days and living in a badly
2 Assumes average victim is 40 years old at exposure and would have lived to 80 with no exposure, equalprobability of dying from the exposure in each year after exposure (no latency, no aging effects)).
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99 199 300 400 500 600 700 800 900 1000
Acute dose (mSv)
0.1094
0.1188
0.1281
0.1375
0.1469
0.1563
0.1657
0.1750
0.1844
0.1938
Solid
Cance
r In
cid
ence
Red is Sigmoid No Threshold
Blue is Linear No Threshold
***
***
*
*
*
*
*
*
**
*
Figure 3: Linear versus Sigmoid NT for RERF Solid Cancers: 0 to 1000 mSv Acute Dose
polluted city has an LLE of 1,150 days.[2] These are the sort of numbers we should comparewith Table 1.
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14 29 45 60 75 90 105 120 135 150
Acute dose (mSv)
0.1045
0.1091
0.1136
0.1182
0.1227
0.1272
0.1318
0.1363
0.1408
0.1454
Solid
Cance
r In
cid
ence
Red is Sigmoid No Threshold
Blue is Linear No Threshold
**
*
** *
*
*
Figure 4: Linear versus Sigmoid NT for RERF Solid Cancers: 0 to 150 mSv Acute Dose
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Dose Logistic LNT Linear Loss Logistic Loss LNT excess riskmSv Fit Fit of Life Expec- of Life Expec- over logistic
Table 1: Linear NT excess cancer incidence vs Sigmoid NT excess cancer incidence
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Figure 5 is a semilog plot of the two models. This gives us a pretty good view of a widedose range but obscures the very large relative difference at the low end. This figure does makethe point that the linear fit is nonsense at the high end. The logistic fit is starting to reduceslope and will end up horizontal at a cancer incidence rate of 1.0.3 To really see the differencebetween the two models at the low end, we need a log-log plot, Figure 6. In this graph I’veswitched to plotting excess cancer incidence. At 0.1 mSv, the SNT curve is almost four ordersof magnitude below the LNT curve and the models are diverging very rapidly.
1.0e-01 1.0e+00 1.0e+01 1.0e+02 1.0e+03 1.0e+04
Acute dose (mSv)
0.1172
0.1344
0.1516
0.1688
0.1860
0.2032
0.2205
0.2377
0.2549
0.2721
Solid
Cance
r In
cidence
Red is Sigmoid No Threshold
Blue is Linear No Threshold
* * ****
*
*
*
*
*
*
* *
***
*
***
Figure 5: Semilog plot of Linear versus Sigmoid NT for RERF Solid Cancers
3 In the real world, extremely high doses will kill via Acute Radiation Syndrome long before the victim getscancer. But here we are only attempting to model cancer incidence. ARS requires its own logistic model
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1.0e-01 1.0e+00 1.0e+01 1.0e+02 1.0e+03 1.0e+04
Acute dose (mSv)
1.0e-09
1.0e-08
1.0e-07
1.0e-06
1.0e-05
1.0e-04
1.0e-03
1.0e-02
1.0e-01
1.0e+00
Exce
ss S
olid
Cance
r In
cidence Red is Sigmoid No Threshold
Blue is Linear No Threshold
Figure 6: Loglog plot of Linear versus Sigmoid NT Excess Cancer Incidence
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3 Handling Chronic Dose
In the great majority of real world radiation releases, the dose is received over an extendedperiod. LNT for which dose rate is irrelevant claims this make no difference. The only thingthat counts is the cumulative dose. This is inconsistent with the fact that people living in highbackground radiation areas accumulate a dose of more than 100 mSv in 20 years. We havelarge populations that have lived in such areas for 50 or more years. For example, in Finland,Figure 7, the average background annual dose is 7.6 mSv, more than double the world average.The average 50 year old Finn accumulates a dose that is more than 200 mSv larger than peopleliving in low background dose areas. It is undisputed that an acute dose of 100 mSv will resultin a statistically observable increase in cancer. Yet there is no discernible increase in cancerincidence in these populations.
Figure 7: European background radiation: source Europen Commission
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The high thorium coastal area of Kerala, India is another example. Here is Dr.Nair’s sum-mary of his study of this population.
The coastal belt of Karunagappally, Kerala is known for its high background ra-diation (HBR) from thorium containing monanzite sand. In coastal panchayats,median outdoor radiation levels are more than 4 mSv/y and, in certain locations onthe coast, it is as high as 70 mSv/year. Although HBR has been repeatedly shownto increase the frequency of chromosome aberrations in the circulating lymphocytesof exposed persons, its carcinogenic effect is still unproven. A cohort of 385,103residents in Karunagappally was established in the 1990’s to evaluate health effectsof HBR. Based on radiation level measurements, a radiation subcohort aged 30-84was analyzed. Cumulative radiation dose for each individual was estimated basedon outdoor and indoor dosimetry of each household, taking into account sex andage specific house occupancy factors. Following 69,958 residents for 10.5 years onthe average, 736,586 person-years of observation were accumulated and 1,379 cancercases including 30 cases of leukemia were identified by the end of 2005. Poissonregression analysis of cohort data, stratified by sex, attained age, follow-up interval,socio-demographic factors and bidi smoking, showed no excess cancer risk from ex-posure to terrestrial gamma radiation. The excess relative risk of cancer excludingleukemia was estimated to be -0.13 per 1000 mSv (95% CI: -0.58, 0.46). In site spe-cific analysis, no cancer site was significantly related to cumulative radiation dose.Leukemia was not significantly related to HBR either.[6]
If we simplistically accumulate dose, sigmoid no threshold will be even farther off than linearno threshold, once a subject’s dose reaches about 220 mSv. The solution is to recognize thatmost of the radiation damage is repaired and the accuracy of that repair depends on dose rate.Our DNA is constantly being damaged and constantly being repaired. Single stand breaks areastonishingly frequent, tens of thousands per cell per day. Almost all these breaks are caused byionized oxygen molecules from metabolism within the cell. MIT researchers observed that 100mSv/y dose rates increased this number by about 12 per day.[9] Breaks that snap only one sideof the chain are repaired almost automatically by the clever chemistry of the double helix itself.
Double strand breaks (DSB) also occur naturally. Endogenous, nonradiogenic causes gener-ate a DSB about once every ten days per cell. Average natural background radiation creates aDSB about every ten thousand days per cell.[3] Clever experiments at UC Berkeley show thatthe two halves migrate to “repair centers”, areas within the cell that are specialized in puttingthe DNA back together.[7] Berkeley actually has pictures of this process, Figure 8. Repair islargely complete in about 2 hours for acute doses below 100 mSv and 10 hours for doses around1000 mSv. These experiments show that, if the “repair center” is only faced with one DSB,the repair process rarely makes a mistake in reconstructing the DNA. But if there are multiple,unrepaired breaks, then the error rate goes up drastically. A few of these errors will survive
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and a few of those will result in a viable mutation that will eventually cause cancer. The keyfeature of this process is it is highly non-linear. The dose received within the repairperiod largely controls the efficacy of repair. This should be a focus of regulation.
Figure 8: UCB pictures of cell repair. There’s a lot going on in this figure. The bright spots inthe screenshots at the top are clusters of damage sensing and repair proteins, known as RadiationInduced Foci (RIF). The graphs at the bottom show that the repair process is over in 2 to aboutten hours depending on the dose. They also show that the number of RIF’s increases far lessrapidly than linearly with the dose. At 0.1 Gy, UCB counted 73 RIF/Gy; at 1.0 Gy, 28 RIF/Gy.Since the damage including double strand breaks (DSB) is presumed to be linear in the dose,this means that as dose rate goes up, more RIF’s will be confronted with more than one DSBand the chances of a bad repair skyrocket.
How to implement that focus? Here’s one possibility:1. Assume an overly long repair time. We know most of the intra-cellular mechanisms operate
on time scales of several hours or less. Radiotherapy effectively assumes a repair time of aday or two in fractionating very high level doses. If we assume a repair time of a month,then we are being extremely conservative.4
2. Apply sigmoid no threshold to each repair time separately, assuming incorrectly that allthe radiation received in that period is received as an acute dose at the start of theperiod. This conservative fabrication allows us to use our acute dose logistic figures to(over-)estimate chronic dose risk.
4 Too much so. Regulators should seriously consider a shorter, more realistic regulatory repair time.
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3. Pick a repair period dose that has an acceptable LLE. This should be done using theALAIB (As Low As Is Beneficial) principle.
For example, under these assumptions, Table 1 tells us each month of 25 mSv per monthdose rate has an LLE of 1 day. We know from Fukushima and Chernobyl that the LLE ofprolonged evacuation is orders of magnitude larger than 1 day. With the possible exception ofpregnant women, there is simply no argument for forcing an evacuation of an area where thedose rate is less than 25 mSv/month, or preventing people from returning to their homes oncethis level is reached. Given the string of conservative assumptions that generated this limit, onecould easily argue for a higher number.
4 Implications of Sigmoid No Threshold
The Sigmoid No Threshold model has several important implications:1. There is a cumulative effect. The model treats each month as a independent event. Thus
the probabilities add. However, we are adding probabilities, not doses. If the dose ratein the first month is 25 mSv per month, and in the second month is 10 mSv/month, andin the third month is 5 mSv/month. then we can add the LLE’s of each of those monthsto end up with 0.956 + 0.132 + 0.030 = 1.118 days.5 This is quite different from the LLEassociated with a dose of 25 + 10 + 5 = 40 mSv or 2.637 days.Suppose a person lives in a area which has a high background dose rate of 6 mSy/y.Then his monthly dose is 0.5 mSv which according to Table 1 has an LLE of 0.0003days. If he lives in this area for 70 years (840 months), the model claims his LLE will be840 · 0.0002 = 0.252 days. The Sigmoid No Threshold model is consistent both with thefact that we can’t see any increase in cancer incidence in high background dose areas, andthe fact that an acute dose of much more than 100 mSv will generate observable increasesin cancer. According to LNT, this dose rate should have increased our septuagarian’schance of becoming a cancer patient by 4%.[10, Table ES-1] This is an easily observablenumber. Gonzalez estimates that an exposed group and a control group of about 500people each should result in a 90% confidence limit.[4]Gonzalez also argues that to see the effects of 10 mSv with a 90% confidence level wouldrequire sample sizes in the millions. This he claims explains the apparent failure to seethe cancers that LNT predicts. But as Figure 7 indicates, we have populations in the tensof millions, if not scores of millions, whose cumulative doses vary by much more than 10mSv. And that’s just in Europe.The assumption of independent repair periods is not consistent with the undisputed ex-istence of inter-period, carryover effects. These can be both positive (e.g. up regulationof immune responses) and negative (e.g. shortening of telemeres). The former appear to
5 LLE is an expected value, so it is proportional to the underlying probabilities. Strictly speaking, we shouldmultiply the probability associated with each succeeding month with the probability of reaching that monthwithout fatal damage. This error is conservative.
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dominate in the low dose rate region. The latter become more significant as the dose rateincreases. The next step would be a model that tries to quantify these inter-dependencies.But given the string of highly conservative assumptions, these secondary adjustmentsneed not be necessary for regulatory purposes, especially since the effects are partiallyoff-setting.
2. Unlike Linear No Threshold, dilution is an effective countermeasure even if it increases theexposed population proportionally. If we are able to dilute from a single person dose of 50mSv’s down to a dose of 1 mSv, even at the cost of increasing the exposed population bya factor of 50, the collective LLE goes from 4.257 days to 50 · 0.001 = 0.05 days. SigmoidNo Threshold accepts the idea of a collective dose, but argues that the impact of that dosefalls off quickly. At 0.5 mSv, the difference between Linear and Sigmoid is more than afactor of 750. And as Figure 6 shows, this difference grows very rapidly at still lower doses.There is no need for the preposterous inconsistency of accepting the Linear No Thresholdhypothesis, but then claiming we can ignore its implications at low dose. UNSCEAR forone appears to hold this indefensible position.[12, page 64]
3. Unlike LNT, measures to spread a release over time makes sense.6 Currently light waterreactor practice is to contain a release until the pressure builds up to near the containmentdesign pressure and then release a large amount of gas over a short period. Under SigmoidNo Threshold, it may make sense to start the release sooner generating a lower releaserate.
4. Unlike Linear No Threshold, the impact of a release depends on the level of existingexposure in the affected area. According to Sigmoid No Threshold, the same release in ahigh background area will cause more response per capita than in a low background area.This is a consequence of ignoring any longer term measures that organisms take to adaptto their environment. However, for all but the highest background areas, this effect willbe marginal.
6 Provided the release period is larger than the assumed repair period. This is a weak point of assuming anoverly long repair period.
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5 Linear No Threshold versus Sigmoid No Threshold
I’d be the last to claim that Sigmoid No Threshold is an accurate model of the exceedinglycomplex biology that is involved in radiation damage and repair.7 But the competition here isnot perfection but LNT. Table 2 summarizes the score in that contest.
Table 2: Linear No Threshold vs Sigmoid No ThresholdLinear Sigmoid
No Threshold No ThresholdModels extremely high dose in a reasonable manner No YesModels mid-range dose in a way that is consistent withuniversally accepted radiotherapy practice
No Yes
Is consistent with the no threshold doctrine Yes YesIs consistent with the risk observed at acute dose of100 mSv and above
Yes Yes
Is consistent with modern understanding of DNAdamage and repair.
No Yes
Is consistent with the lack of discernible increase incancer in high background radiation areas
No Yes
It is the last two that should concern the supporters of LNT. At both Chernobyl andFukushima, the mental and physical stress caused by fear of radiation far outweighed the in-crease in cancer caused by the release. At Fukushima, over 1600 people were killed unnecessarily.8
Much of this must be laid at the feet of LNT and its promoters. These promoters have seen thehuman suffering and death that LNT has caused at least twice. They must know that LNT isnot consistent with either our current understanding of radiation damage and repair nor cancerincidence in high background dose rate areas.9 If there is a workable alternative that avoidsthese critical defects and they choose not to support it, they must share responsibility in theunnecessary suffering that will occur in the next release.
7 I’d also be the last to claim that I have done a good job of implementing Sigmoid No Threshold. Somebodyfar better qualified need to do a much better job of fitting logistic curves to the REFR data and other data sets.
8As of late 2013, rhe number of deaths blamed on the evacuation was put at 1656.[11] Had there been noevacuation, almost no one would have received a dose of 100 mSv.[14] UNSCEAR, using conservative assumptions,estimates that the average dose that would have been received in year 1 in the three towns closest to the plant,Tomioka, Okuma, and Futaba at 51, 47, and 38 mSv respectively,[13][Table C11, page 191] In six of the evacuatedtowns, the projected first year dose was less than 10 mSv. Among UNSCEAR’s conservative assumptions was thegamma dose actually received is 0.6 times the outdoors gamma dose 1 meter above ground as measured from lowflying aircraft. Later studies which compared the outdoors dose rate with actual dosimeter readings in nearbyDate City found that the average dose received was 0.15 times the outdoors aircraft number.[5]
9 This is evident in the contortions that they make to avoid LNT’s very low dose implications. But the bodypolitic hears LNT, not LNT-but-not-really.
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References
[1] B. Cohen. Catalog of risks extended and updated. Health Physics, 61(3):317–335, September1991.
[2] D. Dockery and C. Pope. Lost life expectancy due to air pollution in china. Technicalreport, Swiss re, 2014.
[3] L. Feinendegen, M. Pollycove, and R. Neumann. Hormesis by low dose radiation reffects:Low-dose cancer risk modelling must recognize up-regualtion of protection. Radiation On-cology, 2012. in Therapeutic Nuclear Medicine, Springer, 2012.
[4] A. Gonzalez. The debate on the health effects attributable to low radiation exposure.University of New Hampshire Law Review, 1(1), December 2002.
[5] T. et al Ishikawa. The fukushima health management survey: estimation of external dosesto residents in fukushima prefecture. Scientific Reports, 5, 2015.
[6] M. Nair, B. Rajan, and S. Akiba. Background radiation and cancer incidence in kerala,india, karanagappally cohort study. Health Physics, 96:55–66, January 2009.
[7] T. Neumaier et al. Evidence for formation of dna repair centers and dose-response nonlin-earity in human cells. PNAS early Edition, 2011.
[8] Royal College of Radiologists. Radiotherapy dose fractionation. Technical report, RoyalCollege of Radiologists, 2006.
[9] W. Olipitz, D. Wiktor-Brown, J. Shuga, and B. Pang. Integrated molecular analysis indi-cates undetectable change in dna damage in mice after continuous irradiation at 400 foldnatural background radiation. Environmental Health Perspectives, 120:1130–1136, August2012.
[10] Board on Radiation Effects Research. Health risks from exposure to low levels of ionizingradiation. Technical report, National Research Council, 2006. BEIR VII Phase 2.
[11] T. Otake. Evacuation of fukushima elderly riskier than exposion to radiation. Japan Times,February 2014. 2014-02-20.
[12] UNSCEAR. Sources and effects of ionizing radiation, volume ii. Technical report, UnitedNations Scientific Committee of the Effects of Atomic Radiation, 2011.
[13] W. Weiss. Levels and effects of radiation exposure due to the nuclear accident after the2011 great east japan earthquake. Technical report, United Nations Scientific Committeeof the Effects of Atomic Radiation, February 2014. Vol 1, Scientific Annex A.
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[14] R. Wilson. Evacuation criteria after a nuclear accident. Dose Response, pages 480–499,2012.
