Thinking through Linear With Threshold
Linear No Threshold (LNT), the radiation harm model which is the foundation for our radiation protection regulation is nonsense. It denies our undisputed ability to repair radiation damage. As a result it over-predicts harm in low dose rate situations, such as a nuclear power plant release by many orders of magnitude. But LNT survives. One reason is anti-LNT forces have not coalesced behind a single alternative. Another is that the most commonly suggested alternative, Linear With Threshold (LWT), has much the same problems as LNT.
LWT models accept the L in LNT and focus on the NT. LWT models are rarely completely defined, which at a minimum requires a number specifying the threshold. But there are two main variants:
1) The Threshold is on Dose
2) The Threshold is on Dose Rate.
Threshold on Dose
Threshold on Dose is the way it's usually sketched. Promoters of this model have not thought things through very far. As soon as a person uses up his threshold dose, he's an LNTer. All the usual LNT implications apply. In particular, this model denies our ability to repair any radiation damage no matter how low the dose rate, once the threshold has been exceeded. Figure 1 applies threshold on dose to a idealized nuclear power plant release dose rate profile.
Figure 1. Threshold on dose. The shape of the two areas is immaterial. The area on the right could be 1000 mGy spike or 1mGy/day for 1000 days. The harm is the same.
The only thing that counts is the areas. Let's say the threshold dose is 100 mSv. Suppose the dose rate profile is 2000 mSv delivered all at once (aka acutely). This will have the same effect as an LNT dose of 1900 mSv. The predicted increase in cancer incidence is 19%. Based on the RERF data, this is approximately correct. (By the way, the 1900 mSv spike, will make you very sick.)
Now assume that the 2000 mSv dose is delivered evenly over 1000 days. The LWT harm is still the same as a 1900 mSv LNT dose delivered acutely. The predicted increase in cancer incidence is still 19%. In fact 2 mSv/d is the pre-1950 tolerance dose. 2 mSv/d for 1000 days will result in no detectable harm. Threshold on Dose denies biology in the same way LNT does. It's a non-starter.
Threshold on Dose Rate
Threshold on Dose Rate is a bit more interesting. Whatever the dose rate profile is, just lop off the area under the threshold dose rate. Harm is proportional to the area under the curve that's left.
Figure 2. Threshold on dose rate. The shape of the area above the threshold rate is immaterial. The area above the threshold could be a 1825 mGy spike or an extra 0.5 mGy/day for ten years. The harm is the same.
If we compare, a single spike of 1000 mSv with 1000 mSv spread evenly over say 10 years, we get a big difference in harm. As long as the dose rate is below the threshold, we get zero harm. Threshold on Dose Rate does distinguish between a big acute spike by itself and a protracted chronic dose rate profile with the same cumulative dose.
But it is easy to come up with profiles where this linear model screws up in an obvious manner. Suppose our dose rate threshold is 2 mSv/day, the pre-1950 tolerance dose rate. Consider
a) Profile A which is 2.5 mSv/day for 10 years.
b) Profile B which is 2.0 mSv/day for 10 years plus a spike of 1825 mSv at time zero.
The model claims there is no difference in harm between these two profiles. That's not how our bodies work.
Or compare profiles consisting of a series of spikes. If the spike dose rates are high enough, the area below the threshold dose rate is negligible. We are back to LNT. 1 spike at 1000 mSv is the same as 10 spikes at 100 mSv which is the same as 100 spikes at 10 mSv which is the same as 1000 spikes at 1 mSv and so on. Worse the spacing of the spikes is irrelevant. Whether any of the above patterns was over 1 day or ten years makes no difference. Suppose I have 1000 quick spikes each 1 mSv. I could have those spikes every minute for 1000 minutes. Or one a day for 1000 days. Or one a week for 1000 weeks. The harm would be the same. The body does not operate like that.
The All Important Repair Period
One fundamental problem with both variants of LWT is they ignore the repair period. Any reasonable model of radiation damage and repair must recognize the fact that repair takes time. Any model that does not acknowledge a repair period is nonsense. Simple LWT does not; and therefore comes up with patently ridiculous results.
So let's fix simple LWT by setting a repair period. A repair period of a day would be a defensible choice. Our threshold now is on daily dose. The 2 mSv/day pre-1950 tolerance dose rate would be a good starting point. Each day we toss everything below 2 mSv. Harm is linear in everything that's left. At the end of each day, we reset everything to zero.
This avoids some of the spike profile problems. The timing of the spikes becomes important. They must be at least a repair period apart to be treated separately. But comparing level versus spikey profiles, we end up in the same quandary. Once again consider
a) Profile A which is 2.5 mSv/day for 10 years.
b) Profile B which is 2.0 mSv/day for 10 years plus a spike of 1825 mSv at time zero.
Our improved model still claims there is no difference between these two profiles. This LWT model claims we have a repair system that is perfect up to 2 mSv/day, but has no ability at all to repair any dose above that dose rate. Something happens at 2 mSv/day, that transforms a perfect repair system into a total failure.
This is a better approximation than saying we have no repair system at all; but it is not how our bodies work. And it forces the proponent to argue that there is absolutely zero harm below the threshold dose rate.1 Against a skilled, manipulative debater this is an impossible argument to win, in part because in a strict sense the claim is unprovable.
The LWTer is in the position of defending a model which is a very poor approximation of reality, and which makes an unprovable claim. Perhaps it's better to focus on the L in LNT. That's the part of LNT that implies we have no repair systems. That's an easy target.
About the only way to do this is to introduce hormesis. We know there are one-off situations in which the radiation generates hormetic responses that repair more damage than the radiation causes. But for chronic dose rate profiles, this puts the hormetian in the position of claiming that a release is good for you, and the longer the release the better. That's a stretch. The argument then focuses on disputable hormetian claims rather than LNT's preposterous denial of any repair. Advantage LNTer.
Data beats theory in all of these debates, and to me, the clearest data is Cohen's enormous study of lung cancer from radon in counties all over the USA. The cancer rate is clearly declining up to radon levels of 250 Bq/m3 (more than double the levels found in most buildings). The hormetic effect is small, not enough for me to add radon to my house, but it is easy to explain. Getting a little sun each day will prevent sunburns on the rare occasion when you get too much.
I got into a long debate with some anti-nukers, and they would never accept this simple conclusion, nor could they give me any references supporting their arguments, just outrage that Citizendium would publish this data, and speculation that their must be something wrong with the data. One of the debaters went so far as to dig up maps on smoking in various parts of the USA, and claimed that there was a strong negative correlation between these high-smoking areas and low radon. I pointed out that the cancer study had smoking as a controlled variable, but he didn't understand that.
Citizendium seeks to publish the most effective arguments on each side, be they rational or emotional, but none of these anti's wanted their names associated with their arguments, so I have created a "Read it on the Internet" section with links to the original discussions in a public forum. Let me know if you can improve on our summary. I think it deserves one of your slam-dunk rebuttals. Or maybe Robert Hargraves would like to step in. His lecture slides are where I found the links to this data.
https://citizendium.org/wiki/Fear_of_radiation/Debate_Guide#LNT_and_radon,_Controversy_over_Figure_4
It isn't just radiation regulation which has this problems. You will find similar confusions with both alcohol and meat. Alcohol warnings often stress that there is no safe dose (as far as cancer is concerned) ... particularly for pregnant women. Meat warnings typically include a non-sensical threshold. Because almost all cancers start as a single point of damage, the logical inference is that a single gram (nano-gram, whatever tiny portion you prefer) was responsible. Therefor the only sensible way to describe this is "no safe dose". Once we hear this, it plays with our minds. We can't easily conceive of such tiny units of causality. In the case of meat, the sharp uptick in the dose response curve is at a few hundred grams per week ... hence the warning. But it is the politics of meat and alcohol that determines that "no safe dose" predominates in alcohol circles while threshold thinking dominates in meat warnings. All of these issues are bedevilled by the same problems that you discuss Jack. Almost nobody knows how to think sensibly about these things.