SNT for Dummies

The Sigmoid No Threshold (SNT) model of radiation harm is an important plank in the Gordian Knot Group platform. But it seems I have done a very poor job of explaining just what SNT is. I've gotten some disappointing questions about SNT from the choir. If the choir can't sing SNT, then we haven't got very far.

And it is not only the choir that needs to understand SNT. Far more importantly, Congress and their staffers must. We know these people are talented; but their talents may not lie in radiation harm modelling. So let's take it step by step, and go slowly.

For the missionaries, I can make up a slide deck from this post if there is a demand.

The Individual Dose Rate Profile

In a release, everything starts with each individual's dose rate profile. Figure 1 shows an idealized profile for somebody living in the low dose rate portion of Okuma, the hardest hit town adjacent to Fukushima Daiichi, who does not evacuate, spends all his time outdoors, and does not mask up. (These are the intentionally highly conservative assumptions made by the Underwriter Certification compensation plan.)

Figure 1 Example individual dose rate profile

In future releases, if Underwriter Certification is adopted, the profiles would be based on the actual measurements of the sensors near each resident's home. We can expect the measured profiles to be more complicated than Figure 1 in the early portion of a release. At Fukushima the release was a series of spikes, followed by rapid decay as each puff moved passed a point.

The fact that SNT needs the dose rate through time is sometimes offered as an argument for Linear No Threshold(LNT), the reigning radiation harm model upon which nuclear power regulation is based. LNT only needs the total dose, the area under the dose rate curve. This is nonsense on two levels. Fundamentally SNT and any semi-realistic harm model need the dose rate through time because that's what our bodies respond to. And as a practical matter, the total dose is almost always calculated from the dose rate thru time. In practice, LNT starts with the same data and then throws away what's really important.

Divide Profile into Repair Periods

The first step is to divide the dose-rate profile into repair periods, Figure 2. At the cell level, the repair period is measured in minutes and hours. SNT conservatively assumes a repair period of a day, which is also a convenient measuring interval.

Figure 2. Divide Profile into Repair Periods. SNT uses a day.

For context, I have shown the background dose rate in portions of the coast in Kerala. 173,000 citizens of this area were studied for 15 years. The people in the highest dose rate villages had slightly lower cancer rates than the people in the low dose rate towns, Figure 3. We have not seen any harm until the dose rates get into get into the 20 mSv/d and above range.

Figure 3. Cancer Incidence in Kerala. No detectable harm from 600 mSv over 10 years. (Most of these people have lived with these dose rates their entire lives; not just the time they were in the study.)

Compute the Cancer Mortality associated with each period's dose

Once we have the dose in each period, we can compute the cancer mortality associated with any period. We do that by assuming all the dose in that period was received at the start of the period, that is acutely. In the example in Figure 4 the dose in day 11 is 0.28 mSv. We consult our sigmoid acute dose-harm curve at 0.28 mSv and find that the cancer mortality, the probability of getting mortal cancer from that day's dose, is 0.000000138.

Figure 4. Compute Cancer Mortality for each period

The curve in the inset figure is based on fitting an S-shaped curve to the cancer mortality observed in atom bomb survivors, Figure 5. That's how Sigmoid No Threshold got its name. However, in the inset we are only looking at the very bottom of the S, between a daily dose of 0 and 1 mSv.

Figure 5. SNT(blue) fit to atom bomb survivor cancer mortality. Curve is an S in which the bottom hook is much smaller than the top.

Add the Cancer Mortalities for each Period Up

Unlike LNT which accumulates damage and then converts to harm, SNT converts period damage to period harm (unrepaired damage) and only then accumulates harm, resulting in the increase in cancer mortality shown by the red line in Figure 6.¹

Figure 6. Convert Period Mortalities into Total Mortality, Red Curve, read right}

Actually, it's not quite that simple. SNT assumes each day is a flip of a coin. At the end of the day, the damage from that day is either repaired or it is not. If not, we get mortal cancer. But cancer can only kill us once. So we weight each day's mortality by the probability of not already contacting mortal cancer. In most nuclear plant releases, that probability will be close to 1.0, and the adjustment will be very small.

The hypothesis that what happens in each repair period is independent of whatever happens in any other repair period is easily SNT's most heroic assumption. In a strict sense, it is almost certainly not true. But the test is: does it work? The answer is it works far, far better than LNT, multi-orders of magnitude better on dose rate profiles that occur over protracted periods.

For the purposes of compensation, there is one other adjustment that we should make. The sensors around the plant will measure the total dose rate, which is made up of the background dose rate and the dose rate due to the release. If we are interested in the cancer incidence due only to the release, we need to compute the cancer mortality due to the background radiation and deduct that mortality from the mortality associated with the total dose rate. Since SNT is non-linear, we can't just deduct the background dose rate from the measured dose rate. However, unless you are in a place like Kerala, this adjustment will not change things materially.

Convert Individual Cancer Mortalities into Lost Life Expectancy

For the purposes of compensation and comparison with other sources of electricity, we need to convert the increase in cancer mortality to Lost Life Expectancy (LLE). This can be done on the basis of an overall average. For Americans, the average life years lost to a mortal cancer is about 12. Or we can use a more detailed model based on each individual's sex and age. Either way we simply multiply the SNT cancer mortality for that individual by the average years lost if that person contracts a mortal cancer.

For compensation purposes, we need to multiply each individual's LLE in days by the congressionally mandated value of a lost day. Here we are making the ethical judgement that all lost days are equal. That judgement also allows us to add up all the LLE's to obtain a collective Lost Life Expectancy, which is an important metric of the harm done by the release.

SNT is Easy

This completes our long winded description of SNT. In going so slowly, I have made SNT sound much more complicated than it is. The computer eats this kind of stuff up. Here is the entire code required to turn an individual's daily dose rate profile into his SNT cancer incidence. It’s less than 20 lines.

The only point of cluttering up this piece with some hieroglyphics is to demolish the argument that SNT is too complicated to implement. Once you properly instrument the area around each plant, which you should do regardless of your harm model, SNT is just as easy to enforce as LNT.

So we have a model that is orders of magnitude more accurate than LNT and just as easy to implement. What are we waiting for?

1. Sometimes LNTers will argue for LNT on the grounds that there is a cumulative effect, as if non-LNTers are denying that obvious fact. Of course, there is a cumulative effect. SNT among others claims there is a cumulative effect. The question is what form does the cumulative effect take, and how well does your model describe that effect? There is no way LNT can model both the harm we see when a large dose is received in one shot and the lack of detectable harm when the same or much larger doses are received over prolonged periods.