I really like numbers, and it’s taken me some time to get to them in discussing risk to health from radiation. I also like to know what goes into the numbers, so I’ve taken some time working through Biological Effects of Ionising Radiation (BEIR) VII. Now I’m feeling that I (almost) know what I’m doing, I can start to answer the question: what risk of cancer does a particular exposure to radiation carry?

I’ve considered how radiation standards are developed in two earlier posts. These posts have been among the most difficult I’ve written; it’s no wonder that so many people have a hard time understanding what radiation standards mean. Reporters try to put radiation measurements in perspective by saying that they are some multiple of the standards, sometimes large multiples. But unless we know what sort of harm the standards and increases from them represent, we still lack perspective. That is the relationship I’m trying to illuminate for others and understand better myself.

The allowable exposures to members of the public and to radiation workers are given in the chart by Randall Monroe (XKCD). For a member of the public, 1 millisievert/year (mSv/year). For a radiation worker, 50 mSv/year. Under extreme conditions, the worker’s exposure could go up to 100 mSv while protecting valuable property or 250 mSv in protecting human life. That’s, as the news articles like to say, a factor of 250 in exposure. But what does it mean for the risk of cancer?

Let’s consult BEIR VII again. For this post, I want to make the numbers as plain as possible, so I will omit most qualifications. There are many in BEIR VII, and I will discuss some of them later.

The most directly usable tables are those in Chapter 12 and Annex 12D. They provide the lifetime attributable risk of cancer incidence and mortality for single exposures at various ages. “Lifetime attributable risk” means those cancers attributable to radiation over and above the normal cancer incidence. BEIR VII assumes that the risk is proportional to the amount of exposure, the linear no-threshhold hypothesis. This hypothesis is the subject of some controversy, which BEIR VII addresses and concludes that it is a reasonable assumption. It is a conservative assumption, because it results in a higher calculated risk of cancer than alternative assumptions. So the numbers in this post might be considered an upper bound.

The tables also give the exposures in grays (Gy), rather than sieverts. Gray is the measure of deposited energy, and sievert is the measure of biological effect. For most of what I’m considering, it’s reasonable to assume that the two are numerically equal.

For the public limit, the BEIR VII committee’s preferred estimate is in Table 12-6. 1 mSv per year throughout life, the expectation is that there will be 550 cases of cancer and 290 deaths per 100,000 males, 970 cases and 460 deaths per 100,000 females, due to this incremental radiation exposure.

The worker limit, 50 mSv per year, does not apply to an entire lifetime because people do not work over their entire life. Table 12D-3 provides data for yearly exposures of 1 mGy per year throughout life and 10 mGy per year over ages 18 – 65. It is evident in the table that cancer incidence and death rates are not a simple multiple of the exposures, but I will use that method anyway; it gives a high estimate. For 50 mSv per year exposure for men, the risks for cancer incidence and mortality are 15,295 and 8,500 per 100,000 people; for women, the corresponding numbers are 21,475 and 11,945. But most workers are not exposed over that entire time range, nor do they receive the full 50mSv per year. Although my work with radioactive materials was occasional rather than the regular work of, say, a reactor technician, my typical exposures were under 1 mSv per year.

The lifetime attributable risks of cancer incidence and mortality of the one-time doses, 100 mSv for protection of valuable property and 250 mSv for protection of human life, are found in Tables 12D-1 and 12D-2. If we assume that the workers are male and their age is 40, then 100 mSv gives 648 cancer cases and 337 cancer deaths per 100,000 people exposed; 250 mSv gives 1620 cancer cases and 843 cancer deaths per 100,000 people exposed.

The incidence of genetic mutations is so small that BEIR VII does not include an attempt to measure it.

Doses over a lifetime are not strictly additive, although this claim has been made in the media. The BEIR VII tables indicate different effects for one-time doses and doses over time. Radiation therapy for cancer frequently involved much higher cumulative doses than those expected to cause death in a single exposure.

My next post will consider the likely errors on these numbers, the qualifications stated in BEIR VII, and some questions raised by others about BEIR VII, along with the baseline incidence of cancer. Unfortunately, that last is almost as hard to pull out of the reports as the numbers on radiation effects I’ve given here. For some comparison, Ethel S Gilbert, a radiation epidemiologist at the National Cancer Institute, was quoted in the New York Times on the cancer risk to Americans from fallout from atmospheric nuclear weapons tests. That projection, apparently the same sort of numbers as what I’ve given above, is 11 000 more deaths from solid cancers compared with the normal rate of 40 million cancer fatalities.

Cheryl Rofer holds an A.B. from Ripon College and an M.S. from the University of California at Berkeley, both in chemistry. She is retired from the Los Alamos National Laboratory, where she worked from 1965 through 2001 on tthe nuclear fuel cycle, management of environmental cleanups, and other topics. She has also been involved with cleanups in Estonia and Kazakhstan of former nuclear sites. She is immediate past president of the Los Alamos Committee on Arms Control and International Security and a member of the Board of Trustees of Ripon College (Ripon, Wisconsin). She also blogs at Phronesisaical (http://phronesisaical.blogspot.com/)