Let's consider what each of these graphs mean. Keep in mind that none of these relationships is known to be strictly true, but we think that some of them are closer to the truth than others. That is, all four graphs are models of how radiation might lead to cancer, and we want to know which ones are currently most accepted.

All cancer-exposure relationships start away from the origin. The reason for this is that nothing on this earth is entirely free from radiation. We all experience a background level of radiation that is happening all the time (see below). Also, cancer rates are greater than zero: people who receive background exposures develop cancer at some low rate. We don't know if cancer would disappear in the complete absence of radiation (probably not), so we try to understand how increases in exposure above background level result in increases in cancer rate. Each of these four graphs represents a different kind of model of this relationship.

Model A is the easiest to understand. Under this model, your cancer rate is simply proportional to your dose. This model could not apply across all conceivable doses, because the cancer rate can't exceed 100%, but it could apply to the doses of radiation that interest us.

Model B is the hoped-for model: increases in exposure do not increase cancer rates until the exposure reaches some threshold. We have drawn a linear response to exposures above threshold, but our interest in this model lies chiefly in the existence of a threshold regardless of the form of the curve beyond the threshold.

Model C is one in which cancer rate increases more steeply with increasing dose. That is, doubling your exposure more than doubles your increased risk.

Model D also shows increasing cancer levels with increasing exposure, but the rate of increase declines with exposure.

Which of these models are supported or rejected by the data? Observations on cancer rates (chiefly leukemia, a kind of blood cancer) suggests that model C is correct - the accelerating model. However, increased incidences of cancer from low exposures are so slight that they are difficult to detect, so we aren't terribly confident of the relationship at low doses. A second source of evidence comes from studies on the incidence of chromosome breaks in white blood cells following a person's radiation exposure. (Chromosome breaks do not indicate cancer but are thought to be a first step in cancer formation.) This work supports the linear model A rather than C.

In abbreviated template form, therefore:

Limitations and Complications. All of these predictive models are limited in that they assume a particular form to the relationship between cancer and radiation, and that form is bound to be inaccurate at some level. In practice, the actual relationships may not even be smooth. On top of this, all models ignore factors that may greatly affect cancer rates. For example, the model that best describes the average cancer risk for the population may not apply to any individual in that population: (i) there are time lags - cancer appears long after the exposure (>5 yr for leukemia, 15-25 yr for solid tumors), (ii) the incidence of cancer per dose of radiation is age-dependent, with ages 10-50 being the safest (irradiation of the fetus can lead to mental retardation).

Other abstract models

The four abstract models shown in the graphs above are not the only kinds of abstract models that interest us. A person's genetic make-up can have a tremendous influence on cancer rate, and various "environmental" factors (toxins, diet) may interact with radiation exposure to affect cancer risk. Predictive models can be developed to deal with these aspects of the problem and with countless other dimensions of cancer (such as how radiation causes cancer). The models we have presented are thus a tiny subset of the possible predictive models addressing cancer and radiation.

Measures of radiation

There are many different ways to measure radiation. Each way of measuring radiation is itself a model. Two people who both receive exactly 10 rads of radiation can have different biological responses. Other factors partially determine the biological consequences of 10 rads of radiation, such as a person's age, whether the radiation was received in one large dose or many small doses, and whether the radiation was in the form of beta particles or X rays. Hence, the statement that someone "received 10 rads of radiation" is a summary, or model, of the radiation that that person actually received.

The following list describes some common measures of radiation.

• A roentgen is a measure of radiation according to the number of ions which are produced in a standard mass of air. This metric is from physics.
• A rad (roentgen absorbed dose) is a measure of absorbed energy/roentgen
• A rem (roentgen equivalent man) is the biological response in man which equals one roentgen of x-rays. At low exposures the rad and rem are roughly equivalent.
• A Gray (Gy) equals 100 rads.
• A Sievert (Sv) equals 100 rems.

The physical models

The foregoing evaluations of predictive models were based on data, and the data have come from physical models at several levels. The physical models consist of everything of a physical nature used in evaluating cancer risk - the subjects, the manner in which they were physically treated, and so on. In the case of radiation and cancer, the physical models are important, because the cancer risk may be influenced by many factors, and choice of an inappropriate physical model could greatly mislead us. We are thus cautioned against using a wide range of physical models that might otherwise be employed.

(1) The organism: humans

We know from studies of insects that radiation causes genetic damage. But insects don't develop cancer. Even with mice (which can develop tumors), their biology is sufficiently different from human biology to doubt their utility as a model of human cancer. Human thus make the best models and perhaps the only satisfactory models when studying cancer. And virtually all of the data come from humans. However, because experiments in which people are deliberately exposed to radiation are not permitted, the humans for which we have such data are limited to a few groups: Japanese survivors of atomic bomb blasts, U.S. soldiers exposed to radiation during atomic tests, and victims of diseases whose treatment requires large radiation exposures. So the radiation data are based on the most suitable organisms (humans) but are limited in the extent to which a wide range of humans have been included.

The Japanese Database. After the Japanese surrendered, the surviving atomic bomb victims in Nagasaki and Hiroshima were interviewed. Approximately 6,000 survivors exposed to 1 gy of radiation and 40,000 survivors exposed to .01 gy of radiation were identified, based on their statements of how close they had been to ground zero at the time of detonation. These individuals and their families have been monitored since. However, a recent controversy has arisen over the predominant type of radiation that was received from the bomb blast, so the estimated exposures may have some problems.

(2) The effect of radiation

(A) Leukemia. There are dozens of kinds of cancer, and radiation may well contribute to all of them. Yet most of the radiation-cancer data are for leukemia (an overproliferation of white blood cells). One reason is that leukemia is a relatively common form of cancer, especially so for children. Second, the time lag between radiation exposure and the resulting cancer is shorter for leukemia than for many other cancers, which also contributes to the ease of studying it. The limitation of relying so heavily on leukemia as a "model" cancer is that it may not represent all cancers.

To appreciate the difficulty of studying increases in cancer rates, consider some numbers from the Japanese bomb survivors: the annual number of excess deaths per million people per .01 Gy of exposure from the bomb was

(B) Chromosome Breaks. In view of the enormous sample sizes required for detecting increases in cancer from modest increases in exposure, it is useful to have alternative physical models that give us insight to the risks from radiation. A simple assay that can be applied to large numbers of people is the incidence of chromosome breaks in white blood cells. A sample of blood is drawn, the white cells are cultured, and the chromosomes of the dividing white cells are spread out on a microscope slide. Chromosomes whose "arms" are broken can be identified quite easily. So this assay can be performed on thousands of people, and it has a potential to be quite sensitive, because tens of thousands of chromosome arms can be screened per person, enabling slight increases in the rate of chromosome damage to be detected. Even so, studies have concentrated on people who have received large doses of radiation: Japanese bomb survivors, nuclear shipyard workers in Scotland, uranium miners, and victims of ankylosing spondylitis (treated with 15 Gy). The limitation of this assay is that the form of the relationship between radiation and chromosome breaks need not be similar to that between radiation and cancer.

(3) The Radiation

Our understanding of the cancer risk from above-background radiation is based on haphazard models when it comes to the types of radiation involved in the exposures. As mentioned above, we do not experiment with people to determine the cancer risk of radiation, so we must rely on medical, military and occupational exposures. For the most part, these kinds of exposures are not controlled, and in some cases, there is a fair bit of guesswork in calculating the types of radiation involved. Two conceivable problems arise from this dependence on uncontrolled exposures. First, the different kinds of radiation may have different effects in causing cancer. If the rem and rad indeed accurately accommodate the differences in cancer risk from diverse types of radiation, then this problem is not serious; but the rad and rem are not calculated from cancer risk directly, so this problem may be real. Second, the calculated exposures may themselves be in error in these studies. For example, with the Japanese bomb survivors - the largest and most extensive database for cancer risk from radiation - there is now controversy over whether most of the radiation from the blast was neutrons (quite deadly) or photons (less deadly), and earlier calculations had assumed the latter. If neutrons were more prevalent than assumed, it means that we have overestimated the harmful effects of radiation in this data set. Such a miscalculation in the type of radiation results in a miscalculation of the exposure survivors received (the number of Sieverts or Grays).

(4) The Exposures

Most of the effort in studying the cancer risk from radiation has gone into groups of people who have received large doses. This is not to suggest that we should be complacent about smaller doses, but rather the cancer risk even from large doses is small enough that it takes years of work and tens of thousands to hundreds of thousands of people to detect statistically-significant increases in cancer rate. So we focus on people who have received large exposures and extrapolate to low doses. Of course, by focusing on people who have received large doses, our data do not tell us about which of the predictive models (A-D) apply at low doses. The problem is a classic "catch-22": we want to know about the cancer risk from low doses of radiation, but we need to study people who have received large doses in order to measure the effect. Yet these data don't necessarily tell us what we want to know.

The preceding boxed text on the Japanese bomb survivors indicated the range of exposures studied in that group (0.01 to 1 Gray), and the medical treatment for ankylosing spondylitis involves an accumulated exposure of 15 Gy (given over many years). For comparison, we describe the exposures that an average American can expect to receive each year and a lethal exposure.

Natural forms of radiation exposure come from the sun which gives off UV and cosmic rays. The soil and even natural isotopes in our body (40K) are two other natural sources of radiation. Man-made sources of radiation include X-rays (medicine), bomb testing, nuclear power plants (accidents), radioactive waste, and air travel. (A chest X-ray adds 30 mrem (0.3 mSv) to your annual dose, but a mammogram and gut fluoroscopy each add 2 mSv.) The atmosphere screens cosmic rays to some extent, and the farther one goes up from the earth's surface, the more radiation one is exposed to. And there is an 80-fold increase associated with smoking; however it is directed mostly to alpha particles and is limited to the lining of the lungs. (Is 80-fold the same as 80%?)

Perspective: The 3-Mile Island power plant accident

• the largest exposure was to 260 nearby residents = .2 -.7 mSv
• the average increased exposure within a 10 mi radius = .065 mSv

The average exposure per year for a resident of Harrisburg is 1.16 mSv, and of Denver is 1.93 mSv.

Thus, the worst increased exposure from this accident for these Pennsylvania residents was on the order of a summer-long visit to Denver. The accident shut down the unit for over a year and was very costly, so it was not economically trivial. But we will never be able to see an elevated cancer rate in residents near 3-Mile Island resulting from this accident.

Limitations revisited

In thinking about our knowledge of the cancer risk from radiation, we review the various limitations of the physical models on which our conclusions are based. We also need to be reminded that radiation can have health effects other than cancer, yet we have just considered cancer in this text.

• 1. Radiation may influence cancer rates differently for different cancers, yet most of the physical models consider only leukemia.
• 2. Consequently, studies have been extended to convenient surrogates: chromosome breaks in blood cells.
• 3. The types of radiation vary, and the effects may also vary.
• 4. The baseline rates are small, and it is difficult to get the large samples and the quality control necessary to measure risk.
• 5. Human data are sparse, and the experiments on humans cannot be set up.
• 6. Time lags exist between exposure and the onset of cancer.
• 7. Different age and sex groups vary in sensitivity.
• 8. Dose fractionation: A single big dose has a greater net effect over time than the same dose spread out over small increments.
• 9. Extrapolation from high doses: even modest, above-average exposures to radiation have a small per-person probability of resulting in cancer, so much of the work is based on individuals that were fortuitously exposed to high doses; we thus don't know how to extrapolate to low doses.