Dose response problems in carcinogenesis.

The estimation of risks from exposure to carcinogens is an important problem from the viewpoint of protection of human health. It also poses some very difficult dose-response problems. Two dose-response models may fit experimental data about equally well and yet predict responses that differ by many orders of magnitude at low doses. Mechanisms of carcinogenesis are not sufficiently understood so that the shape of the dose-response curve at low doses can be satisfactorily predicted. Mathematical theories of carcinogenesis and statistical procedures can be of use with dose-reponse problems such as this and, in addition, can lead to a better understanding of the mechanisms of carcinogenesis. In this paper, mathematical dose-response models of carcinogenesis are considered as well as various proposed dose-response procedures for estimating carcinogenic risks at low doses. Areas are suggested in which further work may be useful. These areas include experimental design problems, statistical procedures for use with time-to-occurrence data, and mathematical models that incorporate such biological features as pharmacokinetics of carcinogens, synergistic effects, DNA repair, susceptible subpopulations, and immune reactions.     

Radiation-induced carcinogenesis: mechanistically based differences between gamma-rays and neutrons, and interactions with DMBA

Different types of ionizing radiation produce different dependences of cancer risk on radiation dose/dose rate. Sparsely ionizing radiation (e.g. γ-rays) generally produces linear or upwardly curving dose responses at low doses, and the risk decreases when the dose rate is reduced (direct dose rate effect). Densely ionizing radiation (e.g. neutrons) often produces downwardly curving dose responses, where the risk initially grows with dose, but eventually stabilizes or decreases. When the dose rate is reduced, the risk increases (inverse dose rate effect). These qualitative differences suggest qualitative differences in carcinogenesis mechanisms. We hypothesize that the dominant mechanism for induction of many solid cancers by sparsely ionizing radiation is initiation of stem cells to a pre-malignant state, but for densely ionizing radiation the dominant mechanism is radiation-bystander-effect mediated promotion of already pre-malignant cell clone growth. Here we present a mathematical model based on these assumptions and test it using data on the incidence of dysplastic growths and tumors in the mammary glands of mice exposed to high or low dose rates of γ-rays and neutrons, either with or without pre-treatment with the chemical carcinogen 7,12-dimethylbenz-alpha-anthracene (DMBA). The model provides a mechanistic and quantitative explanation which is consistent with the data and may provide useful insight into human carcinogenesis.     

Estimating radiation-induced cancer risks at very low doses: rationale for using a linear no-threshold approach

The possible cancer risks caused by ionizing radiation doses of ~1 mSv or less are too small to be estimated directly from epidemiological data. The linear no-threshold (LNT) approach to estimating such risks involves using epidemiological data at higher (but still low) doses to establish an “anchor point”, and then extrapolating the excess cancer risk linearly down from this point to the low dose of interest. The study in this issue by Professor Tubiana and colleagues, summarizing a French Academy of Sciences report, argues that such LNT extrapolations systematically give substantial overestimates of the excess cancer risk at very low doses. We suggest that, to the contrary, even if there are significant deviations from linearity in the relevant dose range, potentially caused by the effects of inter-cellular interactions or immune surveillance, we know almost nothing quantitatively about these effects. Consequently, we do not know the magnitude, nor even the direction of any such deviations from linearity—the risks could indeed be lower than those predicted by a linear extrapolation, but they could well be higher.     

Failla memorial lecture. Risk, research, and radiation protection

Radiation protection concerns the risk of stochastic late effects, especially cancer, and limits on radiation exposure both occupationally and for the public tend to be based on these risks. The risks are determined, mainly by expert committees, from the steadily growing information on exposed human populations, especially the survivors of the atomic bombs dropped in Japan in 1945. Risks of cancer estimated up to the early 1980s were in the range 1 to 5 X 10(-2)/Sv, but recent revisions in the dosimetry of the Japanese survivors and additional cycles of epidemiological information suggest values now probably at the high end of this range. These are likely to require an increase in the values used for radiation protection. A major problem with risk estimation is that data are available only for substantial doses and must be extrapolated down to the low-dose region of interest in radiation protection. Thus the shape of the dose-response curve is important, and here we must turn to laboratory research. Of importance are studies involving (1) dose rate, which affects the response to low-LET radiation and often to high-LET radiation as well; (2) radiation quality, since the shapes of the dose-response curves for high- and low-LET radiation differ and thus the RBE, the ratio between them, varies, reaching a maximum value RBEM at low doses; and (3) modifiers of the carcinogenic response, which either enhance or reduce the effect of a given dose. Radiation protection depends both on risk information, and especially also on comparisons with other occupational and public risks, and on research, not only for extrapolations of risk to low doses but also in areas where human information is lacking such as in the effects of radiation quality and in modifications of response.     

The linear no-threshold model does not hold for low-dose ionizing radiation

Almost all of the data on the biological effects of ionizing radiation come from studies of high doses. However, the human population is unlikely to be exposed to such doses. Regulatory limits for radiation exposure are based on the linear no-threshold model, which predicts that the relationship between biological effects and radiation dose is linear, and that any dose has some effect. Chromosomal changes are an important effect of ionizing radiation because of their role in carcinogenesis. Here we exposed pKZ1 mice to single whole-body X-radiation doses as low as 1 microGy. We observed three different phases of response: (1) an induction of inversions at ultra-low doses, (2) a reduction below endogenous inversion frequency at low doses, and (3) an induction of inversions again at higher doses. These results do not fit a linear no-threshold model, and they may have implications for the way in which regulatory standards are presently set and for understanding radiation effects.     

Cancer incidence and mortality after low-dose radiation exposure: epidemiological aspects

Current recommendations for limiting exposure to ionizing radiation are based on the linear-no-threshold (LNT) model for radiation carcinogenesis under which every dose, no matter how low, carries with it some cancer risk. In this review, epidemiological evidences are discussed that the LNT hypothesis is incorrect at low doses. A large set of data was accumulated that showed that cancer risk after ordinarily encountered radiation exposure (natural background radiation, medical X-rays, etc.) is much lower than projections based on the LNT model. The discovery of the low-level radiation hormesis (stimulating effect) implies a non-linear dose-response curve in the low-dose region. The further studies in this field will provide new insights about the mechanisms of radiation carcinogenesis.     

Cancer incidence and mortality after low-dosage radiation exposure: Epidemiological aspects

Current recommendations for limiting exposure to ionizing radiation are based on the linear no-threshold (LNT) model for radiation carcinogenesis under which every dose, no matter how low, bears some cancer risk. In this review, epidemiological evidence is discussed that the LNT hypothesis is incorrect at low doses. A large set of data was accumulated that show that cancer risk after ordinarily encountered radiation exposure (natural background radiation, medical X-rays, etc.) is much lower than estimates based on the LNT model. The discovery of low-level radiation hormesis (stimulating effect) implies a non-linear dose-response curve in the low-dosage region. Further studies in this field will provide new insights into the mechanisms of radiation carcinogenesis.     

Risk estimation for fast neutrons with regard to solid cancer.

In the absence of epidemiological information on the effects of neutrons, their cancer mortality risk coefficient is currently taken as the product of two low-dose extrapolations: the nominal risk coefficient for photons and the presumed maximum relative biological effectiveness of neutrons. This approach is unnecessary. Since linearity in dose is assumed for neutrons at low to moderate effect levels, the risk coefficient can be derived in terms of the excess risk from epidemiological observations at an intermediate dose of gamma rays and an assumed value, R(1), of the neutron RBE relative to this reference dose of gamma rays. Application of this procedure to the A-bomb data requires accounting for the effect of the neutron dose component, which, according to the current dosimetry system, DS86, amounts on average to 11 mGy in the two cities at a total dose of 1 Gy. With R(1) tentatively set to 20 or 50, it is concluded that the neutrons have caused 18% or 35%, respectively, of the total effect at 1 Gy. The excess relative risk (ERR) for neutrons then lies between 8 per Gy and 16 per Gy. Translating these values into risk coefficients in terms of the effective dose, E, requires accounting for the gamma-ray component produced by the neutron field in the human body, which will require a separate analysis. The risk estimate for neutrons will remain essentially unaffected by the current reassessment of the neutron doses in Hiroshima, because the doses are unlikely to change much at the reference dose of 1 Gy.     

The Causes and Prevention of Cancer: The Role of Environment

The idea that synthetic chemicals such as DDT are major contributors to human cancer has been inspired, in part, by Rachel Carson's passionate book, Silent Spring. This chapter discusses evidence showing why this is not true. We also review research on the causes of cancer, and show why much cancer is preventable.Epidemiological evidence indicates several factors likely to have a major effect on reducing rates of cancer: reduction of smoking, increased consumption of fruits and vegetables, and control of infections. Other factors are avoidance of intense sun exposure, increases in physical activity, and reduction of alcohol consumption and possibly red meat. Already, risks of many forms of cancer can be reduced and the potential for further reductions is great. If lung cancer (which is primarily due to smoking) is excluded, cancer death rates are decreasing in the United States for all other cancers combined.Pollution appears to account for less than 1% of human cancer; yet public concern and resource allocation for chemical pollution are very high, in good part because of the use of animal cancer tests in cancer risk assessment. Animal cancer tests, which are done at the maximum tolerated dose (MTD), are being misinterpreted to mean that low doses of synthetic chemicals and industrial pollutants are relevant to human cancer. About half of the chemicals tested, whether synthetic or natural, are carcinogenic to rodents at these high doses. A plausible explanation for the high frequency of positive results is that testing at the MTD frequently can cause chronic cell killing and consequent cell replacement, a risk factor for cancer that can be limited to high doses. Ignoring this greatly exaggerates risks. Scientists must determine mechanisms of carcinogenesis for each substance and revise acceptable dose levels as understanding advances.The vast bulk of chemicals ingested by humans is natural. For example, 99.99% of the pesticides we eat are naturally present in plants to ward off insects and other predators. Half of these natural pesticides tested at the MTD are rodent carcinogens. Reducing exposure to the 0.01% that are synthetic will not reduce cancer rates. On the contrary, although fruits and vegetables contain a wide variety of naturally-occurring chemicals that are rodent carcinogens, inadequate consumption of fruits and vegetables doubles the human cancer risk for most types of cancer. Making them more expensive by reducing synthetic pesticide use will increase cancer. Humans also ingest large numbers of natural chemicals from cooking food. Over a thousand chemicals have been reported in roasted coffee: more than half of those tested (19/28) are rodent carcinogens. There are more rodent carcinogens in a single cup of coffee than potentially carcinogenic pesticide residues in the average American diet in a year, and there are still a thousand chemicals left to test in roasted coffee. This does not mean that coffee is dangerous but rather that animal cancer tests and worst-case risk assessment, build in enormous safety factors and should not be considered true risks.The reason humans can eat the tremendous variety of natural chemical "rodent carcinogens" is that humans, like other animals, are extremely well protected by many general defense enzymes, most of which are inducible (i.e., whenever a defense enzyme is in use, more of it is made). Since the defense enzymes are equally effective against natural and synthetic chemicals one does not expect, nor does one find, a general difference between synthetic and natural chemicals in ability to cause cancer in high-dose rodent tests.The idea that there is an epidemic of human cancer caused by synthetic industrial chemicals is false. In addition, there is a steady rise in life expectancy in the developed countries. Linear extrapolation from the maximum tolerated dose in rodents to low level exposure in humans has led to grossly exaggerated mortality forecasts.Such extrapolations can not be verified by epidemiology. Furthermore, relying on such extrapolations for synthetic chemicals while ignoring the enormous natural background, leads to an imbalanced perception of hazard and allocation of resources. It is the progress of scientific research and technology that will continue to lengthen human life expectancy.Zero exposure to rodent carcinogens cannot be achieved. Low levels of rodent carcinogens of natural origin are ubiquitous in the environment. It is thus impossible to obtain conditions totally free of exposure to rodent carcinogens or to background radiation. Major advances in analytical techniques enable the detection of extremely low concentrations of all substances, whether natural or synthetic, often thousands of times lower than could be detected 30 years ago.Risks compete with risks: society must distinguish between significant and trivial risks. Regulating trivial risks or exposure to substances erroneously inferred to cause cancer at low-doses, can harm health by diverting resources from programs that could be effective in protecting the health of the public. Moreover, wealth creates health: poor people have shorter life expectancy than wealthy people. When money and resources are wasted on trivial problems, society's wealth and hence health is harmed.     

Dynamics of Cellular Responses to Radiation

Understanding the consequences of exposure to low dose ionizing radiation is an important public health concern. While the risk of low dose radiation has been estimated by extrapolation from data at higher doses according to the linear non-threshold model, it has become clear that cellular responses can be very different at low compared to high radiation doses. Important phenomena in this respect include radioadaptive responses as well as low-dose hyper-radiosensitivity (HRS) and increased radioresistance (IRR). With radioadaptive responses, low dose exposure can protect against subsequent challenges, and two mechanisms have been suggested: an intracellular mechanism, inducing cellular changes as a result of the priming radiation, and induction of a protected state by inter-cellular communication. We use mathematical models to examine the effect of these mechanisms on cellular responses to low dose radiation. We find that the intracellular mechanism can account for the occurrence of radioadaptive responses. Interestingly, the same mechanism can also explain the existence of the HRS and IRR phenomena, and successfully describe experimentally observed dose-response relationships for a variety of cell types. This indicates that different, seemingly unrelated, low dose phenomena might be connected and driven by common core processes. With respect to the inter-cellular communication mechanism, we find that it can also account for the occurrence of radioadaptive responses, indicating redundancy in this respect. The model, however, also suggests that the communication mechanism can be vital for the long term survival of cell populations that are continuously exposed to relatively low levels of radiation, which cannot be achieved with the intracellular mechanism in our model. Experimental tests to address our model predictions are proposed.     

The biological effects of diagnostic cardiac imaging on chronically exposed physicians: the importance of being non-ionizing

Ultrasounds and ionizing radiation are extensively used for diagnostic applications in the cardiology clinical practice. This paper reviewed the available information on occupational risk of the cardiologists who perform, every day, cardiac imaging procedures. At the moment, there are no consistent evidence that exposure to medical ultrasound is capable of inducing genetic effects, and representing a serious health hazard for clinical staff. In contrast, exposure to ionizing radiation may result in adverse health effect on clinical cardiologists. Although the current risk estimates are clouded by approximations and extrapolations, most data from cytogenetic studies have reported a detrimental effect on somatic DNA of professionally exposed personnel to chronic low doses of ionizing radiation. Since interventional cardiologists and electro-physiologists have the highest radiation exposure among health professionals, a major awareness is crucial for improving occupational protection. Furthermore, the use of a biological dosimeter could be a reliable tool for the risk quantification on an individual basis.     

The Increase in Animal Mortality Risk following Exposure to Sparsely Ionizing Radiation Is Not Linear Quadratic with Dose

Introduction

The US government regulates allowable radiation exposures relying, in large part, on the seventh report from the committee to estimate the Biological Effect of Ionizing Radiation (BEIR VII), which estimated that most contemporary exposures- protracted or low-dose, carry 1.5 fold less risk of carcinogenesis and mortality per Gy than acute exposures of atomic bomb survivors. This correction is known as the dose and dose rate effectiveness factor for the life span study of atomic bomb survivors (DDREF_LSS). It was calculated by applying a linear-quadratic dose response model to data from Japanese atomic bomb survivors and a limited number of animal studies.

Methods and Results

We argue that the linear-quadratic model does not provide appropriate support to estimate the risk of contemporary exposures. In this work, we re-estimated DDREF_LSS using 15 animal studies that were not included in BEIR VII’s original analysis. Acute exposure data led to a DDREF_LSS estimate from 0.9 to 3.0. By contrast, data that included both acute and protracted exposures led to a DDREF_LSS estimate from 4.8 to infinity. These two estimates are significantly different, violating the assumptions of the linear-quadratic model, which predicts that DDREF_LSS values calculated in either way should be the same.

Conclusions

Therefore, we propose that future estimates of the risk of protracted exposures should be based on direct comparisons of data from acute and protracted exposures, rather than from extrapolations from a linear-quadratic model. The risk of low dose exposures may be extrapolated from these protracted estimates, though we encourage ongoing debate as to whether this is the most valid approach. We also encourage efforts to enlarge the datasets used to estimate the risk of protracted exposures by including both human and animal data, carcinogenesis outcomes, a wider range of exposures, and by making more radiobiology data publicly accessible. We believe that these steps will contribute to better estimates of the risks of contemporary radiation exposures.     

Mouse germ cell mutation tests in genetic risk evaluation of chemical mutagens

That certain environmental chemicals can induce transmissible mutations in germ cells of experimental mammal is clear. The assumption that under certain conditions these chemicals are also likely to be mutagenic to human germ cells is not detectable. However, it is a difficult challenge to determine the level of human exposure at which such chemicals can be produced and used economically without significantly harming human health. Data on transmitted genetic effects in mice are necessary, not only as a measure of endpoints that are considered directly in genetic risk assessment, but also as the standard for evaluating the usefulness of non-germ-cell effects as predictors in genetic risk assessment. To carry out a "real world" genetic risk assessment exercise, in vivo mouse data are being obtained for two model chemicals--ethylene oxide and acrylamide. Both chemicals are capable of inducing transmissible genetic effects in mice; their production and use involve measurable human exposures; and, because they are socially and economically important, they are not likely to be banned altogether despite their mutagenicity. For both chemicals, data are not sufficient for accurate low-dose and low-dose-rate extrapolations.     

Radioresponsiveness at low doses: hyper-radiosensitivity and increased radioresistance in mammalian cells

The rationale for and importance of research on effects after radiation at "low doses" are outlined. Such basic radiobiological studies on induction of repair enzymes, protective mechanisms, priming, and hypersensitivity are certainly all relevant to treatment of cancer (see Section 1, Studies at low doses - relevance to cancer treatment). Included are examples from many groups, using various endpoints to address the possibility of an induced resistance, which has been compared to the adaptive response [M.C. Joiner, P. Lambin, E.P. Malaise, T. Robson, J.E. Arrand, K.A. Skov, B. Marples, Hypersensitivity to very low single radiation doses: its relationship to the adaptive response and induced radioresistance, Mutat. Res. 358 (1996) 171-183.]. This is not intended to be an exhaustive review--rather a re-introduction of concepts such as priming and a short survey of molecular approaches to understanding induced resistance. New data on the response of HT29 cells after treatment (priming) with co-cultured activated neutrophils are included, with protection against X-rays (S1). Analysis of previously published results in various cells lines in terms of increased radioresistance (IRR)/intrinsic sensitivity are presented which complement a study on human tumour lines [P. Lambin, E.P. Malaise, M.C. Joiner, Might intrinsic radioresistance of human tumour cells be induced by radiation?, Int. Radiat. Biol. 69 (1996) 279-290].It is not feasible to extrapolate to low doses from studies at high doses. The biological responses probably vary with dose, LET, and have variable time frames. The above approaches may lead to new types of treatment, or additional means to assess radioresponsiveness of tumours. Studies in many areas of biology would benefit from considerations of different dose regions, as the biological responses vary with dose. There may also be some implications in the fields of radiation protection and carcinogenesis, and the extensions of concepts of hyper-radiosensitivity (HRS)/IRR extended to radiation exposure are considered in Section 2, Possible relevance of IRR concepts to radiation exposure (space). More knowledge on inducible responses could open new approaches for protection and means to assess genetic predisposition. Many endpoints are used currently--clonogenic survival, mutagenesis, chromosome aberrations and more direct--proteins/genes/functions/repair/signals, as well as different biological systems. Because of scant knowledge of the relevant aspects at low doses, such as inducible/protective mechanisms, threshold, priming, dose-rate effects, LET within one system, it is still too early to draw conclusions in the area of radiation exposure. Technological advances may permit much needed studies at low doses in the areas of both treatment and protection.     

International Commission for Protection against Environmental Mutagens and Carcinogens. ICPEMC publication No. 13. The need for biological risk assessment in reaching decisions about carcinogens

The prudent assumption that carcinogen bioassays in rodents predict for human carcinogenicity is examined. It is suggested that in certain cases, as for example the induction of tumors against a high incidence in controls, or in situations in which high dose toxicity may be a critical factor in the induction of cancer, the probability that animal bioassays predict for humans may be low. The term 'biological risk assessment' is introduced to describe that part of risk assessment concerned with the relevance of specific animal results to the induction of human cancer. Biological risk assessment, which is almost entirely dependent on an understanding of carcinogenesis mechanisms, is an important addition to present mathematical modeling used to predict the effects of animal carcinogens that have been demonstrated after high dose exposure, to the effects of the much smaller doses to which humans are perceived to be exposed. Evidence for the conclusions reached by biological risk assessment may sometimes be supported by a careful review of human epidemiological data.     

The protective role of selenium on genetic damage and on cancer

Collectively, results from epidemiologic studies, laboratory bioassays, and human clinical intervention trials clearly support a protective role of selenium against cancer development. Several hypotheses have been proposed to explain these observations. Increased genomic instability, either inherent or induced by exogenous agents (mutagens or carcinogens), has been considered as a primary event leading to neoplastic transformation. This report deals specifically with the evidence for a role of selenium in the inhibition of carcinogen-induced covalent DNA adduct formation and retardation of oxidative damage to DNA, lipids and proteins, and for modulating cellular and molecular events that are critical in cell growth inhibition and in the multi-step carcinogenesis process. At present, the bulk of our knowledge on the role of selenium on genetic stability is based primarily on animal data and from studies conducted in in vitro systems. Studies performed in vitro showed that the dose and form of selenium compounds are critical factors with regard to cellular responses. Inorganic (at doses up to 10microM) and organic selenium compounds (at doses equal to or greater than 10microM) elicit distinctly different cellular responses. The recommended daily allowance (RDA) is 50-70 microgramSe per day for healthy adults; with 40 microgramSe as minimum requirement. Less than 11 microgramSe will definitely put people at risk of deficiency that would be expected to cause genetic damage. Daily doses of 100-200 microgramSe inhibited genetic damage and cancer development in humans. About 400 microgramSe per day is considered an upper limit. Clearly, doses above the RDA are needed to inhibit genetic damage and cancer. However, it has been hypothesized that the intake of excessive doses of selenium may cause oxidative damage, leading to genomic instability. The use of a cocktail consisting of selenium, and other vitamins and minerals appears to be a promising approach to inhibit genetic damage and the development of cancer. It is the author's recommendation that development of mechanism-based hypotheses that can be tested in pilot studies in different populations prior to a large-scale clinical trial in humans, is of paramount importance in order to better understand the role of selenium on genetic stability and cancer.     

A two-mutation model of radiation-induced acute myeloid leukemia using historical mouse data

From studies of the atomic bomb survivors, it is well known that ionizing radiation causes several forms of leukemia. However, since the specific mechanism behind this process remains largely unknown, it is difficult to extrapolate carcinogenic effects at acute high-dose exposures to risk estimates for the chronic low-dose exposures that are important for radiation protection purposes. Recently, it has become clear that the induction of acute myeloid leukemia (AML) in CBA/H mice takes place through two key steps, both involving the Sfpi1 gene. A similar mechanism may play a role in human radiation-induced AML. In the present paper, a two-mutation carcinogenesis model is applied to model AML in several data sets of X-ray- and neutron-exposed CBA/H mice. The models obtained provide good fits to the data. A comparison between the predictions for neutron-induced and X-ray-induced AML yields an RBE for neutrons of approximately 3. The model used is considered to be a first step toward a model for human radiation-induced AML, which could be used to estimate risks of exposure to low doses.     

Increased frequency of spontaneous neoplastic transformation in progeny of bystander cells from cultures exposed to densely ionizing radiation

An increased risk of carcinogenesis caused by exposure to space radiation during prolonged space travel is a limiting factor for human space exploration. Typically, astronauts are exposed to low fluences of ionizing particles that target only a few cells in a tissue at any one time. The propagation of stressful effects from irradiated to neighboring bystander cells and their transmission to progeny cells would be of importance in estimates of the health risks of exposure to space radiation. With relevance to the risk of carcinogenesis, we investigated, in model C3H 10T½ mouse embryo fibroblasts (MEFs), modulation of the spontaneous frequency of neoplastic transformation in the progeny of bystander MEFs that had been in co-culture 10 population doublings earlier with MEFs exposed to moderate doses of densely ionizing iron ions (1 GeV/nucleon) or sparsely ionizing protons (1 GeV). An increase (P<0.05) in neoplastic transformation frequency, likely mediated by intercellular communication through gap junctions, was observed in the progeny of bystander cells that had been in co-culture with cells irradiated with iron ions, but not with protons.     

Two-mutation models for bone cancer due to radium, strontium and plutonium

Data from beagle experiments and radium dial painters were used to derive two-mutation carcinogenesis models for bone cancer induced by the bone-seeking radionuclides radium, strontium and plutonium. For all data, the model fits indicate that at low doses both mutation rates depend linearly and equally strongly on dose rate. For the high-LET alpha-particle emitters, a cell killing term reduces the second mutation rate at high dose rates. In all cases, the combined effect of both mutation rates is a linear-quadratic dose-effect relationship for cancer at low doses. This behavior may lead to experimental data that could be mistaken as showing a threshold below which no cancers are induced. Derived parameters such as toxicity ratios and tumor growth times compare well with values reported in the literature. Furthermore, results for plutonium indicate that rapid burial of the nuclide in the growing bones of juvenile beagles leads to a significant reduction of its toxicity, as was suggested previously. The results for radium in beagles compare well with those for humans and suggest that the models derived for strontium and plutonium in beagles may be translated to humans. The significant model parameters for the accurate animal data could then also be used to fit human epidemiological data.