Michael H. Momeni, PhD
The Chornobyl nuclear reactor accident, 26 April 1986 in Ukraine, and the Fukushima Daiichi nuclear disaster, 11 March 2011 in Japan, exposed both radiation workers and the regional populations. To contain the accident and spread of contamination, in Chornobyl 31 radiation workers died from acute exposures.
These populations were exposed to airborne and ground-deposited radioactive materials. They received internal exposure by inhalation and ingestion of the airborne radioactivity. The scope of this paper is limited to estimation of potential risks to the exposed population from a nuclear reactor accident or from mining and milling of uranium. PRIEM is based on rigorous methods for estimation of the risk of mortality. But, the accuracy of the prediction is dependent on radiation doses to each organ and the accuracy of the age-gender probabilities for each radiation-induced cause.
The earlier versions of this code (PRIM ) was used to estimate "Radiological impacts of Jackpile-Paguate Uranium Mines, An Analysis of Alternatives of Decommissioning", M.H. Momeni, S.Y.H. Tsai, J.Y. Yang, A.B. Gureghian, and C.E. Dungey, Argonne National Laboratory, Argonne, Illinois, Report ANL/ES-131,1983. PRIM was based on the BEIR committee (Biological Effects of Ionizing Radiation, Committee III, 1980) of the National Academy of Sciences. The ANL/ES-131 report and the "Draft environmental impact statement for the Jackpile-Paguate uranium mine reclamation project, Laguna Indian Reservation, Cibola County, New Mexico" [https://archive.org/details/draftenvironment15unit] would indicate the magnitude of this enormous task.
Competitive Analysis of Mortality, Lifetable:
We are at risk throughout the lifetime. The risks include many natural causes including disease and accidents such as car collision. A child born today could survive to ages older than 100 years, but also could die during any year after birth. Among the tools to calculate the survival chances is actuarial table based on lifetable procedure. For efficiency of calculation, we assumed a 100-year life window and divide the span into 5-year periods (age-cohorts), i.e. 20 age cohorts. Those exceeding the 100-year age were combined into a centennial age cohort. We designated each age cohort by gender and racial group. At present, we only have one racial group (All American). Thus, we created 20-age-gender cohorts of male and female for the population.
Any human population in a region is dynamic. The population profile changes by the process of attrition (natural and accidental causes of death) and renewal (birth). We did not include the effects of population migration (in-migration and out-migration).
Causes of Mortality, Non-Radiation Causes:
The causes of death would not be the same for the age-gender cohorts. These causes may be divided into several broad categories, such as non-neoplastic diseases (viral and bacterial infection), accidents (vehicular, airplane etc.) and genetically linked diseases. The probability for each cause is estimated from reported causes of mortality and documented by death certificate. We divided the causes of mortality into two broad categories: neoplastic diseases and all the other causes. We assigned the probability for each mortality category using the nation censuses data. Further, we divided the mortality from neoplasm into the following broad categories: leukemia, cancers of the lung, stomach, intestine, breast, bone, pancreas, liver, urinary and sex organs, and lymphoma. All other neoplasm is combined into one category.
A cohort population P(t,i,j) represents the age- cohort i, gender j; gender j=1 male, j=2 for a female at time t.
The probability of mortality within the 5-year age window is R(i,j,k), where k=1 represents all causes except neoplasm, k=2 leukemia, k=3 cancers of the lung, k=4 stomach, k=5 intestine, k=6 breast, k= 7 bone, k=8 pancreas, k=9 liver, k=10 urinary and sex organs, and k=11 lymphoma. All other neoplasm is combined into one category k=12.
Mortality m(t,i,j,k) among the population cohort P(i,j) from non-radiation-induced risks N(i,j,k) is:
m(t,i,j,k)= P(t,i,j) * N(i,j,k)
Radiation Doses
Procedures for calculation of radiation doses following an accident would require an accurate estimation of the magnitude, type, and duration, and thermal and kinetics of the releases into the environment (Source Term). Transport of the radioactive effluents into the environment, or dispersion, would require knowledge of atmospheric physics, local meteorology, topography and hydrology during and after the release of the effluents.
The concept of radiation dose has been fully developed and cited by many scholars. The three main sources for exposure are external exposure from airborne and ground-deposited radionuclide, inhalation of airborne radioactivity and ingestion of contaminated food and water.
The total dose within any 5-year period, at any time and location, is calculated from the dose rates to the organs of interest at the beginning and the end of that 5-year period. For internal emitters and those radionuclide retained within the body for a long period, such as the bone-seekers, the radiation dose from all pathways of exposure will continue throughout the residual life. The period from the age of the individual to the end of expected life (100 years) is often called the residual life.
Radiation-induced Causes of Mortality:
The magnitude of radiation-induced somatic (stochastic) effects is proportional to the magnitude of the radiation dose, the rate of receiving the dose, and the type of radiation. In addition, for some somatic effects, other factors could change the level of induced effects, such as the age at exposure to radiation, and gender.
Latency and Expression Periods:
Some induced effects are delayed in expression. This period is often referred to as the Latency Period. This period could be as short as a couple of years, for example, induction of leukemia, or more than a decade, such as a carcinoma or an osteosarcoma.
Thus, if the residual life is shorter than the latency period, understandingly, the risk of radiation mortality would be zero. For example, an individual exposed age of 92 would probably die from all the other causes before succumbing to radiation-induced carcinoma.
Probabilities of mortality per unit of radiation dose are dependent on the age at exposure and for some effects also dependent on the gender. The probability mortality each year following the latency period is referred to as the expression period. The probability of radiation-induced mortality within the expression period was assumed to be constant. Thus, the probability of mortality within an age-cohort and for each radiation-induced stochastic effect could be extracted from the lifetime mortality risks.
PRIEM code ( version VII, 2012):
Radiation-induced mortality rate within each age cohort was calculated using the life-table method. The BEIR committee (Biological Effects of Ionizing Radiation) of the National Academy of Sciences, including the Committee VII, has supported a “linear-no-threshold” (LNT) radiation-induced risk model. PRIEM code explicitly assumed a linear-no-threshold relationship between radiation dose and the mortality risks.
The population within each age-gender cohort was subjected to a combined probability of mortality. The population size was limited to those living within the 50-mile radius without the inclusion of people moving into and out of the region.
Mortality m(t,i,j,k) among the cohort population P(t,i,j) from a cause k at risk R(i,j,k)
R(i,j,k) = Dose(t,i,j,k) * PR(i,j,k)
Where, PR(i,j,k) is the mortality probability per unit dose from irradiation of organ k and after the latency period to the end of the expression period.
The code allows using a linear and quadratic method for calculation of radiation-induced risks.
Please see Appendix C: Author Comments on ANL/ES-131.
The Dose(t,i,j,k) to an organ is calculated from the difference of the doses at (t+5) and t. Thus, mortality from cause k is:
m(t,i,j,k) = P(t,i,j) * [N(i,j,k) + PR(i,j,k)]
The total mortality from all causes within a cohort (i, j) at time t is:
M(t,i,j) = ∑ m(t,i,j,k)
The beginning of the analysis is at (t=0), the initial exposure. The time t is incremented by 5 year periods . The survived segment of the population within the cohort i will continue to the cohort (i + 1) at (t + 5) period. Births within each cohort P(t,i,j) will be transferred to a new cohort P(t+5,1,j).
Discussion
PRIEM computer code is based on a competitive analysis of mortality. The mortality from the natural causes, a dominant factor in the population reduction, allows a lower expression of radiation-induced stochastic effects. The exposed population could die prior to frank expression of radiation-induced causes.
This version of PRIEM code is based on additive hazards (absolute risk) model. In earlier versions of PRIEM, both proportional hazards (relative risk) model and the additive hazards were included. But, the two models produce a very different magnitude of risks. The proportional hazard model was not included in this version of the code.
A regional population profile and mortality causes are readily available and extractable from the US Government Census Data. The most difficult task is radiation dosimetry. The doses have to be calculated from the accident source terms (nuclear reactor accident) and release rates from normal operations at uranium mines and mills. These source terms are not known and have to be estimated from the reactor core inventory prior to the event and the kinetics of the releases. The history of the accidents at Chornobyl and the Fukushima Daiichi both indicate the difficulty for determining an order of magnitude estimates for the source terms. The models for dispersion of the effluents are dependent on many environmental factors and are very difficult to validate. The thermal capacity and the kinetic energy for release at Chornobyl reactor accident forced the effluents into higher atmosphere and subjected to air streams inaccessible to ground level meteorology.