A unified formalism for estimating photon absorbed fractions in spherical biovolumes: analytical equations without fitting parameters.

A new analytical formalism, previously developed for estimating electron-absorbed fractions, was extended for estimating photon absorbed fractions in soft-tissue spheres, containing uniformly distributed photon-emitter. Analytical equations were formulated for calculating values of photon-absorbed fractions. The method involves a rescaling procedure with transformation of real biological sizes to unitless effective ones, combining information of photon energy, object's size, and material. Rescaling was applied to large published datasets of photon absorbed fractions in soft-tissue spheres, computed with Monte Carlo codes. A new effect was demonstrated in which the rescaled data formed a single smooth 'unified curve' with saturation. The unified curve for photon absorbed fractions was described analytically, using simple equations without fitting parameters. The new method was tested for a wide range of spheres-from 1 mg up to 1000 kg, and wide range of photon energies-from 0.02 up to 5 MeV. For larger spheres, a close agreement between analytical values and Monte Carlo datasets was demonstrated. For small biovolumes, analytical equations predict higher values than available Monte Carlo data. The unified formalism is now available for direct calculating radiation absorbed fractions in soft-tissue spherical organs and organisms without Monte Carlo codes.

A new analytical method for estimating electron-absorbed fractions in soft-tissue biological volumes.

A new analytical methodology was developed for estimating electron-absorbed fractions in soft-tissue biological volumes from mono-energy emitters, uniformly distributed within these volumes. The approach was originally developed for soft-tissue spheres and was extended to ellipsoids. The method involves a procedure of size rescaling to the electron CSDA ranges. The rescaling was applied to large published datasets of electron-absorbed fractions in soft-tissue spheres. A new effect was demonstrated, i.e., that it is possible to describe the rescaled data on absorbed fractions by a single smooth 'universal curve'. A simple analytical formula is suggested, which describes the curve as a function of a single argument (the so-called rescaled radius) with saturation. Practical application of the method for estimating internal doses to non-human biota was demonstrated. It is concluded that the method provides an effective analytical tool for calculating the electron-absorbed fractions in soft-tissue bio-volumes relevant to various organisms and organs.

Population sensitivities of animals to chronic ionizing radiation-model predictions from mice to elephant.

Model predictions of population response to chronic ionizing radiation (endpoint 'morbidity') were made for 11 species of warm-blooded animals, differing in body mass and lifespan - from mice to elephant. Predictions were made also for 3 bird species (duck, pigeon, and house sparrow). Calculations were based on analytical solutions of the mathematical model, simulating a population response to low-LET ionizing radiation in an ecosystem with a limiting resource (Sazykina, Kryshev, 2016). Model parameters for different species were taken from biological and radioecological databases; allometric relationships were employed for estimating some parameter values. As a threshold of decreased health status in exposed populations ('health threshold'), a 10% reduction in self-repairing capacity of organisms was suggested, associated with a decline in ability to sustain environmental stresses. Results of the modeling demonstrate a general increase of population vulnerability to ionizing radiation in animal species of larger size and longevity. Populations of small widespread species (mice, house sparrow; body mass 20-50 g), which are characterized by intensive metabolism and short lifespan, have calculated 'health thresholds' at dose rates about 6.5-7.5 mGy day-1. Widespread animals with body mass 200-500 g (rat, common pigeon) - demonstrate 'health threshold' values at 4-5 mGy day-1. For populations of animals with body mass 2-5 kg (rabbit, fox, raccoon), the indicators of 10% health decrease are in the range 2-3.4 mGy day-1. For animals with body mass 40-100 kg (wolf, sheep, wild boar), thresholds are within 0.5-0.8 mGy day-1; for herbivorous animals with body mass 200-300 kg (deer, horse) - 0.5-0.6 mGy day-1. The lowest health threshold was estimated for elephant (body mass around 5000 kg) - 0.1 mGy day-1. According to the model results, the differences in population sensitivities of warm-blooded animal species to ionizing radiation are generally depended on the metabolic rate and longevity of organisms, also on individual radiosensitivity of biological tissues. The results of 'health threshold' calculations are formulated as a graded scale of wildlife sensitivities to chronic radiation stress, ranging from potentially vulnerable to more resistant species. Further studies are needed to expand the scale of population sensitivities to radiation, including other groups of wildlife - cold-blooded species, invertebrates, and plants.

Lower thresholds for lifetime health effects in mammals from high-LET radiation - Comparison with chronic low-LET radiation.

Lower threshold dose rates and confidence limits are quantified for lifetime radiation effects in mammalian animals from internally deposited alpha-emitting radionuclides. Extensive datasets on effects from internal alpha-emitters are compiled from the International Radiobiological Archives. In total, the compiled database includes 257 records, which are analyzed by means of non-parametric order statistics. The generic lower threshold for alpha-emitters in mammalian animals (combined datasets) is 6.6·10-5 Gy day-1. Thresholds for individual alpha-emitting elements differ considerably: plutonium and americium - 2.0·10-5 Gy day-1; radium - 2.1·10-4 Gy day-1. Threshold for chronic low-LET radiation is previously estimated at 1·10-3 Gy day-1. For low exposures, the following values of alpha radiation weighting factor wR for internally deposited alpha-emitters in mammals are quantified: wR(α) = 15 as a generic value for the whole group of alpha-emitters; wR(Pu) = 50 for plutonium; wR(Am) = 50 for americium; wR(Ra) = 5 for radium. These values are proposed to serve as radiation weighting factors in calculations of equivalent doses to non-human biota. The lower threshold dose rate for long-lived mammals (dogs) is significantly lower than comparing with the threshold for short-lived mammals (mice): 2.7·10-5 Gy day-1, and 2.0·10-4 Gy day-1, respectively. The difference in thresholds is exactly reflecting the relationship between the natural longevity of these two species. Graded scale of severity in lifetime radiation effects in mammals is developed, based on compiled datasets. Being placed on the severity scale, the effects of internal alpha-emitters are situated in the zones of considerably lower dose rates than effects of the same severity caused by low-LET radiation. RBE values, calculated for effects of equal severity, are found to depend on the intensity of chronic exposure: different RBE values are characteristic for low, moderate, and high lifetime exposures (30, 70, and 13, respectively). The results of the study provide a basis for selecting correct values of radiation weighting factors in dose assessment to non-human biota.

Simulation of population response to ionizing radiation in an ecosystem with a limiting resource--Model and analytical solutions.

A dynamic mathematical model is formulated, predicting the development of radiation effects in a generic animal population, inhabiting an elemental ecosystem 'population-limiting resource'. Differential equations of the model describe the dynamic responses to radiation damage of the following population characteristics: gross biomass; intrinsic fractions of healthy and reversibly damaged tissues in biomass; intrinsic concentrations of the self-repairing pool and the growth factor; and amount of the limiting resource available in the environment. Analytical formulae are found for the steady states of model variables as non-linear functions of the dose rate of chronic radiation exposure. Analytical solutions make it possible to predict the expected severity of radiation effects in a model ecosystem, including such endpoints as morbidity, mortality, life shortening, biosynthesis, and population biomass. Model parameters are selected from species data on lifespan, physiological growth and mortality rates, and individual radiosensitivity. Thresholds for population extinction can be analytically calculated for different animal species, examples are provided for generic mice and wolf populations. The ecosystem model demonstrates a compensatory effect of the environment on the development of radiation effects in wildlife. The model can be employed to construct a preliminary scale 'radiation exposure-population effects' for different animal species; species can be identified, which are vulnerable at a population level to chronic radiation exposure.

Inter-comparison of population models for the calculation of radiation dose effects on wildlife.

An inter-comparison of five models designed to predict the effect of ionizing radiation on populations of non-human wildlife, performed under the IAEA EMRAS II programme, is presented and discussed. A benchmark scenario 'Population response to chronic irradiation' was developed in which stable generic populations of mice, hare/rabbit, wolf/wild dog and deer were modelled as subjected to chronic low-LET radiation with dose rates of 0-5 × 10(-2) Gy day(-1) in increments of 10(-2) Gy day(-1). The duration of exposure simulations was 5 years. Results are given for the size of each surviving population for each of the applied dose rates at the end of the 1st to 5th years of exposure. Despite the theoretical differences in the modelling approaches, the inter-comparison allowed the identification of a series of common findings. At dose rates of about 10(-2) Gy day(-1) for 5 years, the survival of populations of short-lived species was better than that of long-lived species: significant reduction in large mammals was predicted whilst small mammals survive at 80-100 % of the control. Dose rates in excess of 2 × 10(-2) Gy day(-1) for 5 years produced considerable reduction in all populations. From this study, a potential relationship between higher reproduction rates and lower radiation effects at population level can be hypothesized. The work signals the direction for future investigations to validate and improve the predictive ability of different population dose effects models.

Non-parametric estimation of thresholds for radiation effects in vertebrate species under chronic low-LET exposures.

Databases on effects of chronic low-LET radiation exposure were analyzed by non-parametric statistical methods, to estimate the threshold dose rates above which radiation effects can be expected in vertebrate organisms. Data were grouped under three umbrella endpoints: effects on morbidity, reproduction, and life shortening. The data sets were compiled on a simple 'yes' or 'no' basis. Each data set included dose rates at which effects were reported without further details about the size or peculiarity of the effects. In total, the data sets include 84 values for endpoint "morbidity", 77 values for reproduction, and 41 values for life shortening. The dose rates in each set were ranked from low to higher values. The threshold TDR5 for radiation effects of a given umbrella type was estimated as a dose rate below which only a small percentage (5%) of data reported statistically significant radiation effects. The statistical treatment of the data sets was performed using non-parametric order statistics, and the bootstrap method. The resulting thresholds estimated by the order statistics are for morbidity effects 8.1 x 10(-4) Gy day(-1) (2.0 x 10(-4)-1.0 x 10(-3)), reproduction effects 6.0 x 10(-4) Gy day(-1) (4.0 x 10(-4)-1.5 x 10(-3)), and life shortening 3.0 x 10(-3) Gy day(-1) (1.0 x 10(-3)-6.0 x 10(-3)), respectively. The bootstrap method gave slightly lower values: 2.1 x 10(-4) Gy day(-1) (1.4 x 10(-4)-3.2 x 10(-4)) (morbidity), 4.1 x 10(-4) Gy day(-1) (3.0 x 10(-4)-5.7 x 10(-4)) (reproduction), and 1.1 x 10(-3) Gy day(-1) (7.9 x 10(-4)-1.3 x 10(-3)) (life shortening), respectively. The generic threshold dose rate (based on all umbrella types of effects) was estimated at 1.0 x 10(-3) Gy day(-1).

Predicting radionuclide transfer to wild animals: an application of a proposed environmental impact assessment framework to the Chernobyl exclusion zone.

A number of assessment frameworks have been proposed to provide a mechanism to demonstrate protection of the environment from ionising radiation. Whilst some of these are being used for assessment purposes they have largely not been validated against field measurements. In this paper we compare the predictions of transfer parameters recommended by one of these frameworks (FASSET) with observed whole-body 90Sr and radiocaesium activity concentrations in a range of mammal and invertebrate species sampled within the Chernobyl exclusion zone. Predicted activity concentrations were generally within the observed ranges and mean predictions for reference organisms were similar to, or circa one order of magnitude higher than, the observed means. However, some predictions were more than one order of magnitude lower than observed values. No data were available to test predictions for the other radionuclides released by the Chernobyl accident. In a separate paper the outputs of this assessment will be used to estimate doses to reference organisms and compare these to observed radiation induced effects reported within the Chernobyl zone.

A general approach to transform a lake model for one radionuclide (radiocesium) to another (radiostrontium) and critical model tests using data for four Ural lakes contaminated by the fallout from the Kyshtym accident in 1957.

This paper presents results of a model test carried out within the framework of the COMETES project (EU). The aim of the work was to change the structure of the MOIRA lake model for radiocesium so that it can be applied more generally for, in principle, all types of radionuclides and heavy metals. This general lake model is used within the MOIRA decision support system (DSS; MOIRA and COMETES are acronyms for EU-projects). The model is based on a set of differential equations and a specific modelling structure. It incorporates all important fluxes to, from and within lakes in a general manner. Yet the model is driven by a minimum of variables accessible from standard maps and monitoring programs. The model can be separated into two parts, a general part with equations applicable for all types of water pollutants and a substance-specific part. This model has previously been validated for 137Cs from many lakes covering a wide domain and yielded excellent predictive power. The alterations discussed in this work are meant to be general and radiostrontium is used as a typical element. Radiostrontium is known to be more mobile than radiocesium and all abiotic parts of the model handling fixation and mobility have been altered. The new model for 90Sr has been critically tested using data from four lakes heavily contaminated with 90Sr from the Kyshtym accident in the Southern Urals, Russia, using empirical data from a period from 1958 to 1995 for 90Sr in fish (here goldfish), water and sediments.