Radiat Environ Biophys (2015) 54:103–109 DOI 10.1007/s00411-014-0578-x

ORIGINAL PAPER

Modelling the effects of ionizing radiation on survival of animal population: acute versus chronic exposure A. I. Kryshev • T. G. Sazykina

Received: 28 May 2014 / Accepted: 29 November 2014 / Published online: 7 December 2014  Springer-Verlag Berlin Heidelberg 2014

Abstract The objective of the present paper was application of a model, which was originally developed to simulate chronic ionizing radiation effects in a generic isolated population, to the case of acute exposure, and comparison of the dynamic features of radiation effects on the population survival in cases of acute and chronic exposure. Two modes of exposure were considered: acute exposure (2–35 Gy) and chronic lifetime exposure with the same integrated dose. Calculations were made for a generic mice population; however, the model can be applied for other animals with proper selection of parameter values. In case of acute exposure, in the range 2–11 Gy, the population response was in two phases. During a first phase, there was a depletion in population survival; the second phase was a recovery period due to reparation of damage and biosynthesis of new biomass. Model predictions indicate that a generic mice population, living in ideal conditions, has the potential for recovery (within a mouse lifetime period) from acute exposure with dose up to 10–11 Gy, i.e., the population may recover from doses above an LD50 (6.2 Gy). Following acute doses above 14 Gy, however, the mice population went to extinction without recovery. In contrast, under chronic lifetime exposures (500 days), radiation had little effect on population survival up to integrated doses of 14–15 Gy, so the survival of a population subjected to chronic exposure was much better compared with that after an acute exposure with the same dose. Due to the effect of ‘‘wasted radiation’’, the integrated dose of chronic exposure could be about two times higher than acute dose, producing the A. I. Kryshev (&)  T. G. Sazykina Research and Production Association ‘‘Typhoon’’, 4 Pobedy Str., Obninsk, Kaluga Region 249038, Russia e-mail: [email protected]

same effect on survival. It is concluded that the developed generic population model including the repair of radiation damage can be applied both to acute and chronic modes of exposure; results of calculations for generic mice population are in qualitative agreement with published data on radiation effects in mice. Keywords Model  Radiation  Population  Animal  Exposure  Acute  Chronic

Introduction Modern requirements for radiation protection of wildlife are focused on the protection of populations of various representative species (ICRP 2008, 2009, 2014). A main concern of regulations is ensuring radiation protection of biota under conditions of chronic lifetime exposures. In this context, methods and models are to be developed that link effects reported for laboratory conditions to the integrated response on the level of population in ecosystem (Beresford et al. 2008; Andersson et al. 2009). The majority of published radiobiological data refer to radiation effects from acute exposures (Garnier-Laplace et al. 2006; Sazykina and Kryshev 2006; Copplestone et al. 2008); therefore, an important task is adaptation of models to simulate both chronic and acute radiation effects in generic populations with the possibility of model validation based on available experimental data. The objective of the present paper was application of a model, which was originally developed to simulate chronic radiation effects in a generic isolated population (Kryshev et al. 2008; Vives et al. 2012), to the case of acute exposure, including comparison of the dynamics of radiation effects on the population survival in cases of acute and

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chronic exposure. The study was performed within the frame of the International Atomic Energy Agency (IAEA) current Programme MODARIA ‘‘modelling and data for radiological impact assessments’’ (working group 9 ‘‘models for assessing radiation effects on populations of wildlife species’’). More details can be found at http:// www-ns.iaea.org/projects/Modaria).

Materials and methods Modelling approach The effects of ionizing radiation on survival of an animal population were analyzed using a model of an isolated generic animal population subjected to radiation stress, developed in previous papers (Kryshev et al. 2008; Vives et al. 2012). Natural growth of population biomass is described by logistic (Verhulst) model, which suggests that the size of the population is limited by living resources of the local environment. This logistic model of population growth is widely used in ecology for generic modelling of populations of many species. In the present paper, ecological and radiosensitivity parameters used in the calculations were selected for a generic mice population. The model population is considered to be isolated from predators and competing species; parameters of local environment are assumed non-changing with exception of radiation stress. In the absence of radiation stress, the population is considered self-maintained at a constant size and living in stable equilibrium with its local environment. The stable biomass of non-irradiated population is normalized to 1 (or 100 % of the control value). In the model, the population was exposed to ionizing radiation. Considered were the following cases of exposure: acute exposure (doses in the range 2–35 Gy, 1 h of exposure); and chronic lifetime exposure (500 days) with a dose rate p (mGy/day). Lifetime doses of chronic exposures were selected to be equal to doses of acute exposure, for example, the lifetime dose 2 Gy was accumulated at 4 mGy/day of chronic exposure. The following end points were taken into consideration: •

•

Decrease in the population compared with the control following acute exposure with a dose D after 30 and 500 days of exposure; Decrease in the population compared with the control after 500 days of chronic exposure with the same lifetime absorbed dose as acute exposure.

The effects caused by irradiation in an animal population are considered to be the result of superposition of three major processes:

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• • •

Direct damage of biomass by radiation (lethal and reversible), Recovery of reversible damage by means of repairing mechanisms, Recovery of population due to biosynthesis of new healthy biomass.

It is assumed that the biomass of organisms that comprise the exposed population may be in one of the following states: undamaged, reversibly damaged which may be recovered to healthy state by repairing mechanisms, and lethally damaged. Conceptually, a model describing the effects of ionizing radiation on an animal population includes the following dynamical components: a population model which can be run with or without radiation stress; a repairing system which is described as a repairing pool; and a biosynthesis/ reproduction component. Under radiation stress, the living biomass of the investigated population splits in two parts: healthy (X) and reversibly damaged (Y). The repairing system (R) is spent on the recovery of reversibly damaged biomass. The repairing system is also being radiosensitive and can be damaged by radiation. The reproduction/biosynthesis system produces new healthy biomass of the population, and reproduction is itself affected by ionizing radiation. A detailed description of the model is given in a previous publication (Kryshev et al. 2008). In the present paper, a modified version of this model is used, where the control (non-irradiated) values of population biomass, reparation pool, and reproduction capacity are normalized to 1 (100 %). The effect of radiation exposure on the survival of the population is estimated using the values X (healthy biomass in population). Accordingly, the system of differential equations describing the effects of ionizing radiation on population can be written as: dX ¼ a  p  X þ j  y  R þ l  F  ð1  XÞ  X dt dy ¼ a  p  X  e  y  j  y  R; dt dR ¼ ar  p  R  jr  y  R þ lr  R  ð1  RÞ; dt dF ¼ af  p  F þ lf  F  ð1  FÞ  l  F  ð1  XÞ; dt ð1Þ where X is the undamaged (healthy) part of population biomass; y is the fraction of population biomass with reversible damages; R is the repairing pool; F is the intrinsic reproductive/biosynthesis capacity of the population; p is the rate of chronic exposure (mGy/day); a is a parameter characterizing the creation of the initial radiation damage in biomass (mGy-1); ar is a parameter of radiation

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damage of the repairing pool (mGy-1); af is a parameter of radiation damage in the biosysnthesis/reproductive system (mGy-1); j and jr are coefficients of biomass recovery due to activity of the repairing pool (j \ jr); e is the parameter describing the transfer to irreversibly lethal damages; and lr is the self-recovery rate of the repairing pool. Maximum (control) values of the non-irradiated population biomass, repairing pool, and reproductive capacity are each normalized to 1 (100 %). The model calculations were performed for radiation with low-linear energy transfer (LET), so the proportion of non-reparable damages was assumed low (1–2 %) compared with that of reversible damages (Bacq and Alexander 1966; Kudryashov 2008). Initial values for variables were taken equal to 100 % of normal state. In the model, biological parameters for mice were derived from The Animal Ageing and Longevity Database (AnAge database. Available in the Internet: http://geno mics.senescence.info/species). Data on mice radiosensitivity to acute exposure, including LD50/30 = 6.2 Gy, LD100 = 9 Gy, and considerable decrease in fertility above 4 Gy, were taken from (Stabin 2007; Bond and Fliedner 1965); from these data, values for parameters a and e were estimated: a = ln2/ LD50/30 mGy-1 = 1.110-4 mGy-1; e = 0.2 day-1; af = 1.010-3 mGy-1. Considering that for low-LET radiation the ratio ‘‘lethal damage/repaired damage’’ is about 10–20 %, the ratio e/j is about 0.1, and the j value was taken j = 2 day-1. Since the recovery efficiency is less than 100 %, parameter jr is larger than j, and the value for jr was taken as jr = 2.5 day-1. Because the repairing system is somewhat more radiosensitive than the reproduction system, ar is larger than af, and the value for ar was selected as ar = 2.710-3 mGy-1. Growth rates for biomass, repairing, and reproduction pools were taken to be l = 0.065 day-1; lr = 0.085 day-1; and lf = 0.065 day-1. The system of differential equations (Eq. 1) was solved numerically using the Runge–Kutta method in the Mathcad 2001 software package.

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Fig. 1 Dynamics of mice population survival after acute exposure with different doses (depletion and population recovery); 500 days is considered a typical mouse lifetime

biosynthesis of new biomass. The decrease in survival depends on dose, and the remaining population biomass is about 90 % after 2 Gy, about 40 % after 8 Gy, and less than 20 % at exposures higher than 14 Gy. The second phase of population dynamics shows a recovery period during which the population size is gradually restored due to biomass synthesis/reproduction. Complete recovery of the model population within a mice lifetime is predicted by the model for exposures below 10–11 Gy; above 14 Gy of acute exposure the population went to extinction without any recovery. Figure 2 demonstrates the differences between exposed and control mice populations on the 30th and 500th day following acute radiation exposure. The 30th day curve shows an approximately exponential decrease in survival with increasing dose. The shapes of calculated survival

Results and discussion Radiation effects of acute exposure on population survival Acute exposure was modeled as 1-h exposure with integrated dose 2, 4, 6…35 Gy, and the results of the corresponding calculations are shown in Fig. 1. After acute exposure to doses within the range 2–11 Gy, the population response is in two phases: during the first phase, there is an exponential depletion in population survival, while during the second phase there is a recovery period due to

Fig. 2 Relationship between the exposed and control populations of mice at day 30 and 500 after acute exposure

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curves are in good agreement with those of classic experimental survival curves following acute radiation exposures of various living organisms, which can be described by a simple exponential model S(D) = Exp(-kD), where S(D) is the surviving fraction after dose D (see paragraphs 7–14 of Annex J ‘‘Non-stochastic effects of irradiation’’, UNSCEAR 1982). The 500th day curve in Fig. 2 demonstrates a long-term recovery capacity of the modeled mice population: The population exposed to acute doses below 11 Gy is able to recover to its initial (control) size by the 500th day; in contrast, the population exposed to 11–12 Gy recovers only partially by the 500th day with the potential of total long-term recovery; finally, at doses above 14 Gy both 30th and 500th day curves are almost identical, without recovery in exposed population. The experimental evidence of restoration processes after acute irradiation including repair of sublethal damage and repopulation is summarized in Bacq and Alexander (1966, chapter 14 ‘‘processes of restoration after irradiation’’) and in the UNSCEAR 1982 Report (Annex J, paragraphs 17–21). The experimental observations showed that injury from acute exposure to ionizing radiation decreases exponentially with time as far as rats and mice are concerned, for example, the experimentally estimated time necessary for dissipation of half of the amount of injury inflicted by X-irradiation was about 7–12 days for mice (Bacq and Alexander 1966). The shapes of recovery curves and the general dynamics of post-irradiation recovery, obtained with the present model, are in agreement with experimental evidence. Radiation effects of chronic lifetime exposure on population survival Chronic irradiation of a generic mice population was modeled as 500-day exposure with total accumulated dose equal to a corresponding acute dose (2, 4, 6…35 Gy), which corresponds to daily dose rates (p) of 4, 8, 12, and 70 mGy/day, respectively. Survival was calculated using Eq. 1 with dose rates p (mGy/day). The results of these calculations are given in Fig. 3. The calculated dose–effect curve for biomass remains constant close to its control value, at lower dose rates up to approximately 20 mGy/day of lifetime exposure. This behavior demonstrates the capacity of the considered population to repair radiation damages at chronic exposure due to repairing mechanisms. With increasing dose rate of chronic radiation exposure, however, the repairing pool R and reproduction capacity F are gradually decreased. At a dose rate of about 25 mGy/day, the repairing pool decreases close to zero and repairing processes become ineffective. The dotted curve in Fig. 3 is a dose–effect relationship constructed from the empirical Hill model,

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Fig. 3 Dose–effect curves ‘‘population survival versus dose rate of chronic lifetime exposure’’ calculated with Eq. 1 (solid line) and from the empiric Hill equation (Eq. 2) (dotted line)

which is often used for approximation of experimental dose–effect curves for non-human biota (Garnier-Laplace et al. 2006). XðpÞ ¼

1 q ; p 1 þ =p50 

ð2Þ

where p is the dose rate in mGy/day; p50 is the lifetime dose rate corresponding to a 50 % decrease in population biomass; and q is an empirical parameter. For the generic mice population investigated here the values p50 = 39.25 mGy/ day and q = 7.5 give a good fit to the dose–effect curve obtained with Eq. 1. The rapid decrease in population biomass at dose rates above 39 mGy/day is related to considerable depletion of reproduction capacity of population. The results of the present model calculations were compared with available datasets on radiation effects in micetype rodents. Some examples of numerous published data on radiation effects in mice-type rodents, listing the applied dose rates and observed effects, are given in Table 1. Nonstochastic effects of chronic radiation in mammals include effects on morbidity (demonstrating the physiological state of the repairing system), effects on reproduction, and life shortening as a cumulative effect (Sazykina et al. 2009). This comparison of the model predictions with experimental data shows that the model adequately approximates typical dose ranges and severity of effects on repairing system, reproduction, and population survival of mice-type rodents. Comparison of radiation effects on generic population survival from different modes of exposure It is of great interest to examine the change of effectiveness observed in the mouse between the single acute and

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Table 1 Effects of chronic radiation exposure on mice-type rodents (some examples) Dose rate (Gy/day)

Organism

Source of information; effect

Radiation effects on morbidity 1.0 9 10-2

Mouse

(Lorenz et al. 1954); negative changes in blood

1.1 9 10-2

Tundra vole (wild population)

(Maslova et al. 1994); degenerative changes in liver

1.2 9 10 –4.3 9 10

Mouse

(Moskalev and Streltsova 1964); decreased bactericidal activity of blood

1.5 9 10-2

Short-tailed vole (wild population)

(Ilyenko 1974); weakening of resistance to parasites

2.0 9 10-2–8.0 9 10-2

Mouse

(Lorenz et al. 1954); negative changes in blood, increased incidence of tumors

-2

-2

Radiation effects on reproduction 2.4 9 10-3

Mouse

(Leonard et al. 1985); decrease in fecundity

4.0 9 10-3

Mouse

(Moskalev and Streltsova 1964); degenerative changes in ovaries, disturbance of estrous cycle

4.3 9 10-3

Mouse

(Muramatsu et al. 1964); sterility in the later generations

6.0 9 10-3–5.0 9 10-2

Northern red-backed mouse (wild population)

(Ilyenko 1967); decrease in average numbers of living embryos per female

1.0 9 10-2

Mouse

(Lorenz et al. 1954); damage to ovaries

2.0 9 10-2

Albino rat

(Brown 1964); decrease in litter size in later generations

2.0 9 10-2–4.0 9 10-2

Mouse

(Lorenz et al. 1954); ovarian and mammary tumors

4.4 9 10-2

Mouse

(Moskalev and Streltsova 1964); marked morphological negative changes in reproductive organs

5.0 9 10-2

Albino rat

(Brown 1964); sterility of males

6.0 9 10-2

Short-tailed voles (wild population)

(Ilyenko 1967); decreased in numbers of living embryos per female

In addition, numerous authors reported effects of chronic radiation on life shortening in mammals Data in the mouse life shortening at chronic exposure analyzed by UNSCEAR in 1982 Report (Annex K ‘‘Radiation-induced life shortening’’) demonstrated an increasing life-shortening effect following an exponential function of dose rate from 0.01 up to 1 Gy/day

chronic low dose rate exposures (UNSCEAR 1982). Figure 4 demonstrates the differences in population survival (500th day of model calculations) resulting from the two modes of irradiation: acute dose (given at the 1st day) and chronic 500-day exposure with the same integrated dose. Both curves run together up to doses of about 10 Gy, confirming the good capacity of the studied population to recover even from doses above LD50. Above 10–11 Gy, however, the two dose–effect curves diverge, with the curve for chronic exposure showing much less damaging effects compared to that for acute exposure. This divergence of dose–effect curves demonstrates the effect of ‘‘wasted radiation’’ discovered by Mole (1955) and cited in UNSCEAR (1982, Annex K). Mole showed experimentally that under conditions of chronic exposure the radiation dose needed to cause lethal effects in animals is higher than that under acute exposure; the values of ‘‘wasted radiation’’ corresponded to over one-half of the mean accumulated dose (UNSCEAR 1982). Other authors (Grahn et al. 1978) reported that the radiobiological effectiveness for low daily exposures of mice was less than that for single exposures by a factor of 5–10; life shortening was estimated at 0.03–0.06 days/R for the mouse.

Fig. 4 Comparison of dose–effect curves for generic mice populations subjected to acute dose or chronic lifetime exposure with the same integrated doses

Conclusions A model simulating radiation effect in a generic animal population (Kryshev et al. 2008) was applied to calculate effects on population survival in two modes of exposure:

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acute dose (2–35 Gy) and chronic lifetime exposure with the same integrated dose. Calculations were made for a generic mice population. However, the model can be applied for other animals with proper selection of parameter values. In case of acute exposure, in the range 2–11 Gy, the population response is in two phases. During a first phase, there is a depletion in population survival, while the second phase is characterized by a recovery period due to biosynthesis of new biomass. The two-phase response to acute irradiation is confirmed by experimental data on mice and other animals (UNSCEAR 1982). The model predictions presented here indicate that a generic mice population, living in ideal conditions, has a potential for recovery (within a mouse lifetime period) from acute exposure with doses up to 10–11 Gy, i.e., the population may recover from doses above LD50/30 (6.2 Gy) (Bond and Fliedner 1965). Following acute doses above 14 Gy, however, the mice population goes to extinction without recovery. In contrast, under chronic lifetime exposures (500 days), ionizing radiation has little effect on population survival up to integrated doses of 14–15 Gy. In other words, for chronic exposure, the survival of the population is much better than that for acute exposure with the same dose. Due to the effect of ‘‘wasted radiation’’, the integrated dose of chronic exposure could be about two times higher than the acute dose, producing the same effect on survival. The effect of ‘‘wasted radiation’’ was observed for applied doses in the range 11–25 Gy; above 25 Gy, however, the survival went to zero. It is concluded that the generic population model with repairing of radiation damage applied in the present study can adequately simulate in one model the main processes and dose–effect relationships, which are characteristic for acute and chronic modes of exposure. Acknowledgments The authors would like to acknowledge the IAEA-MODARIA Programme and the participants of the MODARIA working group 9, coordinated by Dr. Jordi Vives i Batlle and Dr. Fre´de´ric Alonzo for fruitful discussions on this work.

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