A model of the radionuclide accumulation in fish taking into account the contribution of different tissues and allometry is presented.
The basic model assumptions are as follows.
(i) A fish organism is represented by several compartments in which radionuclides are homogeneously distributed.
(ii) The compartments correspond to three groups of organs or tissues: muscle, bones and organs (kidney, liver, gonads, etc.) differing in metabolic function.
(iii) Two input compartments include gills absorbing contamination from water and digestive tract through which contaminated food is absorbed.
(iv) The absorbed radionuclide is redistributed between organs or tissues according to their metabolic functions.
(v) The elimination of assimilated elements from each group of
organs or tissues differs, reflecting differences in specific
tissues or organs in which elements were accumulated.
(vi) The food and water uptake rates, elimination rate, and growth rate depend on the metabolic rate, which is scaled by fish mass to the
Accumulation of radionuclides in marine organisms is a complicated process that is governed by uptake of radionuclides from water, sediment and food as well as by depuration.
In turn, these processes depend on the chemical properties of elements, their roles in metabolic processes,
the positions of organisms in the food web and marine environmental parameters.
In the case of chronic exposure, the radiological assessment models often assumed an equilibrium approach (Carvalho, 2018),
in which concentration in the organism relates to the concentration in water using a biological accumulation factor (BAF).
However, to describe highly time-dependent transfer processes resulting from accidental releases,
dynamic models for the uptake and retention of activity in marine organisms are necessary (Vives i Batlle et al., 2016).
According to Takata et al. (2019), the effective half-lives of post-Fukushima Dai-ichi Nuclear Power Plant (FDNPP)
accident disequilibrium of
Distribution of accumulated activities of isotopes Cs, Sr and Co in muscle, bone and liver estimated from data (Yankovich, 2003; Yankovich et al., 2010).
A more general approach to the description of the radionuclide accumulation in the tissues of fish is using the physiologically based pharmacokinetic (PBPK) models (Barron et al., 1990; Thomann et al., 1997; Garnier-Laplace et al., 2000; Otero-Muras et al., 2010; Grech et al., 2019). In the PBPK models, the fish organism is represented as three groups of compartments: absorption compartments simulating uptake of contaminants, distribution compartments simulating tissues and organs, and excretion compartments. The exchange of contaminants between compartments is limited by blood flux perfusing compartments. However, these models require a significant number of parameters depending on elements, fish species and marine environments. They must be determined from laboratory experiments (Thomann et al., 1997) or by optimization procedures (Otero-Muras et al., 2010). Note that, with the exception of model Grech et al. (2019), PBPK fish models do not include scaling (allometric) relationships between metabolic rates and organism mass (West et al., 1997; Higley and Bytwerk, 2007; Vives i Batlle et al., 2007; Beresford et al., 2016). Therefore, there is a need to develop a generic model of intermediate complexity between the one-compartment model and the PBPK model taking into account (i) the heterogeneity of the distribution of contamination in fish tissues and (ii) the allometric relationships between metabolic rates and organism mass. Such a model can be used for accidental release simulations without local calibration, which is a complicated task in the circumstances of the accident.
In this paper, a new approach for predicting radionuclide accumulation in fish by taking into account the contributions of different tissues and allometry is presented. The developed multi-compartment kinetic–allometric (MCKA) model is embedded into the box model POSEIDON-R (Lepicard et al., 2004; Maderich et al., 2014a, b; 2018b; Bezhenar et al., 2016), which describes transport of radionuclides in water, accumulation in the sediment, and transfer of radionuclides through the pelagic and benthic food webs. The paper is organized as follows. The MCKA model is described in Sect. 2. The comparison with laboratory experiments is given in Sect. 3. The results of simulation of several radionuclides in the marine environment for regular and accidental releases are described in Sect. 4. The conclusions are presented in Sect. 5.
Here, a simple multi-compartmental model to simulate kinetics of radionuclides in the fish is described.
The basic assumptions are as follows: (i) a fish organism is represented by several compartments in which radionuclides are homogeneously distributed;
(ii) the compartments correspond to three groups of organs or tissues differing in metabolic function: muscle, bones and organs (kidney, liver, gonads, etc.);
(iii) two input compartments include gills which absorb contamination from water and digestive tract through which contaminated food is absorbed;
(iv) the absorbed radionuclide is redistributed between organs or tissues according to their metabolic functions;
(v) the elimination of assimilated elements from each group of organs or tissues differs, reflecting differences in the specific tissues or organs in which elements were accumulated; and
(vi) the food and water uptake rates, elimination rate, and growth rate depend on the metabolic rate, which is scaled by fish mass to the
Schematic of the multi-compartment kinetic–allometric model.
The equation for concentration of radionuclide
The equation for concentration of unabsorbed radionuclide
The activity concentration in the food
Transfer rates
Parameters in allometric relations, standard deviation (SD) of parameters and number of measurements
The food and water uptake rates, elimination rate, and growth rate depend on the metabolic rate,
which in turn is known to scale by the organism mass.
Here, we employed quarter-power scaling for uptake, elimination and growth rates derived from general theory (West et al., 1997).
This theory predicts for all organisms the
The model parameters can be estimated using measurement data and applying the kinetic equations under equilibrium conditions.
Equations (
The assimilation efficiencies are expressed through kinetic coefficients as
Values of BAF for different radionuclides are named as CF (Concentration Factor) in IAEA (2004). Yankovich et al. (2010) provide
The food assimilation efficiency AE
Equation (
Notice that values of AE
Retention of absorbed elements in fish after single feeding was often used to estimate AE
As follows from these solutions,
the decay of activity in the fish organisms includes a fast component with decay constant representing transfer of activity to the fish body and unabsorbed element egestion from the digestive tract, along with a slow component which is governed by elimination constants for
The analytical solutions (Eqs. 28–29) can be compared with laboratory experiments in which depuration of metals from the fish after single feeding was studied.
In the experiment by Mathews and Fisher (2008), the retention of several radioisotopes in juvenile sea bream (
Retention of radionuclides in whole body and tissues of juvenile sea bream (
The solutions were also compared with laboratory experiments for predator fish (Mathews et al., 2008).
In these experiments, the retention of several radioisotopes in sea bream (
Retention of radionuclides in whole bodies of predator fish: sea bream (
Uptake and absorption in fish of elements from water were studied in several laboratory experiments (e.g. Jeffree et al., 2006; Mathews and Fisher, 2008; Mathews et al., 2008).
The modelling of the absorption of elements can be used to estimate an assimilation efficiency AE
Simulated BCF in marine fish during the period of exposition in water. The simulations are compared with isotope measurements by Mathews et al. (2008) in juvenile sea bream (
These solutions were compared with laboratory experiments for prey fish (Mathews et al., 2008) and for predator fish (Jeffree et al., 2006).
In the experiment by Mathews et al. (2008), the uptake of several radioisotopes by juvenile
The parameter
Comparison of the model against laboratory experiments on the retention of absorbed elements in fish after single feeding demonstrated the need to include the kinetic characteristics of the digestive tract in the model when highly non-equilibrium transfer dynamics are expected.
However, for modelling of food uptake in marine environment with multiple feedings the simple equilibrium assumption Eq. (
The results of the sensitivity study suggest that model results are most sensitive to variations of AE
In order to predict the accumulation of radionuclides in fish in the marine environment using the MCKA model described above, it is necessary to calculate changes in concentration in water and in bottom sediments and to calculate the transport of radionuclides through food chains. The POSEIDON-R box model (Lepicard et al., 2004; Maderich et al., 2014a, b; 2018b; Bezhenar et al., 2016) can be used to simulate the marine environment as a system of 3D boxes for the water column, bottom sediment and food web. The water column box is vertically subdivided into layers. The suspended matter settles in the water column. The bottom sediment box is divided into three layers (Fig. S2). The downward burial processes operate in all three sediment layers. Maderich et al. (2018b) described the POSEIDON-R model in detail.
A food web model that includes pelagic and benthic food chains is implemented within the POSEIDON-R box model (Bezhenar et al., 2016). In the food web model, marine organisms are grouped into classes according to trophic level and species type (Fig. S3). The food chains differ between the pelagic zone and the benthic zone. Pelagic organisms comprise primary producers (phytoplankton) and consumers (zooplankton, non-piscivorous (forage) fish and piscivorous fish). In the benthic food chain, radionuclides are transferred from algae and contaminated bottom sediments to deposit-feeding invertebrates, demersal fish and benthic predators. Bottom sediments include both organic and inorganic components. Radioactivity is assumed to be assimilated by benthic organisms from the organic components of the bottom deposits. Other food web components are crustaceans (detritus feeders), molluscs (filter feeders) and coastal predators, which feed throughout the water column in shallow coastal waters. All organisms take in radionuclides both via the food web and directly from the water. Table S9 in the Supplement contains food preferences for organisms in the food web which are used in the model. Details of the transfer of radiocaesium through the marine food web are presented by Bezhenar et al. (2016) and Maderich et al. (2018b).
The POSEIDON-R model can handle different types of radioactive releases: including atmospheric fallout and point sources associated with routine releases from nuclear facilities located directly on the coast or point sources associated with accidental releases (Lepicard et al., 2004). For coastal discharges occurring in the large (“regional”) boxes, “coastal” release boxes are nested into the regional box system. The intermediary boxes between coastal and regional boxes are called “inner” boxes.
Box system around the Forsmark NPP. The numbers denote regional boxes in the box system of the Baltic Sea (Bezhenar et al., 2016). An additional “Inner box” is separated from regional box 68 by the blue line. The coastal box (red rectangle) surrounds the area where cooling water from NPP is discharged.
This section presents the simulation results of
The release rates of
Release rates of
As seen in Fig. 8a, the results of simulation for the concentration of
Similarly, the behaviour of
Comparison between calculated and measured
Following caesium,
The POSEIDON-R model was customized for the north-western Pacific and adjacent seas (the East China Sea, the Yellow Sea, and the East Sea or Sea of Japan) as in (Maderich et al., 2018a).
A total of 188 boxes covered this region.
The boxes around the FDNPP are shown in Fig. 9 with an additional
The historical contamination due to global atmospheric deposition in the period from 1945–2010 was simulated according to Maderich et al. (2014b) with data from the Marine Radioactivity Information System database (MARIS, 2020).
The value of the accidental release was estimated as 160 TBq (16 TBq d
Comparison between calculated and measured
Comparison between calculated and measured
The calculated concentration of
Comparison of the Eqs. (1)–(3) and (7) of the MCKA model and
Eq. (11) of the standard whole-body model demonstrates
that the main difference is found in the description of the whole-body elimination rate
The calculated
In case of the FDNPP accident, the calculated
A new approach to predicting the accumulation of radionuclides in fish by taking into account heterogeneity of distribution of contamination in the organism and dependence of metabolic process rates on the fish mass was developed.
The fish organism was represented by compartments for three groups of tissues or organs (muscle, bone, organs) and two input compartments representing gills and the digestive tract.
The absorbed elements are redistributed between organs or tissues and
then eliminated according to their metabolic function.
The food and water uptake rates, elimination rate, and growth rate depend on the metabolic rate,
which is scaled by the fish mass to the
This model is of intermediate complexity and provides an alternative for the basic/simplistic whole-body models and the highly advanced PBPK models.
The main difference between the MCKA and whole-body models was found in the description of the whole-body elimination rate
The trophic transfer factors (TTF) were calculated for five elements using assimilation efficiencies AE
The developed MCKA model was embedded into the box model POSEIDON-R, which describes the transfer of radionuclides through the pelagic and benthic food webs.
The POSEIDON-R model was applied for the simulation of the transport and fate of
POSEIDON-R code is a part of the decision support system JRODOS for off-site emergency management after nuclear accidents.
Data used in the study are freely available in MARIS, JCAC, MEXT and NRA databases, and in several publications.
The supplement related to this article is available online at:
RB, VM and KOK conducted the literature review and designed the study. RB, VM and KTJ developed the model and performed modelling of laboratory experiments. GdW and KOK collected data for case studies. RB, VM and KOK performed the simulations for case studies. RB, VM, KTJ and GdW analysed results of simulations and wrote the initial article. All authors edited and approved the final article text.
The authors declare that they have no conflict of interest.
Authors are grateful to three anonymous reviewers for useful suggestions that helped to improve the article.
This research has been supported by the Korea Institute of Ocean Science and Technology (grant no. PE99912), the National Research Foundation of Ukraine (Ukraine) (grant nos. 2020.02/0048 and 2020.01/0421) and the International Atomic Energy Agency (grant no. CRP K41017).
This paper was edited by Kenneth Rose and reviewed by three anonymous referees.