Modelling the dynamics of fish contamination by Chernobyl radiocaesium: an analytical solution based on potassium mass balance.

After the sudden fallout from the Chernobyl nuclear accident in 1986, activities and bioaccumulation factors of radiocaesium ((137)Cs, (134)Cs) fluctuated strongly over several years before reaching quasi-equilibrium, with patterns significantly differing among organisms. To model these dynamic relaxation processes based on ecological mechanisms we developed mass balance equations for (137)Cs in an aquatic food chain on the following basis: (a). potassium acts as a biogeochemical analogue ("carrier") of caesium; (b). the concentration of potassium in fish and other animals is effectively constant; (c). the main source of potassium in freshwater fish is the dietary uptake. The model is applicable to linear food chains of any number of trophic levels, while solutions evaluated here include the following food chain compartments: water, invertebrates (fish food), non-piscivorous fish, and piscivorous fish. The activity concentration in the water, which is considered as the secondary source of (137)Cs, is described by multi-component first-order decay function, although two components (fast and slow) are often sufficient to provide agreement with empirical data. In every compartment the turnover rate of caesium is considered as a constant over time. The analytical solution of the model equations describes the (137)Cs activity concentration in every compartment as a series of exponential functions, of which some are derived from the source pattern, and the others determined by the (137)Cs turnover rate in each food chain compartment. The model was tested with post-Chernobyl data from several long-term studies in lakes and provided a reasonable description of important radioecological aspects.