Mathematical relationships between metrics of chemical bioaccumulation in fish

Abstract

Five widely used metrics of bioaccumulation in fish are defined and discussed, namely the octanol-water partition coefficient (K OW ), bioconcentration factor (BCF), bioaccumulation factor (BAF), biomagnification factor (BMF), and trophic magnification factor (TMF). Algebraic relationships between these metrics are developed and discussed using conventional expressions for chemical uptake from water and food and first-order losses by respiration, egestion, biotransformation, and growth dilution. Two BCFs may be defined, namely as an equilibrium partition coefficient K FW or as a nonequilibrium BCF K in which egestion losses are included. Bioaccumulation factors are shown to be the product of the BCF K and a novel equilibrium multiplier M containing 2 ratios, namely, the diet-to-water concentration ratio and the ratio of uptake rate constants for respiration and dietary uptake. Biomagnification factors are shown to be proportional to the lipid-normalized ratio of the predator/prey values of BCF K and the ratio of the equilibrium multipliers. Relationships with TMFs are also discussed. The effects of chemical hydrophobicity, biotransformation, and growth are evaluated by applying the relationships to a range of illustrative chemicals of varying K OW in a linear 4-trophic-level food web with typical values for uptake and loss rate constants. The roles of respiratory and dietary intakes are demonstrated, and even slow rates of biotransformation and growth can significantly affect bioaccumulation. The BCF K s and the values of M can be regarded as the fundamental determinants of bioaccumulation and biomagnification in aquatic food webs. Analyzing data from food webs can be enhanced by plotting logarithmic lipid-normalized concentrations or fugacities as a linear function of trophic level to deduce TMFs. Implications for determining bioaccumulation by laboratory tests for regulatory purposes are discussed.

Bioconcentration and metabolism of pesticides and industrial chemicals in the frog

“…51) Similarly to bioconcentration, theoretical approaches using models have been applied to bioaccumulation. The detailed kinetic analysis was conducted for fish by directly considering dietary uptake, growth dilution, egestion, and metabolism, 52) but such an approach has never been taken for frogs. However, the bioaccumulation factor can be also estimated from the equation "α·F/k D " by using absorption efficiency (α) and feeding rate (F, in g food/g of frog/day).…”

Bioconcentration, bioaccumulation, biomagnification and trophic magnification: a modelling perspective

“…This difference is attributable to the different lipid contents of the diet and sh since Q f is Q C $(L D / L F ). Q C and Q f represent limiting maximum BMFs on a concentration and fugacity or lipid normalized basis respectively as is apparent from eqn (4) and (7). For example, increasing log K OW to 8 and setting biotransformation and growth rates to zero result in a BMF W of 5.98, approaching Q C of 6 and a BMF L of 2.99, approaching Q f of 3.…”

“…It can be viewed as the product of the BCF and a 'multiplier' dependent on the BAF of the diet and the ratio of the rates of dietary uptake and respiratory uptake. 7 The bio-magnication factor BMF is essentially the ratio of the BAFs of the predator and the prey and may involve an increase in both concentration and fugacity. The TMF as the slope of the log concentration vs. trophic position is related to the mean BMF of the species comprising the food web.…”

Review of laboratory‐based terrestrial bioaccumulation assessment approaches for organic chemicals: Current status and future possibilities

“…Aquatic bioconcentration studies may not be appropriate for predicting potential bioaccumulation in terrestrial organisms and ecosystems where dietary exposure, in conjunction with some limited potential for dermal exposure, predominates and different elimination mechanisms are operative (Kelly et al ). However, Mackay et al () present a compelling argument for the importance and relevance of the BCF value, particularly the kinetic BCF value, BCF k , as a principal determinant of chemical concentrations in aquatic food webs. Mackay et al () also highlight what is arguably the most important aspect of any bioaccumulation assessment: “Ultimately, however, it is the absolute concentrations, not their ratios, that are of concern from an exposure and risk assessment perspective.” The concerns highlighted by Kelly et al () do not entirely negate the potential use of aquatic bioconcentration metrics for predicting bioaccumulation in terrestrial food webs but do suggest that chemicals with both a log K OA of 10 6 or higher and a log K OW greater than 10 2 may represent a class of chemicals for which traditional extrapolation of aquatic bioaccumulation metrics to terrestrial organisms is not appropriate, although relatively limited empirical data currently exist to support this hypothesis.…”

“…Aquatic bioconcentration studies may not be appropriate for predicting potential bioaccumulation in terrestrial organisms and ecosystems where dietary exposure, in conjunction with some limited potential for dermal exposure, predominates and different elimination mechanisms are operative (Kelly et al 2007). However, Mackay et al (2013) present a compelling argument for the importance and relevance of the BCF value, particularly the kinetic BCF value, BCF k , as a principal determinant of chemical concentrations in aquatic food webs. Mackay et al (2013) also highlight what is arguably the most important aspect of any bioaccumulation assessment: "Ultimately, however, it is the absolute concentrations, not their ratios, that are of concern from an exposure and risk assessment perspective."…”