A Flux-Based Bioaccumulation Model for Growing Organisms: Integrating Advective-Diffusive Uptake at Exchange Organs into Dynamic Energy Budget Theory.

Bioaccumulation factors in fish vary systematically with body size, food availability, and chemical hydrophobicity, yet widely used fugacity-based models rely on size-independent empirical rate constants and cannot explain these patterns mechanistically. Here we present a flux-based model that resolves this limitation by integrating two complementary exchange theories into the Dynamic Energy Budget framework: Erickson-McKim countercurrent exchange for the respiratory (gill) pathway and plug-flow reactor kinetics for the dietary (gut) pathway. The key methodological advance is requiring simultaneous consistency among four independent flux descriptions at each exchange surface: The advective mass balance, Fick's diffusion law, the one-compartment Dynamic Energy Budget model, and the corresponding exact spatial solution-the countercurrent expression at the gill and the plug-flow expression at the gut. In both pathways, this consistency requirement uniquely determines the effective exposure concentration as a weighted combination of the outflow and body concentrations, where the weighting factor is derived from the exponential concentration profile along the exchange organ rather than postulated. The resulting series-resistance structure places the spatial correction exclusively on the diffusion resistance of each pathway, structurally guaranteeing three properties: The maximum bioconcentration factor equals the thermodynamic partition coefficient, gill and gut assimilation efficiencies are bounded below unity, and elimination rate constants scale inversely with body length for both pathways. This places the two uptake routes on equal mechanistic footing rather than extending a gill-centered formulation to diet as an afterthought. Systematic comparison with fugacity-based models across six diagnostic indicators demonstrates that the present model captures size-, food condition-, and hydrophobicity-dependent bioaccumulation patterns inaccessible to conventional approaches. A preliminary structural validation using mercury bioaccumulation data in blackhead seabream (Acanthopagrus schlegelii), where divalent inorganic mercury (Hg(II)) and methylmercury exhibit contrasting respiratory- and dietary-dominated kinetics, confirms the predicted size dependence of depuration rates and field concentrations.