The relationship between elimination rates and partition coefficients

Rate constants for uptake and elimination of chemicals in organisms are often related to partition coefficients (typically the octanol-water partition coefficient). We show that the well-mixed one-compartment model for toxico-kinetics implies that the elimination rate is inversely proportional to the square root of the partition coefficient. When chemical exchange is limited by diffusion in the boundary layers adjacent to the interface, two-film models are appropriate, which have more complex implications for the relationships between the exchange rates and the partition coefficient. We also show that the popular steady-flux approximation of the two-film model is not a conceptual generalization of the one-compartment model, although it shares the first-order kinetics. We compare the kinetics of a series of models with an increasing number of well-mixed compartments for exchange, such that the two-film model results for an infinite number of compartments. The latter model formulation in terms of partial differential equations, and more in particular its boundary condition at the interface of the two media, is believed to be new. In the steady-flux approximation and in the model with single well-mixed boundary layers and low diffusivities, the elimination rate depends hyperbolically on the partition coefficient. The available data for abiotic systems (SPME fibers) supports a hyperbolic relationship, whereas the data for aquatic biota are less discriminating between a hyperbolic or a square root relationship with the partition coefficient. The daphnia data showed less scatter than the fish data, possibly due to the small variance in body sizes, since elimination rates are inversely proportional to body length. The square root relationship fitted these data best.