### The relationship between elimination rates and partition coefficients

Kooijman, S. A. L. M., Jager, T. and Kooi, B. W. 2004.
The relationship between elimination rates and partition coefficients.
*Chemosphere*, **57**, 745 - 753
#### Abstract

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.