A general approach to the apparent permeability index

The apparent permeability index is widely used as part of a general screening process to study drug absorption, and is routinely obtained from in vitro or ex vivo experiments. A classical example, widely used in the pharmaceutical industry, is the in vitro Caco-2 cell culture model. The index is defined as the initial flux of compound through the membrane (normalized by membrane surface area and donor concentration) and is typically computed by adapting a straight line to the initial portion of the recorded amounts in the receiver compartment, possibly disregarding the first few points when lagging of the transfer process through the membrane is evident. Modeling the transfer process via a two-compartmental system yields an immediate analogue of the common Papp as the initial slope of the receiver quantity, but the two-compartment model often does not match observations well. A three-compartment model, describing the cellular layer as well as donor and receiver compartments, typically better represents the kinetics, but has the disadvantage of always having zero initial flow rate to the receiver compartment: in these circumstances the direct analogue of the Papp index is not informative since it is always zero. In the present work an alternative definition of an apparent permeability index is proposed for three-compartment models, and is shown to reduce to the classical formulation as the cellular layer's volume tends towards zero. This new index characterizes the intrinsic permeability of the membrane to the compound under investigation, can be directly computed in a completely observer-independent fashion, and reduces to the usual Papp when the linear two-compartment representation is sufficient to accurately describe compound kinetics.