Development of appropriate equations for physiologically based pharmacokinetic modeling of permeability-limited and flow-limited transport

Abstract

Although the implementation of a flow-limited, well-stirred tank (WST) single-compartment tissue model in pharmacokinetics and toxicokinetics is widespread, its use is not always justified biophysically or physiologically. The WST model introduces a loss of biophysical detail, specifically the vascular space, which is present in the standard permeability-limited two-subcompartment (PLT) tissue model. To address this loss of detail when evaluating the in vivo kinetics of drugs, toxins, nutrients, and endogenous metabolites, a novel set of physiologically based pharmacokinetic tissue compartment equations is developed through application of an asymptotic approximation to a two-region vascular–extravascular system to arrive at a permeability-limited two-region asymptotically reduced (P-TAR) model and a flow-limited (F-TAR) model. Development of the TAR modeling approach illustrates the importance of relative timescales in PBPK tissue compartment model selection and the conditions under which improved biophysical realism is advantageous. In the permeability-limited regime, the TAR model formulations enable drug or toxicant concentration to be modeled in the vascular and extravascular spaces equivalent to the PLT tissue model while invoking only one state variable to represent the vascular and extravascular spaces. In the flow-limited regime, the F-TAR model is more biophysically realistic than the WST model because it maintains the anatomical distinction between the vascular and extravascular spaces, and hence offers greater pharmacological and physiological insight than the WST model, without introducing additional computational complexity.