Theoretical Examination Seeking Tangible Physical Meanings of Slopes and Intercepts of Plasma Concentration-Time Relationships in Minimal Physiologically Based Pharmacokinetic Models.

ABSTRACT

In minimal physiologically based pharmacokinetic (mPBPK) models, physiological (e.g., cardiac output) and anatomical (e.g., blood/tissue volumes) variables are utilized in the domain of differential equations (DEs) for mechanistic understanding of the plasma concentration-time relationships [Formula see text]. Although fundamental biopharmaceutical variables in terms of distribution (e.g., [Formula see text] and [Formula see text]) and elimination kinetics (e.g., [Formula see text]) in mPBPK provide greater insights in comparison to classical compartment models, an absence of kinetic elucidation of slopes and intercepts in light of such DE model parameters hinders more intuitive appreciation of [Formula see text]. Therefore, this study seeks the tangible physical meanings of slopes and intercepts of the plasma concentration-time relationships in one- and two-tissue mPBPK models (i.e., m2CM and m3CM), with respect to time parameters that are readily understandable in PK analyses, i.e., the mean residence ([Formula see text]) and transit ([Formula see text]) times. Utilizing the explicit equations (EEs) for the slopes, intercepts, and areas of each exponential phase in the m2CM and m3CM, we theoretically and numerically examined the limiting/boundary conditions of such kinetic properties, based on the ratio of the longest tissue [Formula see text] to the [Formula see text] in the body (i.e., [Formula see text]) that is useful for dissecting complex PBPK systems. The kinetic contribution of the area of each exponential phase to the total drug exposure was assessed to identify the elimination phase between the terminal and non-terminal phases of the [Formula see text] in the m2CM and m3CM. This assessment provides improved understanding of the complexities inherent in all PBPK profiles and models.