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

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 C_p(t). Although fundamental biopharmaceutical variables in terms of distribution (e.g., K_p and f_d) and elimination kinetics (e.g., CL) 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 C_p(t). 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 (MRT) and transit (MTT) 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 MTT to the MRT in the body (i.e., K_det= MTT_max/ MRT_B) 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 C_p(t) in the m2CM and m3CM. This assessment provides improved understanding of the complexities inherent in all PBPK profiles and models. Graphical Abstract: [Figure not available: see fulltext.].