Applications of minimal physiologically-based pharmacokinetic models

Abstract

Conventional mammillary models are frequently used for pharmacokinetic (PK) analysis when only blood or plasma data are available. Such models depend on the quality of the drug disposition data and have vague biological features. An alternative minimal-physiologically-based PK (minimal-PBPK) modeling approach is proposed which inherits and lumps major physiologic attributes from whole-body PBPK models. The body and model are represented as actual blood and tissue (usually total body weight) volumes, fractions (f ( d )) of cardiac output with Fick's Law of Perfusion, tissue/blood partitioning (K ( p )), and systemic or intrinsic clearance. Analyzing only blood or plasma concentrations versus time, the minimal-PBPK models parsimoniously generate physiologically-relevant PK parameters which are more easily interpreted than those from mammillary models. The minimal-PBPK models were applied to four types of therapeutic agents and conditions. The models well captured the human PK profiles of 22 selected beta-lactam antibiotics allowing comparison of fitted and calculated K ( p ) values. Adding a classical hepatic compartment with hepatic blood flow allowed joint fitting of oral and intravenous (IV) data for four hepatic elimination drugs (dihydrocodeine, verapamil, repaglinide, midazolam) providing separate estimates of hepatic intrinsic clearance, non-hepatic clearance, and pre-hepatic bioavailability. The basic model was integrated with allometric scaling principles to simultaneously describe moxifloxacin PK in five species with common K ( p ) and f ( d ) values. A basic model assigning clearance to the tissue compartment well characterized plasma concentrations of six monoclonal antibodies in human subjects, providing good concordance of predictions with expected tissue kinetics. The proposed minimal-PBPK modeling approach offers an alternative and more rational basis for assessing PK than compartmental models.

Fig. 1

Paradigm for constructing PBPK models

Fig. 2

Minimal-PBPK model with two tissue compartments. Symbols and physiological restrictions are defined with Eqs. (1–3). The blood compartment in the left box mimics the venous blood as in full PBPK models, but is not utilized in the present model

Fig. 3

Minimal-PBPK model extended with the hepatic compartment. Symbols and physiological restrictions are defined in Table 2

Fig. 4

Basic minimal-PBPK model assigning CL either from tissue (Model A) or plasma compartments (Model B). Symbols and physiological restrictions are defined with Eqs. (9) and (10)

Fig. 5

Pharmacokinetic profiles of 22 beta-lactams in human subjects

Fig. 6

Correlation between estimated (K_p) and calculated partition coefficients K_p (f_up/f_ue) for 22 beta-lactam antibiotics. The line of identity is shown

Fig. 7

Pharmacokinetic profiles for four selected drugs after oral (triangle) and IV (square) dosing

Fig. 8

Pharmacokinetic profiles for moxifloxacin in five species. The dotted line provides fitting with an adjusted b value for man

Fig. 9

Pharmacokinetic profiles for six mAbs given to human subjects and simulated tissue concentrations