A Continuous Intestinal Absorption Model to Predict Drug Enterohepatic Recirculation in Healthy Humans: Nalbuphine as a Model Substrate.

Nalbuphine (NAL) is a κ-agonist/µ-antagonist opioid being developed as an oral extended formulation (ER) for the treatment of chronic cough in idiopathic pulmonary fibrosis and itch in prurigo nodularis. NAL is extensively glucuronidated and likely undergoes enterohepatic recirculation (EHR). The purpose of this work is to develop pharmacokinetic models for NAL absorption and enterohepatic recirculation (EHR). Clinical pharmacokinetic (PK) data sets in healthy subjects from three trials that included IV, oral solution, and ER tablets in fed and fasted state and two published trials were used to parametrize a novel partial differential equation (PDE)-based model, termed "PDE-EHR" model. Experimental inputs included in vitro dissolution and permeability data. The model incorporates a continuous intestinal absorption framework, explicit liver and gall bladder compartments, and compartments for systemic drug disposition. The model was fully PDE-based with well-stirred compartments achieved by rapid diffusion. The PDE-EHR model accurately reproduces NAL concentration-time profiles for all clinical data sets. NAL disposition simulations required inclusion of both parent and glucuronide recirculation. Inclusion of intestinal P-glycoprotein efflux in the simulations suggests that NAL is not expected to be a victim or perpetrator of P-glycoprotein-mediated drug interactions. The PDE-EHR model is a novel tool to predict EHR and food/formulation effects on drug PK. The results strongly suggest that even intravenous dosing studies be conducted in fasted subjects when EHR is suspected. The modeling effort is expected to aid in improved prediction of dosing regimens and drug disposition in patient populations.

Predicting clearance with simple and permeability-limited PBPK frameworks: comparison of well-stirred, dispersion and parallel tube liver models.

One-compartment (1C) and permeability-limited models were used to evaluate the ability of microsomal and hepatocyte intrinsic clearances to predict hepatic clearance. Well-stirred (WSM), parallel tube (PTM), and dispersion (DM) models were evaluated within the liver as well as within whole-body physiologically based pharmacokinetic frameworks. It was shown that a linear combination of well-stirred and parallel-tube average liver blood concentrations accurately approximates dispersion model blood concentrations. Using a flow/permeability-limited model, a large systematic error was observed for acids and no systematic error for bases. A scaling factor that reduced interstitial fluid (ISF) plasma protein binding could greatly decrease the absolute average-fold error (AAFE) for acids. Using a 1C model, a scalar to reduce plasma protein binding decreased the microsomal clearance AAFE for both acids and bases. With a permeability-limited model, only acids required this scalar. The mechanism of the apparent increased cytosolic concentrations for acids remains unknown. We also show that for hepatocyte intrinsic clearance in vitro-in vivo correlations (IVIVCs), a 1C model is mechanistically appropriate since hepatocyte clearance should represent the net clearance from ISF to elimination. A relationship was derived that uses microsomal and hepatocyte intrinsic clearance to solve for an active hepatic uptake clearance, but the results were inconclusive. Finally, the PTM model generally performed better than the WSM or DM models, with no clear advantage between microsomes and hepatocytes. Significance Statement Prediction of drug clearance from microsomes or hepatocytes remains challenging. Various liver models (e.g. WSM, PTM, and DM) have been mathematically incorporated into liver as well as whole-body PBPK frameworks. Although the resulting models allow incorporation of pH partitioning, permeability, and active uptake for prediction of drug clearance, including these processes did not improve clearance predictions for both microsomes and hepatocytes.

Process and System Clearances in Pharmacokinetic Models: Our Basic Clearance Concepts Are Correct.

Clearances are important parameters in pharmacokinetic (PK) models. All clearances in PK models are either process clearances that include diffusion, transport, and metabolism clearances or system clearances that include organ and systemic clearance. Clearance and volume of distribution are two independent parameters that characterize drug disposition in both individual compartments and systems of compartments. In this minireview, we show that systemic and organ clearances are net clearances that can be easily derived by partition analysis. When drugs are eliminated from the central compartment by first-order processes, systemic clearance is constant. When drugs are eliminated from a peripheral compartment, instantaneous systemic clearance will vary with time. However, average clearance and clearance at steady state will be constant and will equal dose divided by area under the curve. We show that peripheral elimination will not have a large impact on most pharmacokinetic analyses and that standard models of organ and systemic clearance are useful and appropriate. SIGNIFICANCE STATEMENT: There are two basic kinds of clearances used in pharmacokinetic models, process and system clearances. We show that organ and systemic clearances are net clearances with blood or plasma as the driving concentration. For linear pharmacokinetics, clearance is constant for elimination from the central compartment but varies with time for peripheral elimination. Despite the different kinds of clearance parameters and models, standard clearance models and concepts remain valid.

The Rat Continuous Intestine Model Predicts the Impact of Particle Size and Transporters on the Oral Absorption of Glyburide.

Oral drug absorption is known to be impacted by the physicochemical properties of drugs, properties of oral formulations, and physiological characteristics of the intestine. The goal of the present study was to develop a mathematical model to predict the impact of particle size, feeding time, and intestinal transporter activity on oral absorption. A previously published rat continuous intestine absorption model was extended for solid drug absorption. The impact of active pharmaceutical ingredient particle size was evaluated with glyburide (GLY) as a model drug. Two particle size suspensions of glyburide were prepared with average particle sizes of 42.7 and 4.1 µm. Each suspension was dosed as a single oral gavage to male Sprague Dawley rats, and concentration-time (C-t) profiles of glyburide were measured with liquid chromatography coupled with tandem mass spectrometry. A continuous rat intestine absorption model was extended to include drug dissolution and was used to predict the absorption kinetics of GLY depending on particle size. Additional literature datasets of rat GLY formulations with particle sizes ranging from 0.25 to 4.0 µm were used for model predictions. The model predicted reasonably well the absorption profiles of GLY based on varying particle size and varying feeding time. The model predicted inhibition of intestinal uptake or efflux transporters depending on the datasets. The three datasets used formulations with different excipients, which may impact the transporter activity. Model simulations indicated that the model provides a facile framework to predict the impact of transporter inhibition on drug C-t profiles. Model simulations can also be conducted to evaluate the impact of an altered intestinal lumen environment. In conclusion, the rat continuous intestine absorption model may provide a useful tool to predict the impact of varying drug formulations on rat oral absorption profiles.

A permeability- and perfusion-based PBPK model for improved prediction of concentration-time profiles.

To improve predictions of concentration-time (C-t) profiles of drugs, a new physiologically based pharmacokinetic modeling framework (termed 'PermQ') has been developed. This model includes permeability into and out of capillaries, cell membranes, and intracellular lipids. New modeling components include (i) lumping of tissues into compartments based on both blood flow and capillary permeability, and (ii) parameterizing clearances in and out of membranes with apparent permeability and membrane partitioning values. Novel observations include the need for a shallow distribution compartment particularly for bases. C-t profiles were modeled for 24 drugs (7 acidic, 5 neutral, and 12 basic) using the same experimental inputs for three different models: Rodgers and Rowland (RR), a perfusion-limited membrane-based model (Kp,mem ), and PermQ. Kp,mem and PermQ can be directly compared since both models have identical tissue partition coefficient parameters. For the 24 molecules used for model development, errors in Vss and t1/2 were reduced by 37% and 43%, respectively, with the PermQ model. Errors in C-t profiles were reduced (increased EOC) by 43%. The improvement was generally greater for bases than for acids and neutrals. Predictions were improved for all 3 models with the use of parameters optimized for the PermQ model. For five drugs in a test set, similar results were observed. These results suggest that prediction of C-t profiles can be improved by including capillary and cellular permeability components for all tissues.

Using partition analysis as a facile method to derive net clearances.

Partition analysis has been described previously by W.W. Cleland to derive net rate constants and simplify the derivation of enzyme kinetic equations. Here, we show that partition analysis can be used to derive elimination and transfer (distribution) net clearances for use in pharmacokinetic models. For elimination clearances, the net clearance approach is exemplified with a mammillary two-compartment model with peripheral elimination, and the established well-stirred and full hepatic clearance models. The intrinsic hepatic clearance associated with an observed average hepatic clearance can be easily calculated with net clearances. Expressions for net transfer clearances are easily derived, including models with explicit membranes (e.g., monolayer permeability and blood-brain barrier models). Together, these approaches can be used to derive equations for physiologically based and hybrid compartmental/ physiologically based models. This tutorial describes how net clearances can be used to derive relationships for simple models as well as increasingly complex models, such as inclusion of active transport and target mediated processes.

Predicting Impact of Food and Feeding Time on Oral Absorption of Drugs with a Novel Rat Continuous Intestinal Absorption Model.

Intricacies in intestinal physiology, drug properties, and food effects should be incorporated into models to predict complex oral drug absorption. A previously published human continuous intestinal absorption model based on the convection-diffusion equation was modified specifically for the male Sprague-Dawley rat in this report. Species-specific physiologic conditions along intestinal length - experimental velocity and pH under fasted and fed conditions, were measured and incorporated into the intestinal absorption model. Concentration-time (C-t) profiles were measured upon a single intravenous and peroral (PO) dose for three drugs: amlodipine (AML), digoxin (DIG), and glyburide (GLY). Absorption profiles were predicted and compared with experimentally collected data under three feeding conditions: 12-hour fasted rats were provided food at two specific times after oral drug dose (1 hour and 2 hours for AML and GLY; 0.5 hours and 1 hour for DIG), or they were provided food for the entire study. Intravenous versus PO C-t profiles suggested absorption even at later times and informed design of appropriate mathematical input functions based on experimental feeding times. With this model, AML, DIG, and GLY oral C-t profiles for all feeding groups were generally well predicted, with exposure overlap coefficients in the range of 0.80-0.97. Efflux transport for DIG and uptake and efflux transport for GLY were included, modeling uptake transporter inhibition in the presence of food. Results indicate that the continuous intestinal rat model incorporates complex physiologic processes and feeding times relative to drug dose into a simple framework to provide accurate prediction of oral absorption. SIGNIFICANCE STATEMENT: A novel rat continuous intestinal model predicts drug absorption with respect to time and intestinal length. Feeding time relative to dose was modeled as a key effect. Experimental fasted/fed intestinal pH and velocity, efflux and uptake transporter expression along intestinal length, and uptake transporter inhibition in the presence of food were modeled. The model uses the pharmacokinetic profiles of three model drugs and provides a novel framework to study food effects on absorption.

Complex Cytochrome P450 Kinetics Due to Multisubstrate Binding and Sequential Metabolism. Part 1. Theoretical Considerations.

Complexities in P450-mediated metabolism kinetics include multisubstrate binding, multiple-product formation, and sequential metabolism. Saturation curves and intrinsic clearances were simulated for single-substrate and multisubstrate models using derived velocity equations and numerical solutions of ordinary differential equations (ODEs). Multisubstrate models focused on sigmoidal kinetics because of their dramatic impact on clearance predictions. These models were combined with multiple-product formation and sequential metabolism, and simulations were performed with random error. Use of single-substrate models to characterize multisubstrate data can result in inaccurate kinetic parameters and poor clearance predictions. Comparing results for use of standard velocity equations with ODEs clearly shows that ODEs are more versatile and provide better parameter estimates. It would be difficult to derive concentration-velocity relationships for complex models, but these relationships can be easily modeled using numerical methods and ODEs. SIGNIFICANCE STATEMENT: The impact of multisubstrate binding, multiple-product formation, and sequential metabolism on the P450 kinetics was investigated. Numerical methods are capable of characterizing complicated P450 kinetics.

Complex Cytochrome P450 Kinetics Due to Multisubstrate Binding and Sequential Metabolism. Part 2. Modeling of Experimental Data.

Three CYP3A4 substrates, midazolam, ticlopidine, and diazepam, display non-Michaelis-Menten kinetics, form multiple primary metabolites, and are sequentially metabolized to secondary metabolites. We generated saturation curves for these compounds and analyzed the resulting datasets using a number of single-substrate and multisubstrate binding models. These models were parameterized using rate equations and numerical solutions of the ordinary differential equations. Multisubstrate binding models provided results superior to single-substrate models, and simultaneous modeling of multiple metabolites provided better results than fitting the individual datasets independently. Although midazolam datasets could be represented using standard two-substrate models, more complex models that include explicit enzyme-product complexes were needed to model the datasets for ticlopidine and diazepam. In vivo clearance predictions improved markedly with the use of in vitro parameters from the complex models versus the Michaelis-Menten equation. The results highlight the need to use sufficiently complex kinetic schemes instead of the Michaelis-Menten equation to generate accurate kinetic parameters. SIGNIFICANCE STATEMENT: The metabolism of midazolam, ticlopidine, and diazepam by CYP3A4 results in multiple metabolites and sequential metabolism. This study evaluates the use of rate equations and numerical methods to characterize the in vitro enzyme kinetics. Use of complex cytochrome P450 kinetic models is necessary to obtain accurate parameter estimates for predicting in vivo disposition.

Numerical Methods for Modeling Enzyme Kinetics.

Differential equations are used to describe time-dependent changes in enzyme kinetics and pharmacokinetics. Analytical and numerical methods can be used to solve differential equations. This chapter describes the use of numerical methods in solving differential equations and its applications in characterizing the complexities observed in enzyme kinetics. A discussion is included on the use of numerical methods to overcome limitations of explicit equations in the analysis of metabolism kinetics, reversible inhibition kinetics, and inactivation kinetics. The chapter describes the advantages of using numerical methods when Michaelis-Menten assumptions do not hold.

Enzyme Kinetics of Oxidative Metabolism-Cytochromes P450.

The cytochrome P450 enzymes (CYPs) are the most important enzymes in the oxidative metabolism of hydrophobic drugs and other foreign compounds (xenobiotics). The versatility of these enzymes results in some unusual kinetic properties, stemming from the simultaneous interaction of multiple substrates with the CYP active site. Often, the CYPs display kinetics that deviate from standard hyperbolic saturation or inhibition kinetics. Non-Michaelis-Menten or "atypical" saturation kinetics include sigmoidal, biphasic, and substrate inhibition kinetics (see Chapter 2 ). Interactions between substrates include competitive inhibition, noncompetitive inhibition, mixed inhibition, partial inhibition, activation, and activation followed by inhibition (see Chapters 4 and 6 ). Models and equations that can result in these kinetic profiles will be presented and discussed.

Case Study 5: Predicting the Drug Interaction Potential for Inhibition of CYP2C8 by Montelukast.

Predicting drug-drug interactions (DDIs) from in vitro data is made difficult by not knowing concentrations of substrate and inhibitor at the target site. For in vivo targets, this is understandable, since intracellular concentrations can differ from extracellular concentrations. More vexing is that the concentration of the drug at the target for some in vitro assays can also be unknown. This uncertainty has resulted in standard in vitro practices that cannot accurately predict human pharmacokinetics. This case study highlights the impact of drug distribution, both in vitro and in vivo, with the example of the drug interaction potential of montelukast.

Time-dependent enzyme inactivation: Numerical analyses of in vitro data and prediction of drug-drug interactions.

Cytochrome P450 (CYP) enzyme kinetics often do not conform to Michaelis-Menten assumptions, and time-dependent inactivation (TDI) of CYPs displays complexities such as multiple substrate binding, partial inactivation, quasi-irreversible inactivation, and sequential metabolism. Additionally, in vitro experimental issues such as lipid partitioning, enzyme concentrations, and inactivator depletion can further complicate the parameterization of in vitro TDI. The traditional replot method used to analyze in vitro TDI datasets is unable to handle complexities in CYP kinetics, and numerical approaches using ordinary differential equations of the kinetic schemes offer several advantages. Improvement in the parameterization of CYP in vitro kinetics has the potential to improve prediction of clinical drug-drug interactions (DDIs). This manuscript discusses various complexities in TDI kinetics of CYPs, and numerical approaches to model these complexities. The extrapolation of CYP in vitro TDI parameters to predict in vivo DDIs with static and dynamic modeling is discussed, along with a discussion on current gaps in knowledge and future directions to improve the prediction of DDI with in vitro data for CYP catalyzed drug metabolism.

A hybrid model to evaluate the impact of active uptake transport on hepatic distribution of atorvastatin in rats.

1. Mathematical modeling remains a useful tool to study the impact of transporters on overall and intracellular drug disposition. The impact of organic anion transporter protein mediated uptake on atorvastatin systemic and intracellular pharmacokinetics, specifically distribution volume, was studied in rats with mathematical modeling and conducting in vivo pharmacokinetic studies for atorvastatin in presence and absence of rifampicin. A previously developed 5-compartment explicit membrane model for the liver was combined with a compartmental model to develop a semi-physiological hybrid model for atorvastatin disposition. 2. Rifampicin treatment resulted in a decrease in systemic clearance and steady-state distribution volume, and an increase in half-life of atorvastatin. The hybrid model predicted higher unbound intracellular liver atorvastatin concentrations than unbound plasma concentrations in both rifampicin treated and untreated groups, indicating involvement of uptake transporters. The intracellular unbound concentrations during the distributive phase were unaffected by rifampicin. The dependence of clearance on blood flow as well as hepatic uptake for atorvastatin (a moderate-to-high extraction ratio drug) can explain this lack of change in intracellular concentrations if there is incomplete inhibition of transport at the tested rifampicin dose. 3. The hybrid model successfully allowed the evaluation of effect of active uptake on intracellular and plasma atorvastatin disposition.

Numerical analysis of time-dependent inhibition kinetics: comparison between rat liver microsomes and rat hepatocyte data for mechanistic model fitting.

Time-dependent inhibition (TDI) may confound drug interaction predictions. Recently, models were generated for an array of TDI kinetic schemes using numerical analysis of microsomal assays. Additionally, a distinct terminal inactivation step was identified for certain mechanism based inhibitors (MBI) following reversible metabolite intermediate complex (MIC) formation. Longer hepatocyte incubations potentially allow analysis of slow TDI and terminal inactivation. In the experiments presented here, we compared the quality of TDI parameterization by numerical analysis between hepatocyte and microsomal data. Rat liver microsomes (RLM), suspended rat hepatocytes (SRH) and sandwich-cultured rat hepatocytes (SCRH) were incubated with the prototypical CYP3A MBI troleandomycin and the substrate midazolam. Data from RLM provided a better model fit as compared to SRH. Increased CYP3A expression after dexamethasone (DEX) induction improved the fit for RLM and SRH. A novel sequential kinetic scheme, defining inhibitor metabolite production prior to MIC formation, improved the fit compared to direct MIC formation. Furthermore, terminal inactivation rate constants were parameterized for RLM and SRH samples with DEX-induced CYP3A. The low expression of CYP3A and experimental error in SCRH resulted in poor data for model fitting. Overall, RLM generated data better suited for elucidation of TDI mechanisms by numerical analysis.

Prediction of Tissue-Plasma Partition Coefficients Using Microsomal Partitioning: Incorporation into Physiologically based Pharmacokinetic Models and Steady-State Volume of Distribution Predictions.

Drug distribution is a necessary component of models to predict human pharmacokinetics. A new membrane-based tissue-plasma partition coefficient (K p) method (K p,mem) to predict unbound tissue to plasma partition coefficients (K pu) was developed using in vitro membrane partitioning [fraction unbound in microsomes (f um)], plasma protein binding, and log P The resulting K p values were used in a physiologically based pharmacokinetic (PBPK) model to predict the steady-state volume of distribution (V ss) and concentration-time (C-t) profiles for 19 drugs. These results were compared with K p predictions using a standard method [the differential phospholipid K p prediction method (K p,dPL)], which differentiates between acidic and neutral phospholipids. The K p,mem method was parameterized using published rat K pu data and tissue lipid composition. The K pu values were well predicted with R 2 = 0.8. When used in a PBPK model, the V ss predictions were within 2-fold error for 12 of 19 drugs for K p,mem versus 11 of 19 for Kp,dPL With one outlier removed for K p,mem and two for K p,dPL, the V ss predictions for R 2 were 0.80 and 0.79 for the K p,mem and K p,dPL methods, respectively. The C-t profiles were also predicted and compared. Overall, the K p,mem method predicted the V ss and C-t profiles equally or better than the K p,dPL method. An advantage of using f um to parameterize membrane partitioning is that f um data are used for clearance prediction and are, therefore, generated early in the discovery/development process. Also, the method provides a mechanistically sound basis for membrane partitioning and permeability for further improving PBPK models. SIGNIFICANCE STATEMENT: A new method to predict tissue-plasma partition coefficients was developed. The method provides a more mechanistic basis to model membrane partitioning.

Impact of Lipid Partitioning on the Design, Analysis, and Interpretation of Microsomal Time-Dependent Inactivation.

Nonspecific drug partitioning into microsomal membranes must be considered for in vitro-in vivo correlations. This work evaluated the effect of including lipid partitioning in the analysis of complex TDI kinetics with numerical methods. The covariance between lipid partitioning and multiple inhibitor binding was evaluated. Simulations were performed to test the impact of lipid partitioning on the interpretation of TDI kinetics, and experimental TDI datasets for paroxetine (PAR) and itraconazole (ITZ) were modeled. For most kinetic schemes, modeling lipid partitioning results in statistically better fits. For MM-IL simulations (KI,u = 0.1 µM, kinact = 0.1 minute-1), concurrent modeling of lipid partitioning for an fumic range (0.01, 0.1, and 0.5) resulted in better fits compared with post hoc correction (AICc: -526 vs. -496, -579 vs. -499, and -636 vs. -579, respectively). Similar results were obtained with EII-IL. Lipid partitioning may be misinterpreted as double binding, leading to incorrect parameter estimates. For the MM-IL datasets, when fumic = 0.02, MM-IL, and EII model fits were indistinguishable (δAICc = 3). For less partitioned datasets (fumic = 0.1 or 0.5), the inclusion of partitioning resulted in better models. The inclusion of lipid partitioning can lead to markedly different estimates of KI,u and kinact A reasonable alternate experimental design is nondilution TDI assays, with post hoc fumic incorporation. The best fit models for PAR (MIC-M-IL) and ITZ (MIC-EII-M-IL and MIC-EII-M-Seq-IL) were consistent with their reported mechanism and kinetics. Overall, experimental fumic values should be concurrently incorporated into TDI models with complex kinetics, when dilution protocols are used.

Methods to Predict Volume of Distribution.

PURPOSE OF REVIEW: Prior to human studies, knowledge of drug disposition in the body is useful to inform decisions on drug safety and efficacy, first in human dosing, and dosing regimen design. It is therefore of interest to develop predictive models for primary pharmacokinetic parameters, clearance, and volume of distribution. The volume of distribution of a drug is determined by the physiological properties of the body and physiochemical properties of the drug, and is used to determine secondary parameters, including the half-life. The purpose of this review is to provide an overview of current methods for the prediction of volume of distribution of drugs, discuss a comparison between the methods, and identify deficiencies in current predictive methods for future improvement. RECENT FINDINGS: Several volumes of distribution prediction methods are discussed, including preclinical extrapolation, physiological methods, tissue composition-based models to predict tissue:plasma partition coefficients, and quantitative structure-activity relationships. Key factors that impact the prediction of volume of distribution, such as permeability, transport, and accuracy of experimental inputs, are discussed. A comparison of current methods indicates that in general, all methods predict drug volume of distribution with an absolute average fold error of 2-fold. Currently, the use of composition-based PBPK models is preferred to models requiring in vivo input. SUMMARY: Composition-based models perfusion-limited PBPK models are commonly used at present for prediction of tissue:plasma partition coefficients and volume of distribution, respectively. A better mechanistic understanding of important drug distribution processes will result in improvements in all modeling approaches.

Molecular Modeling of Drug-Transporter Interactions-An International Transporter Consortium Perspective.

Membrane transporters play diverse roles in the pharmacokinetics and pharmacodynamics of small-molecule drugs. Understanding the mechanisms of drug-transporter interactions at the molecular level is, therefore, essential for the design of drugs with optimal therapeutic effects. This white paper examines recent progress, applications, and challenges of molecular modeling of membrane transporters, including modeling techniques that are centered on the structures of transporter ligands, and those focusing on the structures of the transporters. The goals of this article are to illustrate current best practices and future opportunities in using molecular modeling techniques to understand and predict transporter-mediated effects on drug disposition and efficacy.Membrane transporters from the solute carrier (SLC) and ATP-binding cassette (ABC) superfamilies regulate the cellular uptake, efflux, and homeostasis of many essential nutrients and significantly impact the pharmacokinetics of drugs; further, they may provide targets for novel therapeutics as well as facilitate prodrug approaches. Because of their often broad substrate selectivity they are also implicated in many undesirable and sometimes life-threatening drug-drug interactions (DDIs).5,6.

Improved Predictions of Drug-Drug Interactions Mediated by Time-Dependent Inhibition of CYP3A.

Time-dependent inactivation (TDI) of cytochrome P450s (CYPs) is a leading cause of clinical drug-drug interactions (DDIs). Current methods tend to overpredict DDIs. In this study, a numerical approach was used to model complex CYP3A TDI in human-liver microsomes. The inhibitors evaluated included troleandomycin (TAO), erythromycin (ERY), verapamil (VER), and diltiazem (DTZ) along with the primary metabolites N-demethyl erythromycin (NDE), norverapamil (NV), and N-desmethyl diltiazem (NDD). The complexities incorporated into the models included multiple-binding kinetics, quasi-irreversible inactivation, sequential metabolism, inhibitor depletion, and membrane partitioning. The resulting inactivation parameters were incorporated into static in vitro-in vivo correlation (IVIVC) models to predict clinical DDIs. For 77 clinically observed DDIs, with a hepatic-CYP3A-synthesis-rate constant of 0.000 146 min-1, the average fold difference between the observed and predicted DDIs was 3.17 for the standard replot method and 1.45 for the numerical method. Similar results were obtained using a synthesis-rate constant of 0.000 32 min-1. These results suggest that numerical methods can successfully model complex in vitro TDI kinetics and that the resulting DDI predictions are more accurate than those obtained with the standard replot approach.