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PubMed1999

Analysis of PBPK models for risk characterization.

Adoption of a Bayesian framework for risk characterization permits the seamless integration of different kinds of information available in order to choose and parameterize risk models. It also becomes easy to disentangle uncertainty from variability, through hierarchical statistical modeling. Appropriate numerical techniques can be found, for example, in the recently developed arsenal of Markov chain, Monte Carlo simulations. The developments in this area can actually be viewed as extensions of the traditional or standard Monte Carlo methods for uncertainty analysis. Following a brief review of the techniques, examples of Bayesian analyses of physiologically-based pharmacokinetic models are presented for tetrachloroethylene and dichloromethane. The discussion touches on some open problems and perspectives for the proposed methods.

Bayes Theorem↗
PubMed2000

Statistical analysis of Fisher et al. PBPK model of trichloroethylene kinetics.

Two physiologically based pharmacokinetic models for trichloroethylene (TCE) in mice and humans were calibrated with new toxicokinetic data sets. Calibration is an important step in model development, essential to a legitimate use of models for research or regulatory purposes. A Bayesian statistical framework was used to combine prior information about the model parameters with the data likelihood to yield posterior parameter distributions. For mice, these distributions represent uncertainty. For humans, the use of a population statistical model yielded estimates of both variability and uncertainty in human toxicokinetics of TCE. After adjustment of the models by Markov chain Monte Carlo sampling, the mouse model agreed with a large part of the data. Yet, some data on secondary metabolites were not fit well. The posterior parameter distributions obtained for mice were quite narrow (coefficient of variation [CV] of about 10 or 20%), but these CVs might be underestimated because of the incomplete fit of the model. The data fit, for humans, was better than for mice. Yet, some improvement of the model is needed to correctly describe trichloroethanol concentrations over long time periods. Posterior uncertainties about the population means corresponded to 10-20% CV. In terms of human population variability, volumes and flows varied across subject by approximately 20% CV. The variability was somewhat higher for partition coefficients (between 30 and 40%) and much higher for the metabolic parameters (standard deviations representing about a factor of 2). Finally, the analysis points to differences between human males and females in the toxicokinetics of TCE. The significance of these differences in terms of risk remains to be investigated.

Animals↗
PubMed2000

Statistical analysis of Clewell et al. PBPK model of trichloroethylene kinetics.

A physiologically based pharmacokinetic model for trichloroethylene (TCE) in rodents and humans was calibrated with published toxicokinetic data sets. A Bayesian statistical framework was used to combine previous information about the model parameters with the data likelihood, to yield posterior parameter distributions. The use of the hierarchical statistical model yielded estimates of both variability between experimental groups and uncertainty in TCE toxicokinetics. After adjustment of the model by Markov chain Monte Carlo sampling, estimates of variability for the animal or human metabolic parameters ranged from a factor of 1.5-2 (geometric standard deviation [GSD]). Uncertainty was of the same order as variability for animals and higher than variability for humans. The model was used to make posterior predictions for several measures of cancer risk. These predictions were affected by both uncertainties and variability and exhibited GSDs ranging from 2 to 6 in mice and rats and from 2 to 10 for humans.

Animals↗
PubMed2003

Whole body pharmacokinetic models.

The aim of the current review is to summarise the present status of physiologically based pharmacokinetic (PBPK) modelling and its applications in drug research, and thus serve as a reference point to people interested in the methodology. The review is structured into three major sections. The first discusses the existing methodologies and techniques of PBPK model development. The second describes some of the most interesting PBPK model implementations published. The final section is devoted to a discussion of the current limitations and the possible future developments of the PBPK modelling approach. The current review is focused on papers dealing with the pharmacokinetics and/or toxicokinetics of medicinal compounds; references discussing PBPK models of environmental compounds are mentioned only if they represent considerable methodological developments or reveal interesting interpretations and/or applications.The major conclusion of the review is that, despite its significant potential, PBPK modelling has not seen the development and implementation it deserves, especially in the drug discovery, research and development processes. The main reason for this is that the successful development and implementation of a PBPK model is seen to require the investment of significant experience, effort, time and resources. Yet, a substantial body of PBPK-related research has been accumulated that can facilitate the PBPK modelling and implementation process. What is probably lagging behind is the expertise component, where the demand for appropriately qualified staff far outreaches availability.

Humans↗
PubMed2006

A novel strategy for physiologically based predictions of human pharmacokinetics.

BACKGROUND: The major aim of this study was to develop a strategy for predicting human pharmacokinetics using physiologically based pharmacokinetic (PBPK) modelling. This was compared with allometry (of plasma concentration-time profiles using the Dedrick approach), in order to determine the best approaches and strategies for the prediction of human pharmacokinetics. METHODS: PBPK and Dedrick predictions were made for 19 F. Hoffmann-La Roche compounds. A strategy for the prediction of human pharmacokinetics using PBPK modelling was proposed in this study. Predicted values (pharmacokinetic parameters, plasma concentrations) were compared with observed values obtained after intravenous and oral administration in order to assess the accuracy of the prediction methods. RESULTS: By following the proposed strategy for PBPK, a prediction would have been made prospectively for approximately 70% of the compounds. The prediction accuracy for these compounds in terms of the percentage of compounds with an average-fold error of <2-fold was 83%, 50%, 75%, 67%, 92% and 100% for apparent oral clearance (CL/F), apparent volume of distribution during terminal phase after oral administration (V(z)/F), terminal elimination half-life (t(1/2)), peak plasma concentration (C(max)), area under the plasma concentration-time curve (AUC) and time to reach C(max) (t(max)), respectively. For the other 30% compounds, unacceptable prediction accuracy was obtained in animals; therefore, a prospective prediction of human pharmacokinetics would not have been made using PBPK. For these compounds, prediction accuracy was also poor using the Dedrick approach. In the majority of cases, PBPK gave more accurate predictions of pharmacokinetic parameters and plasma concentration-time profiles than the Dedrick approach. CONCLUSIONS: Based on the dataset evaluated in this study, PBPK gave reasonable predictions of human pharmacokinetics using preclinical data and is the recommended approach in the majority of cases. In addition, PBPK modelling is a useful tool to gain insights into the properties of a compound. Thus, PBPK can guide experimental efforts to obtain the relevant information necessary to understand the compound's properties before entry into human, ultimately resulting in a higher level of prediction accuracy.

Animals↗
PubMed2002

Prediction of pharmacokinetics prior to in vivo studies. II. Generic physiologically based pharmacokinetic models of drug disposition.

Many in vitro data on physicochemical properties and specific absorption, distribution, metabolism, and elimination (ADME) processes are already available at early stages of drug discovery. These data about new drug candidates could be integrated/connected in physiologically based pharmacokinetic (PBPK) models to estimate a priori the overall plasma and tissue kinetic behaviors under in vivo conditions. The objective of the present study was to illustrate that generic PBPK models integrating such data can be developed in drug discovery prior to any in vivo studies. This approach was illustrated with three example compounds, including two lipophilic bases (diazepam, propranolol) and one neutral more hydrophilic drug (ethoxybenzamide). Distribution and liver metabolism were the processes integrated in the generic rat PBPK models of disposition. Tissue:plasma partition coefficients (P(t:p)s) used for description of distribution were estimated from established tissue composition-based equations, which need only in vitro data on drug lipophilicity and plasma protein binding as sole input parameters. Furthermore, data on intrinsic clearance (CL(int)) determined in vitro with hepatocytes were scaled to the in vivo situation to estimate hepatic metabolic clearance. These prediction approaches were both incorporated in the PBPK models to enable automated estimation of distribution and liver metabolism for each drug studied. The generic PBPK models suggested can simulate a priori concentration-time profiles of plasma and several tissues after intravenous administrations to rat. The results indicate that most of the simulated concentration-time profiles of plasma and 10 tissues are in reasonable agreement with the corresponding experimental data determined in vivo (less than a factor of two). However, some more relevant deviations were observed for specific tissues (brain and gut for diazepam; liver and gut for ethoxybenzamide; lung for propranolol) because of important ADME processes were probably neglected in the PBPK models of these drugs. In this context, generic PBPK models were also used for mechanistic evaluations of pharmacokinetics for generating research hypotheses to understand these deviations. Overall, the present generic and integrative PBPK approach of drug disposition suggested as a tool for a priori simulations and mechanistic evaluations of pharmacokinetics has the potential to improve the selection and optimization of new drug candidates.

Animals↗
PubMed1995

Perspectives in pharmacokinetics. Physiologically based pharmacokinetic modeling as a tool for drug development.

Since the pioneering work of Haggard and Teorell in the first half of the 20th century, and of Bischoff and Dedrick in the late 1960s, physiologically based pharmacokinetic (PBPK) modeling has gone through cycles of general acceptance, and of healthy skepticism. Recently, however, the trend in the pharmaceuticals industry has been away from PBPK models. This is understandable when one considers the time and effort necessary to develop, test, and implement a typical PBPK model, and the fact that in the present-day environment for drug development, efficacy and safety must be demonstrated and drugs brought to market more rapidly. Although there are many modeling tools available to the pharmacokineticist today, many of which are preferable to PBPK modeling in most circumstances, there are several situations in which PBPK modeling provides distinct benefits that outweigh the drawbacks of increased time and effort for implementation. In this Commentary, we draw on our experience with this modeling technique in an industry setting to provide guidelines on when PBPK modeling techniques could be applied in an industrial setting to satisfy the needs of regulatory customers. We hope these guidelines will assist researchers in deciding when to apply PBPK modeling techniques. It is our contention that PBPK modeling should be viewed as one of many modeling tools for drug development.

Animals↗
PubMed1996

A distributed parameter physiologically-based pharmacokinetic model for dermal and inhalation exposure to volatile organic compounds.

Estimates of dermal dose from exposures to toxic chemicals are typically derived using models that assume instantaneous establishment of steady-state dermal mass flux. However, dermal absorption theory indicates that this assumption is invalid for short-term exposures to volatile organic chemicals (VOCs). A generalized distributed parameter physiologically-based pharmacokinetic model (DP-PBPK), which describes unsteady state dermal mass flux via a partial differential equation (Fickian diffusion), has been developed for inhalation and dermal absorption of VOCs. In the present study, the DP-PBPK model has been parameterized for chloroform, and compared with two simpler PBPK models of chloroform. The latter are lumped parameter models, employing ordinary differential equations, that do not account for the dermal absorption time lag associated with the accumulation of permeant chemical in tissue represented by permeability coefficients. All three models were evaluated by comparing simulated post-exposure exhaled breath concentration profiles with measured concentrations following environmental chloroform exposures. The DP-PBPK model predicted a time-lag in the exhaled breath concentration profile, consistent with the experimental data. The DP-PBPK model also predicted significant volatilization of chloroform, for a simulated dermal exposure scenario. The end-exposure dermal dose predicted by the DP-PBPK model is similar to that predicted by the EPA recommended method for short-term exposures, and is significantly greater than the end-exposure dose predicted by the lumped parameter models. However, the net dermal dose predicted by the DP-PBPK model is substantially less than that predicted by the EPA method, due to the post-exposure volatilization predicted by the DP-PBPK model. Moreover, the net dermal dose of chloroform predicted by all three models was nearly the same, even though the lumped parameter models did not predict substantial volatilization.

Absorption↗
PubMedDate not supplied

An approach for incorporating tissue composition data into physiologically based pharmacokinetic models.

The objective of this study was to develop an approach for incorporating tissue composition data into physiologically based pharmacokinetic (PBPK) models in order to facilitate "built-in" calculation of tissue: air partition coefficients (PCs) of volatile organic chemicals. The approach involved characterizing tissue compartments within PBPK models as a mixture of neutral lipids, phospholipids, and water (instead of using the conventional description of them as "empty" boxes). This approach enabled automated calculation of the tissue solubility of chemicals from n-octanol and water solubility data, since these data approximate those of solubility in tissue lipids and water. Tissue solubility was divided by the saturable vapor concentration at 37 degrees C to estimate the tissue: air PCs within PBPK models, according to the method of Poulin and Krishnan (1995c). The highest and lowest lipid and water levels for human muscle, liver, and adipose tissues were obtained from the literature and incorporated within the tissue composition-based PBPK model to calculate the tissue: air PCs of dichloromethane (DCM) and simulate the pharmacokinetics of DCM in humans. The PC values predicted for human tissues were comparable to those estimated using rat tissues in cases where the relative levels of lipids and water were comparable in both species. These results suggest that the default assumption of using rat tissue: air PCs in human PBPK models may be acceptable for certain tissues (liver, adipose tissues), but questionable for others (e.g., muscle). The PBPK modeling exercise indicated that the interindividual differences in tissue dose arising from variations of tissue: air PCs may not be reflected sufficiently by venous blood concentrations. Overall, the present approach of incorporating tissue composition data into PBPK models would not only enhance the biological basis of these models but also provide a means of evaluating the impact of interindividual and interspecies differences in tissue composition on the tissue dose surrogates used in PBPK-based risk assessments.

Adipose Tissue↗
PubMed1997

Physiologically based pharmacokinetic modeling of a ternary mixture of alkyl benzenes in rats and humans.

The objective of the present study was to develop a physiologically based pharmacokinetic (PBPK) model for a ternary mixture of alkyl benzenes [toluene (TOL), m-xylene (XYL), and ethylbenzene (EBZ)] in rats and humans. The approach involved the development of the mixture PBPK model in the rat and extrapolation to humans by substituting rat physiological parameters and blood:air partition coefficients in the model with those of humans, scaling maximal velocity for metabolism on the basis of body weight0.75 and keeping all other model parameters species-invariant. The development of the PBPK model for the ternary mixture in the rat was accomplished by initially validating or refining the existing PBPK models for TOL, XYL, and EBZ and linking the individual chemical models via the hepatic metabolism term. Accordingly, the Michaelis-Menten equation for each solvent was modified to test four possible mechanisms of metabolic interaction (i.e., no interaction, competitive inhibition, noncompetitive inhibition, and uncompetitive inhibition). The metabolic inhibition constant (Ki) for each binary pair of alkyl benzenes was estimated by fitting the binary chemical PBPK model simulations to previously published data on blood concentrations of TOL, XYL, and EBZ in rats exposed for 4 hr to a binary combination of 100 or 200 ppm of each of these solvents. Competitive metabolic inhibition appeared to be the most plausible mechanism of interaction at relevant exposure concentrations for all binary mixtures of alkyl benzenes in the rat (Ki,TOL-XYL = 0.17; Ki,TOL-EBZ = 0.79; Ki,XYL-TOL = 0.77; Ki,XYL-EBZ = 1.50; Ki,EBZ-TOL = 0.33; Ki,EBZ-XYL = 0.23 mg/L). Incorporating the Ki values obtained with the binary chemical mixtures, the PBPK model for the ternary mixture simulated adequately the time course of the venous blood concentrations of TOL, XYL, and EBZ in rats exposed to a mixture containing 100 ppm each of these solvents. Following the validation of the ternary mixture model in the rat, it was scaled to predict the kinetics of TOL, XYL, and EBZ in blood and alveolar air of human volunteers exposed for 7 hr to a combination of 17, 33, and 33 ppm, respectively, of these solvents. Model simulations and experimental data obtained in humans indicated that exposure to atmospheric concentrations of TOL, XYL, and EBZ that remain within the permissible concentrations for a mixture would not result in biologically significant modifications of their pharmacokinetics. Overall, this study demonstrates the utility of PBPK models in the prediction of the kinetics of components of chemical mixtures, by accounting for mechanisms of binary chemical interactions.

Animals↗
PubMed2002

Use of a hybrid computational fluid dynamics and physiologically based inhalation model for interspecies dosimetry comparisons of ester vapors.

Numerous inhalation studies have demonstrated that exposure to high concentrations of a wide range of volatile acids and esters results in cytotoxicity to the nasal olfactory epithelium. Previously, a hybrid computational fluid dynamics (CFD) and physiologically based pharmacokinetic (PBPK) dosimetry model was constructed to estimate the regional tissue dose of organic acids in the rodent and human nasal cavity. This study extends this methodology to a representative volatile organic ester, ethyl acrylate (EA). An in vitro exposure of explants of rat olfactory epithelium to EA with and without an esterase inhibitor demonstrated that the organic acid, acrylic acid, released by nasal esterases is primarily responsible for the olfactory cytotoxicity. Estimates of the steady-state concentration of acrylic acid in olfactory tissue were made for the rat nasal cavity by using data from a series of short-term in vivo studies and from the results of CFD-PBPK computer modeling. Appropriate parameterization of the CFD-PBPK model for the human nasal cavity and to accommodate human systemic anatomy, metabolism, and physiology allowed interspecies dose comparisons. The CFD-PBPK model simulations indicate that the olfactory epithelium of the human nasal cavity is exposed to at least 18-fold lower tissue concentrations of acid released from EA than the olfactory epithelium of the rat nasal cavity under the same exposure conditions. The magnitude of this difference varies with the specific exposure scenario that is simulated and with the specific dataset of human esterase activity used for the simulations. The increased olfactory tissue dose in rats relative to humans may be attributed to both the vulnerable location of the rodent olfactory tissue (comprising greater than 50% of the nasal cavity) and the high concentration of rat olfactory esterase activity (comparable to liver esterase activity) relative to human olfactory tissue. These studies suggest that the human olfactory epithelium is protected from vapors of organic esters significantly better than rat olfactory epithelium due to substantive differences in nasal anatomy, nasal and systemic metabolism, systemic physiology, and air flow. Although the accumulation of acrylic acid in the nasal tissues may be a primary concern for nasal irritation and human risk assessment, acute animal inhalation studies to evaluate lethality (LD50-type studies) conducted at very high vapor concentrations of ethyl acrylate indicated that a different mechanism is primarily responsible for mortality. The rodent studies demonstrated that systemic tissue nonprotein sulfhydryl depletion is a primary cause of death at exposure concentrations more than two orders of magnitude above the concentrations that induce nasal irritation. The CFD-PBPK model adequately simulated the severe depletion of glutathione in systemic tissues (e.g., liver and lung) associated with acute inhalation exposures in the 500-1000 ppm range. These results indicate that the CFD-PBPK model can simulate both the low-dose nasal tissue dosimetry associated with irritation and the high-dose systemic tissue dosimetry associated with mortality. In addition, the comparison of simulation results for ethyl acetate and acetone to nasal deposition data suggests that the CFD-PBPK model has general utility as a tool for dosimetry estimates for a wide range of other esters and slowly metabolized vapors.

Acrylates↗
PubMed1995

Development of physiologically based pharmacokinetic and physiologically based pharmacodynamic models for applications in toxicology and risk assessment.

Pharmacokinetics (PK) involves the study of the rates of absorption, distribution, excretion, and biotransformation of chemicals and their metabolites. PK models can be used to reconstruct extensive time-course data sets based on a small number of kinetic parameters. These models can be used to predict the results of new experiments and integrate studies on kinetics, disposition and metabolism in various animal species [1]. The 2 main approaches that have been pursued in developing PK models are: (1) data-based compartmental modeling; and (2) physiologically based compartmental modeling. Data-based models rely on the collection of time-course concentration data and fitting these data with mathematical models. Compartments in these models do not necessarily reflect the anatomy and physiology of the animal, and the kinetic constants derived from these models do not have obvious physiological or biochemical counterparts. In physiologically based pharmacokinetic (PBPK) models, compartments correspond more closely to actual anatomical structures, defined with respect to their volumes, blood flows, chemical binding (partitioning) characteristics, and ability to metabolize or excrete the compounds of interest. Because the kinetic parameters of these models reflect tissue blood flows, partitioning, and biochemical constants, these models are more readily scaled from one animal species to another [2]. PBPK models have been used to understand the disposition of chemicals in the body for almost 70 years. Their more widespread application in toxicology dates back only 15 years or so to models developed for polychlorinated biphenyls and other persistent lipophilic compounds. Quantitative applications of PBPK models in risk assessment date to the development of a number of PBPK models for methylene chloride in the mid 1980s. The burgeoning use of PBPK models in toxicology research and chemical risk assessment today is primarily related to their ability to make more accurate predictions of target tissue dose for different exposure situations in different animal species, including humans. This overview includes a discussion of the development of these PBPK models in toxicology and speculates about future applications of PBPK and physiologically based pharmacodynamic (PBPD) models in chemical risk assessment.

Animals↗
PubMed1996

Incorporating Monte Carlo simulation into physiologically based pharmacokinetic models using advanced continuous simulation language (ACSL): a computational method.

Biologically based models with physiological parameters are becoming more popular as a tool to estimate target tissue doses from chemical exposures. However, the majority of current physiologically based pharmacokinetic (PBPK) models do not take into account the uncertainty and/or variability within the various model parameters. Consideration of uncertainty is important to evaluate the predictive ability and complexity of a model as well as identification of parameters which contribute disproportionately to variability in model output. In order to estimate the uncertainty in PBPK model output, a versatile and simple computational method is presented which can be readily incorporated into the majority of PBPK models without extensive additions to model computer code. In this paper, a separate computer program for Monte Carlo simulation is furnished that randomly samples values for model parameters and writes them into a run-time language (command file) format which can then be utilized to execute individual PBPK models. Modifications to the PBPK model allow the desired output to be written to a data file for statistical analysis. The method presented in this paper is applied to a simple PBPK model for benzene disposition.

Algorithms↗
PubMed2003

Toxicokinetic modeling and its applications in chemical risk assessment.

In recent years physiologically based pharmacokinetic (PBPK) modeling has found frequent application in risk assessments where PBPK models serve as important adjuncts to studies on modes of action of xenobiotics. In this regard, studies on mode of action provide insight into both the sites/mechanisms of action and the form of the xenobiotic associated with toxic responses. Validated PBPK models permit calculation of tissue doses of xenobiotics and metabolites for a variety of conditions, i.e. at low-doses, in different animal species, and in different members of a human population. In this manner, these PBPK models support the low-dose and interspecies extrapolations that are important components of current risk assessment methodologies. PBPK models are sometimes referred to as physiological toxicokinetic (PT) models to emphasize their application with compounds causing toxic responses. Pharmacokinetic (PK) modeling in general has a rich history. Data-based PK compartmental models were developed in the 1930's when only primitive tools were available for solving sets of differential equations. These models were expanded in the 1960's and 1970's to accommodate new observations on dose-dependent elimination and flow-limited metabolism. The application of clearance concepts brought many new insights about the disposition of drugs in the body. In the 1970's PBPK/PT models were developed to evaluate metabolism of volatile compounds of occupational importance, and, for the first time, dose-dependent processes in toxicology were included in PBPK models in order to assess the conditions under which saturation of metabolic and elimination processes lead to non-linear dose response relationships. In the 1980's insights from chemical engineers and occupational toxicology were combined to develop PBPK/PT models to support risk assessment with methylene chloride and other solvents. The 1990's witnessed explosive growth in risk assessment applications of PBPK/PT models and in applying sensitivity and variability methods to evaluate model performance. Some of the compounds examined in detail include butadiene, styrene, glycol ethers, dioxins and organic esters/aids. This paper outlines the history of PBPK/PT modeling, emphasizes more recent applications of PBPK/TK models in health risk assessment, and discusses the risk assessment perspective provided by modern uses of these modeling approaches.

Animals↗
PubMed2003

Reduction and lumping of physiologically based pharmacokinetic models: prediction of the disposition of fentanyl and pethidine in humans by successively simplified models.

Physiologically based pharmacokinetic (PBPK) models can be used to predict drug disposition in humans from animal data and the influence of disease or other changes in physiology on the pharmacokinetics of a drug. The potential usefulness of a PBPK model must however be balanced against the considerable effort needed for its development. Proposed methods to simplify PBPK modeling include predicting the necessary tissue:blood partition coefficients (kp) from physicochemical data on the drug instead of determining them in vivo, formal lumping of model compartments, and replacing the various kp values of the organs and tissues by only two values, for "fat" and "lean" tissues, respectively. The aim of this study was to investigate the effects of simplifying complex PBPK models on their ability to predict drug disposition in humans. Arterial plasma concentration curves of fentanyl and pethidine were simulated by means of a number of successively reduced models. Median absolute prediction errors were used to evaluate the performance of each model, in relation to arterial plasma concentration data from clinical studies, and the Wilcoxon matched pairs test was used for comparison of predictions. An originally diffusion-limited model for fentanyl was simplified to perfusion-limitation, and this model was either lumped, reducing 11 organ/tissue compartments to six, or changed to a model based on only two kp values, those of fat (used for fat and lungs) and muscle (used for all other tissues). None of these simplifications appreciably changed the predictions of arterial drug concentrations in the 10 patients. Perfusion-limited models for pethidine were set up using either experimentally determined [Gabrielsson et al. 1986] or theoretically calculated [Davis and Mapleson 1993] kp values, and predictions using the former were found to be significantly better. Lumping of the models did not appreciably change the predictions; however, going from a full set of kp values to only two ("fat" and "lean") had an adverse effect. Using a kp for lungs determined either in rats or indirectly in humans [Persson et al. 1988], i.e., a total of three kp values, improved these predictions. In conclusion, this study strongly suggested that complex PBPK models for lipophilic basic drugs may be considerably reduced with marginal loss of power to predict standard plasma pharmacokinetics in humans. Determination of only two or three kp values instead of a "full" set can mean an important reduction of experimental work to define a basic model. Organs of particular pharmacological or toxicological interest should of course be investigated separately as needed. This study also suggests and applies a simple method for statistical evaluation of the predictions of PBPK models.

Adult↗