Interspecies Extrapolation of Physiological Pharmacokinetic Parameter Distributions

Three methods (multiplicative, additive, and allometric) were developed to extrapolate physiological model parameter distributions across species, specifically from rats to humans. In the multiplicative approach, the rat model parameters are multiplied by the ratio of the mean values between humans and rats. Additive scaling of the distributions is denned by adding the difference between the average human value and the average rat value to each rat value. Finally, allometric scaling relies on established extrapolation relationships using power functions of body weight. A physiologically-based pharmacokinetic model was fitted independently to rat and human benzene disposition data. Human model parameters obtained by extrapolation and by fitting were used to predict the total bone marrow exposure to benzene and the quantity of metabolites produced in bone marrow. We found that extrapolations poorly predict the human data relative to the human model. In addition, the prediction performance depends largely on the quantity of interest. The extrapolated models underpredict bone marrow exposure to benzene relative to the human model. Yet, predictions of the quantity of metabolite produced in bone marrow are closer to the human model predictions. These results indicate that the multiplicative and allometric techniques were able to extrapolate the model parameter distributions, but also that rats do not provide a good kinetic model of benzene disposition in humans.     

A Pharmacokinetic Study of Occupational and Environmental Benzene Exposure with Regard to Gender

Using physiologically-based pharmacokinetic (PBPK) modeling, occupational, personal, and environmental benzene exposure scenarios are simulated for adult men and women. This research identifies differences in internal exposure due to physiological and biochemical gender differences. Physiological and chemical-specific model parameters were obtained from other studies reported in the literature and medical texts for the subjects of interest. Women were found to have a higher blood/air partition coefficient and maximum velocity of metabolism for benzene than men (the two most sensitive parameters affecting gender-specific differences). Additionally, women generally have a higher body fat percentage than men. These factors influence the internal exposure incurred by the subjects and should be considered when conducting a risk assessment. Results demonstrated that physicochemical gender differences result in women metabolizing 23–26% more benzene than men when subject to the same exposure scenario even though benzene blood concentration levels are generally higher in men. These results suggest that women may be at significantly higher risk for certain effects of benzene exposure. Thus, exposure standards based on data from male subjects may not be protective for the female population.     

Steady-State Solutions to PBPK Models and Their Applications to Risk Assessment I: Route-to-Route Extrapolation of Volatile Chemicals

Although analysis of in vivo pharmacokinetic data necessitates use of time-dependent physiologically-based pharmacokinetic (PBPK) models, risk assessment applications are often driven primarily by steady-state and/or integrated (e.g., AUC) dosimetry. To that end, we present an analysis of steady-state solutions to a PBPK model for a generic volatile chemical metabolized in the liver. We derive an equivalent model that is much simpler and contains many fewer parameters than the full PBPK model. The state of the system can be specified by two state variables-the rate of metabolism and the rate of clearance by exhalation. For a given oral dose rate or inhalation exposure concentration, the system state only depends on the blood-air partition coefficient, metabolic constants, and the rates of blood flow to the liver and of alveolar ventilation. At exposures where metabolism is close to linear, only the effective first-order metabolic rate is needed. Furthermore, in this case, the relationship between cumulative exposure and average internal dose (e.g., AUCs) remains the same for time-varying exposures. We apply our analysis to oral-inhalation route extrapolation, showing that for any dose metric, route equivalence only depends on the parameters that determine the system state. Even if the appropriate dose metric is unknown, bounds can be placed on the route-to-route equivalence with very limited data. We illustrate this analysis by showing that it reproduces exactly the PBPK-model-based route-to-route extrapolation in EPA's 2000 risk assessment for vinyl chloride. Overall, we find that in many cases, steady-state solutions exactly reproduce or closely approximate the solutions using the full PBPK model, while being substantially more transparent. Subsequent work will examine the utility of steady-state solutions for analyzing cross-species extrapolation and intraspecies variability.     

A new mathematical approach for the estimation of the AUC and its variability under different experimental designs in preclinical studies

The aim of the present work was to develop a new mathematical method for estimating the area under the curve (AUC) and its variability that could be applied in different preclinical experimental designs and amenable to be implemented in standard calculation worksheets. In order to assess the usefulness of the new approach, different experimental scenarios were studied and the results were compared with those obtained with commonly used software: WinNonlin® and Phoenix WinNonlin®. The results do not show statistical differences among the AUC values obtained by both procedures, but the new method appears to be a better estimator of the AUC standard error, measured as the coverage of 95% confidence interval. In this way, the new proposed method demonstrates to be as useful as WinNonlin® software when it was applicable. Copyright © 2011 John Wiley & Sons, Ltd.     

Individual Prior Information in a Physiological Model of 2H8-Toluene Kinetics: An Empirical Bayes Estimation Strategy

Physiologically-based toxicokinetic (PBTK) models are widely used to quantify whole-body kinetics of various substances. However, since they attempt to reproduce anatomical structures and physiological events, they have a high number of parameters. Their identification from kinetic data alone is often impossible, and other information about the parameters is needed to render the model identifiable. The most commonly used approach consists of independently measuring, or taking from literature sources, some of the parameters, fixing them in the kinetic model, and then performing model identification on a reduced number of less certain parameters. This results in a substantial reduction of the degrees of freedom of the model. In this study, we show that this method results in final estimates of the free parameters whose precision is overestimated. We then compared this approach with an empirical Bayes approach, which takes into account not only the mean value, but also the error associated with the independently determined parameters. Blood and breath ²H₈-toluene washout curves, obtained in 17 subjects, were analyzed with a previously presented PBTK model suitable for person-specific dosimetry. Model parameters with the greatest effect on predicted levels were alveolar ventilation rate Q_PC, fat tissue fraction V_FC, blood-air partition coefficient K_b, fraction of cardiac output to fat Q_a/co and rate of extrahepatic metabolism V_max-p. Differences in the measured and Bayesian-fitted values of Q_PC, V_FC and K_b were significant (p < 0.05), and the precision of the fitted values V_max-p and Q_a/co went from 11 ± 5% to 75 ± 170% (NS) and from 8 ± 2% to 9 ± 2% (p < 0.05) respectively. The empirical Bayes approach did not result in less reliable parameter estimates: rather, it pointed out that the precision of parameter estimates can be overly optimistic when other parameters in the model, either directly measured or taken from literature sources, are treated as known without error. In conclusion, an empirical Bayes approach to parameter estimation resulted in a better model fit, different final parameter estimates, and more realistic parameter precisions.     

The Impact of Cytochrome P450 2E1-Dependent Metabolic Variance on a Risk-Relevant Pharmacokinetic Outcome in Humans

Risk assessments include assumptions about sensitive subpopulations, such as the fraction of the general population that is sensitive and the extent that biochemical or physiological attributes influence sensitivity. Uncertainty factors (UF) account for both pharmacokinetic (PK) and pharmacodynamic (PD) components, allowing the inclusion of risk-relevant information to replace default assumptions about PK and PD variance (uncertainty). Large numbers of human organ donor samples and recent advances in methods to extrapolate in vitro enzyme expression and activity data to the intact human enable the investigation of the impact of PK variability on human susceptibility. The hepatotoxicity of trichloroethylene (TCE) is mediated by acid metabolites formed by cytochrome P450 2E1 (CYP2E1) oxidation, and differences in the CYP2E1 expression are hypothesized to affect susceptibility to TCE's liver injury. This study was designed specifically to examine the contribution of statistically quantified variance in enzyme content and activity on the risk of hepatotoxic injury among adult humans. We combined data sets describing (1) the microsomal protein content of human liver, (2) the CYP2E1 content of human liver microsomal protein, and (3) the in vitro Vmax for TCE oxidation by humans. The 5th and 95th percentiles of the resulting distribution (TCE oxidized per minute per gram liver) differed by approximately sixfold. These values were converted to mg TCE oxidized/h/kg body mass and incorporated in a human PBPK model. Simulations of 8-hour inhalation exposure to 50 ppm and oral exposure to 5 micro g TCE/L in 2 L drinking water showed that the amount of TCE oxidized in the liver differs by 2% or less under extreme values of CYP2E1 expression and activity (here, selected as the 5th and 95th percentiles of the resulting distribution). This indicates that differences in enzyme expression and TCE oxidation among the central 90% of the adult human population account for approximately 2% of the difference in production of the risk-relevant PK outcome for TCE-mediated liver injury. Integration of in vitro metabolism information into physiological models may reduce the uncertainties associated with risk contributions of differences in enzyme expression and the UF that represent PK variability.     

Modeling Human Interindividual Variability in Metabolism and Risk: The Example of 4-Aminobiphenyl

We investigate, through modeling, the impact of interindividual heterogeneity in the metabolism of 4-aminobiphenyl (ABP) and in physiological factors on human cancer risk: A physiological pharmacokinetic model was used to quantify the time course of the formation of the proximate carcinogen, N-hydroxy-4-ABP and the DNA-binding of the active species in the bladder. The metabolic and physiologic model parameters were randomly varied, via Monte Carlo simulations, to reproduce interindividual variability. The sampling means for most parameters were scaled from values developed by Kadlubar et al. (Cancer Res., 51 : 4371, 1991) for dogs; variances were obtained primarily from published human data (e.g., measurements of ABP N-oxidation, and arylamine N-acetylation in human liver tissue). In 500 simulations, theoretically representing 500 humans, DNA-adduct levels in the bladder of the most susceptible individuals are ten thousand times higher than for the least susceptible, and the 5th and 95th percentiles differ by a factor of 160. DNA binding for the most susceptible individual (with low urine pH, low N-acetylation and high N-oxidation activities) is theoretically one million-fold higher than for the least susceptible (with high urine pH, high N-acetylation and low N-oxidation activities). The simulations also suggest that the four factors contributing most significantly to interindividual differences in DNA-binding of ABP in human bladder are urine pH, ABP N-oxidation, ABP N-acetylation and urination frequency.     

Physiologically-Based Pharmacokinetic Model for Trichloroethylene Considering Enterohepatic Recirculation of Major Metabolites

Trichloroacetic acid (TCA) is major metabolite of trichloroethylene (TRI) thought to contribute to its hepatocarcinogenic effects in mice. Recent studies have shown that peak blood concentrations of TCA in rats do not occur until approximately 12 hours following an oral dose of TRI. However, blood concentrations of TRI reach maximum within an hour and are nondetectable after 2 hours.⁽¹⁾ The results of study which examined the enterohepatic recirculation (EHC) of the principle TRI metabolited⁽²⁾ was used to develop physiologically-based pharmacokinetic model for TRI, which includes enterohepatic recirculation of its metabolites. The model quantitatively predicts the uptake, distribution and elimination of TRI, trichloroethanol, trichloroethanol-glucuronide, and TCA and includes production of metabolites through the enterohepatic recirculation pathway. Physiologic parameters used in the model were obtained from the literature.^(3.4) Parameters for TRI metabolism were taken from Fisher et al.⁽⁵⁾ Other kinetic parameters were found in the literature or estimated from experimental data.⁽²⁾ The model was calibrated to data from experiments of an earlier study where TRI was orally administered⁽²⁾ Verification of the model was conducted using data on the enterohepatic recirculation of TCEOH and TCA⁽²⁾ chloral hydrate data (infusion doses) from Merdink,⁽¹⁾ and TRI data from Templin(l) and Larson and Bull.⁽¹⁾     

Differences in Pharmacokinetics Between Children and Adults—II. Children''s Variability in Drug Elimination Half-Lives and in Some Parameters Needed for Physiologically-Based Pharmacokinetic Modeling

In earlier work we assembled a database of classical pharmacokinetic parameters (e.g., elimination half-lives; volumes of distribution) in children and adults. These data were then analyzed to define mean differences between adults and children of various age groups. In this article, we first analyze the variability in half-life observations where individual data exist. The major findings are as follows. The age groups defined in the earlier analysis of arithmetic mean data (0-1 week premature; 0-1 week full term; 1 week to 2 months; 2-6 months; 6 months to 2 years; 2-12 years; and 12-18 years) are reasonable for depicting child/adult pharmacokinetic differences, but data for some of the earliest age groups are highly variable. The fraction of individual children's half-lives observed to exceed the adult mean half-life by more than the 3.2-fold uncertainty factor commonly attributed to interindividual pharmacokinetic variability is 27% (16/59) for the 0-1 week age group, and 19% (5/26) in the 1 week to 2 month age group, compared to 0/87 for all the other age groups combined between 2 months and 18 years. Children within specific age groups appear to differ from adults with respect to the amount of variability and the form of the distribution of half-lives across the population. The data indicate departure from simple unimodal distributions, particularly in the 1 week to 2 month age group, suggesting that key developmental steps affecting drug removal tend to occur in that period. Finally, in preparation for age-dependent physiologically-based pharmacokinetic modeling, nationally representative NHANES III data are analyzed for distributions of body size and fat content. The data from about age 3 to age 10 reveal important departures from simple unimodal distributional forms-in the direction suggesting a subpopulation of children that are markedly heavier than those in the major mode. For risk assessment modeling, this means that analysts will need to consider "mixed" distributions (e.g., two or more normal or log-normal modes) in which the proportions of children falling within the major versus highweight/fat modes in the mixture changes as a function of age. Biologically, the most natural interpretation of this is that these subpopulations represent children who have or have not yet received particular signals for change in growth pattern. These apparently distinct subpopulations would be expected to exhibit different disposition of xenobiotics, particularly those that are highly lipophilic and poorly metabolized.     

Cardiac Sensitization Thresholds of Halon Replacement Chemicals Predicted in Humans by Physiologically-Based Pharmacokinetic Modeling

Human exposure to halons and halon replacement chemicals is often regulated on the basis of cardiac sensitization potential. The dose-response data obtained from animal testing are used to determine the no observable adverse effect level (NOAEL) and lowest observable adverse effect level (LOAEL) values. This approach alone does not provide the information necessary to evaluate the cardiac sensitization potential for the chemical of interest under a variety of exposure concentrations and durations. In order to provide a tool for decision-makers and regulators tasked with setting exposure guidelines for halon replacement chemicals, a quantitative approach was established which allowed exposures to be assessed in terms of the chemical concentrations in blood during the exposure. A physiologically-based pharmacokinetic (PBPK) model was used to simulate blood concentrations of Halon 1301 (bromotrifluoromethane, CF₃Br), HFC-125 (pentafluoroethane, CHF₂CF₃), HFC-227ea (heptafluoropropane, CF₃CHFCF₃), HCFC-123 (dichlorotrifluoroethane, CHCl₂CF₃), and CF₃I (trifluoroiodomethane) during inhalation exposures. This work demonstrates a quantitative approach for use in linking chemical inhalation exposures to the levels of chemical in blood achieved during the exposure.