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

Ecological risk assessment methods for oxidative by-products in the oxidation degradation process of emerging pollutants: A review

The inherent toxicity and persistence of emerging contaminants such as antibiotics and endocrine disruptors pose substantial threats to the environment. Advanced oxidation processes (AOPs) employed for oxidative degradation could yield toxic oxidation by-products (OBPs), including organic acids and aromatic hydrocarbons. Despite their typically low concentrations, OBPs require scrutiny owing to their potential health risks. Although effective assessment methodologies are available, a comprehensive review focusing on the ecological and environmental effects of these pollutants is lacking. This study offers a succinct overview of existing ecotoxicological exposure assessments for emerging organic pollutants. Further, it encapsulates principal dose-response assessment techniques and provides a comparative analysis of several methods. The straightforward assessment factor method evaluates risk based on exposure and species sensitivity and is suitable for preliminary assessments of single pollutants; Species Sensitivity Distribution (SSD) compares species sensitivities to OBPs, emphasizing the importance of species-specific toxicological responses; microcosm and mesocosm methods simulate and predict the effects of OBPs on aquatic life by considering environmental diversity and biological community structures and are ideal for assessing the toxicity of multiple OBPs; the ecological risk analysis model employs mathematical and probabilistic approaches to comprehensively and accurately assess exposures and effects, accounting for the complexities and uncertainties inherent in ecotoxicological evaluations. Different risk characterization techniques are outlined in this study, including the risk quotient (RQ), which is ideal for quantifying and comparing risks; probabilistic ecological risk assessment (PERA), suitable for managing significant uncertainty; and the Environmental Pollution Index (EPI), the preferred method for quantitative assessment of OBP pollution levels. The merits and limitations of each of these quantitative assessment tools are evaluated, providing a comprehensive view of their applications in risk analysis. In addition, pressing contemporary challenges are identified and trajectories and pivotal issues suggested for future research.

Effects and risk assessment of halogenated bisphenol A derivatives on human follicle stimulating hormone receptor: An interdisciplinary study

Halogenated bisphenol A (BPA) derivatives are produced during disinfection treatment of drinking water or are synthesized as flame retardants (TCBPA or TBBPA). BPA is considered as an endocrine disruptor especially on human follicle-stimulating hormone receptor (FSHR). Using a global experimental approach, we assessed the effect of halogenated BPA derivatives on FSHR activity and estimated the risk of halogenated BPA derivatives to the reproductive health of exposed populations. For the first time, we show that FSHR binds halogenated BPA derivatives, at 10 nM, a concentration lower than those requires to modulate the activity of nuclear receptors and/or steroidogenesis enzymes. Indeed, bioluminescence assays show that FSHR response is lowered up to 42.36 % in the presence of BPA, up to 32.79 % by chlorinated BPA derivatives and up to 27.04 % by brominated BPA derivatives, at non-cytotoxic concentrations and without modification of basal receptor activity. Moreover, molecular docking, molecular dynamics simulations, and site-directed mutagenesis experiments demonstrate that the halogenated BPA derivatives bind the FSHR transmembrane domain reducing the signal transduction efficiency which lowers the cellular cAMP production and in fine disrupts the physiological effect of FSH. The potential reproductive health risk of exposed individuals was estimated by comparing urinary concentrations (through a collection of human biomonitoring data) with the lowest effective concentrations derived from in vitro cell assays. Our results suggest a potentially high concern for the risk of inhibition of the FSHR pathway. This global approach based on FSHR activity could enable the rapid characterization of the toxicity of halogenated BPA derivatives (or other compounds) and assess the associated risk of exposure to these halogenated BPA derivatives.

ADME characterization and PBK model development of 3 highly protein-bound UV filters through topical application

Estimating human exposure in the safety assessment of chemicals is crucial. Physiologically based kinetic (PBK) models which combine information on exposure, physiology, and chemical properties, describing the absorption, distribution, metabolism, and excretion (ADME) processes of a chemical, can be used to calculate internal exposure metrics such as maximum concentration and area under the concentration-time curve in plasma or tissues of a test chemical in next-generation risk assessment. This article demonstrates the development of PBK models for 3 UV filters, specifically octyl methoxycinnamate, octocrylene, and 4-methylbenzylidene camphor. The models were parameterized entirely based on data obtained from in vitro and/or in silico methods in a bottom-up modeling approach and then validated based on human dermal pharmacokinetic (PK) data. The 3 UV filters are "difficult to test" in in vitro test systems due to high lipophilicity, high binding affinity for proteins, and nonspecific binding, for example, toward plastic. This research work presents critical considerations in ADME data generation, interpretation, and parameterization to assure valid PBK model development to increase confidence in using PBK modeling to help make safety decisions in the absence of human PK data. The developed PBK models of the 3 chemicals successfully simulated the plasma concentration profiles of clinical PK data following dermal application, indicating the reliability of the ADME data generated and the parameters determined. The study also provides insights and lessons learned for characterizing ADME and developing PBK models for highly lipophilic and protein-bound chemicals in the future.

Development, testing, parameterisation, and calibration of a human PBK model for the plasticiser, di (2-ethylhexyl) adipate (DEHA) using in silico, in vitro and human biomonitoring data

Introduction: A physiologically based biokinetic model for di (2-ethylhexyl) adipate (DEHA) based on a refined model for di-(2-propylheptyl) phthalate (DPHP) was developed to interpret the metabolism and biokinetics of DEHA following a single oral dosage of 50 mg to two male and two female volunteers. Methods: The model was parameterized using in vitro and in silico methods such as, measured intrinsic hepatic clearance scaled from in vitro to in vivo and algorithmically predicted parameters such as plasma unbound fraction and tissue:blood partition coefficients (PCs). Calibration of the DEHA model was achieved using concentrations of specific downstream metabolites of DEHA excreted in urine. The total fractions of ingested DEHA eliminated as specific metabolites were estimated and were sufficient for interpreting the human biomonitoring data. Results: The specific metabolites of DEHA, mono-2-ethyl-5-hydroxyhexyl adipate (5OH-MEHA), mono-2-ethyl-5-oxohexyl adipate (5oxo-MEHA), mono-5-carboxy-2-ethylpentyl adipate (5cx-MEPA) only accounted for ∼0.45% of the ingested DEHA. Importantly, the measurements of adipic acid, a non-specific metabolite of DEHA, proved to be important in model calibration. Discussion: The very prominent trends in the urinary excretion of the metabolites, 5cx-MEPA and 5OH-MEHA allowed the important absorption mechanisms of DEHA to be modelled. The model should be useful for the study of exposure to DEHA of the general human population.

Development, testing, parameterisation, and calibration of a human PBPK model for the plasticiser, di-(2-ethylhexyl) terephthalate (DEHTP) using in silico, in vitro and human biomonitoring data

A physiologically based pharmacokinetic model for di-(2-ethylhexyl) terephthalate (DEHTP) based on a refined model for di-(2-propylheptyl) phthalate (DPHP) was developed to interpret the metabolism and biokinetics of DEHTP following a single oral dose of 50 mg to three male volunteers. In vitro and in silico methods were used to generate parameters for the model. For example, measured intrinsic hepatic clearance scaled from in vitro to in vivo and plasma unbound fraction and tissue:blood partition coefficients (PCs) were predicted algorithmically. Whereas the development and calibration of the DPHP model was based upon two data streams, blood concentrations of parent chemical and first metabolite and the urinary excretion of metabolites, the model for DEHTP was calibrated against a single data stream, the urinary excretion of metabolites. Despite the model form and structure being identical significant quantitative differences in lymphatic uptake between the models were observed. In contrast to DPHP the fraction of ingested DEHTP entering lymphatic circulation was much greater and of a similar magnitude to that entering the liver with evidence for the dual uptake mechanisms discernible in the urinary excretion data. Further, the absolute amounts absorbed by the study participants, were much higher for DEHTP relative to DPHP. The in silico algorithm for predicting protein binding performed poorly with an error of more than two orders of magnitude. The extent of plasma protein binding has important implications for the persistence of parent chemical in venous blood-inferences on the behaviour of this class of highly lipophilic chemicals, based on calculations of chemical properties, should be made with extreme caution. Attempting read across for this class of highly lipophilic chemicals should be undertaken with caution since basic adjustments to PCs and metabolism parameters would be insufficient, even when the structure of the model itself is appropriate. Therefore, validation of a model parameterized entirely with in vitro and in silico derived parameters would need to be calibrated against several human biomonitoring data streams to constitute a data rich source chemical to afford confidence for future evaluations of other similar chemicals using the read-across approach.

Towards best use and regulatory acceptance of generic physiologically based kinetic (PBK) models for in vitro-to-in vivo extrapolation (IVIVE) in chemical risk assessment

With an increasing need to incorporate new approach methodologies (NAMs) in chemical risk assessment and the concomitant need to phase out animal testing, the interpretation of in vitro assay readouts for quantitative hazard characterisation becomes more important. Physiologically based kinetic (PBK) models, which simulate the fate of chemicals in tissues of the body, play an essential role in extrapolating in vitro effect concentrations to in vivo bioequivalent exposures. As PBK-based testing approaches evolve, it will become essential to standardise PBK modelling approaches towards a consensus approach that can be used in quantitative in vitro-to-in vivo extrapolation (QIVIVE) studies for regulatory chemical risk assessment based on in vitro assays. Based on results of an ECETOC expert workshop, steps are recommended that can improve regulatory adoption: (1) define context and implementation, taking into consideration model complexity for building fit-for-purpose PBK models, (2) harmonise physiological input parameters and their distribution and define criteria for quality chemical-specific parameters, especially in the absence of in vivo data, (3) apply Good Modelling Practices (GMP) to achieve transparency and design a stepwise approach for PBK model development for risk assessors, (4) evaluate model predictions using alternatives to in vivo PK data including read-across approaches, (5) use case studies to facilitate discussions between modellers and regulators of chemical risk assessment. Proof-of-concepts of generic PBK modelling approaches are published in the scientific literature at an increasing rate. Working on the previously proposed steps is, therefore, needed to gain confidence in PBK modelling approaches for regulatory use.

PBPK Modeling to Simulate the Fate of Compounds in Living Organisms

Pharmacokinetics study the fate of xenobiotics in a living organism. Physiologically based pharmacokinetic (PBPK) models provide realistic descriptions of xenobiotics' absorption, distribution, metabolism, and excretion processes. They model the body as a set of homogeneous compartments representing organs, and their parameters refer to anatomical, physiological, biochemical, and physicochemical entities. They offer a quantitative mechanistic framework to understand and simulate the time-course of the concentration of a substance in various organs and body fluids. These models are well suited for performing extrapolations inherent to toxicology and pharmacology (e.g., between species or doses) and for integrating data obtained from various sources (e.g., in vitro or in vivo experiments, structure-activity models). In this chapter, we describe the practical development and basic use of a PBPK model from model building to model simulations, through implementation with an easily accessible free software.

High-throughput PBTK models for in vitro to in vivo extrapolation

INTRODUCTION

Toxicity data are unavailable for many thousands of chemicals in commerce and the environment. Therefore, risk assessors need to rapidly screen these chemicals for potential risk to public health. High-throughput screening (HTS) for in vitro bioactivity, when used with high-throughput toxicokinetic (HTTK) data and models, allows characterization of these thousands of chemicals.

AREAS COVERED

This review covers generic physiologically based toxicokinetic (PBTK) models and high-throughput PBTK modeling for in vitro-in vivo extrapolation (IVIVE) of HTS data. We focus on 'httk', a public, open-source set of computational modeling tools and in vitro toxicokinetic (TK) data.

EXPERT OPINION

HTTK benefits chemical risk assessors with its ability to support rapid chemical screening/prioritization, perform IVIVE, and provide provisional TK modeling for large numbers of chemicals using only limited chemical-specific data. Although generic TK model design can increase prediction uncertainty, these models provide offsetting benefits by increasing model implementation accuracy. Also, public distribution of the models and data enhances reproducibility. For the httk package, the modular and open-source design can enable the tool to be used and continuously improved by a broad user community in support of the critical need for high-throughput chemical prioritization and rapid dose estimation to facilitate rapid hazard assessments.

Evaluation of Placental Transfer and Tissue Distribution of cis- and Trans-Permethrin in Pregnant Rats and Fetuses Using a Physiological-Based Pharmacokinetic Model

Biomonitoring studies have highlighted the exposure of pregnant women to pyrethroids based on the measurement of their metabolites in urine. Pyrethroids can cross the placental barrier and be distributed in the fetus as some pyrethroids were also measured in the meconium of newborns. Prenatal exposure to pyrethroids is suspected to alter the neurodevelopment of children, and animal studies have shown that early life exposure to permethrin, one of the most commonly used pyrethroid in household applications, can alter the brain development. This study aimed to characterize the fetal permethrin exposure throughout gestation in rats. We developed a pregnancy physiologically based pharmacokinetic (pPBPK) model that describes the maternal and fetal kinetics of the cis- and trans- isomers of permethrin during the whole gestation period. Pregnant Sprague-Dawley rats were exposed daily to permethrin (50 mg/kg) by oral route from the start of gestation to day 20. Permethrin isomers were quantified in the feces, kidney, mammary gland, fat, and placenta in dams and in both maternal and fetal blood, brain, and liver. Cis- and trans-permethrin were quantified in fetal blood and tissues, with higher concentrations for the cis-isomer. The pPBPK model was fitted to the toxicokinetic maternal and fetal data in a Bayesian framework. Several parameters were adjusted, such as hepatic clearances, partition coefficients, and intestinal absorption. Our work allowed to estimate the prenatal exposure to permethrin in rats, especially in the fetal brain, and to quantitatively estimate the placental transfer. These transfers could be extrapolated to humans and be incorporated in a human pPBPK model to estimate the fetal exposure to permethrin from biomonitoring data.

In vitro-in silico-based probabilistic risk assessment of combined exposure to bisphenol A and its analogues by integrating ToxCast high-throughput in vitro assays with in vitro to in vivo extrapolation (IVIVE) via physiologically based pharmacokinetic (PBPK) modeling

Combined risk assessment of endocrine effects of bisphenol A (BPA) and its analogues, such as bisphenols S, F, and AF (BPS, BPF, and BPAF), is challenging due to lack of related common toxicity metrics. This study conducted a population-based in vitro-to-in vivo extrapolation using physiologically based pharmacokinetic (PBPK) models coupled with Monte Carlo simulations to convert ToxCast in vitro estrogen receptor (ER) assays to human equivalent doses (HEDs). The ER pathway-based HEDs were compared with HEDs from animal studies and used to assess the combined risks for different populations across different countries/regions in a probabilistic manner. The estimated ER pathway-based HEDs for the four bisphenols (BPs) matched the animal-derived HEDs. The HEDs for the ER gene transcription (the common biological process target among BPs) were 0.40 (2.5th-97.5th percentiles: 0.06-5.42), 4.43 (0.69-53.84), 3.30 (0.51-626.57), and 1.12 (0.16-9.73) mg/kg/day for BPA, BPS, BPF, and BPAF, respectively. Results suggest a potentially moderate concern for combined risks of activating the ER pathway for toddlers and adults with high dietary exposures. This study presents in vitro-based credible HEDs for the four BPs and represents an advancement in the application of in vitro-in silico-based alternative approaches in human health risk assessment.

Development and evaluation of a harmonized whole body physiologically based pharmacokinetic (PBPK) model for flutamide in rats and its extrapolation to humans

By their definition, inadvertent exposure to endocrine disrupting compounds (EDCs) intervenes with the endocrine signalling system, even at low dose. On the one hand, some EDCs are used as important pharmaceutical drugs that one would not want to dismiss. On the other hand, these pharmaceutical drugs are having off-target effects and increasingly significant exposure to the general population with unwanted health implications. Flutamide, one of the top pharmaceutical products marketed all over the world for the treatment of prostate cancer, is also a pollutant. Its therapeutic action mainly depends on targeting the androgen receptors and inhibiting the androgen action that is essential for growth and survival of prostate tissue. Currently flutamide is of concern with respect to its categorization as an endocrine disruptor. In this work we have developed a physiologically based pharmacokinetic (PBPK) model of flutamide that could serve as a standard tool for its human risk assessment. First we built the model for rat (where many parameters have been measured). The rat PBPK model was extrapolated to human where the re-parameterization involved human-specific physiology, metabolic kinetics derived from in-vitro studies, and the partition coefficient same as the rat model. We have harmonized the model by integrating different sets of in-vitro, in-vivo and physiological data into a PBPK model. Then the model was used to simulate different exposure scenarios and the results were compared against the observed data. Both uncertainty and sensitivity analysis was done. Since this new whole-body PBPK model can predict flutamide concentrations not only in plasma but also in various organs, the model may have clinical applications in efficacy and safety assessment of flutamide. The model can also be used for reverse dosimetry in the context of interpreting the available biomonitoring data to estimate the degree to which the population is currently being exposed, and a tool for the pharmaceutical companies to validate the estimated Permitted Daily Exposure (PDE) for flutamide.

Modeling Pharmacokinetics

Pharmacokinetics is the study of the fate of xenobiotics in a living organism. Physiologically based pharmacokinetic (PBPK) models provide realistic descriptions of xenobiotics' absorption, distribution, metabolism, and excretion processes. They model the body as a set of homogeneous compartments representing organs, and their parameters refer to anatomical, physiological, biochemical, and physicochemical entities. They offer a quantitative mechanistic framework to understand and simulate the time-course of the concentration of a substance in various organs and body fluids. These models are well suited for performing extrapolations inherent to toxicology and pharmacology (e.g., between species or doses) and for integrating data obtained from various sources (e.g., in vitro or in vivo experiments, structure-activity models). In this chapter, we describe the practical development and basic use of a PBPK model from model building to model simulations, through implementation with an easily accessible free software.

Evaluation and calibration of high-throughput predictions of chemical distribution to tissues

Toxicokinetics (TK) provides critical information for integrating chemical toxicity and exposure assessments in order to determine potential chemical risk (i.e., the margin between toxic doses and plausible exposures). For thousands of chemicals that are present in our environment, in vivo TK data are lacking. The publicly available R package "httk" (version 1.8, named for "high throughput TK") draws from a database of in vitro data and physico-chemical properties in order to run physiologically-based TK (PBTK) models for 553 compounds. The PBTK model parameters include tissue:plasma partition coefficients (Kp) which the httk software predicts using the model of Schmitt (Toxicol In Vitro 22 (2):457-467, 2008). In this paper we evaluated and modified httk predictions, and quantified confidence using in vivo literature data. We used 964 rat Kp measured by in vivo experiments for 143 compounds. Initially, predicted Kp were significantly larger than measured Kp for many lipophilic compounds (log10 octanol:water partition coefficient > 3). Hence the approach for predicting Kp was revised to account for possible deficiencies in the in vitro protein binding assay, and the method for predicting membrane affinity was revised. These changes yielded improvements ranging from a factor of 10 to nearly a factor of 10,000 for 83 Kp across 23 compounds with only 3 Kp worsening by more than a factor of 10. The vast majority (92%) of Kp were predicted within a factor of 10 of the measured value (overall root mean squared error of 0.59 on log10-transformed scale). After applying the adjustments, regressions were performed to calibrate and evaluate the predictions for 12 tissues. Predictions for some tissues (e.g., spleen, bone, gut, lung) were observed to be better than predictions for other tissues (e.g., skin, brain, fat), indicating that confidence in the application of in silico tools to predict chemical partitioning varies depending upon the tissues involved. Our calibrated model was then evaluated using a second data set of human in vivo measurements of volume of distribution (Vss) for 498 compounds reviewed by Obach et al. (Drug Metab Dispos 36(7):1385-1405, 2008). We found that calibration of the model improved performance: a regression of the measured values as a function of the predictions has a slope of 1.03, intercept of - 0.04, and R2 of 0.43. Through careful evaluation of predictive methods for chemical partitioning into tissues, we have improved and calibrated these methods and quantified confidence for TK predictions in humans and rats.

Physiologically based pharmacokinetic models of small molecules and therapeutic antibodies: a mini-review on fundamental concepts and applications

The mechanisms of absorption, distribution, metabolism and elimination of small and large molecule therapeutics differ significantly from one another and can be explored within the framework of a physiologically based pharmacokinetic (PBPK) model. This paper briefly reviews fundamental approaches to PBPK modeling, in which drug kinetics within tissues and organs are explicitly represented using physiologically meaningful parameters. The differences in PBPK models applied to small/large molecule drugs are highlighted, thus elucidating differences in absorption, distribution and elimination properties between these two classes of drugs in a systematic manner. The absorption of small and large molecules differs with respect to their common extravascular routes of delivery (oral versus subcutaneous). The role of the lymphatic system in drug distribution, and the involvement of tissues as sites of elimination (through catabolism and target mediated drug disposition) are unique features of antibody distribution and elimination that differ from small molecules, which are commonly distributed into the tissues but are eliminated primarily by liver metabolism. Fundamental differences exist in the ability to predict human pharmacokinetics based upon preclinical data due to differing mechanisms governing small and large molecule disposition. These differences have influence on the evolving utilization of PBPK modeling in the discovery and development of small and large molecule therapeutics.

Ontogeny of plasma proteins, albumin and binding of diazepam, cyclosporine, and deltamethrin

BACKGROUND

To characterize the ontogeny of plasma albumin and total proteins, due to the lack of a comprehensive pediatric database. Secondly, to establish the magnitude and duration of maturational changes in binding of highly-bound drugs/chemicals.

METHODS

Anonymized plasma samples from 296 donors were pooled in 6 age brackets from birth to adolescence. Total protein and albumin levels were measured in each age group, as was the age-dependency of plasma binding of diazepam (DZP), cyclosporine (CYC), and deltamethrin (DLM), a pyrethroid insecticide.

RESULTS

Plasma levels of albumin and total proteins steadily increased for the first 1-3 y of life. Unbound DZP and CYC fractions were elevated three- to fourfold in neonates, but decreased to adult levels after 1 and 3 y, respectively. Unbound DLM levels exceeded those in adults for just 1 mo.

CONCLUSION

Neonates and infants under 1-3 y may be at risk from increased amounts of free drug, when given standard doses of some highly-bound drugs. Pyrethroid insecticides might be anticipated to pose increased risk for 1 mo.

In silico toxicology: computational methods for the prediction of chemical toxicity

Determining the toxicity of chemicals is necessary to identify their harmful effects on humans, animals, plants, or the environment. It is also one of the main steps in drug design. Animal models have been used for a long time for toxicity testing. However, in vivo animal tests are constrained by time, ethical considerations, and financial burden. Therefore, computational methods for estimating the toxicity of chemicals are considered useful. In silico toxicology is one type of toxicity assessment that uses computational methods to analyze, simulate, visualize, or predict the toxicity of chemicals. In silico toxicology aims to complement existing toxicity tests to predict toxicity, prioritize chemicals, guide toxicity tests, and minimize late-stage failures in drugs design. There are various methods for generating models to predict toxicity endpoints. We provide a comprehensive overview, explain, and compare the strengths and weaknesses of the existing modeling methods and algorithms for toxicity prediction with a particular (but not exclusive) emphasis on computational tools that can implement these methods and refer to expert systems that deploy the prediction models. Finally, we briefly review a number of new research directions in in silico toxicology and provide recommendations for designing in silico models. WIREs Comput Mol Sci 2016, 6:147-172. doi: 10.1002/wcms.1240 For further resources related to this article, please visit the WIREs website.

Malaria Prevention, Mefloquine Neurotoxicity, Neuropsychiatric Illness, and Risk-Benefit Analysis in the Australian Defence Force

The Australian Defence Force (ADF) has used mefloquine for malaria chemoprophylaxis since 1990. Mefloquine has been found to be a plausible cause of a chronic central nervous system toxicity syndrome and a confounding factor in the diagnosis of existing neuropsychiatric illnesses prevalent in the ADF such as posttraumatic stress disorder and traumatic brain injury. Overall health risks appear to have been mitigated by restricting the drug's use; however serious risks were realised when significant numbers of ADF personnel were subjected to clinical trials involving the drug. The full extent of the exposure, health impacts for affected individuals, and consequences for ADF health management including mental health are not yet known, but mefloquine may have caused or aggravated neuropsychiatric illness in large numbers of patients who were subsequently misdiagnosed and mistreated or otherwise failed to receive proper care. Findings in relation to chronic mefloquine neurotoxicity were foreseeable, but this eventuality appears not to have been considered during risk-benefit analyses. Thorough analysis by the ADF would have identified this long-term risk as well as other qualitative risk factors. Historical exposure of ADF personnel to mefloquine neurotoxicity now also necessitates ongoing risk monitoring and management in the overall context of broader health policies.

Correlation-based prediction of tissue-to-plasma partition coefficients using readily available input parameters

1.

RATIONALE

Tissue-to-plasma partition coefficients (Kp) that characterize the tissue distribution of a drug are important input parameters in physiologically based pharmacokinetic (PBPK) models. The aim of this study was to develop an empirically derived Kp prediction algorithm using input parameters that are available early in the investigation of a compound. 2.

METHODS

The algorithm development dataset (n = 97 compounds) was divided according to acidic/basic properties. Using multiple stepwise regression, the experimentally derived Kp values were correlated with the rat volume of distribution at steady state (Vss) and one or more physicochemical parameters (e.g. lipophilicity, degree of ionization and protein binding) to account for inter-organ variability of tissue distribution. 3.

RESULTS

Prediction equations for the value of Kp were developed for 11 tissues. Validation of this model using a test dataset (n = 20 compounds) demonstrated that 65% of the predicted Kp values were within a two-fold error deviation from the experimental values. The developed algorithms had greater prediction accuracy compared to an existing empirically derived and a mechanistic tissue-composition algorithm. 4.

CONCLUSIONS

This innovative method uses readily available input parameters with reasonable prediction accuracy and will thus enhance both the usability and the confidence in the outputs of PBPK models.

Systems biology tools for toxicology

An important goal of toxicology is to understand and predict the adverse effects of drugs and other xenobiotics. For pharmaceuticals, such effects often emerge unexpectedly in man even when absent from trials in vitro and in animals. Although drugs and xenobiotics act on molecules, it is their perturbation of intracellular networks that matters. The tremendous complexity of these networks makes it difficult to understand the effects of xenobiotics on their ability to function. Because systems biology integrates data concerning molecules and their interactions into an understanding of network behaviour, it should be able to assist toxicology in this respect. This review identifies how in silico systems biology tools, such as kinetic modelling, and metabolic control, robustness and flux analyse, may indeed help understanding network-mediated toxicity. It also shows how these approaches function by implementing them vis-à-vis the glutathione network, which is important for the detoxification of reactive drug metabolites. The tools enable the appreciation of the steady state concept for the detoxification network and make it possible to simulate and then understand effects of perturbations of the macromolecules in the pathway that are counterintuitive. We review how a glutathione model has been used to explain the impact of perturbation of the pathway at various molecular sites, as would be the effect of single-nucleotide polymorphisms. We focus on how the mutations impact the levels of glutathione and of two candidate biomarkers of hepatic glutathione status. We conclude this review by sketching how the various systems biology tools may help in the various phases of drug development in the pharmaceutical industry.

Application of physiologically based pharmacokinetic models in chemical risk assessment

Post-exposure risk assessment of chemical and environmental stressors is a public health challenge. Linking exposure to health outcomes is a 4-step process: exposure assessment, hazard identification, dose response assessment, and risk characterization. This process is increasingly adopting "in silico" tools such as physiologically based pharmacokinetic (PBPK) models to fine-tune exposure assessments and determine internal doses in target organs/tissues. Many excellent PBPK models have been developed. But most, because of their scientific sophistication, have found limited field application-health assessors rarely use them. Over the years, government agencies, stakeholders/partners, and the scientific community have attempted to use these models or their underlying principles in combination with other practical procedures. During the past two decades, through cooperative agreements and contracts at several research and higher education institutions, ATSDR funded translational research has encouraged the use of various types of models. Such collaborative efforts have led to the development and use of transparent and user-friendly models. The "human PBPK model toolkit" is one such project. While not necessarily state of the art, this toolkit is sufficiently accurate for screening purposes. Highlighted in this paper are some selected examples of environmental and occupational exposure assessments of chemicals and their mixtures.

Simulation of human intravenous and oral pharmacokinetics of 21 diverse compounds using physiologically based pharmacokinetic modelling

BACKGROUND

The importance of predicting human pharmacokinetics during compound selection has been recognized in the pharmaceutical industry. To this end there are many different approaches that are applied.

METHODS

In this study we compared the accuracy of physiologically based pharmacokinetic (PBPK) methodologies implemented in GastroPlus™ with the one-compartment approach routinely used at Pfizer for human pharmacokinetic plasma concentration-time profile prediction. Twenty-one Pfizer compounds were selected based on the availability of relevant preclinical and clinical data. Intravenous and oral human simulations were performed for each compound. To understand any mispredictions, simulations were also performed using the observed clearance (CL) value as input into the model.

RESULTS

The simulation results using PBPK were shown to be superior to those obtained via traditional one-compartment analyses. In many cases, this difference was statistically significant. Specifically, the results showed that the PBPK approach was able to accurately predict passive distribution and absorption processes. Some issues and limitations remain with respect to the prediction of CL and active transport processes and these need to be improved to further increase the utility of PBPK modelling. A particular advantage of the PBPK approach is its ability to accurately predict the multiphasic shape of the pharmacokinetic profiles for many of the compounds tested.

CONCLUSION

The results from this evaluation demonstrate the utility of PBPK methodology for the prediction of human pharmacokinetics. This methodology can be applied at different stages to enhance the understanding of the compounds in a particular chemical series, guide experiments, aid candidate selection and inform clinical trial design.

A systems biology approach to dynamic modeling and inter-subject variability of statin pharmacokinetics in human hepatocytes

Background

The individual character of pharmacokinetics is of great importance in the risk assessment of new drug leads in pharmacological research. Amongst others, it is severely influenced by the properties and inter-individual variability of the enzymes and transporters of the drug detoxification system of the liver. Predicting individual drug biotransformation capacity requires quantitative and detailed models.

Results

In this contribution we present the de novo deterministic modeling of atorvastatin biotransformation based on comprehensive published knowledge on involved metabolic and transport pathways as well as physicochemical properties. The model was evaluated on primary human hepatocytes and parameter identifiability analysis was performed under multiple experimental constraints. Dynamic simulations of atorvastatin biotransformation considering the inter-individual variability of the two major involved enzymes CYP3A4 and UGT1A3 based on quantitative protein expression data in a large human liver bank (n = 150) highlighted the variability in the individual biotransformation profiles and therefore also points to the individuality of pharmacokinetics.

Conclusions

A dynamic model for the biotransformation of atorvastatin has been developed using quantitative metabolite measurements in primary human hepatocytes. The model comprises kinetics for transport processes and metabolic enzymes as well as population liver expression data allowing us to assess the impact of inter-individual variability of concentrations of key proteins. Application of computational tools for parameter sensitivity analysis enabled us to considerably improve the validity of the model and to create a consistent framework for precise computer-aided simulations in toxicology.

A physiologically based pharmacokinetic model for atrazine and its main metabolites in the adult male C57BL/6 mouse

Atrazine (ATR) is a chlorotriazine herbicide that is widely used and relatively persistent in the environment. In laboratory rodents, excessive exposure to ATR is detrimental to the reproductive, immune, and nervous systems. To better understand the toxicokinetics of ATR and to fill the need for a mouse model, a physiologically based pharmacokinetic (PBPK) model for ATR and its main chlorotriazine metabolites (Cl-TRIs) desethyl atrazine (DE), desisopropyl atrazine (DIP), and didealkyl atrazine (DACT) was developed for the adult male C57BL/6 mouse. Taking advantage of all relevant and recently made available mouse-specific data, a flow-limited PBPK model was constructed. The ATR and DACT sub-models included blood, brain, liver, kidney, richly and slowly perfused tissue compartments, as well as plasma protein binding and red blood cell binding, whereas the DE and DIP sub-models were constructed as simple five-compartment models. The model adequately simulated plasma levels of ATR and Cl-TRIs and urinary dosimetry of Cl-TRIs at four single oral dose levels (250, 125, 25, and 5mg/kg). Additionally, the model adequately described the dose dependency of brain and liver ATR and DACT concentrations. Cumulative urinary DACT amounts were accurately predicted across a wide dose range, suggesting the model's potential use for extrapolation to human exposures by performing reverse dosimetry. The model was validated using previously reported data for plasma ATR and DACT in mice and rats. Overall, besides being the first mouse PBPK model for ATR and its Cl-TRIs, this model, by analogy, provides insights into tissue dosimetry for rats. The model could be used in tissue dosimetry prediction and as an aid in the exposure assessment to this widely used herbicide.

Physiologically based pharmacokinetic (PBPK) models for lifetime exposure to PCB 153 in male and female harbor porpoises (Phocoena phocoena): model development and evaluation

Physiologically based pharmacokinetic (PBPK) models were developed for the most persistent polychlorinated biphenyl (PCB 153) in male and female harbor porpoises (Phocoena phocoena) to elucidate processes such as uptake, distribution, and elimination. Due to its limited metabolic capacities, long life span, and top position in marine food chains, this species is highly sensitive to pollution. The models consist of 5 compartments, liver, blubber, kidney, brain, and a compartment which accounts for the rest of the body, all connected through blood. All physiological and biochemical parameters were extracted from the literature, except for the brain/blood partition coefficient and rate of excretion, which were both fitted to data sets used for validation of the models. These data sets were compiled from our own analyses performed with GC-MS on tissue samples of harbor porpoises. The intake of PCB 153 was from milk from birth to 4 months, and after weaning fish was the main food source. Overall, these models reveal that concentrations of PCB 153 in males increase with age but suggest that, as the animals grow older, metabolic transformation can be a possible pathway for elimination as well. In contrast, the model for females confirms that gestation and lactation are key processes for eliminating PCB 153 as body burdens decrease with age. These PBPK models are capable of simulating the bioaccumulation of PCB 153 during the entire life span of approximately 20 years of the harbor porpoises.

Approaches for applications of physiologically based pharmacokinetic models in risk assessment

Physiologically based pharmacokinetic (PBPK) models are particularly useful for simulating exposures to environmental toxicants for which, unlike pharmaceuticals, there is often little or no human data available to estimate the internal dose of a putative toxic moiety in a target tissue or an appropriate surrogate. This article reviews the current state of knowledge and approaches for application of PBPK models in the process of deriving reference dose, reference concentration, and cancer risk estimates. Examples drawn from previous U.S. Environmental Protection Agency (EPA) risk assessments and human health risk assessments in peer-reviewed literature illustrate the ways and means of using PBPK models to quantify the pharmacokinetic component of the interspecies and intraspecies uncertainty factors as well as to conduct route to route, high dose to low dose and duration extrapolations. The choice of the appropriate dose metric is key to the use of the PBPK models for the various applications in risk assessment. Issues related to whether uncertainty factors are most appropriately applied before or after derivation of human equivalent dose (or concentration) continue to be explored. Scientific progress in the understanding of life stage and genetic differences in dosimetry and their impacts on variability in susceptibility, as well as ongoing development of analytical methods to characterize uncertainty in PBPK models, will make their use in risk assessment increasingly likely. As such, it is anticipated that when PBPK models are used to express adverse tissue responses in terms of the internal target tissue dose of the toxic moiety rather than the external concentration, the scientific basis of, and confidence in, risk assessments will be enhanced.

Physiologically based pharmacokinetic modelling: a sub-compartmentalized model of tissue distribution

We present a sub-compartmentalized model of drug distribution in tissue that extends existing approaches based on the well-stirred tissue model. It is specified in terms of differential equations that explicitly account for the drug concentration in erythrocytes, plasma, interstitial and cellular space. Assuming, in addition, steady state drug distribution and by lumping the different sub-compartments, established models to predict tissue-plasma partition coefficients can be derived in an intriguingly simple way. This direct link is exploited to explicitly construct and parameterize the sub-compartmentalized model for moderate to strong bases, acids, neutrals and zwitterions. The derivation highlights the contributions of the different tissue constituents and provides a simple and transparent framework for the construction of novel tissue distribution models.

Acute Toluene Exposure and Rat Visual Function in Proportion to Momentary Brain Concentration

Acute exposure to toluene was assessed in two experiments to determine the relationship between brain toluene concentration and changes in neurophysiological function. The concentration of toluene in brain tissue at the time of assessment was estimated using a physiologically based pharmacokinetic model. Brain neurophysiological function was measured using pattern-elicited visual evoked potentials (VEP) recorded from electrodes located over visual cortex of adult male Long-Evans rats. In the first experiment, VEPs were recorded before and during exposure to control air or toluene at 1000 ppm for 4 h, 2000 ppm for 2 h, 3000 ppm for 1.3 h, or 4000 ppm for 1 h. In the second experiment, VEPs were recorded during and after exposure to clean air or 3000 or 4000 ppm toluene. In both experiments, the response amplitude of the major spectral component of the VEP (F2 at twice the stimulus rate in steady-state responses) was reduced by toluene. A logistic function was fit to baseline-adjusted F2 amplitudes from the first experiment that described a significant relationship between brain toluene concentration and VEP amplitude deficits. In the second experiment, 3000 ppm caused equivalent VEP deficits during or after exposure as a function of estimated brain concentration, but 4000 ppm showed a rapid partial adaptation to the acute effects of toluene after exposure. In general, however, the neurophysiological deficits caused by acute toluene exposure could be described by estimates of the momentary concentration of toluene in the brain at the time of VEP evaluation.

Development of a non-invasive biomonitoring approach to determine exposure to the organophosphorus insecticide chlorpyrifos in rat saliva

Non-invasive biomonitoring approaches are being developed using reliable portable analytical systems to quantify dosimetry utilizing readily obtainable body fluids, such as saliva. In the current study, rats were given single oral gavage doses (1, 10, or 50 mg/kg) of the insecticide chlorpyrifos (CPF). Saliva and blood were then collected from groups of animals (4/time-point) at 3, 6, and 12 h post-dosing, and were analyzed for the CPF metabolite trichloropyridinol (TCP). Trichloropyridinol was detected in both blood and saliva at all doses and the TCP concentration in blood exceeded saliva, although the kinetics in blood and saliva were comparable. A physiologically based pharmacokinetic and pharmacodynamic (PBPK/PD) model for CPF incorporated a compartment model to describe the time-course of TCP in blood and saliva. The model adequately simulated the experimental results over the dose ranges evaluated. A rapid and sensitive sequential injection (SI) electrochemical immunoassay was developed to monitor TCP, and the reported detection limit for TCP was 6 ng/L (in water). Computer model simulation in the range of the Allowable Daily Intake (ADI) or Reference Dose (RfD) for CPF (0.01-0.003 mg/kg/day) suggests that the electrochemical immunoassay has adequate sensitivity to detect and quantify TCP in saliva at these low exposure levels. However, to validate this approach, further studies are needed to more fully understand the pharmacokinetics of CPF and TCP excretion in saliva. These initial findings suggest that the utilization of saliva as a biomonitoring matrix, coupled to real-time quantitation and PBPK/PD modeling represents a novel approach with broad application for evaluating both occupational and environmental exposures to CPF.

Evaluation of physiologically based pharmacokinetic models for use in risk assessment

Physiologically based pharmacokinetic (PBPK) models are sophisticated dosimetry models that offer great flexibility in modeling exposure scenarios for which there are limited data. This is particularly of relevance to assessing human exposure to environmental toxicants, which often requires a number of extrapolations across species, route, or dose levels. The continued development of PBPK models ensures that regulatory agencies will increasingly experience the need to evaluate available models for their application in risk assessment. To date, there are few published criteria or well-defined standards for evaluating these models. Herein, important considerations for evaluating such models are described. The evaluation of PBPK models intended for risk assessment applications should include a consideration of: model purpose, model structure, mathematical representation, parameter estimation, computer implementation, predictive capacity and statistical analyses. Model purpose and structure require qualitative checks on the biological plausibility of a model. Mathematical representation, parameter estimation, computer implementation involve an assessment of the coding of the model, as well as the selection and justification of the physical, physicochemical and biochemical parameters chosen to represent a biological organism. Finally, the predictive capacity and sensitivity, variability and uncertainty of the model are analysed so that the applicability of a model for risk assessment can be determined. Published in 2007 by John Wiley & Sons, Ltd.

The virtual laboratory approach to pharmacokinetics: design principles and concepts

Modeling and simulation in pharmacokinetics has turned into the focus of pharmaceutical companies, driven by the emerging consensus that in silico predictions, combined with in vitro data, have the potential to significantly increase insight into pharmacokinetic processes. To support in silico methodology adequately, software tools need to be user-friendly and, at the same time, flexible. In brief, the software has to allow the modeling of ideas that go beyond the current knowledge--in the form of a virtual laboratory. In this review, we present and discuss the necessary design principles and concepts required to do this. They have been implemented in the software package MEDICI-PK, demonstrating its feasibility and advantages.

Hierarchical models for probabilistic dose–response assessment

Probabilistic risk assessment is gaining acceptance as the most appropriate way to characterize and communicate uncertainties in estimates of human health risk and/or reference levels of exposure such as benchmark doses. Although probabilistic techniques are well established in the exposure-assessment component of the National Research Council's risk-assessment paradigm, they are less well developed in the dose-response-assessment component. This paper proposes the use of hierarchical statistical models as tools for implementing probabilistic dose-response assessments, in that such models provide a natural connection between the pharmacokinetic (PK) and pharmacodynamic (PD) components of dose-response models. The results show that incorporating internal dose information into dose-response assessments via the coupling of PK and PD models in a hierarchical structure can reduce the uncertainty in the dose-response assessment of risk. However, information on the mean of the internal dose distribution is sufficient; having information on the variance of internal dose does not affect the uncertainty in the resulting estimates of excess risks or benchmark doses. In addition, the complexity of a PK model of internal dose does not affect how the variability in risk is measured via the ultimate endpoint.

Use of a chemical probe to increase safety for human volunteers in toxicokinetic studies

To avoid interspecies extrapolation in toxicokinetics and drug development, it is convenient to directly develop human data. In that case, exposure dose should pose null or negligible risk to the exposed individual, but still be sufficiently high to allow quantification. We propose to reduce the dose received by human volunteers during exposure, and to compensate for loss of information by exposing the same volunteers to a nontoxic agent. This method was applied to develop 1,3-butadiene (BD) exposure protocols for humans. To study the potential of such a procedure, we worked with simulated data. Three exposure times (20, 10, and 5 minutes) and four exposure concentrations (2, 1, 0.8, and 0.5 ppm) were used to define 12 inhalation exposure scenarios for BD. Isoflurane was used as a probe, with simulated exposure of 20 subjects to 20 ppm isoflurane during 15 minutes. Isoflurane or BD-exhaled air concentrations were supposed to be measured 10 times. A three-compartment physiological toxicokinetic model was used to jointly describe BD and isoflurane data. For each subject, BD data were analyzed, in a Bayesian framework, either alone or together with the isoflurane data. The precision of BD metabolic rate constant or fraction metabolized was increased, and bias reduced, when BD and probe data were considered jointly. An exposure to 10 ppm x min BD and 300 ppm x min isoflurane gave equivalent precision and bias as a unique exposure to 40 ppm x min BD. The BD dose received by volunteers could therefore be at least quartered if BD exposure was supplemented with that of a probe.

Applications of dosimetry modeling to assessment of neurotoxic risk

Risk assessment procedures can be improved through better understanding and use of tissue dose information and linking tissue dose level to adverse outcomes. For volatile organic compounds, such as toluene and trichloroethylene (TCE), blood and brain concentrations can be estimated with physiologically based pharmacokinetic (PBPK) models. Acute changes in the function of the nervous system can be linked to the concentration of test compounds in the blood or brain at the time of neurological assessment. This set of information enables application to a number of risk assessment situations. For example, we have used this approach to recommend duration adjustments for acute exposure guideline levels (AEGLs) for TCE such that the exposure limits for each exposure duration yield identical tissue concentrations at the end of the exposure period. We have also used information on tissue concentration at the time of assessment to compare sensitivity across species, adjusting for species-specific pharmacokinetic differences. Finally this approach has enabled us to compare the relative sensitivity of different compounds on a tissue dose basis, leading to expression of acute solvent effects as ethanol-dose equivalents for purposes of estimating cost-benefit relationships of various environmental control options.

Allometric principles for interspecies extrapolation in toxicological risk assessment--empirical investigations

Four types of data (toxicokinetic data of pharmaceuticals from six species including humans, LD(50) values from eight animal species, long-term NOAEL values of pesticides from mice, rats, and dogs, and toxicity data on anti-neoplastic agents from six species including humans) were used for interspecies comparisons. Species differences with regard to kinetic parameters and toxicity were evaluated and the concordance with predictions by allometric scaling according to caloric demand (allometric exponent 0.75) or to body weight (allometric exponent 1) was checked. For LD(50) values, agreement was poor for both allometric concepts. Recently reported concordance of LD(50) species differences with body weight scaling could be traced back to biased data selection. The other three datasets are clearly in agreement with the allometric scaling according to caloric demand. Caloric demand scaling is thus proposed as a generic interspecies extrapolation method in the absence of substance-specific data. Moreover, the evaluated data make it possible to describe uncertainty associated with the process of interspecies extrapolation by allometric rules.

Noninvasive biomonitoring approaches to determine dosimetry and risk following acute chemical exposure: analysis of lead or organophosphate insecticide in saliva

There is a need to develop approaches for assessing risk associated with acute exposures to a broad range of metals and chemical agents and to rapidly determine the potential implications to human health. Noninvasive biomonitoring approaches are being developed using reliable portable analytical systems to quantitate dosimetry utilizing readily obtainable body fluids, such as saliva. Saliva has been used to evaluate a broad range of biomarkers, drugs, and environmental contaminants, including heavy metals and pesticides. To advance the application of noninvasive biomonitoring a microfluidic/electrochemical device has also been developed for the analysis of lead (Pb), using square-wave anodic stripping voltametry. The system demonstrates a linear response over a broad concentration range (1-2000 ppb) and is capable of quantitating saliva Pb in rats orally administered acute doses of Pb acetate. Appropriate pharmacokinetic analyses have been used to quantitate systemic dosimetry based on determination of saliva Pb concentrations. In addition, saliva has recently been used to quantitate dosimetry following exposure to the organophosphate insecticide chlorpyrifos in a rodent model system by measuring the major metabolite, trichloropyridinol, and saliva cholinesterase inhibition following acute exposures. These results suggest that technology developed for noninvasive biomonitoring can provide a sensitive and portable analytical tool capable of assessing exposure and risk in real-time. By coupling these noninvasive technologies with pharmacokinetic modeling it is feasible to rapidly quantitate acute exposure to a broad range of chemical agents. In summary, it is envisioned that once fully developed, these monitoring and modeling approaches will be useful for evaluating acute exposure and health risk.

Predicting blood:air partition coefficients using theoretical molecular descriptors

Three regression methods, namely ridge regression (RR), partial least squares (PLS), and principal components regression (PCR), were used to develop models for the prediction of rat blood:air partition coefficient for increasingly diverse data sets. Initially, modeling was performed for a set of 13 chlorocarbons. To this set, 10 additional hydrophobic compounds were added, including aromatic and non-aromatic hydrocarbons. A set of 16 hydrophilic compounds was also modeled separately. Finally, all 39 compounds were combined into one data set for which comprehensive models were developed. A large set of diverse, theoretical molecular descriptors was calculated for use in the current study. The topostructural (TS), topochemical (TC), and geometrical or 3-dimensional (3D) indices were used hierarchically in model development. In addition, single-class models were developed using the TS, TC, and 3D descriptors. In most cases, RR outperformed PLS and PCR, and the models developed using TC indices were superior to those developed using other classes of descriptors.

Comparison of models for the estimation of biological partition coefficients

Several models have been published for calculating blood-air, tissue-air, or tissue-blood partition coefficients of volatile organic chemicals in human or rat tissues, from functions of their octanol-water partition coefficients or solubilities in vegetable oil and water. In this work, the relative accuracy, strengths, and limitations of the various models are examined. Comparison of predicted human tissue-air and tissue-blood partition coefficients with experimental values has been made for 12 chemicals, covering a wide range of lipophilicity (acetone, isopropanol, diethylether, methylene dichloride, benzene, toluene, trichloroethylene, trichloroethane, n-pentane, cyclohexane, n-hexane, and n-heptane). Seven published models for human tissue-air and 10 models for tissue-blood partition coefficients have been compared. Fewer models are available for predicting rat tissue-air and rat tissue-blood partition coefficients, but a similar comparison has been made. The ratio of predicted to experimental partition coefficients and their mean, R(mean), and the mean magnitude of the difference between predicted and experimental values of log(10) P, E, were used to assess the accuracy of each model. For the test set the most accurate for human blood-air partition coefficients were the empirical equations of Meulenberg and Vijverberg (R(mean) = 1.1 +/- 0.46, E = 0.156) and the empirical solvation equation of Abraham and Weathersby (1994) (R(mean) = 0.93 +/- 0.38, E = 0.166). For rat blood, predictions are much less accurate due to difficulties in modeling the effects of protein binding, which are much larger. Overall, for rat blood-air partition coefficients the equation of Meulenberg and Vijverberg (1999) (R(mean) = 0.74 +/- 0.50, E = 0.236) was the most accurate. The tissue-composition-based equations of Poulin and Krishnan, using solubilities in vegetable oil, performed well for human liver-air partition coefficients (R(mean) = 1.21 +/- 0.28, E = 0.079) for log(octanol-water partition coefficients) > 0.7 and for fat-air partition coefficients, but overestimated solubilities in human kidney and brain tissues (e.g., for kidney tissue, R = 1.88 +/- 0.58, E = 0.255). The equations of Meulenberg and Vijverberg (2000a), Abraham and Weathersby (1994), and Paterson and Mackay (1989) also performed moderately well for human tissue-air partition coefficients. For rat muscle-air, liver-air, and fat-air partition coefficients the model of Poulin and Krishnan (1996a) gave the most accurate predictions. For tissue-blood partition coefficients, generally good agreement with experimental values is obtained by the empirical model of Balaz and Lukacova (1999) (e.g., for human kidney, R(mean) = 1.15 +/- 0.38, E = 0.085) and, if solubility in fat is known, by the equations of Fiserova-Bergerova and Diaz (1986) (e.g., for human muscle, R(mean) = 1.10 +/- 0.39, E = 0.107). The equations of DeJongh et al. (1997) gave the most accurate predictions for rat muscle-blood, liver-blood and fat-blood partition coefficients (e.g., for rat muscle R(mean) = 1.03 +/- 0.39, E = 0.149), but predictions were less accurate than for human tissue-blood partition coefficients, attributable to difficulties in modeling the effect of protein binding. The choice of equation for use in physiologically based pharmacokinetic (PBPK) models depends on the species, tissue, and chemical lipophilicity.

A comparison of Haber's rule at different ages using a physiologically based pharmacokinetic (PBPK) model for chloroform in rats

Haber's rule as commonly interpreted in inhalation toxicology, can be stated as exposure concentration times duration equals a constant biological effect, or C x t=k. In other words, identical products of concentration and duration lead to the same effect. The goals of this paper are to develop a biological and pharmacokinetic modeling approach for chloroform, and to evaluate Haber's rule for different ages by taking into account the physiological changes due to growth and aging in rats. Three-dimensional dose-response surfaces for liver toxicity were generated for each age group of interest: adolescent, adult, and senescent rats. The three-dimensional surfaces were then characterized with a generalized description of Haber's rule for each age group. The simulations suggest that adolescent rats need higher exposure levels in order to achieve similar levels of liver damage compared to adults or senescent rats, if the comparison is made using the same exposure length. In summary, a pharmacokinetic modeling approach with a biological framework including the chemical's mode of action, was used to relate concentration, exposure duration and effect. Major advantages of this approach include: the potential ability to extrapolate to humans, the inclusion of aging in the simulations, and the ability to summarize the results using a generalized form of Haber's rule.