A Bayesian population PBPK model for multiroute chloroform exposure

Exploring Route-Specific Pharmacokinetics of PFAS in Mice by Coupling in Vivo Tests and Physiologically Based Toxicokinetic Models

BACKGROUND

Oral ingestion, inhalation, and skin contact are important exposure routes for humans to uptake per- and polyfluoroalkyl substances (PFAS). However, nasal and dermal exposure to PFAS remains unclear, and accurately predicting internal body burden of PFAS in humans via multiple exposure pathways is urgently required.

OBJECTIVES

We aimed to develop multiple physiologically based toxicokinetic (PBTK) models to unveil the route-specific pharmacokinetics and bioavailability of PFAS via respective oral, nasal, and dermal exposure pathways using a mouse model and sought to predict the internal concentrations in various tissues through multiple exposure routes and extrapolate it to humans.

METHODS

Mice were administered the mixed solution of perfluorohexane sulfonate, perfluorooctane sulfonate, and perfluorooctanoic acid through oral, nasal, and dermal exposure separately or jointly. The time-dependent concentrations of PFAS in plasma and tissues were determined to calibrate and validate the individual and combined PBTK models, which were applied in single- and repeated-dose scenarios.

RESULTS

The developed route-specific PBTK models successfully simulated the tissue concentrations of PFAS in mice following single or joint exposure routes as well as long-term repeated dose scenarios. The time to peak concentration of PFAS in plasma via dermal exposure was much longer (34.1-83.0 h) than that via nasal exposure (0.960 h). The bioavailability of PFAS via oral exposure was the highest (73.2%-98.0%), followed by nasal (33.9%-66.8%) and dermal exposure (4.59%-7.80%). This model was extrapolated to predict internal levels in human under real environment.

DISCUSSION

Based on these data, we predict the following: PFAS were absorbed quickly via nasal exposure, whereas a distinct hysteresis effect was observed for dermal exposure. Almost all the PFAS to which mice were exposed via gastrointestinal route were absorbed into plasma, which exhibited the highest bioavailability. Exhalation clearance greatly depressed the bioavailability of PFAS via nasal exposure, whereas the lowest bioavailability in dermal exposure was because of the interception of PFAS within the skin layers. https://doi.org/10.1289/EHP11969.

Reconstruction of exposure to methylene diphenyl-4,4'-diisocyanate (MDI) aerosol using computational fluid dynamics, physiologically based toxicokinetics and statistical modeling

OBJECTIVES

This study employed computational fluid dynamics (CFD), physiologically based toxicokinetics (PBTK), and statistical modeling to reconstruct exposure to methylene diphenyl-4,4'-diisocyanate (MDI) aerosol. By utilizing a validated CFD model, human respiratory deposition of MDI aerosol in different workload conditions was investigated, while a PBTK model was calibrated using experimental rat data. Biomonitoring data and Markov Chain Monte Carlo (MCMC) simulation were utilized for exposure assessment.

RESULTS

Deposition fraction of MDI in the respiratory tract at the light, moderate, and heavy activity were 0.038, 0.079, and 0.153, respectively. Converged MCMC results as the posterior means and prior values were obtained for several PBTK model parameters. In our study, we calibrated a rat model to investigate the transport, absorption, and elimination of 4,4'-MDI via inhalation exposure. The calibration process successfully captured experimental data in the lungs, liver, blood, and kidneys, allowing for a reasonable representation of MDI distribution within the rat model. Our calibrated model also represents MDI dynamics in the bloodstream, facilitating the assessment of bioavailability. For human exposure, we validated the model for recent and long-term MDI exposure using data from relevant studies.

CONCLUSION

Our computational models provide reasonable insights into MDI exposure, contributing to informed risk assessment and the development of effective exposure reduction strategies.

Bayesian PBPK modeling using R/Stan/Torsten and Julia/SciML/Turing.Jl

Physiologically-based pharmacokinetic (PBPK) models are mechanistic models that are built based on an investigator's prior knowledge of the in vivo system of interest. Bayesian inference incorporates an investigator's prior knowledge of parameters while using the data to update this knowledge. As such, Bayesian tools are well-suited to infer PBPK model parameters using the strong prior knowledge available while quantifying the uncertainty on these parameters. This tutorial demonstrates a full population Bayesian PBPK analysis framework using R/Stan/Torsten and Julia/SciML/Turing.jl.

Human health risk assessment for contaminated sites: A retrospective review

Soil contamination is a serious global hazard as contaminants can migrate to the human body through the soil, water, air, and food, threatening human health. Human Health Risk Assessment (HHRA) is a commonly used method for estimating the magnitude and probability of adverse health effects in humans that may be exposed to contaminants in contaminated environmental media in the present or future. Such estimations have improved for decades with various risk assessment frameworks and well-established models. However, the existing literature does not provide a comprehensive overview of the methods and models of HHRA that are needed to grasp the current status of HHRA and future research directions. Thus, this paper aims to systematically review the HHRA approaches and models, particularly those related to contaminated sites from peer-reviewed literature and guidelines. The approaches and models focus on methods used in hazard identification, toxicity databases in dose-response assessment, approaches and fate and transport models in exposure assessment, risk characterization, and uncertainty characterization. The features and applicability of the most commonly used HHRA tools are also described. The future research trend for HHRA for contaminated sites is also forecasted. The transition from animal experiments to new methods in risk identification, the integration and update and sharing of existing toxicity databases, the integration of human biomonitoring into the risk assessment process, and the integration of migration and transformation models and risk assessment are the way forward for risk assessment in the future. This review provides readers with an overall understanding of HHRA and a grasp of its developmental direction.

Human skin responses to environmental pollutants: A review of current scientific models

Whatever the exposure route, chemical, physical and biological pollutants modify the whole organism response, leading to nerve, cardiac, respiratory, reproductive, and skin system pathologies. Skin acts as a barrier for preventing pollutant modifications. This review aims to present the available scientific models, which help investigate the impact of pollution on the skin. The research question was "Which experimental models illustrate the impact of pollution on the skin in humans?" The review covered a period of 10 years following a PECO statement on in vitro, ex vivo, in vivo and in silico models. Of 582 retrieved articles, 118 articles were eligible. In oral and inhalation routes, dermal exposure had an important impact at both local and systemic levels. Healthy skin models included primary cells, cell lines, co-cultures, reconstructed human epidermis, and skin explants. In silico models estimated skin exposure and permeability. All pollutants affected the skin by altering elasticity, thickness, the structure of epidermal barrier strength, and dermal extracellular integrity. Some specific models concerned wound healing or the skin aging process. Underlying mechanisms were an exacerbated inflammatory skin reaction with the modulation of several cytokines and oxidative stress responses, ending with apoptosis. Pathological skin models revealed the consequences of environmental pollutants on psoriasis, atopic dermatitis, and tumour development. Finally, scientific models were used for evaluating the safety and efficacy of potential skin formulations in preventing the skin aging process or skin irritation after repeated contact. The review gives an overview of scientific skin models used to assess the effects of pollutants. Chemical and physical pollutants were mainly represented while biological contaminants were little studied. In future developments, cell hypoxia and microbiota models may be considered as more representative of clinical situations. Models considering humidity and temperature variations may reflect the impact of these changes.

Determination of priority control factors for the management of soil trace metal(loid)s based on source-oriented health risk assessment

Trace metal(loid)s (TMs) in soils can seriously threaten the ecological environment and human health. With the limitation of resources and costs, determining priority control factor is critical for managing soil TM pollution. To explore the pollution characteristics, source apportionment, and human health risk of TMs, a total of 209 surface soil samples were collected from Anqing City, China. Results showed that all the average values of TM concentration, except for Cr, were higher than their corresponding background value. Using a Positive matrix factorization model coupled with Correlation analysis, four sources (including agricultural sources, atmospheric deposition sources, industrial sources, and natural sources) were identified as the determinants for the accumulation of soil TMs, with the contribution rates of 12.4%, 8.1%, 64.1%, and 15.4%, respectively. The assessment of probabilistic health risks revealed that Non- carcinogenic risks of all populations were acceptable (HI < 1), while Carcinogenic risks were all at a high level (TCR > 10E-04). Agricultural pollution and As were identified as priority control factors, according to the analysis results of the relationship among TMs, pollution sources and health risks. Our findings provide scientific support for decision-makers to formulate target control policies and reduce management costs of soil pollution.

Bayesian Refinement of the Permeability-Limited Physiologically Based Pharmacokinetic Model for Perfluorooctanoic Acid in Male Rats

Physiologically based pharmacokinetic (PBPK) modeling is a powerful technique to inform risk assessment of xenobiotic substances such as perfluorooctanoic acid (PFOA). In our previous study, a permeability-limited PBPK model was developed to simulate the toxicokinetics and tissue distribution of PFOA in male rats. However, due to limited information on some key model parameters (e.g., protein binding and active transport rates), the uncertainty of the permeability-limited PBPK model was quite high. To address this issue, a hierarchical Bayesian analysis with Markov chain Monte Carlo (MCMC) was applied to reduce the uncertainty of parameters and improve the performance of the PBPK model. With the optimized posterior parameters, the PBPK model was evaluated by comparing its prediction with experimental data from three different studies. The results show that the uncertainties of the posterior model parameters were reduced substantially. In addition, most of the PBPK model predictions were improved: with the posterior parameters, most of the predicted plasma toxicokinetics (e.g., half-life) and tissue distribution fell well within a factor of 2.0 of the experimental data. Finally, the Bayesian framework could provide insights into the molecular mechanisms driving PFOA toxicokinetics: PFOA-protein binding, membrane permeability, and active transport.

Key Factors for Improving the Carcinogenic Risk Assessment of PAH Inhalation Exposure by Monte Carlo Simulation

Monte Carlo simulation (MCS) is a computational technique widely used in exposure and risk assessment. However, the result of traditional health risk assessment based on the MCS method has always been questioned due to the uncertainty introduced in parameter estimation and the difficulty in result validation. Herein, data from a large-scale investigation of individual polycyclic aromatic hydrocarbon (PAH) exposure was used to explore the key factors for improving the MCS method. Research participants were selected using a statistical sampling method in a typical PAH polluted city. Atmospheric PAH concentrations from 25 sampling sites in the area were detected by GC-MS and exposure parameters of participants were collected by field measurement. The incremental lifetime cancer risk (ILCR) of participants was calculated based on the measured data and considered to be the actual carcinogenic risk of the population. Predicted risks were evaluated by traditional assessment method based on MCS and three improved models including concentration-adjusted, age-stratified, and correlated-parameter-adjusted Monte Carlo methods. The goodness of fit of the models was evaluated quantitatively by comparing with the actual risk. The results showed that the average risk derived by traditional and age-stratified Monte Carlo simulation was 2.6 times higher, and the standard deviation was 3.7 times higher than the actual values. In contrast, the predicted risks of concentration- and correlated-parameter-adjusted models were in good agreement with the actual ILCR. The results of the comparison suggested that accurate simulation of exposure concentration and adjustment of correlated parameters could greatly improve the MCS. The research also reveals that the social factors related to exposure and potential relationship between variables are important issues affecting risk assessment, which require full consideration in assessment and further study in future research.

Bayesian population physiologically-based pharmacokinetic model for robustness evaluation of withdrawal time in tilapia aquaculture administrated to florfenicol

The antimicrobial residues of aquacultural production is a growing public concern, leading to reexamine the method for establishing robust withdrawal time and ensuring food safety. Our study aims to develop the optimizing population physiologically-based pharmacokinetic (PBPK) model for assessing florfenicol residues in the tilapia tissues, and for evaluating the robustness of the withdrawal time (WT). Fitting with published pharmacokinetic profiles that experimented under temperatures of 22 and 28 °C, a PBPK model was constructed by applying with the Bayesian Markov chain Monte Carol (MCMC) algorithm to estimate WTs under different physiological, environmental and dosing scenarios. Results show that the MCMC algorithm improves the estimates of uncertainty and variability of PBPK-related parameters, and optimizes the simulation of the PBPK model. It is noteworthy that posterior sets generated from temperature-associated datasets to be respectively used for simulating residues under corresponding temperature conditions. Simulating the residues under regulated regimen and overdosing scenarios for Taiwan, the estimated WTs were 12-16 days at 22 °C and 9-12 days at 28 °C, while for the USA, the estimated WTs were 14-18 and 11-14 days, respectively. Comparison with the regulated WT of 15 days, results indicate that the current WT has well robustness and resilience in the environment of higher temperatures. The optimal Bayesian population PBPK model provides effective analysis for determining WTs under scenario-specific conditions. It is a new insight into the increasing body of literature on developing the Bayesian-PBPK model and has practical implications for improving the regulation of food safety.

Estimating seasonal variations of realistic exposure doses and risks to organs due to ambient particulate matter -bound metals of Delhi

This study aims to calculate deposition of PM_2.5 -bound hazardous metals in different organs after inhalation of particulate matter for the Delhi (India), and to estimate risks to organs following inhalation. Bio-accessible fractions of three PM-associated carcinogenic metals (As, Pb &Cd) were calculated using the metal values in simulated lung fluids. Depositions of metals in different organs were calculated using an integrated model consists of HRT and PBPK models. The calculation indicates that the major or significant deposition of metal Pb occurs in tissues, such as bone, muscle and blood. Most of the depositions of Cd happens in lung whereas most of the depositions of As happens in lung, muscle and skin. Most of the deposition of studied metals was found in lung (45% for arsenic and 70% for cadmium of their bio -dissolved contents). The following order of depositions of metals in different tissues were found (from highest deposition to smallest deposition): As: Lung > muscle = liver; Pb: bone > blood > muscle; Cd: lung > intestine. The combined exposures of PM_2.5 and its associated metals were found to give interaction-based hazard index greater than 1 for several months of the year, indicating a chance of health risk. Hazard quotient (HQ) <1 was seen for ingestion and dermal pathways, indicating no cause of concern. Findings indicate the need for doing periodic monitoring and estimating deposition doses and exposure risks of PM-associated metals to lungs and other organs for protecting human health.

High inter-species differences of 12378-polychlorinated dibenzo-p-dioxin between humans and mice

Although huge interspecies differences in the response to dioxins have been acknowledged, toxic equivalency factors derived from rodent studies are often used to assess human health risk. To determine interspecies differences, we first developed a toxicokinetic model in humans by measuring dioxin concentrations in environmental and biomonitoring samples from Southern China. Significant positive correlations between dioxin concentrations in blood and age were observed for seven dioxin congeners, indicating an age-dependent elimination rate. Based on toxicokinetic models in humans, the half-lives of 15 dioxin congeners were estimated to be 1.60-28.55 years. In consideration that the highest contribution to total toxic equivalency in blood samples was by 12378-polychlorinated dibenzo-p-dioxin (P₅CDD), this study developed a physiologically based pharmacokinetic (PBPK) model of 12378-P₅CDD levels in the liver, kidney, and fat of C57/6J mice exposed to a single oral dose, and the half-life was estimated to be 26.1 days. Based on estimated half-lives in humans and mice, we determined that the interspecies difference of 12378-P₅CDD was 71, much higher than the default usually used in risk assessment. These results could reduce the uncertainty human risk assessment of 12378-P₅CDD, and our approach could be used to estimate the interspecies differences of other dioxin congeners.

Development of a generic lifelong physiologically based biokinetic model for exposome studies

The current study within the frame of the HEALS project aims at the development of a lifelong physiologically based biokinetic (PBBK) model for exposome studies. The aim was to deliver a comprehensive modelling framework for addressing a large chemical space. Towards this aim, the delivered model can easily adapt parameters from existing ad-hoc models or complete the missing compound specific parameters using advanced quantitative structure activity relationship (QSAR). All major human organs are included, as well as arterial, venous, and portal blood compartments. Xenobiotics and their metabolites are linked through the metabolizing tissues. This is mainly the liver, but also other sites of metabolism might be considered (intestine, brain, skin, placenta) based on the presence or not of the enzymes involved in the metabolism of the compound of interest. Each tissue is described by three mass balance equations for (a) red blood cells, (b) plasma and interstitial tissue and (c) cells respectively. The anthropometric parameters of the models are time dependent, so as to provide a lifetime internal dose assessment, as well as to describe the continuously changing physiology of the mother and the developing fetus. An additional component of flexibility is that the biokinetic processes that relate to metabolism are related with either Michaelis-Menten kinetics, as well as intrinsic clearance kinetics. The capability of the model is demonstrated in the assessment of internal exposure and the prediction of expected biomonitored levels in urine for three major compounds within the HEALS project, namely bisphenol A (BPA), Bis(2-ethylhexyl) phthalate (DEHP) and cadmium (Cd). The results indicated that the predicted urinary levels fit very well with the ones from human biomonitoring (HBM) studies; internal exposure to plasticizers is very low (in the range of ng/L), while internal exposure to Cd is in the range of μg/L.

Critical assessment and integration of separate lines of evidence for risk assessment of chemical mixtures

Humans are exposed to multiple chemicals on a daily basis instead of to just a single chemical, yet the majority of existing toxicity data comes from single-chemical exposure. Multiple factors must be considered such as the route, concentration, duration, and the timing of exposure when determining toxicity to the organism. The need for adequate model systems (in vivo, in vitro, in silico and mathematical) is paramount for better understanding of chemical mixture toxicity. Currently, shortcomings plague each model system as investigators struggle to find the appropriate balance of rigor, reproducibility and appropriateness in mixture toxicity studies. Significant questions exist when comparing single-to mixture-chemical toxicity concerning additivity, synergism, potentiation, or antagonism. Dose/concentration relevance is a major consideration and should be subthreshold for better accuracy in toxicity assessment. Previous work was limited by the technology and methodology of the time, but recent advances have resulted in significant progress in the study of mixture toxicology. Novel technologies have added insight to data obtained from in vivo studies for predictive toxicity testing. These include new in vitro models: omics-related tools, organs-on-a-chip and 3D cell culture, and in silico methods. Taken together, all these modern methodologies improve the understanding of the multiple toxicity pathways associated with adverse outcomes (e.g., adverse outcome pathways), thus allowing investigators to better predict risks linked to exposure to chemical mixtures. As technology and knowledge advance, our ability to harness and integrate separate streams of evidence regarding outcomes associated with chemical mixture exposure improves. As many national and international organizations are currently stressing, studies on chemical mixture toxicity are of primary importance.

Bayesian evaluation of a physiologically based pharmacokinetic (PBPK) model for perfluorooctane sulfonate (PFOS) to characterize the interspecies uncertainty between mice, rats, monkeys, and humans: Development and performance verification

A challenge in the risk assessment of perfluorooctane sulfonate (PFOS) is the large interspecies differences in its toxicokinetics that results in substantial uncertainty in the dosimetry and toxicity extrapolation from animals to humans. To address this challenge, the objective of this study was to develop an open-source physiologically based pharmacokinetic (PBPK) model accounting for species-specific toxicokinetic parameters of PFOS. Considering available knowledge about the toxicokinetic properties of PFOS, a PBPK model for PFOS in mice, rats, monkeys, and humans after intravenous and oral administrations was created. Available species-specific toxicokinetic data were used for model calibration and optimization, and independent datasets were used for model evaluation. Bayesian statistical analysis using Markov chain Monte Carlo (MCMC) simulation was performed to optimize the model and to characterize the uncertainty and interspecies variability of chemical-specific parameters. The model predictions well correlated with the majority of datasets for all four species, and the model was validated with independent data in rats, monkeys, and humans. The model was applied to predict human equivalent doses (HEDs) based on reported points of departure in selected critical toxicity studies in rats and monkeys following U.S. EPA's guidelines. The lower bounds of the model-derived HEDs were overall lower than the HEDs estimated by U.S. EPA (e.g., 0.2 vs. 1.3 μg/kg/day based on the rat plasma data). This integrated and comparative analysis provides an important step towards improving interspecies extrapolation and quantitative risk assessment of PFOS, and this open-source model provides a foundation for developing models for other perfluoroalkyl substances.

Physiology-based toxicokinetic modelling in the frame of the European Human Biomonitoring Initiative

Given the opportunities provided by internal dosimetry modelling in the interpretation of human biomonitoring (HBM) data, the assessment of the links between exposure to chemicals and observed HBM data can be effectively supported by PBTK modelling. This paper gives a comprehensive review of available human PBTK models for compounds selected as a priority by the European Human Biomonitoring Initiative (HBM4EU). We highlight their advantages and deficiencies and suggest steps for advanced internal dose modelling. The review of the available PBTK models highlighted the conceptual differences between older models compared to the ones developed recently, reflecting commensurate differences in research questions. Due to the lack of coordinated strategies for deriving useful biomonitoring data for toxicokinetic properties, significant problems in model parameterisation still remain; these are further increased by the lack of human toxicokinetic data due to ethics issues. Finally, questions arise as well as to the extent they are really representative of interindividual variability. QSARs for toxicokinetic properties is a complementary approach for PBTK model parameterisation, especially for data poor chemicals. This approach could be expanded to model chemico-biological interactions such as intestinal absorption and renal clearance; this could serve the development of more complex generic PBTK models that could be applied to newly derived chemicals. Another gap identified is the framework for mixture interaction terms among compounds that could eventually interact in metabolism. From the review it was concluded that efforts should be shifted toward the development of generic multi-compartmental and multi-route models, supported by targeted biomonitoring coupled with parameterisation by both QSAR approach and experimental (in-vivo and in-vitro) data for newly developed and data poor compounds.

PBTK model for assessment of operator exposure to haloxyfop using human biomonitoring and toxicokinetic data

Physiologically-based toxicokinetic (PBTK) models are mathematical representations of chemical absorption, distribution, metabolism and excretion (ADME) in animals. Each parameter in a PBTK model describes a physiological, physicochemical or biochemical process that affects ADME. Distributions can be assigned to the model parameters to describe population variability and uncertainty. In this study to assess potential crop sprayer operator exposure to the herbicide haloxyfop, a permeability-limited PBTK model was constructed with parameter uncertainty and variability, and calibrated using Bayesian analysis via Markov chain Monte Carlo methods. A hierarchical statistical model was developed to reconstruct operator exposure using available measurement data: experimentally determined octanol/water partition coefficient, mouse and human toxicokinetic data as well as human biomonitoring data from seven operators who participated in a field study. A chemical risk assessment was performed by comparing the estimated systemic exposure to the acceptable operator exposure level (AOEL). The analysis suggested that in one of the seven operators, the model estimates systemic exposure to haloxyfop of 49.04 ± 10.19 SD μg/kg bw in relation to an AOEL of 5.0 μg/kg bw/day. This does not represent a safety concern as this predicted exposure is well within the 100-fold uncertainty factor applied to the No Observed Adverse Effect Level (NOAEL) in animals. In addition, given the availability of human toxicokinetic data, the 10x uncertainty factor for interspecies differences in ADME could be reduced (EFSA, 2006). Thus the AOEL could potentially be raised tenfold from 5.0 to 50.0 μg/kg bw/day.

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 (K_p) 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 K_p measured by in vivo experiments for 143 compounds. Initially, predicted K_p were significantly larger than measured K_p for many lipophilic compounds (log₁₀ octanol:water partition coefficient > 3). Hence the approach for predicting K_p 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 K_p across 23 compounds with only 3 K_p worsening by more than a factor of 10. The vast majority (92%) of K_p 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 (V_ss) 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.

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.

Probabilistic modeling of aggregate lead exposure in children of urban China using an adapted IEUBK model

Lead, a ubiquitous pollutant throughout the environment, is confirmed to be neurotoxic for children by pulmonary and oral routes. As preschool children in China continue to be exposed to lead, we analyzed the available biomonitoring data for preschool children in urban China collected in the period 2004-2014 through a literature review. To identify apportionment of lead exposure sources for urban children in China, we modified the IEUBK model with a Monte Carlo module to assess the uncertainty and variability of the model output based on limited available exposure data and compared the simulated blood lead levels with the observed ones obtained through literature review. Although children's blood lead levels in urban China decreased statistically over time for the included studies, changes in blood lead levels in three economic zones and seven age groups except for two age-specific groups were no longer significant. The GM-predicted BLLs and the GM-observed BLLs agreed within 1μg/dL for all fourteen cities. The 95% CIs for the predicted GMs and the observed distribution (GM±GSD) overlapped substantially. These results demonstrated the plausibility of blood lead prediction provided by the adapted IEUBK model. Lead exposure estimates for diet, soil/dust, air, and drinking water were 12.01±6.27μg/day, 2.69±0.89μg/day, 0.20±0.15μg/day, and 0.029±0.012μg/day, respectively. These findings showed that the reduction of lead concentrations in grains and vegetables would be beneficial to limit the risk of dietary lead exposure for a large proportion of preschool children in urban China.

Using publicly available data, a physiologically-based pharmacokinetic model and Bayesian simulation to improve arsenic non-cancer dose-response

Publicly available data can potentially examine the relationship between environmental exposure and public health, however, it has not yet been widely applied. Arsenic is of environmental concern, and previous studies mathematically parameterized exposure duration to create a link between duration of exposure and increase in risk. However, since the dose metric emerging from exposure duration is not a linear or explicit variable, it is difficult to address the effects of exposure duration simply by using mathematical functions. To relate cumulative dose metric to public health requires a lifetime physiologically-based pharmacokinetic (PBPK) model, yet this model is not available at a population level. In this study, the data from the U.S. total diet study (TDS, 2006-2011) was employed to assess exposure: daily dietary intakes for total arsenic (tAs) and inorganic arsenic (iAs) were estimated to be 0.15 and 0.028μg/kg/day, respectively. Meanwhile, using National Health and Nutrition Examination Survey (NHANES, 2011-2012) data, the fraction of urinary As(III) levels (geometric mean: 0.31μg/L) in tAs (geometric mean: 7.75μg/L) was firstly reported to be approximately 4%. Together with Bayesian technique, the assessed exposure and urinary As(III) concentration were input to successfully optimize a lifetime population PBPK model. Finally, this optimized PBPK model was used to derive an oral reference dose (Rfd) of 0.8μg/kg/day for iAs exposure. Our study also suggests the previous approach (by using mathematical functions to account for exposure duration) may result in a conservative Rfd estimation.

Combining the 'bottom up' and 'top down' approaches in pharmacokinetic modelling: fitting PBPK models to observed clinical data

Pharmacokinetic models range from being entirely exploratory and empirical, to semi-mechanistic and ultimately complex physiologically based pharmacokinetic (PBPK) models. This choice is conditional on the modelling purpose as well as the amount and quality of the available data. The main advantage of PBPK models is that they can be used to extrapolate outside the studied population and experimental conditions. The trade-off for this advantage is a complex system of differential equations with a considerable number of model parameters. When these parameters cannot be informed from in vitro or in silico experiments they are usually optimized with respect to observed clinical data. Parameter estimation in complex models is a challenging task associated with many methodological issues which are discussed here with specific recommendations. Concepts such as structural and practical identifiability are described with regards to PBPK modelling and the value of experimental design and sensitivity analyses is sketched out. Parameter estimation approaches are discussed, while we also highlight the importance of not neglecting the covariance structure between model parameters and the uncertainty and population variability that is associated with them. Finally the possibility of using model order reduction techniques and minimal semi-mechanistic models that retain the physiological-mechanistic nature only in the parts of the model which are relevant to the desired modelling purpose is emphasized. Careful attention to all the above issues allows us to integrate successfully information from in vitro or in silico experiments together with information deriving from observed clinical data and develop mechanistically sound models with clinical relevance.

Uncertainties in human health risk assessment of environmental contaminants: A review and perspective

Addressing uncertainties in human health risk assessment is a critical issue when evaluating the effects of contaminants on public health. A range of uncertainties exist through the source-to-outcome continuum, including exposure assessment, hazard and risk characterisation. While various strategies have been applied to characterising uncertainty, classical approaches largely rely on how to maximise the available resources. Expert judgement, defaults and tools for characterising quantitative uncertainty attempt to fill the gap between data and regulation requirements. The experiences of researching 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD) illustrated uncertainty sources and how to maximise available information to determine uncertainties, and thereby provide an 'adequate' protection to contaminant exposure. As regulatory requirements and recurring issues increase, the assessment of complex scenarios involving a large number of chemicals requires more sophisticated tools. Recent advances in exposure and toxicology science provide a large data set for environmental contaminants and public health. In particular, biomonitoring information, in vitro data streams and computational toxicology are the crucial factors in the NexGen risk assessment, as well as uncertainties minimisation. Although in this review we cannot yet predict how the exposure science and modern toxicology will develop in the long-term, current techniques from emerging science can be integrated to improve decision-making.

Incorporation of stochastic variability in mechanistic population pharmacokinetic models: handling the physiological constraints using normal transformations

The utilisation of physiologically-based pharmacokinetic models for the analysis of population data is an approach with progressively increasing impact. However, as we move from empirical to complex mechanistic model structures, incorporation of stochastic variability in model parameters can be challenging due to the physiological constraints that may arise. Here, we investigated the most common types of constraints faced in mechanistic pharmacokinetic modelling and explored techniques for handling them during a population data analysis. An efficient way to impose stochastic variability on the parameters of interest without neglecting the underlying physiological constraints is through the assumption that they follow a distribution with support and properties matching the underlying physiology. It was found that two distributions that arise through transformations of the normal, the logit-normal generalisation and the logistic-normal, are excellent for such an application as not only they can satisfy the physiological constraints but also offer high flexibility during characterisation of the parameters' distribution. The statistical properties and practical advantages/disadvantages of these distributions for such an application were clearly displayed in the context of different modelling examples. Finally, a simulation study clearly illustrated the practical gains of the utilisation of the described techniques, as omission of population variability in physiological systems parameters leads to a biased/misplaced stochastic model with mechanistically incorrect variance structure. The current methodological work aims to facilitate the use of mechanistic/physiologically-based models for the analysis of population pharmacokinetic clinical data.

A Novel Method for Assessing Drug Degradation Product Safety Using Physiologically-Based Pharmacokinetic Models and Stochastic Risk Assessment

Patient safety risk due to toxic degradation products is a potentially critical quality issue for a small group of useful drug substances. Although the pharmacokinetics of toxic drug degradation products may impact product safety, these data are frequently unavailable. The objective of this study is to incorporate the prediction capability of physiologically based pharmacokinetic (PBPK) models into a rational drug degradation product risk assessment procedure using a series of model drug degradants (substituted anilines). The PBPK models were parameterized using a combination of experimental and literature data and computational methods. The impact of model parameter uncertainty was incorporated into stochastic risk assessment procedure for estimating human safe exposure levels based on the novel use of a statistical metric called "PROB" for comparing probability that a human toxicity-target tissue exposure exceeds the rat exposure level at a critical no-observed-adverse-effect level. When compared with traditional risk assessment calculations, this novel PBPK approach appeared to provide a rational basis for drug instability risk assessment by focusing on target tissue exposure and leveraging physiological, biochemical, biophysical knowledge of compounds and species.

Influence of Sexual Dimorphism on Pulmonary Inflammatory Response in Adult Mice Exposed to Chloroform

Chloroform is an organic solvent used as an intermediate in the synthesis of various fluorocarbons. Despite its widespread use in industry and agriculture, exposure to chloroform can cause illnesses such as cancer, especially in the liver and kidneys. The aim of the study was to analyze the effects of chloroform on redox imbalance and pulmonary inflammatory response in adult C57BL/6 mice. Forty animals were divided into 4 groups (N = 10): female (FCG) and male (MCG) controls, and females (FEG) and males (MEG) exposed to chloroform (7.0 ppm) 3 times/d for 20 minutes for 5 days. Total and differential cell counts, oxidative damage analysis, and protein carbonyl and antioxidant enzyme catalase (CAT) activity measurements were performed. Morphometric analyses included alveolar area (Aa) and volume density of alveolar septa (Vv) measurements. Compared to FCG and MCG, inflammatory cell influx, oxidative damage to lipids and proteins, and CAT activity were higher in FEG and MEG, respectively. Oxidative damage and enzyme CAT activity were higher in FEG than in FCG. The Aa was higher in FEG and MEG than in FCG and MCG, respectively. The Vv was lower in FEG and MEG than in FCG and MCG, respectively. This study highlights the risks of occupational chloroform exposure at low concentrations and the intensity of oxidative damage related to gender. The results validate a model of acute exposure that provides cellular and biochemical data through short-term exposure to chloroform.

An analysis of whole body tracer kinetics in dynamic PET studies with application to image-based blood input function extraction

In a positron emission tomography (PET) study, the local uptake of the tracer is dependent on vascular delivery and retention. For dynamic studies the measured uptake time-course information can be best interpreted when knowledge of the time-course of tracer in the blood is available. This is certainly true for the most established tracers such as 18F-Fluorodeoxyglucose (FDG) and 15O-Water (H2O). Since direct sampling of blood as part of PET studies is increasingly impractical, there is ongoing interest in image-extraction of blood time-course information. But analysis of PET-measured blood pool signals is complicated because they will typically involve a combination of arterial, venous and tissue information. Thus, a careful appreciation of these components is needed to interpret the available data. To facilitate this process, we propose a novel Markov chain model for representation of the circulation of a tracer atom in the body. The model represents both arterial and venous time-course patterns. Under reasonable conditions equilibration of tracer activity in arterial and venous blood is achieved by the end of the PET study-consistent with empirical measurement. Statistical inference for Markov model parameters is a challenge. A penalized nonlinear least squares process, incorporating a generalized cross-validation score, is proposed. Random effects analysis is used to adaptively specify the structure of the penalty function based on historical samples of directly measured blood data. A collection of arterially sampled data from PET studies with FDG and H2O is used to illustrate the methodology. These data analyses are highly supportive of the overall modeling approach. An adaptation of the model to the problem of extraction of arterial blood signals from imaging data is also developed and promising preliminary results for cerebral and thoracic imaging studies with FDG and H2O are obtained.

Using Bayesian-PBPK modeling for assessment of inter-individual variability and subgroup stratification

Purpose

Inter-individual variability in clinical endpoints and occurrence of potentially severe adverse effects represent an enormous challenge in drug development at all phases of (pre-)clinical research. To ensure patient safety it is important to identify adverse events or critical subgroups within the population as early as possible. Hence, a comprehensive understanding of the processes governing pharmacokinetics and pharmacodynamics is of utmost importance. In this paper we combine Bayesian statistics with detailed mechanistic physiologically-based pharmacokinetic (PBPK) models. On the example of pravastatin we demonstrate that this combination provides a powerful tool to investigate inter-individual variability in groups of patients and to identify clinically relevant homogenous subgroups in an unsupervised approach. Since PBPK models allow the identification of physiological, drug-specific and genotype-specific knowledge separately, our approach supports knowledge-based extrapolation to other drugs or populations.

Methods

PBPK models are based on generic distribution models and extensive collections of physiological parameters and allow a mechanistic investigation of drug distribution and drug action. To systematically account for parameter variability within patient populations, a Bayesian-PBPK approach is developed rigorously quantifying the probability of a parameter given the amount of information contained in the measured data. Since these parameter distributions are high-dimensional, a Markov chain Monte Carlo algorithm is used, where the physiological and drug-specific parameters are considered in separate blocks.

Results

Considering pravastatin pharmacokinetics as an application example, Bayesian-PBPK is used to investigate inter-individual variability in a cohort of 10 patients. Correlation analyses infer structural information about the PBPK model. Moreover, homogeneous subpopulations are identified a posteriori by examining the parameter distributions, which can even be assigned to a polymorphism in the hepatic organ anion transporter OATP1B1.

Conclusions

The presented Bayesian-PBPK approach systematically characterizes inter-individual variability within a population by updating prior knowledge about physiological parameters with new experimental data. Moreover, clinically relevant homogeneous subpopulations can be mechanistically identified. The large scale PBPK model separates physiological and drug-specific knowledge which allows, in combination with Bayesian approaches, the iterative assessment of specific populations by integrating information from several drugs.

Electronic supplementary material

The online version of this article (doi:10.1186/2193-9616-1-6) contains supplementary material, which is available to authorized users.

A multi-route model of nicotine-cotinine pharmacokinetics, pharmacodynamics and brain nicotinic acetylcholine receptor binding in humans

The pharmacokinetics of nicotine, the pharmacologically active alkaloid in tobacco responsible for addiction, are well characterized in humans. We developed a physiologically based pharmacokinetic/pharmacodynamic model of nicotine pharmacokinetics, brain dosimetry and brain nicotinic acetylcholine receptor (nAChRs) occupancy. A Bayesian framework was applied to optimize model parameters against multiple human data sets. The resulting model was consistent with both calibration and test data sets, but in general underestimated variability. A pharmacodynamic model relating nicotine levels to increases in heart rate as a proxy for the pharmacological effects of nicotine accurately described the nicotine related changes in heart rate and the development and decay of tolerance to nicotine. The PBPK model was utilized to quantitatively capture the combined impact of variation in physiological and metabolic parameters, nicotine availability and smoking compensation on the change in number of cigarettes smoked and toxicant exposure in a population of 10,000 people presented with a reduced toxicant (50%), reduced nicotine (50%) cigarette Across the population, toxicant exposure is reduced in some but not all smokers. Reductions are not in proportion to reductions in toxicant yields, largely due to partial compensation in response to reduced nicotine yields. This framework can be used as a key element of a dosimetry-driven risk assessment strategy for cigarette smoke constituents.

Development of lead source-specific exposure standards based on aggregate exposure assessment: Bayesian inversion from biomonitoring information to multipathway exposure

Exposure of children to lead is of great concern, and the exposure standards for different media are important for protecting public safety. However, these media-specific standards often fail to ensure the safety of children even when environmental lead levels are lower than the quality standards since humans are often exposed to lead via multiple pathways. To establish exposure standards to protect children from hazards associated with exposure to lead, an analytical tool for assessing aggregate exposure to lead based on Bayesian hierarchical model was developed, and then was used to update the external lead exposure of diet, paint, soil, air and drinking water using the blood lead levels in Chinese children aged 1-6 years. On the basis of updated external exposure, the source allocations for diet, paint, soil, air, and drinking water in China were 65.80 ± 7.92%, 16.98 ± 7.88%, 13.65 ± 5.05%, 3.36 ± 1.75%, and 0.20 ± 0.14%, respectively. Based on the estimated source allocations, the exposure standards were evaluated to be 0.2 μg/m(3), 24.25 mg/kg, 0.027 μg/L, 0.051 μg/mg, 0.042 μg/mg, 38.02 μg/mg for air, soil, water, grains, vegetables, and paint, respectively. Since the standards setting procedure was based on the multipathway aggregate exposure assessment of lead, the newly proposed exposure standards should ensure the safety of children.

Modeling of absorption

Absorption takes place when a compound enters an organism, which occurs as soon as the molecules enter the first cellular bilayer(s) in the tissue(s) to which is it exposed. At that point, the compound is no longer part of the environment (which includes the alimentary canal for oral exposure), but has become part of the organism. If absorption is prevented or limited, then toxicological effects are also prevented or limited. Thus, modeling absorption is the first step in simulating/predicting potential toxicological effects. Simulation software used to model absorption of compounds of various types has advanced considerably over the past 15 years. There can be strong interactions between absorption and pharmacokinetics (PK), requiring state-of-the-art simulation computer programs that combine absorption with either compartmental pharmacokinetics (PK) or physiologically based pharmacokinetics (PBPK). Pharmacodynamic (PD) models for therapeutic and adverse effects are also often linked to the absorption and PK simulations, providing PK/PD or PBPK/PD capabilities in a single package. These programs simulate the interactions among a variety of factors including the physicochemical properties of the molecule of interest, the physiologies of the organisms, and in some cases, environmental factors, to produce estimates of the time course of absorption and disposition of both toxic and nontoxic substances, as well as their pharmacodynamic effects.