Parameter variability and the interpretation of physiologically based pharmacokinetic modeling results

Does the Systemic Plasma Profile Inform the Liver Profile? Analysis Using a Physiologically Based Pharmacokinetic Model and Individual Compounds

The physiologically based pharmacokinetic (PBPK) model for liver transporter substrates has been established previously and used for predicting drug-drug interactions (DDI) and for clinical practice guidance. So far, nearly all the published PBPK models for liver transporter substrates have one or more hepatic clearance processes (i.e., active uptake, passive diffusion, metabolism, and biliary excretion) estimated by fitting observed systemic data. The estimated hepatic clearance processes are then used to predict liver concentrations and DDI involving either systemic or liver concentration. However, the accuracy and precision of such predictions are unclear. In this study, we try to address this question by using the PBPK model to generate simulated compounds for which we know both systemic and liver profiles. We then developed an approach to assess the accuracy and precision of predicted liver concentration. With hepatic clearance processes estimated using plasma data, model predictions of liver are typically accurate (i.e., true value is bounded by predicted maximum and minimum); however, only for a few compounds are predictions also precise. The results of the current study indicate that extra attention is required when using the current PBPK approach to predict liver concentration and DDI for transporter substrates dependent upon liver concentrations.

Heterogeneous dynamics, robustness/fragility trade-offs, and the eradication of the macroparasitic disease, lymphatic filariasis

BACKGROUND

The current WHO-led initiative to eradicate the macroparasitic disease, lymphatic filariasis (LF), based on single-dose annual mass drug administration (MDA) represents one of the largest health programs devised to reduce the burden of tropical diseases. However, despite the advances made in instituting large-scale MDA programs in affected countries, a challenge to meeting the goal of global eradication is the heterogeneous transmission of LF across endemic regions, and the impact that such complexity may have on the effort required to interrupt transmission in all socioecological settings.

METHODS

Here, we apply a Bayesian computer simulation procedure to fit transmission models of LF to field data assembled from 18 sites across the major LF endemic regions of Africa, Asia and Papua New Guinea, reflecting different ecological and vector characteristics, to investigate the impacts and implications of transmission heterogeneity and complexity on filarial infection dynamics, system robustness and control.

RESULTS

We find firstly that LF elimination thresholds varied significantly between the 18 study communities owing to site variations in transmission and initial ecological parameters. We highlight how this variation in thresholds lead to the need for applying variable durations of interventions across endemic communities for achieving LF elimination; however, a major new result is the finding that filarial population responses to interventions ultimately reflect outcomes of interplays between dynamics and the biological architectures and processes that generate robustness/fragility trade-offs in parasite transmission. Intervention simulations carried out in this study further show how understanding these factors is also key to the design of options that would effectively eliminate LF from all settings. In this regard, we find how including vector control into MDA programs may not only offer a countermeasure that will reliably increase system fragility globally across all settings and hence provide a control option robust to differential locality-specific transmission dynamics, but by simultaneously reducing transmission regime variability also permit more reliable macroscopic predictions of intervention effects.

CONCLUSIONS

Our results imply that a new approach, combining adaptive modelling of parasite transmission with the use of biological robustness as a design principle, is required if we are to both enhance understanding of complex parasitic infections and delineate options to facilitate their elimination effectively.

PCDD/Fs in plasma of individuals living near a hazardous waste incinerator. A comparison of measured levels and estimated concentrations by PBPK modeling

The construction of the first and, until now, only hazardous waste incinerator (HWI) in Spain finished in 1998. To assess its potential impact on the population living in the vicinity, a surveillance program was established. It includes the periodical biomonitoring of PCDD/Fs body burden. On the basis of this program, in 2012 we determined the levels of PCDD/Fs in plasma of nonoccupationally exposed individuals living near the HWI. The results were compared with those of the baseline study, and with those of two previous surveys (2002 and 2007). A multicompartment, physiologically based pharmacokinetic (PBPK) model was also applied to estimate the levels of PCDD/Fs in plasma. The model was validated by comparing the results with our experimental data (baseline, 2002, 2007, and 2012). The current mean concentration was 6.18 pg I-TEQ/g lipid, with a range between 2.03 and 18.8 pg I-TEQ/g lipid. In 1998 (baseline), the mean concentration of PCDD/Fs in plasma was 27.0 pg I-TEQ/g lipid (reduction of 77%, p < 0.001). Significant reductions were also noted in our previous 2002 and 2007 surveys, with mean concentrations of 15.7 and 9.36 pg I-TEQ/g lipid, respectively. However, the comparison between simulated (using the PBPK model) and experimental results was very successful, as PCDD/F values in plasma were very similar (7.95 vs 6.18 pg I-TEQ/g lipid). The levels of PCDD/Fs in plasma of nonoccupationally exposed individuals living near the HWI here assessed are comparatively lower than most recently reported values.

Addressing human variability in next-generation human health risk assessments of environmental chemicals

BACKGROUND

Characterizing variability in the extent and nature of responses to environmental exposures is a critical aspect of human health risk assessment.

OBJECTIVE

Our goal was to explore how next-generation human health risk assessments may better characterize variability in the context of the conceptual framework for the source-to-outcome continuum.

METHODS

This review was informed by a National Research Council workshop titled "Biological Factors that Underlie Individual Susceptibility to Environmental Stressors and Their Implications for Decision-Making." We considered current experimental and in silico approaches, and emerging data streams (such as genetically defined human cells lines, genetically diverse rodent models, human omic profiling, and genome-wide association studies) that are providing new types of information and models relevant for assessing interindividual variability for application to human health risk assessments of environmental chemicals.

DISCUSSION

One challenge for characterizing variability is the wide range of sources of inherent biological variability (e.g., genetic and epigenetic variants) among individuals. A second challenge is that each particular pair of health outcomes and chemical exposures involves combinations of these sources, which may be further compounded by extrinsic factors (e.g., diet, psychosocial stressors, other exogenous chemical exposures). A third challenge is that different decision contexts present distinct needs regarding the identification-and extent of characterization-of interindividual variability in the human population.

CONCLUSIONS

Despite these inherent challenges, opportunities exist to incorporate evidence from emerging data streams for addressing interindividual variability in a range of decision-making contexts.

Geographic and ecologic heterogeneity in elimination thresholds for the major vector-borne helminthic disease, lymphatic filariasis

Background

Large-scale intervention programmes to control or eliminate several infectious diseases are currently underway worldwide. However, a major unresolved question remains: what are reasonable stopping points for these programmes? Recent theoretical work has highlighted how the ecological complexity and heterogeneity inherent in the transmission dynamics of macroparasites can result in elimination thresholds that vary between local communities. Here, we examine the empirical evidence for this hypothesis and its implications for the global elimination of the major macroparasitic disease, lymphatic filariasis, by applying a novel Bayesian computer simulation procedure to fit a dynamic model of the transmission of this parasitic disease to field data from nine villages with different ecological and geographical characteristics. Baseline lymphatic filariasis microfilarial age-prevalence data from three geographically distinct endemic regions, across which the major vector populations implicated in parasite transmission also differed, were used to fit and calibrate the relevant vector-specific filariasis transmission models. Ensembles of parasite elimination thresholds, generated using the Bayesian fitting procedure, were then examined in order to evaluate site-specific heterogeneity in the values of these thresholds and investigate the ecological factors that may underlie such variability

Results

We show that parameters of density-dependent functions relating to immunity, parasite establishment, as well as parasite aggregation, varied significantly between the nine different settings, contributing to locally varying filarial elimination thresholds. Parasite elimination thresholds predicted for the settings in which the mosquito vector is anopheline were, however, found to be higher than those in which the mosquito is culicine, substantiating our previous theoretical findings. The results also indicate that the probability that the parasite will be eliminated following six rounds of Mass Drug Administration with diethylcarbamazine and albendazole decreases markedly but non-linearly as the annual biting rate and parasite reproduction number increases.

Conclusions

This paper shows that specific ecological conditions in a community can lead to significant local differences in population dynamics and, consequently, elimination threshold estimates for lymphatic filariasis. These findings, and the difficulty of measuring the key local parameters (infection aggregation and acquired immunity) governing differences in transmission thresholds between communities, mean that it is necessary for us to rethink the utility of the current anticipatory approaches for achieving the elimination of filariasis both locally and globally.

The application of a Bayesian approach to the analysis of a complex, mechanistically based model

The Bayesian approach has been suggested as a suitable method in the context of mechanistic pharmacokinetic-pharmacodynamic (PK-PD) modeling, as it allows for efficient use of both data and prior knowledge regarding the drug or disease state. However, to this day, published examples of its application to real PK-PD problems have been scarce. We present an example of a fully Bayesian re-analysis of a previously published mechanistic model describing the time course of circulating neutrophils in stroke patients and healthy individuals. While priors could be established for all population parameters in the model, not all variability terms were known with any degree of precision. A sensitivity analysis around the assigned priors used was performed by testing three different sets of prior values for the population variance terms for which no data were available in the literature: "informative", "semi-informative", and "noninformative", respectively. For all variability terms, inverse gamma distributions were used. It was possible to fit the model to the data using the "informative" priors. However, when the "semi-informative" and "noninformative" priors were used, it was impossible to accomplish convergence due to severe correlations between parameters. In addition, due to the complexity of the model, the process of defining priors and running the Markov chains was very time-consuming. We conclude that the present analysis represents a first example of the fully transparent application of Bayesian methods to a complex, mechanistic PK-PD problem with real data. The approach is time-consuming, but enables us to make use of all available information from data and scientific evidence. Thereby, it shows potential both for detection of data gaps and for more reliable predictions of various outcomes and "what if" scenarios.

Occupational exposure limits in the context of solvent mixtures, consumption of ethanol, and target tissue dose

Individuals are exposed to mixtures, and never to single chemicals. Depending on the composition of the elements of mixtures, significant toxicological interactions between the components may occur. These interactions are complex and often difficult to predict, ranging from synergistic to additive and subadditive interactions. The nature of the interactions needs to be evaluated as the target tissue dose of the active form of each chemical. PBPK modeling is an effective tool for determining the target tissue dose and evaluating these interactions when data are available for model development. Some of the interactions are pharmacokinetic in nature, affecting the disposition of other chemicals in the body. Other interactions can be pharmacodynamic in nature, altering the effects that other chemicals have on the organism. For many organic solvents, these interactions occur principally at the level of the metabolizing enzyme, cytochrome P-450 2E1 (CYP2E1). Many solvents are known to induce or inhibit CYP2E1, or both. Mixtures may be comprised of concomitant exposures to chemicals or from components encountered separately on-the-job, off-the-job, through the diet, and otherwise. Examples of mixtures where the exposure to separate components occurs off the job will be discussed, with special emphasis on ethanol consumption as a modifier of solvent pharmacokinetics. The present practice of the linear extrapolation of the toxicity of individual mixture components in the interpretation of occupational exposure limits will also be critiqued.

Physiologically-based pharmacokinetic and toxicokinetic models in cancer risk assessment

Physiologically-based pharmacokinetic (PBPK) and toxicokinetic models are increasingly being used for the conduct of high dose to low dose and interspecies extrapolations required in cancer risk assessment. These models, by simulating tissue dose of toxic chemicals, help address the uncertainty associated with the default approaches for interspecies and high dose to low dose extrapolations. The applicability of PBPK models in cancer risk assessment has been demonstrated with a number of chemicals (e.g., acrylonitrile, 2-butoxyethanol, chloroform, 1,4-dioxane, methyl chloroform, methylene chloride, styrene, trichloroethylene, tetrachloroethylene, vinyl chloride, vinyl acetate). Recent advances in PBPK modeling facilitate the consideration of population distribution of parameter values, age-dependent changes in physiology and metabolism, multi-route exposures as well as multichemical interactions for application in cancer risk assessment. Whereas the average values for various input parameters have been used to evaluate the age-dependency of tissue dose, the Markov Chain Monte Carlo technique can be applied to address variability and uncertainty in parameter estimates, thus facilitating a more accurate estimation of cancer risk in the population. The PBPK models also uniquely facilitate the simulation of tissue dose, and thereby cancer risks, associated with multi-route and multichemical exposure situations. Overall, the recent advances reviewed in this article point to the continued enhancement of the scientific basis and applicability of PBPK models in cancer risk assessment.

Reconstructing population exposures from dose biomarkers: inhalation of trichloroethylene (TCE) as a case study

Physiologically based pharmacokinetic (PBPK) modeling is a well-established toxicological tool designed to relate exposure to a target tissue dose. The emergence of federal and state programs for environmental health tracking and the availability of exposure monitoring through biomarkers creates the opportunity to apply PBPK models to estimate exposures to environmental contaminants from urine, blood, and tissue samples. However, reconstructing exposures for large populations is complicated by often having too few biomarker samples, large uncertainties about exposures, and large interindividual variability. In this paper, we use an illustrative case study to identify some of these difficulties, and for a process for confronting them by reconstructing population-scale exposures using Bayesian inference. The application consists of interpreting biomarker data from eight adult males with controlled exposures to trichloroethylene (TCE) as if the biomarkers were random samples from a large population with unknown exposure conditions. The TCE concentrations in blood from the individuals fell into two distinctly different groups even though the individuals were simultaneously in a single exposure chamber. We successfully reconstructed the exposure scenarios for both subgroups - although the reconstruction of one subgroup is different than what is believed to be the true experimental conditions. We were however unable to predict with high certainty the concentration of TCE in air.

Whole body pharmacokinetic models

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

The Bayesian population approach to physiological toxicokinetic-toxicodynamic models--an example using the MCSim software

The calibration of physiologically based toxicokinetic models against experimental data encompasses the merging of prior knowledge with information present in the data. This prior knowledge is manifested in the scientific literature and associated with various degrees of uncertainty. The most convenient way to combine these sources of information is via the use of Bayesian statistical methods. Furthermore, toxicokinetic models are subject to both inter- and intra-individual variability. This variability may be handled statistically by the use of a population model. The MCSim software, which is available for free download on the Internet, permits the use of a population model in combination with a Bayesian statistical approach. An example of the use of MCSim in a recent model-based risk assessment of dichloromethane (DCM) is given and discussed.

Physiologically based modeling of the inhalation kinetics of styrene in humans using a bayesian population approach

Animal studies have implicated styrene as toxic to the central nervous system and its major metabolite styrene-7,8-oxide as a carcinogen. Therefore, a reliable estimate of the metabolic capacity for styrene in humans is of interest. However, the available models describing styrene kinetics in humans lack rigorous statistical validation and also ignore the population variability in metabolism. The population variability may be estimated by the use of population models. Furthermore, the statistical validation of pharmacokinetic models may be improved by use of Bayesian methods. These two approaches may be combined and recently have been gaining interest in the toxicology literature. A population-based physiologically based pharmacokinetic (PBPK) model for styrene was developed. The model was calibrated to extensive human toxicokinetic data from three previous studies in which 24 volunteers were exposed to 50-386 ppm of styrene at rest and various levels of exercise. Model fitting was performed in a Bayesian framework using Markov chain Monte Carlo simulation. The uncertainty around the partition coefficients and metabolic parameters for styrene was reduced. The metabolic capacity for styrene in humans was estimated to be 0.92 micromol/l kg(-1), with a lognormal standard deviation of 1.66. The estimated Vmax is 40% higher than previously estimated, whereas the population standard deviation is estimated for the first time.

Modelling and simulation of variability and uncertainty in toxicokinetics and pharmacokinetics

Two important methodological issues within the framework of the variability and uncertainty analysis of toxicokinetic and pharmacokinetic systems are discussed: (i) modelling and simulation of the existing physiologic variability in a population; and (ii) modelling and simulation of variability and uncertainty when there is insufficient or not well defined (e.g. small sample, semiquantitative, qualitative and vague) information available. Physiologically based pharmacokinetic models are especially suited for separating and characterising the physiologic variability from the overall variability and uncertainty in the system. Monte Carlo sampling should draw from multivariate distributions, which reflect all levels of existing dependencies in the intact organism. The population characteristics should be taken into account. A fuzzy simulation approach is proposed to model variability and uncertainty when there is semiquantitative, qualitative and vague information about the model parameters and their statistical distributions cannot be defined reliably.

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

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

Analysis of PBPK models for risk characterization

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

Population toxicokinetics of benzene

In assessing the distribution and metabolism of toxic compounds in the body, measurements are not always feasible for ethical or technical reasons. Computer modeling offers a reasonable alternative, but the variability and complexity of biological systems pose unique challenges in model building and adjustment. Recent tools from population pharmacokinetics, Bayesian statistical inference, and physiological modeling can be brought together to solve these problems. As an example, we modeled the distribution and metabolism of benzene in humans. We derive statistical distributions for the parameters of a physiological model of benzene, on the basis of existing data. The model adequately fits both prior physiological information and experimental data. An estimate of the relationship between benzene exposure (up to 10 ppm) and fraction metabolized in the bone marrow is obtained and is shown to be linear for the subjects studied. Our median population estimate for the fraction of benzene metabolized, independent of exposure levels, is 52% (90% confidence interval, 47-67%). At levels approaching occupational inhalation exposure (continuous 1 ppm exposure), the estimated quantity metabolized in the bone marrow ranges from 2 to 40 mg/day.