Quantitative Characterization of Population-Wide Tissue- and Metabolite-Specific Variability in Perchloroethylene Toxicokinetics in Male Mice

Abstract

Quantification of interindividual variability is a continuing challenge in risk assessment, particularly for compounds with complex metabolism and multi-organ toxicity. Toxicokinetic variability for perchloroethylene (perc) was previously characterized across 3 mouse strains and in 1 mouse strain with various degrees of liver steatosis. To further characterize the role of genetic variability in toxicokinetics of perc, we applied Bayesian population physiologically based pharmacokinetic (PBPK) modeling to the data on perc and metabolites in blood/plasma and tissues of male mice from 45 inbred strains from the Collaborative Cross (CC) mouse population. After identifying the most influential PBPK parameters based on global sensitivity analysis, we fit the model with a hierarchical Bayesian population analysis using Markov chain Monte Carlo simulation. We found that the data from 3 commonly used strains were not representative of the full range of variability in perc and metabolite blood/plasma and tissue concentrations across the CC population. Using interstrain variability as a surrogate for human interindividual variability, we calculated dose-dependent, chemical-, and tissue-specific toxicokinetic variability factors (TKVFs) as candidate science-based replacements for the default uncertainty factor for human toxicokinetic variability of 10^0.5. We found that toxicokinetic variability factors for glutathione conjugation metabolites of perc showed the greatest variability, often exceeding the default, whereas those for oxidative metabolites and perc itself were generally less than the default. Overall, we demonstrate how a combination of a population-based mouse model such as the CC with Bayesian population PBPK modeling can reduce uncertainty in human toxicokinetic variability and increase accuracy and precision in quantitative risk assessment.

Perchloroethylene (perc) is an environmental toxicant of significant public health concern because it is a high-production volume industrial chemical that persists in the environment and has a potential for causing serious health effects in multiple organs in humans and animals (Cichocki et al., 2016; IARC, 2014; Luo et al., 2018b; USEPA, 2011a,b). Perc exposure is associated with numerous cancer and noncancer toxicities, and is classified by IARC as a probable human carcinogen (Group 2A; IARC, 2014), based on sufficient evidence for carcinogenesis from chronic studies in rodents and limited epidemiologic data supporting an association between perc exposure and cancer of the bladder, esophagus, kidney, and cervix. Among the noncancer toxicities in several organs associated with perc exposure (USEPA, 2011b), neurotoxicity is the most sensitive pathway in humans and is well correlated with parent compound concentrations at the target site (Bushnell et al., 2005; USEPA, 2011a). Understanding perc metabolism is especially important toxicologically, because a number of observed cancer and noncancer endpoints are associated with its specific metabolites or metabolic pathways. Perc and its metabolites trichloroacetic acid (TCA) and dichloroacetic acid were associated with similar effects in the liver of rodents, including hepatomegaly in rats and mice and hepatocarcinogenicity in multiple strains and both sexes of mice but not in rats (DeAngelo et al., 1999, 2008 JISA, 1993; NCI, 1977; NTP, 1986; Pereira, 1996). On the other hand, tubular toxicity in the kidney of both mice and rats, and kidney tumors in rats (JISA, 1993; NTP, 1986) are thought to be associated with the perc metabolism by glutathione (GSH) conjugation, based on the production in the kidney of nephrotoxic and genotoxic metabolites from this pathway (Lash and Parker, 2001).

The metabolism of perc is complex with multiple tissues directly involved and extensive interorgan transport. Except for neurological effects, toxicity is largely attributed to specific metabolites or metabolic pathways rather than the parent compound (Bushnell et al., 2005; Lash et al., 2000). The extent of perc metabolism through cytochrome P450-mediated oxidation and glutathione-S-transferase (GST)-mediated GSH conjugation pathways and the interindividual differences in formation of liver- and kidney-toxic metabolites of perc are critical challenges for accurately characterizing its toxicokinetics (Boyes et al., 2009; Chiu et al., 2007a, 2009a; Sweeney et al., 2009). Investigation of the toxicokinetics of perc and its metabolites in multiple tissues is essential for understanding of risks associated perc exposure, because biologically effective tissue doses of perc and its specific metabolites modulate organ-specific adverse effects (Cichocki et al., 2016, 2017b; Guyton et al., 2014; Lash and Parker, 2001; Lash et al., 2014; Luo et al., 2018b, 2019).

Population heterogeneity in susceptibility to adverse effects of chemicals, including genetic polymorphisms, age, sex, diet, and underlying disease state, confounds human health assessments (Bois, 2010). Understanding population variability in toxicokinetics and toxicodynamics is critical to refining the risk-based evaluations for perc; however, addressing the population variability in toxicokinetics has been identified as one of the most important impediments to robust dose-response assessment of perc (NRC, 2009; Zeise et al., 2013). The current approaches to risk assessment are largely limited to applying default uncertainty factors to account for uncertainty associated with interindividual variability (Stedeford et al., 2007). Based on the recommendations of the National Research Council, the U.S. Environmental Protection Agency (U.S. EPA) and World Health Organization/International Programme on Chemical Safety (NRC, 2006; USEPA, 2014; WHO/IPCS, 2005; Zeise et al., 2013), population physiologically based pharmacokinetic (PBPK) modeling has been used to replace such default factors with values derived from chemical-specific data to quantitate the impact of interindividual variability in several U.S. EPA assessments, including trichlorethylene, a chemical structurally similar to perc (Chiu et al., 2009b; Evans et al., 2009; Hack, 2006; USEPA, 2011a). However, determining the appropriate chemical-specific adjustment factors is a difficult task for chemicals that are subject to multiple metabolic pathways and elicit metabolism-dependent tissue-specific effects. Given the limited available human toxicokinetic data on perc, mouse population modeling as a surrogate to characterize and quantify the extent of human variability may provide an avenue to address this challenge (Chiu et al., 2014; Luo et al., 2018c; Rusyn et al., 2010). Multistrain panels of genetically diverse mouse strains have been previously evaluated to characterize interstrain variability of trichloroethylene and perc (Bradford et al., 2011; Cichocki et al., 2017c; Luo et al., 2018a,c; Venkatratnam et al., 2017). For trichlorethylene, the data from a genetically diverse mouse population have been combined with population PBPK modeling and the results showed remarkable concordance with those based on modeling of human data (Chiu et al., 2014).

The recent demonstration of complex and highly variable metabolism of perc using 45 collaborative Cross (CC) mouse strains (Cichocki et al., 2017b; Luo et al., 2019) provides the means to apply a population PBPK modeling approach to studies of toxicokinetics of perc and increase confidence in characterization of interstrain toxicokinetic variability and uncertainty. This information may be used to replace the default uncertainty factor for perc with TKVFs based on metabolite-, and organ-specific data.

MATERIALS AND METHODS

An overall workflow describing the steps of PBPK modeling processes and their inputs and outputs is visualized in Figure 1. PBPK modeling and methods of each step are described in detail in the following sections.

Figure 1.

A workflow describing the steps of modeling processes and their inputs and outputs. The “starting point” is the previously published 3-strain model (Dalaijamts et al., 2018), which calibrated 27 model parameters. “Preliminary modeling” was performed by Bayesian Markov chain Monte Carlo (MCMC) calibration of all 58 parameters using 3 representative strains—B6C3F1, C57BL/6J, and CC001—the latter 2 of which had toxicokinetic (TK) data on glutathione conjugates. “Global sensitivity analysis” was performed using the posteriors from this 3-strain calibration, and the 43 most “sensitive parameters” were identified. The “final modeling” used MCMC to calibrate these parameters to data from all 48 strains. Samples were drawn from the posterior parameters using Monte Carlo simulation to evaluate model fit and make predictions as to different dose metrics as well as inter-individual variability in the form of TK variability factors.

 

PBPK Model Structure

The perc PBPK model was previously described in detail (Chiu and Ginsberg, 2011; Dalaijamts et al., 2018, 2020), and includes submodels that describe the metabolism of perc, as well as downstream metabolism and elimination. Each of sub-models includes individual tissue compartments, which are aimed at providing tissue-specific dose metrics of perc and its metabolites (Supplementary Figure 1).

Model Parameters and Baseline Values

All PBPK model parameters, including physiological measurements (eg, volumes and flows) and chemical disposition data from in vitro studies (eg, partition coefficients [PCs], binding coefficients, and metabolism and clearance rates), and the detailed descriptions of their baseline values and sources are provided in (Supplementary Table 1), and are the same as previously reported (Dalaijamts et al., 2018).

In Vivo Toxicokinetic Data

The sources of toxicokinetic data used for model calibration in this study are summarized in Figure 2. The in vivo data from perc toxicokinetic studies in B6C3F1 (Gargas, 1988; Gearhart et al., 1993; Odum et al., 1988; Reitz et al., 1996), Swiss-Webster (SW; Philip et al., 2007), and C57BL/6J (Cichocki et al., 2017a, 2019) strains were summarized in (Chiu and Ginsberg, 2011; Dalaijamts et al., 2018). The additional study of Cichocki et al. (2017c) reported in vivo data on toxicokinetics of perc, administered as a single dose of 1000 mg perc/kg of bodyweight (b.w.) by oral gavage, and its oxidative and GSH conjugation metabolites trichlorovinyl GSH (TCVG), trichlorovinyl cysteine (TCVC), and N-acetylated trichlorovinyl cysteine (NAcTCVC) in serum, liver and kidney in male mice from 45 inbred strains of the CC.

Figure 2.

Summary of the in vivo toxicokinetic data used for population analysis (“final modeling” in Figure 1) in terms of strain, study, route of exposure, doses of perchloroethylene administered, and available toxicokinetic data.

Parameter Selection for Estimation

Previous studies (Dalaijamts et al., 2018, 2020) calibrated only a subset of the available toxicokinetic parameters (27 out of 58), with the remainder fixed as baseline values. Here, we posited that the inclusion of a larger population of mouse strains would necessitate additional parameters being calibrated. Because calibrating all 58 parameters in almost 50 strains was not feasible computationally, we used global sensitivity analysis to identify which parameters could be fixed and which required calibration (Hsieh et al., 2018; McNally et al., 2011).

Global sensitivity analysis aims to evaluate the contribution of an individual model input factor (parameter) or its interactions with multiple inputs to the range of outputs (predictions) of PBPK model. Model parameters were analyzed using the extended Fourier Amplitude Sensitivity Test method from the workflow proposed previously (Hsieh et al., 2018; McNally et al., 2011) to obtain the quantitative, variance-based measures of sensitivity, calculating so-called Sobol sensitivity indices (SIs). This method produces 2 sensitivity indices for each parameter. The main (first order) effect sensitivity index, S_i, quantifies the importance of the parameter in isolation, whereas the total effect sensitivity index, S_Ti, quantifies the interactions with other model parameters in addition to the main effect. The difference between S_Ti and S_i is therefore a measure of interactions.

Global sensitivity analysis requires an input distribution for each of the parameters being analyzed. We found that utilizing each parameter’s prior distribution (Supplementary Table 2), we could not achieve adequate convergence because many parameters had extremely wide distributions. We therefore conducted an exploratory Bayesian analysis with all 58 parameters using only 3 strains: B6C3F1, C57BL/6J, and CC0001. The resulting posterior distributions were approximated by normal distributions truncated at their 95% CIs (Supplementary Table 2), representing the “reasonable range” of values over which the global sensitivity analysis was performed. Comparison of prior and posterior parameter distributions from the preliminary Bayesian analysis are shown in Supplementary Figure 2.

Our global sensitivity analysis produced sensitivity indexes for model predicted concentrations at the first 3 time points (1, 2, and 4 h) of perc and its oxidative (TCA) and GSH conjugation metabolites (TCVG, TCVC, and NAcTCVC) in blood (plasma for TCA) and tissues (liver, kidney, and fat). The use of earlier time points was to investigate the parameter sensitivities during the phases of greatest change (ie, uptake, distribution and elimination) and to avoid the regions where sensitivity measures reflect sampling variability and noise. Two experiments of oral exposure to perc, 300 mg/kg b.w. in C57BL/6J mice and 1000 mg/kg b.w. in CC001/Unc mice, were modeled. Convergence of SIs was estimated by computing the range of 95% CIs (from random phase shift) of each index (S_Ti and S_i) across replications for each parameter at numbers of sample size up to 10,000 (resulting in over 1,000,000 model evaluations). The convergence index <0.1 was used as a measure of acceptable convergence as described in Hsieh et al. (2018). Heatmaps were used to visualize the results from the SA at each time point. Cutoff points of 0.01 and 0.05 were assigned as criteria of selection as “influential” to model outputs for main and total effects, respectively. Parameters with any SIs above these cut-points were selected for calibration, and the remainder fixed at baseline values.

Bayesian Approach to Calibration of PBPK Model Parameters

The hierarchical Bayesian population statistical model was applied for PBPK model calibration and estimation of model parameters and their uncertainty and variability as previously described (Bois, 2000a,b; Chiu et al., 2009b; Hack, 2006) and the updated conceptual representation described in Dalaijamts et al. (2018, 2020) was used.

Prior distributions for model parameters

The most influential parameters selected from GSA were then estimated by Markov Chain Monte Carlo (MCMC) sampling using a Bayesian approach. The assumptions of prior distributions reflecting the uncertainty in the population mean and variance of previously assigned parameters were previously described (Chiu and Ginsberg, 2011; Chiu et al., 2009b; Dalaijamts et al., 2018). A priori knowledge of M_θ and V_θ is available in the form of “standard” values for some parameters. Uncertainty in the population means M_θ was acknowledged under the form of a priori log-normal or log-uniform distributions depending on available information, whereas prior distributions of population variances V_θ a standard inverse gamma distribution, with parameters α = 1 and β=V₀. Parameter prior uncertainty distributions of population mean and population variability for the selected parameters are summarized below and described in detail in Supplementary Table 3.

Uncertainty distributions for the population mean of the PBPK model parameters involve informative (for parameters with independent data) and non-informative (for parameters without independent data) prior distributions. Informative prior distributions for the population mean of parameters were centered on either baseline values of model parameters or the posterior means from the previously published multi-strain mouse PBPK model of trichloroethylene (Chiu et al., 2014) for cardiac output, pulmonary perfusion rate, fat volume, tissue specific blood PCs of perc and TCA, and parameters of plasma binding and constants of urinary and metabolic clearance of TCA. For parameters without independent data (uninformative), either a truncated normal distribution centered on baseline values with high SD (conjugate PCs) or log-uniform distributions with upper and lower bounds separated by at least 10⁴ (absorption and metabolism/clearance of perc metabolites) priors were set as to minimize potential bias. We also improved parameter identifiability through use of informative priors based on posteriors from previous models for some parameters (Supplementary Table 1). Overall, we followed the approach recommended by Garcia et al. (2015), which found that global identifiability in PBPK models could only be assured through Bayesian analysis with truncated priors.

The error distributions for the likelihood of each toxicokinetic prediction were assumed to be independent and lognormally distributed, with log-scale mean zero and variance ${\mathit{\delta }}^2$. The variance vector ${\mathit{\delta }}^2$ were assigned log-uniform prior distributions. The detailed description of likelihood of the toxicokinetic data and their nondetects included in the analysis can be found in the previous model by Dalaijamts et al. (2018).

Estimation of posterior parameter distributions

Hierarchical Metropolis-Hastings algorithms within the Gibbs sampler (Gelfand and Adrian, 1990; Geman and Geman, 1984) was used in MCMC simulation. The MCMC algorithm draws a sample along a Markov chain, which is constructed to have the posterior distribution as its long-run stationary distribution (Andrieu et al., 2003; Krauss et al., 2013; van Ravenzwaaij et al., 2018). The MCMC simulation, thereby, generates posterior parameter values at the population level, and parameter values for the strains used in the experiments. Posterior model predictions were made following MCMC calibration using the strain-specific posterior parameter values as well as posterior predictions for a “random strain” accounting for both interstrain variability and parameter uncertainty (Hack et al., 2006).

Computations

PBPK modeling in conjunction with statistical modeling, including the MC/MCMC simulations and model output predictions, in all stages of the flow diagram (Figure 1) was performed using GNU MCSim v.5.6.5 software (Bois, 2009). To check convergence, we used 4 independent MCMC with different starting values. Parallelized computation for independent Markov chains was performed in the Unix/Linux environment on a high-performance computing cluster comprising machines with Intel Xeon 2.4 GHz E5-2670 v2 (Broadwell-EP) 14-core processors and 64 GB of DRAM each run out up to the number of iterations converged (1 of every 10th iteration was recorded). The evaluation of convergence of the MCMC simulations was carried out using the R “coda” package v.0.19-1 (Plummer et al., 2006). The global sensitivity analysis and its visual inspection were performed using R-based “pksensi” package v.1.2 developed from our lab (Hsieh et al., 2018). All other statistical analyses and visualizations of the study results were carried out in R v.3.6. Model code are available in a GitHub repository https://github.com/ChimkaD/PBPK-perc. MCMC and MC simulation output files have been deposited on the Dryad repository https://doi.org/10.5061/dryad.brv15dv94.

Model Evaluation

Evaluation of convergence

Convergence of the Markov chains to the posterior distribution was monitored using analysis of variance as described by Gelman et al. (1996). The Gelman and Rubin shrink factors (potential scale reduction factor, R), a ratio of an upper bound and a lower bound of the variance in the target distribution, and Brooks-Gelman multivariate shrink factor are used to assess whether the independent MCMC chains have converged to a common distribution. As multiple, independent chains move closer together toward the same distribution, the ratio declines to unity. A convergence diagnostic potential scale reduction factor, R, of 1.2 or less has been proposed as a criterion for acceptable convergence (Gelman et al., 2004). A visual inspection for dependency of posterior parameter distributions using cross correlations and convergence of the chains using traces and probability density functions for each posterior parameter distributions was performed as an additional diagnostic.

Evaluation of posterior parameter distributions

Posterior distributions of the population parameters were checked as to whether they appear reasonable given the prior distributions, while posterior distributions of the strain-specific parameters were estimated to see variability across strains. Inconsistency between the prior and posterior distributions of population mean parameters may indicate insufficiently broad priors (ie, overconfidence in their specification), misspecification of the model structure (eg, leading to pathological parameter estimates), or measurement error.

Evaluation of model fit

The posterior parameter distributions at both population (“random strain”) and strain-specific levels were used to make model predictions of internal toxicokinetics of perc and metabolites. At a population level, samples of the population parameters (means and variances) were used, and “random” strains were sampled from appropriate distributions using these population means and variances. Thus, the predictions were only conditioned on the population-level parameter distributions, representing a distribution across all the strains, and not on the specific predictions for that dataset. These strains then represent the predicted population distribution, incorporating variability in the population as well as uncertainty in the population means and variances and therefore compare predictions for the overall mouse population. In contrast to population level, strain-specific prediction was sampled from posterior parameter distribution of the specific strain, those predictions are compared only with those datasets from the specific strain. All population and strain-specific toxicokinetic predictions were evaluated by comparing with in vivo blood (plasma for TCA) and tissue-specific concentration-time course data of perc and its metabolites.

Residual error estimated for each in vivo measurement provides some quantitative measure of the degree to which there were deviations due to intrastudy variability, interindividual variability, and measurement and model errors, including any difficulties fitting multiple dose levels in the same study using the same model parameters. Estimated residual error with geometric SD of more than 3-fold was assumed to indicate that the model prediction does not fit the in vivo measurement adequately.

Model Predictions of Dose Metrics

The current PBPK model was applied to characterize uncertainty and variability in internal dose metrics of exposure to perc. Population variability and uncertainty in dose metrics, including perc metabolism and toxicokinetics (AUC = area under the concentration-time curve) of perc and its oxidative and GSH-conjugation metabolites, were characterized using population-generated posterior parameter distribution. Posterior dose metrics were predicted following the scheme depicted in Supplementary Figure 3 based on previously developed methods by Chiu et al. (2009b) with the specific interest of estimating the contributions from both uncertainty in population parameters and variability within the population. Out of 4 chains of MCMC simulation, 100 sets of population mean (µ_θ), and variance (V_θ) of parameter posteriors were randomly selected representing the uncertainty in the population parameters. The sets of posterior parameter distributions (θ_ij) of 500 random strains were generated through MC simulation from each set of population parameters of the selected samples in the framework of their distributions—each of which represents the population variability. Consequently, a total of 50 000 individuals, representing 500 random strains (variability) each for 100 different populations (uncertainty), were generated. PBPK model prediction of posterior dosimetry (y_ij) used exposure scenarios of a single doses of 10, 100, or 1000 mg/kg aqueous based oral gavage of Perc (E) for mouse population with normal distributions of measured body weight (φ) of CC mice. All dose metrics were estimated at 24 h postexposure.

To replace the default subfactor of 3.16 (or 10^0.5 out of the uncertainty factor of 10) for interindividual variability of TK with the relevant scientific data, in silico-derived quantitative measure of population variability and uncertainty in the internal dose metrics estimated in this study were used to derive a chemical-specific adjustment factor, so called a “toxicokinetic variability factor (TKVF),” for each chemical in target organs. The TKVF is defined as the ratio between the internal dose metrics in a “sensitive” individual (eg, 95th or 99th percentile) in a population to that in a “typical” individual (eg, median) (WHO/IPCS, 2005, 2014). Here, we calculated both the TKVF₉₅ for a 95th percentile individual and the TKVF₉₉ corresponding to a 99th percentile individual, consistent with WHO/IPCS (2014) guidance as well as previous analyses (Luo et al., 2018a; USEPA, 2011a).

RESULTS

 

Global Sensitivity Analysis

The global sensitivity analysis was conducted for 58 parameters across 30 toxicokinetic predictions at 1, 2, and 4 h of exposure in 2 mouse strains. Convergence indices of the 58 parameters were < 0.1 after 10 000 iterations are shown in Supplementary Figure 4 and ranked in Supplementary Figure 5. The resulting quantitative measures of the main (S_i) and total (S_Ti) effects of the variance-based analysis in model parameters for each output for C57BL/6J and CC001 mouse strains are visualized in heatmaps in Supplementary Figure 6. The rankings of maximum S_i and S_Ti of model outputs across 58 model parameters are shown in Supplementary Figure 7. A total of 43 parameters were ranked as “influential” based on the cutoffs described in Materials and Methods section and were selected for PBPK model calibration.

Convergence of MCMC Simulation

Four Markov chains were run up to 120 000 iterations each to obtain convergence. The first 30 000 iterations for each chain were discarded as “burn-in” iterations, ie, iterations for which the simulation had not yet converged, and the remainder used for inferences. For the remaining iterations, the convergence diagnostic “R” were <1.2 for all population parameters (with the exception of lnkaD, which was 1.24) and multivariate R was 1.17, indicating adequate convergence. Traces of 4 chains were well mixed for most parameters, which were hardly distinguishable by visual inspection for most model parameters. Traces and probability densities of posterior uncertainty distributions for each calibrated parameter population mean, their cross-correlations, and log-likelihood of chains are provided in Supplementary Table 4 and Figure 8.

Posterior Parameter Distributions

Comparison of the prior and posterior distributions of the parameter population mean and geometric SDs is shown in Supplementary Figure 9. The posterior parameter distributions of population mean were also compared with those from the previous analyses (Dalaijamts et al., 2018, 2020). There is a general consistency between the posterior distributions of population mean parameters in the current model and the corresponding priors as well as, the posteriors of previous model from (Dalaijamts et al., 2018, Supplementary Figure 9a). All posteriors uncertainty distributions of population means are narrower than the corresponding informative and noninformative priors, indicating that substantial information on almost all parameters has been gained from the experimental data in the updated posteriors. For oral exposure, because the gastrointestinal absorption parameters are highly uncertain and experimental data of exposure to oil based oral gavage of perc were from only the B6C3F1 strain of mice, parameters of oil based oral exposure are not well updated a posteriori. Posteriors of absorption parameters for aqueous based oral gavage of perc were well updated and even narrower than those of previous model given the experiments from multi-strains. Posteriors of population mean parameters of oxidative metabolism of perc are more consistent with those predicted in the previous model in 3 strains than those in the model for 3 diets, which shifted into the tails of corresponding priors in previous models. Overall, the current Bayesian population PBPK model provides reasonable posterior population estimates with no indications either that prior distributions were overly restrictive or that model specification errors led to erroneous parameter estimates.

Substantial variability in model parameters across strains was present (Supplementary Figure 10). For instance, posterior parameter distributions of the absorption rate of perc across strains vary up to 6.7-fold, and tissue: blood PCs may vary more than 10-fold. Variability of oxidative and conjugative metabolism parameters of perc is also high across strains. The population variability across strains for these parameters is evident in the analysis of population geometric SD, in which posterior distributions were shifted largely from the corresponding priors (Supplementary Figure 9b). The summary statistics of posterior uncertainty distributions of population geometric mean and population geometric SD are provided in Supplementary Table 4.

Posterior Model Predictions

Model fitting

A goodness of model fit was first evaluated by comparison between medians of model predictions of toxicokinetics of perc and its metabolites over time-points of measurement using strain-specific parameter posteriors and median values of the in vivo data (Figure 3A). Most of the median predictions (83.3%) were within 2-fold of the data, indicating a good model fit. The residuals from the predicted result versus experimental values are plotted across strains in Figure 3A and stratified for perc and its metabolites in Figure 3B. PBPK model predicted toxicokinetics more accurately in B6C3F1 and SW mice, likely due to the much greater amount of data on each of these strains than on CC strains. Based on estimated median residuals and their distribution (the inset boxplot), we further found that model prediction of perc toxicokinetics was most accurate and precise in B6C3F1 mice, while accurate or precise prediction of TCA was also observed in C57BL/6J mice (Figure 3B). Deviation of model prediction of toxicokinetics from the observations was greater for GSH-conjugates in either C57BL/6J or CC strains. PBPK model predictions of organ-specific toxicokinetics across strains are plotted against observations for each chemical in Supplementary Figure 11. Posterior distributions of the geometric SD for the estimated residual error in each in vivo measurement are shown in Figure 3C. These results demonstrate improvement over residual errors from the previous model (Dalaijamts et al., 2018); summary statistics are presented in Supplementary Table 5. Overall, model predictions of toxicokinetic data fit in vivo measurements with the estimated residual errors of <2.3-fold geometric SD, indicating an adequate fit.

Figure 3.

Global evaluation of goodness of model fit of the physiologically based pharmacokinetic simulation results. A, scatter plot of overall comparison of medians of strain-specific model predictions (y-axis) with medians of observed toxicokinetic data (x-axis), with error distributions (inset). The diagonal line indicates where data and predictions are equal, and the gray bands indicate 2- and 3-fold differences. B, strain-specific residual error distributions of toxicokinetics of perchloroethylene and its metabolites. C, posterior distributions of geometric SD of estimated residual error (95% CIs, pink) in the current model update was plotted against those estimated in the previous model (Dalaijamts et al., 2018; gray lines). Vertical dashed line indicates 3-fold error.

PBPK model predictions (using population-generated “random strain” parameter posteriori) of concentration-time course of perc and its oxidative (TCA) and GSH-conjugation (TCVG, TCVC, and NAcTCVC) metabolites in blood (plasma for TCA), liver and kidney were compared with in vivo observations in the population of 45 CC strains (Cichocki et al., 2017c; Luo et al., 2019) at 1–24 h postexposure to a single dose of 1000 mg/kg aqueous-based oral gavage of perc in Figure 4. Population posterior prediction of concentration-time relationships reflects the range of interstrain variability over time. The range of predictions for perc and all metabolites in blood (plasma for TCA) and tissues in the current population model are consistent with the variation in the experimental data across CC strains. The medians predicted by the model overlap with those of observations for all chemicals in all tissues. Strain-specific posterior predictions were compared with in vivo data from Cichocki et al. (2017c) for each of 45 CC strains separately in Supplementary Figure 12. Model predictions were visualized using either median or 95% CIs of uncertainty distribution (Supplementary Figure 12A) or point estimates of the last simulation for each of 4 Markov chains (Supplementary Figure 12B) of posterior parameters. Overall, the model predicted time-dependence for perc and metabolites was consistent with the data.

Figure 4.

Predicted and observed concentration-time profiles for toxicokinetic data on perchloroethylene (perc), trichloroacetic acid, and glutathione conjugates from 45 strains of male Collaborative Cross (CC) mice administered a single dose of 1000 mg/kg aqueous based oral gavage of perc. Individual CC strain data are depicted by open circles and light gray lines, and their median and 95% CI shown as solid circles and error bars. The reported limits of detection (LODs) are shown by the horizontal dashed line, with data points reported to be <LOD shown by inverted triangles. Population-level predictions include the median (solid line), interquartile range (dotted line), and 95% CI (blue shading).

Posterior dose metric predictions

PBPK model prediction of uncertainty and variability in the internal dose metrics of perc exposure, including perc disposition, metabolism, and area under the organ-specific concentration-time curves (AUC) of perc and its metabolites, using parameter posteriors of population-generated random strains was summarized in Supplementary Tables 6 and 7. The internal dose metrics were estimated across 500 random strains at 36 h postoral exposures to single doses of 10, 100, and 1000 mg perc/kg b.w. (Supplementary Figure 13). At the population level, a clear dose-dependence is evident in the overall disposition of perc, with increasing amounts of perc excreted unchanged and decreasing amounts of oxidative metabolism as dose increased (Supplementary Figure 14).

Population mean and variability of total perc disposition and AUCs across mouse strains was compared with the uncertainty distribution of those predicted for disease-associated (fatty liver disease and steatohepatitis) variability in toxicokinetics of perc (Dalaijamts et al., 2020) in Figure 5. A clear variability across different strains and disease states is shown in all dose metrics. Notably, the excretion of unchanged perc decreased, whereas TCA production increased in the diseased C57BL/6J mice. In contrast, C57BL/6J-control mice have the highest excretion of perc, while B6C3F1/J and SW mice were somewhere between them (Figure 5A). In comparison of body burden of perc and metabolites, liver of diseased mice has the highest burden of perc, which was 3-fold above the population mean, whereas kidney of diseased mice has the highest burden of TCA. By contrast, B6C3F1/J mice have lowest perc in liver and TCA in kidney (Figure 5B). For GSH conjugation, AUCs of each metabolite were clearly distinguished across tissues, with relatively high concentrations of TCVG and TCVC in liver and kidney in all mice, respectively, compared with other 2 tissues (Figure 5B). Across all dose metrics and tissues, population variability across the larger population of strains analyzed here was greater than that associated with liver disease states or across the three “standard” starins, showing the importance of including a relatively large genetically diverse population when estimating population variability.

Figure 5.

Perchloroethylene (perc) dose metric predictions for overall population distribution as compared with selected individual strains calculated 36 h postoral exposure to 1000 mg perc/kg b.w. single dose. The top 2 rows for each panel show the population mean (geometric mean and 95% CI in top line) and population distribution (median, 11th and 99th percentile variability across mouse population) of selected dose metrics predicted by the current physiologically based pharmacokinetic model. Strain/disease-specific predictions (median and 95% CI) from Dalaijamts et al. (2020) are shown for comparison (solid dots and shapes are used for normal or healthy mouse strains and, gray and white squares are used for diseased mice). A, Prediction of total disposition of perc, including unchanged perc excreted, total trichloroacetic acid (TCA) produced, and total glutathione (GSH) conjugation. B, Area under the curve of perc and its oxidative and GSH conjugation metabolites in blood (plasma for TCA), liver and kidney.

Chemical-specific TKVF

In addition, TKVFs were calculated at the 95th and 99th percentile strains at 3 different dose levels to translate population variability of perc disposition and organ-specific AUCs of perc and its metabolites for use in the risk assessment of perc. The median and 95% CI of uncertainty distributions of TKVF₉₅ and TKVF₉₉ across 100 simulations derived from the current PBPK model predictions for each of 10, 100, and 1000 mg perc/kg b.w. oral doses are summarized in Supplementary Tables 6 and 7. The median and uncertainty distributions of TKVF₉₉ for interstrain variability in perc total disposition through exhalation and metabolic clearances derived from the current population PBPK model are shown in Figure 6A (see Supplementary Figure 15A for corresponding TKVF95 values). For comparison, the results derived from the (nonphysiologically based) compartmental model for the CC strains (Luo et al., 2019) are also shown. With increasing dose, PBPK modeled variability in TCA production increases and variability in excretion of unchanged perc decreases, although in all cases, the TKVFs remain lower than the default uncertainty factor of 3.16. For total GSH conjugation, the TKVF was the larger, with little dose-dependence, but the CI still overlapped the default value. The results of applying the compartmental model (Luo et al., 2019) were similar to the PBPK model-based results for 1000 mg/kg, but did not capture the dose-dependence evident for unchanged perc and TCA.

Figure 6.

Chemical-, tissue-, and dose-specific toxicokinetic variability factor (TKVF) predictions based modeled interstrain variability. For each dose metric, dots and error bars denote the median and 95% CI of uncertainty distributions across 100 simulations of in silico TKVFs (ratios of 99th percentile/50th percentile strain) across 500 random strains, predicted at single 10 (white dot), 100 (gray dot), and 1000 (solid dot) mg perchloroethylene/kg b.w. oral doses. Solid diamonds denote TKVFs derived from the compartmental model by (Luo et al., 2019). Open squares and open diamonds denote empirical TKVFs from (Cichocki et al., 2017c) and based on (Luo et al., 2019), respectively.

In Figure 6B, the median and 95% CI of uncertainty distributions of TKVF₉₉ in organ-specific AUCs derived from the current population PBPK model were compared with point estimates derived from estimates based on empirical data from CC strains (Cichocki et al., 2017c; Luo et al., 2019; see Supplementary Figure 15B for corresponding TKVF95 values). For perc, the CIs for the TKVF₉₉ values derived from the current PBPK model overlapped with the default value, and are similar to those from matching empirical studies. In contrast, TKVF₉₉ in AUCs of TCA was dose-dependent, significantly below the default uncertainty factor at lower doses, but overlapping with it at the highest dose. The empirical values derived by Cichocki et al. (2017c, open squares) and Luo et al. (2019) were inconsistent for TCA in plasma, while the predictions for TCA in liver and kidney were more similar. For GSH conjugation metabolites, the median TKVF₉₉ was greater than the default uncertainty factor in all conjugates and tissues except for blood TCVG. The largest variation was found in TCVC followed by NAcTCVC in liver with the median TKVF₉₉s of up to 14- and 6.7-fold and upper confidence bounds of 31- and 10-fold, respectively. Empirically derived TKVF₉₉ values from Luo et al. (2019) were either similar to or less than the PBPK model-derived TKVFs, with a very large discrepancy for TCVC in liver, showing the importance of PBPK modeling to provide more accurate predictions for toxicokinetic variability (Figure 6B).

DISCUSSION

Addressing interindividual variability remains one of the most pressing challenges in public health and risk assessment (NRC, 2009; Zeise et al., 2013), with the urgent need to better “deal with the individual genetic, epigenetic, and biological variability in the establishment of research strategies for studying public health and environmental toxicology” (NIEHS, 2020). Although progress has been made recently in developing “high throughput” approaches to estimate toxicokinetic variability (Ring et al., 2017), these approaches cannot be applied for chemicals that require metabolic activation to elicit toxicity or that have multiple target organs. We have previously demonstrated for the solvent trichloroethylene that coupling toxicokinetic data from a population of mouse strains (Bradford et al., 2011; Venkatratnam et al., 2017) with population PBPK modeling offers an accurate surrogate for estimating human toxicokinetic variability (Chiu et al., 2014). The emergence of the genetically defined mouse populations such as the CC (Threadgill and Churchill, 2012), and the genetically diverse such as diversity outbred (DO; Churchill et al., 2012) has opened the door to numerous other studies showing how these population-based models offer a promising approach to address challenges in risk assessment (Aylor et al., 2011; Bogue et al., 2015; Durrant et al., 2011; Ferris et al., 2013; Kovacs et al., 2011; Logan et al., 2013; Neuner et al., 2019; Rasmussen et al., 2014; Rogala et al., 2014; Saul et al., 2019). This study represents the largest effort to date to use a population mouse model—almost 50 CC strains—in combination with population PBPK modeling in order to quantify population variability in toxicokinetics of a high-profile chemical.

The complexity of perc metabolism combined with the use of a large population of CC strains created significant challenge for application of PBPK modeling. In particular, a population PBPK model requires numerous parameters to be estimated since each model parameter must be estimated for each experimental subject/group and for the population as a whole, and the presence of almost 50 different strains led to a substantial computational burden. To reduce this burden, the most common practice is to fix “known” physiological variables and estimate the remaining chemical-specific parameters, but this approach is usually not rigorously justified and thus prone to bias (Sheiner, 1984; Sheiner and Ludden, 1992). Moreover, given the diversity of the CC population, it is not clear that “known” model parameters that have been previously used in PBPK modeling are necessarily appropriate—indeed we found that our previous model appeared to inappropriately “fix” a number of parameters, leading to poor model fits to some CC strains. Sensitivity analyses provide an objective means to evaluate the influence of PBPK model parameters and identify those less influential to model outputs to be fixed (Ratto et al., 2007; Zhang et al., 2015). Specifically, global sensitivity analysis has been recently recognized as a reliable approach for improving the efficiency of Bayesian PBPK model calibration maintaining prediction accuracy and precision with minimal bias in parameter estimation (Hsieh et al., 2018). However, global sensitivity analysis itself can also be computationally intensive, and our application here necessitated a 2-step approach in which a preliminary model calibrating all model parameters was developed with a small number of strains in order to provide analysis inputs. In the end, our global sensitivity analysis was able to identify 15 out of 58 parameters for which the PBPK model had low sensitivity, and therefore could be fixed to baseline values, leaving 43 parameters for calibration. After applying global sensitivity analysis, our Bayesian population PBPK model was successfully calibrated to organ-specific toxicokinetic profiles of perc, and its oxidative and conjugation metabolites, with the accurate prediction of the concentration-time courses of all chemicals in blood (plasma for TCA) and liver and kidney, and the precise prediction of the range of population variation.

Taking advantage of incorporating the recently published population-level toxicokinetic data of perc and both its oxidative and GSH conjugation metabolites in target organs in multiple strains of CC mouse (Cichocki et al., 2017c; Luo et al., 2019), we have demonstrated the power of population PBPK modeling in data-derived estimates for TK uncertainty and variability. Although empirical approaches can provide estimates of variability in tissue-specific concentrations, and compartmental models can provide predictions of metabolic flux, PBPK models have the dual additional advantages of being able to make predictions of tissue-specific chronic cumulative concentrations (eg, AUC) as well as at different dose levels.

Perhaps the greatest impact of our approach would be on risk assessment practice, where uncertainty or safety factors of 10 (or subfactors of 10^0.5) are applied to convert the no-observed-adverse-effect level (NOAEL) for noncancer endpoints into a human intake to allow for possible interindividual differences between typical and sensitive humans (WHO, 1999). The default uncertainty factor to address population variability consists with an equal subdivision into 10^0.5 (3.16) for toxicokinetics and 10^0.5 (3.16) for toxicodynamics. Existing examples of applying population PBPK modeling to quantify interindividual variability rely on the (rare) availability of human toxicokinetic data, whereas we are proposing that mouse population-based data and models can serve as an experimentally derived surrogate for human populations. For example, the extent of interindividual variability observed among inbred mouse strains used a single high oral dose of trichloroethylene well approximated that predicted from PBPK models calibrated to population toxicokinetic data in humans that included both occupational (Monster et al., 1976) and environmentally relevant exposures (Chiu et al., 2007b). Previous attempts at characterizing toxicokinetic variability of (Bois et al., 1996; Chiu and Ginsberg, 2011; Covington et al., 2007; Gelman et al., 1996) were hindered by inadequate experimental data, particularly for GSH conjugation and for tissue dosimetry, leading to substantial uncertainty in the ultimate risk assessments. Subsequently, a “harmonized” PBPK model rendered to the conclusions that perc metabolism to GSH conjugation may be high or low in humans, with high uncertainty and/or variability without accurate characterization (Chiu and Ginsberg, 2011). Our recent empirical data on perc toxicokinetics from multistrain inbred CC mice exposed to a single oral high dose (Cichocki et al., 2017c; Luo et al., 2019), which the oxidative metabolism of perc is likely to be saturated (Buben and O’Flaherty, 1985) and consequently results in greater formation of GSH conjugates in mice, may be more relevant to humans, whose oxidative capacity is less than mice, in case of lack of available human in vivo data on blood or tissue levels of GSH conjugation metabolites for more direct comparison. Therefore, population-based PBPK modeling of rodent-derived toxicokinetic data is useful for understanding interindividual variability in toxicokinetics among the human population.

Under these assumptions, we have demonstrated convincingly that population variability is highly dependent on both the putative active agent (eg, parent or specific metabolite) in the target tissue and exposure levels that lead to saturation in clearance, and that the use of a “one-size-fits-all” default uncertainty factor of 3.16 for toxicokinetic variability may not be adequately protective. Moreover, we found that more empirical approaches, including use of nonphysiological compartmental approaches, not only sometimes substantially underestimated toxicokinetic variability, but also could not characterize the dose-dependence in toxicokinetic variability evident for some dose metrics. To illustrate the application of TKVFs, in Table 1 we suggest TKVF values from among those in Supplementary Tables 6 and 7 for the target human health hazard endpoints used in EPA’s 2020 risk evaluation of perc (USEPA, 2020), based on the target tissue and available dose metrics. In general, we suggest that tissue-specific dose metrics be preferred if available due to their higher specificity, and because they account for potential interindividual differences in tissue partitioning. If metrics for a particular tissue are unavailable, then blood-based metrics are potential surrogate, with flux-based metrics (eg, total GSH conjugation) being the least specific. Additionally, we have used the usual default assumption that the parent compound is the active moiety unless there is evidence to suggest otherwise (ie, for liver and kidney).

Table 1.

Suggested Toxicokinetic Variability Factors (TKVFs) for Human Health Hazard Endpoints in Perchloroethylene Risk Evaluation by U.S. EPA (2020)

Target Organ System	Suggested Dose Metric	TKVF99 (Median [95% CI])
Central nervous system	Perc in blood	2.0 [1.7, 2.4]
Kidney	TCVC in kidney	3.7 [3.0-4.8]
Liver	TCA in liver	2.1 [1.0-2.5]
Immune/hematological	Perc in blood	2.0 [1.7, 2.4]
Reproductive	Perc in blood	2.0 [1.7, 2.4]
Developmental	Perc in blood	2.0 [1.7, 2.4]

Abbreviation: TKVF₉₉ = toxicokinetic variability factor protective of 99% of the population.

Our study has a number of important limitations, the most important of which is that only genetic variability from different strains is accounted for. As our previous work on diet-related variability showed (Dalaijamts et al., 2020), pre-existing disease states and other nongenetic factors may have substantial impacts on chemical toxicokinetics, and no experimental resource is currently available to address more than a narrow range of such factors. Additionally, the accuracy of the CC mouse population in reproducing human variability has only been demonstrated in a few cases—additional case studies in which both human and mouse variability data are available and can be compared are needed to further validate this assumption. Moreover, as our PBPK model of population variability in organ-specific TK of perc is limited to blood as a central compartment of whole body, liver, and kidney as targets of metabolic and organ-specific toxicity, future studies in examining the interindividual variability of parent perc in brain as a target of neurotoxicity are warranted. Finally, it is acknowledged that this approach takes a high level of effort, both with respect to in vivo studies in a large number of mouse strains as well as the complexity of the PBPK modeling approach required. However, while routine use of mouse population-based TKVFs may be unlikely, it may be necessary in cases of complex metabolism and high existing exposure levels where more accuracy and precision are needed in a chemical risk assessment.

In summary, a population-based PBPK model has successfully predicted tissue-specific internal dose metrics of perc exposure with the accurate central estimate of population mean and precise characterization of population variability of unchanged perc and its oxidative and GSH conjugation metabolism. We demonstrated that the combination of PBPK modeling refined by population-wide experimental TK data and Bayesian statistical analysis provides a means of filling gaps in risk assessment of perc to quantitatively characterize the nature and extent of human interindividual variability for toxicologically relevant internal dose metrics in target organs. Our results provide additional support for the use of population-based experimental models in the absence of TK variability data in human populations to address the critical issue of interindividual variability in chemical risk assessments so as ensure adequate human health protection.

SUPPLEMENTARY DATA

Supplementary data are available at Toxicological Sciences online.

DECLARATION OF CONFLICTING INTERESTS

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

 

Dryad Digital Repository DOI: http://doi:10.5061/dryad.brv15dv94