Estimation of species- and sex-specific PFAS pharmacokinetics in mice, rats, and non-human primates using a Bayesian hierarchical methodology

Abstract

The carbon chain length, degree of fluorination, and functional group of per- and polyfluoroalkyl substances (PFAS) influences the bioaccumulation and half-lives of these substances in humans and laboratory animals. Pharmacokinetic (PK) studies using laboratory animals characterize the absorption, distribution, metabolism, and excretion (ADME) of a PFAS and can provide the underlying data for inter-species extrapolation to inform human pharmacokinetics. However, variations in ADME arise due to differences in protein binding and renal and hepatobiliary clearance mechanisms. In particular, sex- and species-specific differences in active transporter abundance and PFAS binding affinity challenge body weight-based extrapolation assumptions from animal models to human PK parameters. Because these protein-dependent changes in ADME do not always scale with species body weight, classic allometric scaling assumptions can fail to account for species-specific transporter-mediated clearance. In addition, study-dependent differences in pharmacokinetic modeling approaches and parameterization techniques can result in large differences among the PK parameters reported in the literature. To better quantify PFAS pharmacokinetics and characterize the underlying uncertainty, we implemented a Bayesian inference hierarchical model to estimate PFAS PK parameters for multiple species (mice, rats, and non-human primates) using numerous single-dose animal studies. Through an alternative parameterization of the one- and two-compartment models, this method improved parameter identifiability and allowed for the use of prior information on PFAS absorption rate, clearance, and volume of distribution. Using reported time-course concentration data, we estimated sex-specific clearance, volume of distribution, and half-life across mice, rats, and non-human primates using a consistent modeling methodology for eight PFAS: PFHxA, PFHxS, PFNA, PFDA, PFBS, PFBA, PFOA, and PFOS. The resulting comparison to available human data demonstrated that standard volume of distribution body-mass scaling (BW¹) for PFAS generally agrees with reported human values while standard assumptions for allometric scaling of clearance (BW^3/4) are not appropriate for most of the PFAS investigated in this study. In addition, we demonstrated that there may be considerable differences in clearance for PFAS in some species when comparing across different sexes and routes of exposure.

1. Introduction

Per- and polyfluoroalkyl substances (PFAS) are a large group of synthetic chemicals that have been widely used in a variety of products including non-stick cookware, stain-resistant fabrics, and fire-fighting foams (Gluge et al., 2020). The unique physicochemical properties that make them suitable for these industrial purposes also lead to increased chemical and biological stability, and in many cases, a tendency for bioaccumulation. These properties, coupled with wide-spread usage, have led to their extensive environmental presence (Bonato et al., 2020; Kurwadkar et al., 2022). Within the large universe of known PFAS, perfluoroalkyl sulphonic acids (PFSAs) and perfluoroalkyl carboxylic acids (PFCAs) are readily found in the environment (Nakayama et al., 2019) and can have unique properties that influence the absorption, distribution, metabolism, and excretion (ADME) of these compounds. For example, some PFSAs and PFCAs have the ability to bind to plasma proteins (Smeltz et al., 2023) and/or utilize organic anion transporters (OATS) and organic anion-transporting polypeptides (OATPs) for transporter-mediated tissue distribution (Niu et al., 2023). Additionally, these compounds are generally found to be rabidly absorbed (ATSDR, 2021) and do not appear to be readily metabolized (Lau, 2015). These ADME properties can result in unique pharmacokinetic parameters for this class of chemicals.

In April of 2024, the U.S. EPA Office of Water (EPA/OW) finalized the National Primary Drinking Water Regulation (NPDWR) and established maximum contaminant levels (MCLs) for perfluorooctanesulfonic acid (PFOS) and perfluorooctanoate (PFOA). At this time, the Office of Water also established a hazard index approach for co-exposure to perfluorobutanesulfonic acid (PFBS), perfluorononanoic acid (PFNA), perfluorohexanesulfonic acid (PFHxS), and Hexafluoropropylene oxide dimer acid (HFPO-DA, commonly known as Gen X) (U.S. Environmental Protection Agency, 2024). Concurrently, the Integrated Risk Information System (IRIS) program is developing a series of five PFAS Toxicological Reviews for perfluorobutanoic acid (PFBA), perfluorohexanoic acid (PFHxA), perfluorohexanesulfonic acid (PFHxS), perfluorononanoic acid (PFNA), perfluorodecanoic acid (PFDA), and their associated salts. Species- and PFAS-specific PK parameters, such as half-life and clearance, in mice, rats, and non-human primates are critical in these assessments for facilitating species-specific internal dosimetry predictions (U.S. Environmental Protection Agency, 2014) and estimating how long these chemicals remain inside the body following exposure. These predictions allow for the examination of animal bioassay dose response data in terms of internal dose, which reduces uncertainty in subsequently calculated human equivalent doses (U.S. Environmental Protection Agency, 2014). However, as summarized by ATSDR (2021) and evidenced across the publicly available IRIS assessments (U.S. Environmental Protection Agency, 2021b; U.S. Environmental Protection Agency, 2022; U.S. Environmental Protection Agency, 2023), the species-specific half-lives and clearances for a given PFAS reported in different studies can vary by orders of magnitude depending on the study design and methods used for analyzing the measured concentration vs. time data. In addition, half-lives reported across species can vary widely, depending on the chemical structure of the PFAS.

There are three primary approaches for utilizing PK data from numerous sources to address the variability originating from different analysis methodologies and different experimental conditions. In the first “completely pooled” method, all datasets are pooled together, and one determines a single set of PK parameter values that best describes all the data. While this method makes use of all available data, important information regarding study-to-study variability along with possible route of exposure- and dose-dependent effects will be lost. Conversely, each dataset can be fit individually using a unique set of parameter values. This “completely un-pooled” method will give N values of each PK parameter (one for each of N datasets) and is analogous to the summary of PK parameters presented by ATSDR (2021). The third option, known as partial-pooling (Gelman and Hill, 2006), utilizes a Bayesian hierarchical approach where the fitted parameters for each dataset are sampled from a single population-level distribution to capture the similarities between each study, while still allowing for dataset- and study-specific parameters to characterize the inherent variability that exists from dataset to dataset across different studies. Because studies can employ different dose levels and routes of exposure, each resulting set of concentration time-course observations within a study can be considered a different dataset. This method results in a single posterior probability distribution (hereafter referred to as a “posterior”) for each pharmacokinetic parameter at the population level while also providing distributional estimates for each time-course concentration within a given exposure scenario. Within a partially-pooled or hierarchical model, the population mean of a fitted parameter characterizes the average value of the parameter across all levels of the hierarchy, while the population variance characterizes the spread or variability of the fitted parameters across the different levels of the hierarchy.

To better characterize PFAS pharmacokinetics for use in risk assessments, we implemented a partially-pooled method in the form of a Bayesian hierarchical model to develop population-based PK parameter estimates for mice, rats, and non-human primates for eight PFAS of interest: PFBA, PFBS, PFHxA, PFHxS, PFOA, PFOS, PFNA, and PFDA. These PFAS were chosen as they represented the EPA priorities under the 2021–2024 PFAS Strategic Roadmap investigated by EPA/OW and the IRIS program. Similar to previous hierarchical Bayesian methods for pooling PK data (Chiu et al., 2009; Zurlinden et al., 2016; Zurlinden and Reisfeld, 2016; Chiu et al., 2022), this approach conducted a meta-analysis to combine time-course concentration datasets from multiple studies to fit classical one- and two-compartment PK models, incorporated prior knowledge of PFAS pharmacokinetics, and characterized parameter uncertainty based on the available data. This partial-pooling of data across multiple studies and dosing regimens differs from a previous Bayesian hierarchical pharmacokinetic analysis for PFOA (Wambaugh et al., 2008) where a multi-level model was used to characterize rat inter-individual variability. The results from the current study allow for (i) the determination of critical PK parameters such as clearance and half-life for each PFAS/species/sex combination, (ii) the investigation of inter-species PK parameter value extrapolation for the selected PFAS, and (iii) the ability to compare PK parameter values derived for each dataset to investigate the unique ADME properties of these chemicals.

2. Materials and methods

2.1. Pharmacokinetic model

To select blood (serum) concentration vs. time datasets used for fitting, we conducted a systematic literature search to identify publications that describe PK studies in mice, rats, or non-human primates that administered at least one of the PFAS of interest (PFBA, PFBS, PFHxA, PFHxS, PFOA, PFOS, PFNA, or PFDA) either intravenously or through oral gavage. The identification of published PK data was conducted as part of an overall systematic literature search for information on various PFAS (U.S. Environmental Protection Agency, 2021b) which limited in vivo animal studies to those published prior to 2021.

Once time-course concentration data were extracted from the literature, we fit one- and two-compartment models (Fig. 1) using these measured blood concentration datasets as the observed central compartment concentrations for each combination of PFAS, species, and sex available. A summary of the analytical solutions for each model are outlined below. See Appendix A for derivation of these analytical solutions from their respective governing equations. In the resulting one- and two-compartment equations, the use of a tilde signifies a mass-normalized pharmacokinetic parameter such as systemic clearance (${\tilde{C}}_{\text{L}}$, L/kg/d) and volume of distribution (${\tilde{V}}_{\text{d}}$, L/kg).

Fig. 1.

Schematics of models used for this analysis: A) “One-compartment” model and B) “Two-compartment” model. In both cases, the number of compartments (one vs. two) refers to the number of compartments that PFAS distributes to within the body (Bourne, 1995). Model A includes a single “central” body compartment, representing the blood where observed PFAS concentrations are measured. Model B includes both the central compartment and a tissue compartment to capture a net distribution out of the central to tissues with which there is a rate-limited exchange. For route of exposure, intravenous (IV) doses are applied directly to the central compartment while gavage doses are applied to an absorption compartment with an absorption constant $\left(k_{\text{a}}\right)$ to describe transport of PFAS from the gastrointestinal tract to the central compartment. In the case of the two-compartment model, transfer between the central compartment and a generalized tissue compartment is governed by inflow and outflow rate constants ($k_{12}$ and $k_{21}$). Excretion from the central compartment is described by a first-order excretion rate constant $\left(k_{\text{e}}\right)$ for both models.

2.2. One-compartment model

The closed-form solution (see Appendix A for derivation) to the one-compartment system of ordinary differential equations is given by

$$C_{\text{IV}}(t)=\frac{D}{{\tilde{V}}_{\text{d}}•M(t)}{e}^{-k_{\text{e}}t}$$ (1)

$$C_{\text{gavage}}(t)=\frac{f_{\text{a}}•D}{{\tilde{V}}_{\text{d}}•M(t)}•\frac{k_{\text{a}}}{k_{\text{a}}-k_{\text{e}}}\left(e^{-k_{\text{e}}t}-e^{-k_{\text{a}}t}\right)$$ (2)

$$k_{\text{e}}=\frac{{\tilde{C}}_L}{{\tilde{V}}_{\text{d}}}$$ (3)

where $C_{\text{IV}}(t)$ and $C_{\text{gavage}}(t)$ represent the time-dependent predicted concentrations (mg/L) in the central compartment (which represents the blood) following an intravenous (IV) or gavage route of exposure, respectively; ${\tilde{V}}_{\text{d}}$ is the mass-normalized central compartment volume or volume of distribution (L/kg); $f_{\text{a}}$ is the fraction absorbed (unitless, gavage only); $k_{\text{a}}$ is the absorption rate constant (d⁻¹, gavage only); $k_{\text{e}}$ is the elimination rate constant $\left({\text{d}}^{-1}\right)$; ${\tilde{C}}_L$ is the mass-normalized systemic clearance (L/kg/d); $D$ is the applied initial dose (mg); and $M(t)$ is the time-dependent mass (kg) of the animal. For Eq. 1–3, $k_{\text{a}}$, $f_{\text{a}}$, ${\tilde{V}}_{\text{d}}$, and ${\tilde{C}}_{\text{L}}$ represent the parameters that are fit using the available pharmacokinetic data. Finally, for the one-compartment model, the half-life was calculated as $t_{\frac{1}{2}}=\text{log}(2)•{\tilde{V}}_{\text{d}}/{\tilde{C}}_{\text{L}}$ where ${\tilde{V}}_{\text{d}}$ and ${\tilde{C}}_{\text{L}}$ are the selected (“fit”) values for the volume of distribution and clearance parameters, respectively, and “log” denotes the natural (base e) logarithm.

2.3. Two-compartment model

The closed-form solution (see Appendix A for derivation) of the two-compartment system of ordinary differential equations is given by

$$k_{21}=R•k_{12}$$ (4)

$${\tilde{V}}_{\text{C}}=R•\frac{{\tilde{V}}_{d,ss}}{R+1}$$ (5)

$$k_{\text{e}}=\frac{{\tilde{C}}_L}{{\tilde{V}}_{\text{c}}}$$ (6)

$$\alpha +\beta =k_{21}+k_{\text{e}}+k_{12}$$ (7)

$$\alpha •\beta =k_{\text{e}}•k_{21}$$ (8)

$$C_{\text{iv}}(t)=\frac{D}{{\tilde{V}}_{\text{c}}•M(t)}\left(\frac{k_{21}-\alpha }{\beta -\alpha }{e}^{-\alpha •t}+\frac{k_{21}-\beta }{\alpha -\beta }{e}^{-\beta •t}\right)$$ (9)

$$A=\frac{k_{\text{a}}•\left(k_{21}-\alpha \right)}{\left(k_{\text{a}}-\alpha \right)(\beta -\alpha )}$$ (10)

$$B=\frac{k_{\text{a}}•\left(k_{21}-\beta \right)}{\left(k_{\text{a}}-\beta \right)(\alpha -\beta )}$$ (11)

$$\left.C_{\text{gavage}}(t)=\frac{f_{\text{a}}D}{{\tilde{V}}_{\text{c}}•M(t)}\left(A•e^{-\alpha t}+B•e^{-\beta t}-(A+B)•e^{-k_{a}t}\right)\right)$$ (12)

where $C_{\text{iv}}(t)$ (Eq. 9) and $C_{\text{gavage}}(t)$ (Eq. 12) represent the time-dependent predicted concentrations in the blood following an IV or gavage route of exposure, respectively. For Eq. 4–12, the variables fit using the available pharmacokinetic data are ${\tilde{V}}_{\text{d},\text{ss}}$ (L/kg) (the steady-state volume of distribution); $R$ (unitless), the ratio of central compartment volume $\left({\tilde{V}}_{\text{C}}\right)$ to tissue compartment volume $\left({\tilde{V}}_{\text{T}}\right)$; $k_{12}\left({\text{d}}^{-1}\right)$, the rate of transfer from central to tissue compartment; $f_{\text{a}}$, the fraction absorbed (unitless, gavage only); $k_{\text{a}}$, the absorption constant (${\text{d}}^{-1}$, gavage only); and ${\tilde{C}}_L$, the systemic clearance (L/kg/d). For the two-compartment model, ${\tilde{V}}_{\text{d},\text{ss}}$ is defined as the sum of the central and tissue compartments (Shargel and Yu, 2016). The known applied dose (mg) and time-dependent mass (kg) of the animal are represented as $D$ and $M(t)$, respectively. See Appendix B for further details on the reparameterization of Eq. 4–12. Finally, the steady-state half-life $(t_{\frac{1}{2}})$ for the two-compartment model was calculated using the model derived ${\tilde{C}}_L$ and ${\tilde{V}}_{\text{d},\text{ss}}$ where $\frac{t_1}{2}=\text{log}(2)•{\tilde{V}}_{\text{d},\text{ss}}/{\tilde{C}}_{\text{L}}$ where “log” denotes the natural (base e) logarithm.

Depending on the route of exposure, the model-predicted concentration $\left(C_{\text{P}}\right)$ is given by

$$C_{\text{P}}=\left\{\begin{array}{l}{C}_{\text{IV}},\text{for IV route}\\ C_{\text{gavage}},\text{for gavage route}\end{array}\right.$$ (13)

In the case of Tatum-Gibbs et al. (2011), background levels of PFNA were found in the control animals. These sex-specific control animal PFNA concentrations were assumed to be a steady-state background concentration and were subtracted from the reported blood concentrations in the dosed animals. No other studies reported background levels of PFAS in control animals. Finally, the methods accounting for body mass changes in the rat over time, $M(t)$, are described in Appendix A using animal growth curves presented in NTP (2020) for Sprague-Dawley rats and NTP (2017) for Wistar rats.

2.3.1. Hierarchical Bayesian modeling

When multiple studies provided time-course concentration data for a particular species, sex, and PFAS, we estimated the pharmacokinetic parameters for both model structures described by Eq. 1–12 using a hierarchical Bayesian approach. Similar to previous hierarchical pharmacokinetic parameterizations (Chiu et al., 2009; Zurlinden et al., 2016; Zurlinden and Reisfeld, 2016; Zurlinden and Reisfeld, 2017; Hsieh et al., 2021; Chiu et al., 2022), this involved determining the population-level model parameters and the likelihood of the observed data. For a detailed description of the hierarchical Bayesian methods, please see Appendix A.

2.4. Priors for population means and standard deviations hyperparameters

All log-transformed population mean parameters $\left({\mathrm{M}}_{\theta }\right)$ except the population $f_a$ mode, were estimated using normal prior distributions. Details of these priors are summarized in Table 1. The prior used for mean clearance across both models was derived from all summary clearance values for mice, rats, and non-human primates reported by ATSDR (2021) which results in a clearance prior with a geometric mean of 0.06 L/kg/d and geometric standard deviation (GSD) of 14.5. We defined a weakly informative prior on the volume of distribution based on the values reported by ATSDR (2021). Therefore, the volume of distribution prior is centered at 0.22 L/kg with a GSD of 4.5 to allow for a broad range of volumes of distribution to be sampled (Table 1). This allowed data for a PFAS that is highly bound to plasma proteins to inform a lower volume of distribution while a PFAS with greater tissue distribution could still have a volume of distribution greater than one. Using these priors, the resulting median and 95th equal-tailed interval for the half-life prior $\left(t_{\frac{1}{2}}=\text{log}2\frac{{\tilde{V}}_d}{{\tilde{C}}_L}\right)$ was 2.58 (6.3 × 10⁻³–1.1 × 10³) days. In addition, model priors for the two-compartment parameters ($k_{12}$ and $R$) were chosen such that $k_{12}\ll 1$ and $R\gg 1$. This choice of priors reduced the autocorrelation between $k_{12}$ and $R$ during sampling which increases the posterior effective sample size. Therefore, the two-compartment model behaves as a one-compartment model given these priors, ensuring that true two-compartment model behavior is only exhibited when strongly driven by the observed data. Finally, absorption priors were chosen to reflect knowledge of rapid absorption relative to elimination presented by ATSDR (2021) where absorption half-lives across PFOA, PFHxA, PFBA, and PFBS were shown to be less than 1 h with the median reported absorption half-life of ~0.206 h (0.0086 days). Using $k_a=\text{log}(2)/0.0086$ provides a median absorption rate of ~81 d⁻¹.

Table 1.

Prior distributions for the hyperparameters describing the means of the pharmacokinetic parameters used in the one- and two-compartment model formulations. All instances of log represent a natural log and ${\sigma }_{\theta }=\text{log}GS{D}_{\theta }$ for each log-transformed normal distribution.

Parameter (units)	Summary	Prior distribution	2.5th - 97.5th percentile	Two-compartment model only
${\text{M}}_{{\tilde{C}}_{\text{L}}}(\text{L}/\text{kg}/\text{d})$	Clearance	${\text{logM}}_{CLC}\sim \text{N}(\text{log}(0.06),2.68)$	0.00031–11.5
${\text{M}}_{{\tilde{V}}_d}(\text{L}/\text{kg})$	Volume of distributiona	${\text{logM}}_{V_d}\sim \text{N}(\text{log}(0.22),1.5)$	0.01–4.2
${\text{M}}_{k_{12}}({\text{d}}^{-1})$	Rate of transfer from central to tissue compartment	${\text{logM}}_{k_{12}}\sim \text{N}(\text{log}(0.01),1.5)$	5.3 × 10−4−1.9 × 10−1	✓
${\text{M}}_R(\text{unitless})$	Ratio of volumes for central and deep compartments	${\text{logM}}_R\sim \text{N}(\text{log}(100),1.5)$	5.2–1892	✓
${\text{M}}_{k_a}({\text{d}}^{-1})$	Absorption rate constant	${\text{logM}}_{k_a}\sim \text{N}(\text{log}(81),0.25)$	50–132
${\omega }_{f_a}(\text{unitless})$	Fraction absorbed	${\omega }_{f_a}\sim \text{Beta}(6,1.5)$	0.47–0.98

^aFor a one-compartment model, this represents the volume of distribution calculated from the central compartment $\left(V_C\right)$. For a two-compartment model, this is the steady-state volume of distribution $\left(V_{d,ss}=V_C+V_T=V_C•(1+1/R)\right)$.

Population standard deviations for all log-transformed parameters except $f_a$ were estimated using half-normal prior distributions (Gelman and Hill, 2006; Rover et al., 2021). This weakly informative half-normal prior regularizes, i.e. constrains, the population mean which allows for stronger pooling of estimates while also allowing for heterogeneity in the dataset-level parameters if discrepancies exist between datasets in the underlying observed data. As outlined by Rover et al. (2021), the HalfNormal(0.5) prior on the population standard deviation for log-transformed parameters provides a wide range of lower-level parameter heterogeneity and allows for sampling in both the stronger pooling region (similar parameters across datasets) and in the un-pooled region (disparate parameter distributions across datasets).

2.5. Bayesian summary

When more than two datasets existed for a given PFAS/species/sex combination, we implemented the hierarchical framework described above and summarized in Fig. 2 and Appendix A.

Fig. 2.

Summary of hierarchical modeling framework (similar to Fig. 3 of Chiu et al. (2009)). Squares represent fixed prior distributions or observed values while circles represent the unobserved or random variables. The triangle $\left(C_{\text{P},j}\right)$ represents the closed-form solution to the concentration vs. time pharmacokinetic model for each dataset $(i)$ and time $(j)$. Dataset-level $(i)$ parameters are sampled from the population-level parameters for $f_{a,i}$ (fraction absorbed) and ${\theta }_i$ where ${\theta }_i\in \left\{k_{\text{a},i},{\tilde{V}}_{\text{d},i},{\tilde{C}}_{\text{L},i}\right\}$ for a one-compartment model and ${\theta }_i\in \left\{k_{\text{a},i},{\tilde{V}}_{\text{d},i},{\tilde{C}}_{\text{L},i},k_{12,i},R_i\right\}$ for a two-compartment model. The fraction absorbed beta-distribution population mode $\left({\omega }_{f_a}\right)$ and ‘concentration’ $\left({\kappa }_{f_a}\right)$ priors are described in depth in Appendix A. The population for each PFAS/species/sex combination consists of time-course datasets where each dataset comprises PFAS serum concentrations presented as either summary-level or individual animal data following a single IV or gavage dose.

However, for some PFAS, species, and sex combinations, data were only available from one or two datasets in a single study, e.g., one or two doses total in a single species. In these instances, a single-level Bayesian model (complete pooling) was implemented with priors for each pharmacokinetic parameter being the same as those described in Table 1. Finally, this hierarchical framework aims to characterize dataset-to-dataset variability as opposed to inter-individual variability because not every study reported individual animal data.

2.5.1. Allometric scaling for inter-species extrapolation

To evaluate pharmacokinetic parameters across species, we fit an allometric scaling model for the clearance and volume of distribution. Here, we used the following body weight (mass) allometric power-law model:

$$Y_s=a•M_s^b$$ (14)

where $M_s$ is the species-specific mass (kg) and $Y_s$ represents the species $(s)$ specific pharmacokinetic parameter of interest adjusted for body weight, e.g., clearance ($C_{\text{L}}$, L/d) or volume of distribution ($V_d$, $\text{L}$). The parameters $a$ and $b$ are the constants for the power law model. Historically, $a$ represents a chemical-specific scaling coefficient while the power law coefficient, $b$, is set to 1 when scaling volume of distribution and 0.75 when scaling clearance (U.S. Environmental Protection Agency, 2011). For volume of distribution, $b=1$ indicates the volume of distribution is directly proportional to body weight. However, $b=0.75$ for clearance stems from the observation that inter-species metabolic rates are proportional to body weight to the $\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$4$}\right.$ power through Kleiber’s rule (Kleiber, 1932), with this property reviewed across numerous species in Thommen et al. (2019). This observation for cellular metabolic scaling has demonstrated utility for inter-species extrapolation of clearance and is used as the default method for the derivation of oral reference doses (U.S. Environmental Protection Agency, 2011).

To investigate how the pharmacokinetic parameters derived from the Bayesian analysis are described by classical allometric scaling, we linearly reparametrized Eq. 14 as:

$$\text{log}{Y}_{p,sex}^{pred}=\text{log}{a}_{p,sex}+b•\text{log}{M}_s$$ (15)

where $\text{log}{Y}_{p,sex}^{pred}$ is the allometrically-scaled log-transformed pharmacokinetic parameter ($\text{log}{C}_{\text{L}}$ or $\text{log}{V}_d$) and $\text{log}{a}_{p,sex}$ is the log-transformed scaling coefficient for each PFAS $(p)$ and sex. $\text{Log}{M}_s$ is the log-transformed mass for each species $(s)$. For these fits, $M_s$ is defined as:

$$M_s=\left\{\begin{array}{l}0.025\text{kg},|\text{for}s=\text{mouse}\\ 0.25\text{kg},|\text{for}s=\text{rat}\\ 2.6\text{kg},|\text{for}\text{s}=\text{primate}\end{array}\right.$$ (16)

where reference body weights for mice and rats are determined from (U. S. Environmental Protection Agency, 1988) and (Chengelis et al., 2009) for primates. For mice and rats, these species-specific animal masses represent default values used by EPA for pharmacokinetic modeling while the primate mass represents the average mass of cynomolgus monkeys (the primate species used for these PK studies) reported in Chengelis et al. (2009). The values in Eq. 16 are similar to the masses used for fitting the PK models. Finally, $b$ is the power coefficient and is fixed depending on which pharmacokinetic parameter is analyzed: $b=1$ for $V_d$ and $b=0.75$ for $C_L$. Therefore, only $a_{p,sex}$ was determined for the allometric scaling of volume of distribution and clearance by fitting a sex- and PFAS-specific $a_{p,sex}$ from Eq. 15 using the default priors of the Bayesian Model-Building Interface in Python (Bambi) which formulated the following regression model

$$\begin{array}{l}\text{log}{a}_{p,sex}\sim \text{N}ormal(0,28.67),\\ \text{log}{Y}_{p,sex}^{obs}\sim Normal\left(\text{log}{Y}_{p,sex}^{pred},\sigma \right),\\ \sigma \sim \text{HalfStudentT}(4,3.02).\end{array}$$ (17)

where $\text{log}{a}_{p,sex}$ is the log-intercept for each individual PFAS, $\text{log}{Y}_{p,sex}^{obs}$ is the mean log-transformed MCMC determined pharmacokinetic parameter ($V_d$ or $C_L$), $\text{log}{Y}_{p,sex}^{obs}$ is the predicted allometrically scaled pharmacokinetic parameter from Eq. 15, and $\sigma$ is the regression model error.

2.5.2. Comparing clearances through a region of practical equivalence (ROPE)

Unlike frequentist methods where differences in conditions are tested against a single null hypothesis (zero) through a p-value, the region of practical equivalence (ROPE) defines an area around the null that is deemed “practically equivalent” and determines if the effect of interest falls sufficiently far away from zero in order to reject the null hypothesis. (Kruschke, 2015; Kruschke, 2018). By defining a comparator parameter using the posterior probability distributions for the desired conditions to test, the most credible values of this comparator parameter e.g., the 95 % HDI, can be compared to the ROPE to aid in decision making. The HDI + ROPE decision rule (Kruschke, 2018) determines if any of the most credible comparator parameters (95 % HDI) fall within the ROPE, i.e., the null region. Once this relationship is established, Kruschke (2018) provides the following rules for the decision making process:

1. The entire 95 % HDI of the comparator parameter falls within the ROPE: accept, the groups are the same for practical purposes.

2. The entire 95 % HDI of the comparator parameter falls outside the ROPE: reject, the groups are not the same for practical purposes.

3. Some portion of the comparator 95 % HDI falls inside and outside the ROPE: withhold a decision.

To evaluate differences in clearance between two conditions, we defined our null region or region of practical equivalence as a 20 % difference in clearance (Kruschke, 2018). As reviewed in (Little, 2015) and (Kruschke, 2018), acceptance criteria for whether two conditions are the same should be risk based where higher risks dictate a smaller ROPE and smaller risks dictate a larger ROPE. A 20 % difference in parameters represents a moderate risk (Little, 2015) and is in line with the confidence interval acceptance criteria for bioequivalence studies used in U.S. Food and Drug Administration Center for Drug Evaluation and Research and Center for Biologics Evaluation and Research (2016). The ramifications of a 20 % difference in clearance are realized through predicted steady-state serum concentration where a 20 % difference in clearance results in a 20 % change in the steady state serum concentration. For each comparison, the comparator parameter $(\rho )$ was determined as a fractional change in clearance given by

$$\rho =\frac{{\tilde{C}}_{L,1}}{{\tilde{C}}_{L,2}}$$ (18)

where ${\tilde{C}}_{L,1}$ represents the clearance posterior distribution in scenario one and ${\tilde{C}}_{L,1}$ is the clearance posterior distribution in scenario two. To test for a 20 % change in clearance, the ROPE is defined from 0.8 to 1.2 so that the “null-hypothesis” is defined as a 20 % change in clearance and overlap with the ROPE is determined from the 95 % HDI of $\rho$. In this study we tested two comparisons: 1) Sex-dependent differences in population clearance with ${\tilde{C}}_{L,1}=\text{Female}$, ${\tilde{C}}_{L,2}=\text{Male}$, and 2) Within-study differences in routes of exposure where ${\tilde{C}}_{L,1}=\text{IV}$ and ${\tilde{C}}_{L,2}=\text{gavage}$.

2.5.3. Software and computing platform

Graphical extraction of concentration vs. time data was conducted using Webplot digitizer (Rohatgi, 2022). All MCMC modeling, statistical analysis, and post-processing was conducted in Python v3.12 with PyMC v. 5.7.2 (Salvatier et al., 2016; Abril-Pla et al., 2023) used for all MCMC sampling. Allometric scaling through linear regression utilized Bambi (Capretto et al., 2022), a Bayesian model-building interface implemented in PyMC. Post-processing of inference data objects from PyMC was done using ArviZ v. 0.16.1 (Kumar et al., 2019) with plotting and visualizations using Matplotlib v3.7.1 (Hunter, 2007). Each PFAS analysis is conducted in a PFAS-specific Jupyter notebook with python code and accompanying Jupyter notebooks for each PFAS available in a GitHub repository at https://github.com/USEPA/CPHEA-Animal-PFAS-PK. All calculations were performed on a 64-bit CentOS Linux operating system (RHEL 8.9) on a Dell Precision 7920 containing an Intel Xeon Silver 4216 processor and 94 GB of RAM.

3. Results

Extracted time-course concentration data (individual animal and summary-level concentrations) are available in the GitHub repository. Prior and posterior predictive checks for the MCMC simulations are available in Appendix B while time-course fits to the extracted data are available in Appendix C.

3.1. Pharmacokinetic modeling results

Following the review of the literature, we extracted time-course blood (serum) PK data for mice, rats, and non-human primates from 20 studies (Table 2) resulting in 48 PFAS/species/sex combinations for which we fit a population PK model. Out of the 48 PFAS/species/sex fits, six were chosen to be best fit using a one-compartment model while a two-compartment model was selected as the most appropriate model for the remaining 42. Models were selected by the lowest EPLD between one- and two-compartment fits following LOO cross validation.

Table 2.

Summary of available blood (serum) time-course pharmacokinetic studies for the selected PFAS. For each study, the letter designates which species was studied for each PFAS across mouse (M), rat (R), and non-human primate (P).

Study	PFBA	PFBS	PFHxA	PFHxS	PFOA	PFOS	PFNA	PFDA
Butenhoff et al. (2004)					P
Chang et al. (2012)						M,R,P
Chang et al. (2008)	M,R,P
Chengelis et al. (2009)		R,P	R,P
Daikin (2010)			M
Dzierlenga et al. (2019)			R		R			R
Gannon et al. (2011)			M,R
Huang et al. (2019)		R		R		R
Iwabuchi et al. (2017)			R		R	R	R
Kemper (2003)					R
Kim et al. (2016)				R	R	R
Kim et al. (2018)				R
Kim et al. (2019)							R	R
Kudo et al. (2002)					R
Lau et al. (2020)		M
Lou et al. (2009)					M
Ohmori et al. (2003)					R		R	R
Olsen et al. (2009)		R,P
Sundström et al. (2012)				M,R,P
Tatum-Gibbs et al. (2011)							M,R

For the majority of fits, the 95 % credible interval was contained within a 3-fold error of the measured concentrations (Fig. B.1). However, reported PFBS concentrations in the individual mice and primates used for parameter determination could vary by more than an order of magnitude following the same administered dose and time point which resulted in a mean square log error greater than 0.5 for both species across males and females (PFBS fits in Appendix C). When investigating parameter uncertainty, specifically clearance, the largest posterior geometric standard deviations pertained to PFAS/species/sex combinations that contained substantial route- and dose-specific differences in clearance (PFBS, PFHxS, PFOA, PFOS). Apart from the model chosen for PFOA PK behavior in the male rat, the LOO-CV selected models predicted the observed serum concentrations across multiple orders of magnitude with central estimates falling within the 3-fold error bounds (Fig. B.1). However, the over prediction of the lowest serum concentrations for PFOA (Fig. B.1) indicates that neither model is appropriate for predicting these lowest internal concentrations.

Posterior distributions of PK parameters demonstrated similar body-weight normalized volumes of distribution $\left({\tilde{V}}_d\right)$ across each PFAS, but with body-weight normalized clearances $\left({\tilde{C}}_L\right)$ that could span orders of magnitude (Fig. 3 and Table 3). In addition, scaling clearance $\left(C_L\right)$ by $M_s^{0.75}$ resulted in a species-dependent effect on the allometrically-scaled clearance (Fig. B.6).

Fig. 3.

Mean and 95 % credible intervals for clearance (${\tilde{C}}_L$, L/kg/d), steady-state volume of distribution (${\tilde{V}}_d$, L/kg), and steady state half-life ($t_{1/2}$, d). Posterior population distributions for clearance (top row), steady-state volume of distribution (middle row), and half-life (bottom row) across mouse (left column), rat (middle column), non-human primate (right column).

Table 3.

Summary clearance $\left({\tilde{C}}_L\right)$, volume of distribution $\left({\tilde{V}}_d\right)$, and half-life $\left(t_{\frac{1}{2}}\right)$ pharmacokinetic parameters for mice, rats, and non-human primate. Values for each parameter are presented as means (95 % credible interval) of the posterior probability distribution. When a value is not presented for fa, both oral and IV data were not available for that specific PFAS/species/sex combination and the value was set to 1. Time-course pharmacokinetic data for PFDA in mice and primates and PFNA in primates were not available and the corresponding parameters could not be derived.

PFAS	Species	Sex	fa	${\tilde{C}}_L$ (ml/kg/d)	${\tilde{V}}_d$ (ml/kg)	$t_{\frac{1}{2}}$ (d)
	rat	Male	0.815 (0.556, 1)	528.7 (102.5, 981)	216.7 (82.94, 346.5)	0.348 (0.052, 0.744)
		Female	0.814 (0.561, 0.999)	1889 (427, 3364)	221.4 (68.47, 390.3)	0.098 (0.013, 0.216)
PFBA	mouse	Male	–	298.2 (137.8, 466.8)	288 (114.5, 472.2)	0.724 (0.195, 1.336)
		Female	–	866.6 (378.6, 1385)	214.1 (102.1, 331.7)	0.186 (0.064, 0.343)
	primate	Male	–	2061 (1546, 2576)	592.2 (335.5, 869.2)	0.197 (0.148, 0.248)
		Female	–	1341 (964.6, 1742)	436.9 (232.2, 649.6)	0.284 (0.229, 0.337)
	rat	Male	0.795 (0.523, 0.998)	1330 (782.2, 1944)	223.9 (132, 337.6)	0.12 (0.065, 0.189)
		Female	0.854 (0.632, 0.999)	5361 (3223, 7606)	305.1 (195.7, 427.8)	0.041 (0.022, 0.063)
PFBS	mouse	Male	–	1150 (927.9, 1394)	309.5 (216.6, 403.8)	0.186 (0.154, 0.221)
		Female	–	1963 (1342, 2613)	356.9 (206.5, 513.7)	0.125 (0.099, 0.154)
	primate	Male	–	361 (142.2, 609.2)	270 (94.44, 479.8)	0.564 (0.135, 1.077)
		Female	–	443.7 (125.2, 771.3)	298.5 (97.43, 543.5)	0.528 (0.101, 1.055)
	rat	Male	0.911 (0.786, 0.999)	3118 (2622, 3597)	426.4 (292.3, 557.7)	0.095 (0.066, 0.124)
		Female	0.836 (0.603, 0.999)	8115 (4532, 1.17e+04)	387.8 (215.2, 576.8)	0.034 (0.017, 0.053)
PFHxA	mouse	Male	–	2207 (1841, 2595)	686.9 (401.1, 1038)	0.215 (0.141, 0.309)
		Female	–	4441 (2865, 6069)	1525 (211.9, 3665)	0.251 (0.025, 0.63)
	primate	Male	–	4686 (2778, 6877)	827.4 (383.3, 1342)	0.121 (0.09, 0.16)
		Female	–	5042 (3839, 6335)	392.6 (255.3, 541.2)	0.054 (0.045, 0.063)
	rat	Male	0.869 (0.667, 1)	4.79 (3.39, 6.19)	201.6 (134.3, 265.6)	29.71 (18.35, 42.11)
PFHxS		Female	0.896 (0.728, 0.999)	98.21 (65.05, 134.6)	239.6 (158.7, 319.5)	1.744 (0.961, 2.588)
	mouse	Male	–	3.81 (3.49, 4.13)	150.6 (133.8, 168)	27.4 (25.62, 29.45)
		Female	–	3.14 (2.95, 3.32)	120.7 (111.1, 130.4)	26.66 (25.44, 27.95)
	primate	Male	–	1.17 (0.6, 1.7)	272 (234.6, 311.8)	177.6 (90.56, 296.9)
		Female	–	2.1 (1.7, 2.48)	222.9 (191.2, 252.9)	74.38 (56.84, 93.43)
	rat	Male	0.928 (0.824, 0.999)	15.07 (8.31, 22.63)	289.4 (190.5, 380.1)	14.2 (6.291, 23.18)
		Female	0.894 (0.735, 1)	666.3 (474.4, 859)	648.6 (282.3, 1183)	0.69 (0.271, 1.31)
PFOA	mouse	Male	–	6.94 (6.08, 7.77)	252.2 (206, 303.8)	25.63 (20.12, 31.97)
		Female	–	12.38 (3.28, 25.4)	298.5 (76.39, 569.5)	21.45 (2.501, 53.1)
	primate	Male	–	10.83 (8.06, 13.71)	179 (124.3, 236.2)	11.45 (9.765, 13.26)
		Female	–	4.64 (3.95, 5.39)	169.4 (140.5, 199.1)	25.34 (21.67, 29.26)
	rat	Male	0.853 (0.641, 0.999)	5.51 (3.66, 7.39)	441.9 (289.3, 608.6)	57.08 (33.41, 85.94)
		Female	0.885 (0.69, 0.999)	4.64 (2.48, 6.86)	345.7 (214.8, 476.4)	54.73 (25.33, 89.66)
PFOS	mouse	Male	–	5.59 (5.18, 6.01)	286 (257, 315.2)	35.49 (32.35, 38.55)
		Female	–	5.79 (5.41, 6.2)	274.2 (247.4, 299.9)	32.81 (30.25, 35.3)
	primate	Male	–	1.1 (0.86, 1.34)	212.1 (189.5, 232.2)	135.9 (100.5, 178.8)
		Female	–	1.91 (1.56, 2.25)	262.8 (235, 291.9)	96.3 (74.73, 120.3)
	rat	Male	0.863 (0.646, 1)	3.3 (1.73, 5.03)	239.8 (130.4, 355.2)	53.72 (22.22, 90.98)
PFNA		Female	0.937 (0.841, 1)	68.17 (58.8, 77.35)	277.8 (225.9, 330.6)	2.831 (2.284, 3.348)
	mouse	Male	–	3.93 (0.83, 6.35)	602.6 (508.5, 729.3)	227.5 (46.7, 445.9)
		Female	–	4.19 (3.1, 5.24)	348.4 (304.1, 395.1)	59.44 (39.45, 84.55)
PFDA	rat	Male	0.849 (0.62, 1)	3.46 (1.68, 5.54)	405.5 (249.2, 579)	88.41 (35.63, 153.3)
		Female	0.867 (0.655, 1)	3.22 (1.78, 4.82)	300.7 (188.2, 446.4)	68.78 (27.72, 116.2)

Because half-life is proportional to ${\tilde{V}}_d/{\tilde{C}}_L$, and ${\tilde{V}}_d$ remained generally consistent for PFAS across species, the large differences in PFAS-specific half-life are driven mainly by differences in systemic clearance. Here, a distinct reduction in clearance is observed across all species when transitioning between PFAS with 5‑carbon fluoroalkyl chain (PFHxA) or less (PFBS/PFBA) and a 6‑carbon fluoroalkyl chain (PFHxS) or greater.

Finally, a prior sensitivity analysis demonstrated that estimations of clearance, volume of distribution, and half-life were not meaningfully impacted by different choices of population mean and variance priors (see sensitivity analysis notebook within in supplemental code). Briefly, this sensitivity analysis demonstrated that the weakly informative priors for these pharmacokinetic parameters based on previous knowledge of PFAS pharmacokinetics did not significantly impact the resulting posterior distributions. In addition, a prior predictive check on the observed data showed that the 95 % credible intervals for concentrations predicted from the priors chosen for this analysis (Table 1) contained the observed data and were not biased towards any measured concentrations (Appendix B).

3.2. Clearance and volume of distribution allometric scaling

Allometric scaling (Eq. 14) using the population mean volume of distribution $\left(V_d\right)$ posterior distribution showed good agreement with the human values reported by Chiu et al. (2022) (central estimates within a factor of two) using a power-law coefficient of $b=1$ (Fig. 4A, Table 4). In addition, any sex-dependent differences in $V_d$ across mice, rats, and non-human primates were negligible as evidenced by the fits having very similar scaling coefficients $\left(a_{p,sex}\right)$. Similar cross-species volumes of distributions are to be expected for PFAS owing to the high degree of serum protein binding and distribution primarily to rapidly perfused tissues. These results demonstrate the reasonableness in using the non-human primate ${\tilde{V}}_d$ for human-specific PK calculations.

Fig. 4.

Allometric scaling of volume of distribution (A) and clearance (B). Mean fits from the Bayesian allometric scaling fits are shown for male (solid line) and female (dashed lines) and compared to mice (blue circles), rats (orange triangles), and non-human primates (green squares) for males (closed symbols) and females (open symbols). Using a body weight of 80 kg, mean model fits are extrapolated to humans and compared to human values reported for PFHxS, PFOA, PFOS, and PFNA (Chiu et al., 2022), PFBA (U.S. Environmental Protection Agency, 2022), PFBS (U.S. Environmental Protection Agency, 2021), and PFHxA (U.S. Environmental Protection Agency, 2023) (red diamonds). PFDA is excluded from the allometric scaling fits because only rat concentration data were available. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Table 4.

Predicted human volume of distribution (${\tilde{V}}_d$, L/kg) and clearance (${\tilde{C}}_L$, L/kg/y) through allometric scaling for male (M) and female (F). Previously reported pharmacokinetic parameters are given for comparison with the accompanying source. Calculations assume an 80 kg human and clearances are converted to L/kg/y to aid in comparison across sources.

PFAS	Volume of Distribution (L/kg)			Clearance (L/kg/y)			Human Source
	M	F	Reported Human ${\tilde{V}}_d$	M	F	Reported Human ${\tilde{C}}_L$
PFBA	0.33 (0.2–0.53)	0.28 (0.17–0.45)	–	59.5 (13.2–247)	112 (25.4–489)	43.8	U.S. Environmental Protection Agency (2022) - IRIS
PFBS	0.27 (0.17–0.43)	0.32 (0.2–0.52)	–	71.4 (15–287)	144 (33.9–608)	1.31	U.S. Environmental Protection Agency (2021)
PFHxA	0.63 (0.39–1.0)	0.62 (0.38–0.99)	–	275 (66.1–1150)	490 (116–2080)	16.2	U.S. Environmental Protection Agency (2023) - IRIS
PFHxS	0.2 (0.13–0.33)	0.19 (0.12–0.31)	0.29 (0.17–0.45)	0.24 (0.053–0.98)	0.753 (0.162–2.99)	0.025 (0.012–0.039)
PFOA	0.24 (0.15–0.38)	0.32 (0.2–0.52)	0.43 (0.32–0.59)	0.911 (0.208–4.07)	2.94 (0.665–12.2)	0.095 (0.074–0.13)	Chiu et al. (2022)
PFOS	0.3 (0.19–0.49)	0.29 (0.18–0.48)	0.32 (0.22–0.47)	0.28 (0.063–1.25)	0.322 (0.072–1.33)	0.066 (0.048–0.092)
PFNA	0.38 (0.2–0.68)	0.31 (0.17–0.56)	0.19 (0.11–0.3)	0.233 (0.039–1.5)	1.1 (0.19–7.19)	0.056 (0.033–0.093)

With the exception of PFBA, comparing the best available human clearance values $\left(C_L\right)$ presented by Chiu et al. (2022) (PFHxS, PFOA, PFOS, PFNA), U.S. Environmental Protection Agency (2021) (PFBS), U.S. Environmental Protection Agency (2023) (PFHxA), and U.S. Environmental Protection Agency (2022) (PFBA) to the current results where clearance is estimated through allometric scaling (power-law coefficient of $b=0.75$) demonstrates that allometric scaling does not reliably predict human clearance for the selected PFAS (Fig. 4B, Table 4). Furthermore, clearance $\left(C_L\right)$ for the longer chained PFAS (PFHxS, PFOA, PFOS, and PFNA) did not substantially change with increasing species body weight (Fig. 4) and in some cases, decreased from rats to primates to humans (female PFOA).

For both pharmacokinetic parameters predicted through allometric scaling ($V_d$ and $C_L$), we used a human body weight of 80 kg (U.S. Environmental Protection Agency, 2011a) to convert to a per kg volume of distribution $\left({\tilde{V}}_d\right)$ and clearance $\left({\tilde{C}}_L\right)$ for comparison to the reported human values in Table 4. Finally, allometric scaling of PFDA was excluded because only rat pharmacokinetic data were available.

3.3. Quantitating differences in clearance

Using a ±20% difference in clearance as the ROPE, we compared clearances from two scenarios: 1) female vs. male and 2) intravenous vs gavage routes of exposure (Fig. 5). The largest differences in clearance between sexes was seen in rats, where female rats had substantially greater clearance for PFBS, PFHxA, PFHxS, PFOA, and PFNA (Fig. 5A). The mean relative difference in clearance for these five chemicals in female rats ranged from two to 32 times larger compared to male clearance. For PFBA, clearance in female rats was greater, but 95 % credible interval estimates of $\rho$ overlapped with the ROPE while estimates of $\rho$ (relative sex-specific clearance values) for PFOS and PFDA indicated no significant differences in clearance between the rat sexes. For mice, only PFHxA demonstrated a significantly higher clearance for females compared to males. However, even though none of the confidence interval estimates of $\rho$ excluded the ROPE for the remaining PFAS, the central estimates of $\rho$ indicated that female mouse clearance was higher for several chemicals (PFBA, PFBS, PFOA and PFNA). For PFOS in mice, the entire 95 % C.I. was contained within the ROPE indicating equivalent PFOS clearances for male and female mice. For non-human primates, sex-specific differences in $\rho$ did not follow the same trends. The central estimate for male non-human primate PFOA clearance was twice as large as that for females, while the central estimate for PFOS female clearance was about 50 % larger than that for males.

Fig. 5.

Comparison of clearances using a 20% difference in clearance as the ROPE (shaded blue with dash-dot border) with $\rho =C_{L,1}/C_{L,2}$ expressed as a ${\text{log}}_2$ fold change. Subfigure A compares $C_{L,1}=\text{female}$ and $C_{L,2}=\text{male}$ results pooled by species and chemical where values to the right of the blue region indicate higher female clearance compared to male. Subfigure B compares $C_{L,1}=\text{IV}$ and $C_{L,2}=\text{gavage}$ for rats on the level of single exposure in a study (dose [mg/kg], sex) where values to the right of the blue region indicate higher IV clearance. In the figures, the mean and 95 % HDI for each $\rho$ is plotted and ${\text{log}}_2\rho >0$ indicates $C_{L,1}>C_{L,2}$ while ${\text{log}}_2\rho <0$ represents $C_{L,2}>C_{L,1}$. A filled symbol signifies the entire 95 % HDI falls outside the ROPE, indicating a practical difference between $C_{L,1}$ and $C_{L,2}$. Comparatively, open symbols indicate overlap between the 95 % HDI and the ROPE and no decision is made about a difference in clearances. Finally, an ‘x’ signifies the entire 95 % HDI falls within the ROPE and indicates no difference between $C_{L,1}$ and $C_{L,2}$. For intravenous vs gavage comparisons, only studies that tested the same dose across both routes of exposure were compared. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

When comparing pharmacokinetics across different routes of exposures, the general expectation is that systemic clearance should be independent of the route, i.e., once a chemical distributes through the body, it should clear from the body at the same rate regardless of the route of exposure. However, several studies have reported bioavailability values, calculated as the dose-normalized ratio of the areas under the curve (AUCs) for gavage and IV exposures, greater than 100 % (Kim et al., 2016; Dzierlenga et al., 2019; Huang et al., 2019), indicating that there is more chemical in circulation following gavage dosing than following IV dosing. Using the ROPE+HDI method, we investigated differences in clearance between gavage and IV routes of exposure. These route-specific comparisons demonstrated that IV routes of exposure generally produced larger clearances than gavage routes of exposure in the rat, which was the only species for which dose-matched routes of exposure were available (Fig. 5B). The ROPE+HDI results shown in Fig. 5B highlight this effect for PFBA (Chang et al., 2008), PFBS (Huang et al., 2019), PFHxS (Kim et al., 2016; Kim et al., 2018), PFOA (Kemper, 2003), PFOS (Huang et al., 2019), and PFDA (Dzierlenga et al., 2019), where a significant difference between IV and gavage clearance was determined for female rats when comparing the same dose within a study. These instances of greater PFAS clearance following IV compared to gavage corresponded to datasets where the reported dose normalized AUC for gavage is greater than the dose normalized AUC for IV indicating $f_a>1$.

4. Discussion

By incorporating observed concentration vs. time data from 20 studies across eight PFAS of interest, the hierarchical Bayesian analysis characterized population- and dataset-level uncertainty and variability in PFAS PK parameters using single dose pharmacokinetic studies published in the literature. Posterior population mean, population variance, and dataset-level parameters provide insights into the uncertainty of the pharmacokinetic parameters and allow for propagation of that uncertainty into PFAS pharmacokinetic predictions. The distributional estimate of the population mean PK parameter provides the central estimate and estimated uncertainty of the true population mean while the population variance (presented as a geometric standard deviation in Table B.4) quantitates dataset-to-dataset variation and describes the heterogeneity in parameter values across available datasets. Finally, dataset-level parameters describe how PK parameters derived from each time-course dataset deviate from the population mean. Taken together, the resulting posterior probability distributions account for several sources of uncertainty, such as those pertaining to the observed data (e. g., inter- and intra-study variability, study-specific measurement error, etc.), and those involving underlying model assumptions (e.g. only fitting one- vs. two-compartment classical PK models). Using these posterior PK distributions, we characterized differences in population-level PFAS PK across mice, rats, primates, and humans to demonstrate a breakdown in allometric scaling assumptions for clearance in several PFAS. In addition, comparisons of dataset-level posterior distributions demonstrated significant differences in clearance within a population depending on the PFAS route of exposure. Results from this study inform current internal dose predictions for PFAS in animals and help identify data gaps and possible changes to model structure to better characterize PFAS pharmacokinetics.

4.1. Population-based modeling of PFAS pharmacokinetics

The partial pooling of PK data ensured clearance calculated from less robust datasets, e.g. shorter measured time, fewer time points, and fewer animals did not unduly influence the population PK parameters for each PFAS/species/sex combination. For example, Sundström et al. (2012) determined clearances of 40.32 ml/d/kg for male rats and 119 ml/d/kg for female rats following an IV administration of PFHxS. Comparatively, Huang et al. (2019) calculated a much lower clearances for IV administration of PFHxS of 4.73 ml/d/kg for male rats and 65.5 ml/d/kg for female rats. Differences in study-specific PFHxS clearance will arise from variations in study designs, such as different applied doses, number of animals dosed, study duration, and pharmacokinetic model assumptions. Taking each study- or dataset-specific clearance independently represents a completely un-pooled approach where it is difficult to know which study’s set of PK parameters should be utilized for internal dosimetry calculations. By pooling data across these studies, outlier datasets will not overly influence the population clearance derived from the remaining datasets. Ultimately, we determined a PFHxS population level clearance (95 % C.I.) of 4.5 (3.2–5.7) ml/d/kg for male rats and 98.4 (68.8–127) ml/d/kg for female rats which resembles the lower clearance for male rats presented in Huang et al. (2019) while agreeing with the higher clearance for female rats presented by Sundström et al. (2012). These estimates utilize observations from several datasets across four different studies and assign a probability distribution to the clearance based on the observed PFHxS pharmacokinetics.

Additionally, physiologically based pharmacokinetic (PBPK) models do exist for some PFAS, but they do not cover the PFAS space as comprehensively as this study and require substantially more resources to parameterize compared to a classical PK analysis. However, when comparing clearance results from this study (15.1 ± 3.8 ml/kg/d) to the probabilistic population-based PBPK model for PFOA in male rats presented in Cheng and Ng (2021) (25.2 ± 1.6), we find that the Cheng and Ng (2021) reported clearance and in vivo clearance in Kemper (2003) (20.9 ± 3.8) are within the 90 % credible intervals for the population-level male rat PFOA clearance from this analysis. While the central estimates for clearance between this analysis and Cheng and Ng (2021) are similar, the larger range of doses and study-to-study variability from seven studies will contribute to larger uncertainty for the population-level clearance value.

4.2. Inter-species clearance extrapolation through allometric scaling

As outlined in U.S. Environmental Protection Agency (2014) guidelines, ratios of systemic clearance can be used to derive inter-species extrapolation factors for predictions of internal dose. For PFBS, predicted human clearance based on body mass to the ¾ power scaling agrees with the values reported by U.S. Environmental Protection Agency (2022) within a factor of two for the central estimates. However, the default approach of predicting human clearance using allometric scaling by body weight significantly overpredicts the observed human clearance for most PFAS investigated here (PFBS, PFHxA, PFHxS, PFOA, PFOS, PFNA). In some cases, this human-predicted value was several orders of magnitude higher than any reported human value (Table 4). In addition, clearance across female rats, female non-human primates, and humans either stays the same or decreases for the longer chain PFHxA, PFHxS, PFOA, and PFNA indicating a maximal absolute (liter per day) clearance is reached regardless of species size.

One possible explanation for an overprediction of human clearance following extrapolation from animal-derived clearances is that PFAS internal dosimetry in the animal tends to be much higher than typically seen for humans in the general population. For example, the lowest animal serum concentrations measured for PFOA in this study were on the order of 1–10 μg/L after 80 days following a 0.1 mg/kg dose in male rats (Kemper, 2003). Comparatively, serum concentrations of PFOA following environmentally relevant exposures in humans are on the order of 0.002–0.2 μg/L (Lynch et al., 2023). PFAS clearance is limited by extensive binding to plasma proteins (Ng and Hungerbuhler, 2014; Cheng and Ng, 2017), increased tissue distribution through membrane lipid binding (Allendorf et al., 2021), and active renal resorption (Wambaugh et al., 2013; Cheng and Ng, 2017) mediated by organic anion transporters (Zhao et al., 2023). Under a saturable renal resorption hypothesis, fitting the one- and two-compartment PK models using data sets from the higher dose experiments would overestimate PFAS clearance at (lower) environmentally relevant doses (Felmlee et al., 2013). However, while saturation of renal resorption might explain higher clearance in animals compared to humans (when scaled by body mass to the ¾ power), many of the animal PK data sets do not show higher clearance at higher vs. lower doses (Fig. B.2) and have elimination phases consistent with a constant clearance rather than one that decreases as blood concentration decreases. This could indicate that the animal internal dosimetry following a single large external dose is not representative of repeated dosing at much lower external doses for some PFAS.

Species dependent differences in the high affinity PFAS transporters responsible for renal excretion provide another explanation for observed inter-species PFAS clearance differences. For example, Niu et al. (2023) reviewed the renal transporters most likely to impact PFAS renal resorption and highlighted organic anion transporting polypeptides (OATP) for rats and humans as apical membrane transporters with the ability to facilitate resorption in the proximal tubule for numerous PFAS. When comparing PFOS and PFHxS OATP rat vs. human in vitro transporter efficiency through ratios of maximum transport rate to affinity constant $\left(V_{max}/K_M\right)$, Zhao et al. (2017) determined that OATP $V_{max}/K_M$ was significantly higher for humans compared to rats. Comparatively, Niu et al. (2023) identified OAT3 as a basolateral membrane transporter responsible for transporting PFAS out of the blood and into the proximal tubule. For PFOA, Nakagawa et al. (2008) determined the rOat3 $V_{max}/K_M$ in rats to be twice that of hOAT3 for humans. Taken together, a higher $V_{max}/K_M$ for rats compared to humans on the basolateral (blood facing) membrane and a lower $V_{max}/K_M$ for rats compared to humans on the apical (urine facing) membrane would lead to a net higher renal clearance in the rat compared to human. Furthermore, not all PFAS investigated in this study have been shown to be substrates for human OATs. Ryu et al. (2024) demonstrated that PFBA and PFOS were not in vitro substrates for these renal transporters. Interestingly, PFBA and PFOS were the best candidates for inter-species extrapolation (Fig. 3B) through default approaches indicating inter-species differences in OAT transporter affinity may play a significant role in the species-specific effect on clearance. Additional explanations for departure from the default allometric approaches could also be attributed to other kidney transporters such as OATP4C1, MDR1, BCRP, MRP2, and MRP3 for which species differences were not evaluated in vitro. While this simplistic view of species-specific differences in apical vs. basolateral membrane transporter efficiency begins to explain the inability to extrapolate PFAS through classical allometric scaling, complex transporter interactions exist elsewhere in the body that may also contribute to inter-species differences in systemic clearance. Overall, active transporters expressed at different levels across different species and sexes and with differing affinities to each PFAS mean that it will be difficult to extrapolate systemic clearance across species using body mass alone.

4.3. Sex-dependent differences in PFAS clearance

From Fig. 5A, we determined that the primary difference between male and female clearance occurred in the rat which is in line with previous studies looking at male and female matched PK results (Vanden Heuvel et al., 1992; Kudo et al., 2002; Dzierlenga et al., 2019; Huang et al., 2019). Interestingly, this sex-dependent difference is not consistently observed across mice and non-human primates indicating that there may be something unique about male vs. female rats such as a sex hormone-dependence on kidney transporters. For example, male rat castration significantly reduces Oat3 expression in the male rat renal cortex (Ljubojevic et al., 2004) and reduces Oatl1a1 expression in the male mouse (Cheng et al., 2006) and male rat (Gotoh et al., 2002) kidneys. For each species, transporter expression is restored following supplementation with testosterone. While these studies only demonstrate sex-hormone effect on renal transporters, Kudo et al. (2002) demonstrated a positive correlation between basolateral Oat2/Oat3 expression and renal PFOA clearance in male and female rats.

While there are limited pharmacokinetic datasets for PFAS in non-human primates, the sex-dependent effect in primates appears to be much more muted as compared to rats. For comparison in humans, Jain and Ducatman (2022) evaluated PFAS serum concentrations in the US population measured as part of ongoing biomonitoring by NHANES and demonstrated sex- and age-dependent differences in serum concentrations for PFOA, PFNA, PFHxS, and PFOS. At early ages (<12 years), serum concentrations in males and females are similar. However, serum concentrations for these PFAS begin to diverge during teenage years with female concentrations generally decreasing from age 12 until age 30–35, while concentrations in males are approximately constant over this range. Concentrations in females then begin to increase but remain lower than males until age 50–60. While the largest difference between males and females is during the woman’s reproductive lifespan (approximately age 12–50) and menstrual fluid loss seems a likely explanatory mechanism, the fact that PFAS concentrations begin to trend upward in women between ages 35 and 40, when menopause does not usually occur until age 50, provides reason to consider alternative mechanisms for PFAS clearance. Concentrations of PFOS in women remained mostly below those of men until age 75, although this was not the case for PFOA, PFNA and PFHxS (Jain and Ducatman, 2022). Further, while concentration differences between males and females is indicative of greater clearance in females, exposure levels have not been evaluated for these populations and may also be lower for females than males, contributing to the observed concentration differences. Changes in body weight over time are also expected to impact serum concentrations and the trends for these may also be sex-dependent. Finally, while it seems likely that menstrual fluid which includes the serum proteins to which PFAS binds will contain PFAS at similar concentrations as blood serum, experimental confirmation of this assumption is not available, and it is possible that some of the PFAS initially lost with fluid from the uterus is resorbed before the fluid completely leaves the woman’s body. Nevertheless, the NHANES data reported by Jain and Ducatman (2022) is strongly indicative of menstrual fluid loss as a mechanism of elimination, leading to higher clearance in women. A follow up study in humans (Jain and Ducatman, 2023) found that increased estrogen during hormone replacement therapy resulted in increased PFAS concentrations, relative to those not using hormone replacement, both after natural menopause and after hysterectomies, indicating that hormonal regulation of urinary or fecal excretion was not likely to explain the male-female difference.

Overall, menstrual fluid loss in humans is on the order of 0.03 mL/kg-d (calculated from results of Verner and Longnecker (2015)) which means that it will only significantly impact clearance when clearance by other routes (in males) is below 0.15 mL/kg-d, i.e., for longer-chain PFAS. This will also be a factor for the cynomolgus monkeys used as the non-human primates in these studies, which also menstruate (Kerber and Reese, 1969). Results from this study demonstrate two PFAS with the lowest clearance in monkeys (PFHxS and PFOS) both showed close to double the clearance in females vs. males (PFHxS does not reach the ROPE criteria established for practical significance due to the Sundström et al. (2012) inter-individual variability). On the other hand, male monkeys had higher clearance for PFOA than female monkeys (10.8 vs. 4.64 ml/kg/d). This difference of ~6 mL/kg-d is far greater than the difference of 0.9 mL/kg-d estimated for PFHxS and PFOS. Hence, other mechanisms besides menstrual fluid loss appear to be active for non-human primates, leading to sex-specific results. Irrespective of the mechanism, the apparent difference in clearance of PFAS in human females during reproductive years vs males is consistently in the same direction – higher in females – though the magnitude and duration of the difference varies among the PFAS evaluated, as illustrated by Jain and Ducatman (2022).

4.4. Route of exposure can impact clearance

As summarized in Fig. 5B, when comparing population mean posterior clearances from the same dose in a given study, clearance following IV dosing was often significantly greater (as evidenced through rejection of the null hypotheses using the ROPE+HDI decision) than clearance following gavage dosing for some PFAS in female rats. Because the beta distribution prior ensures $f_a\le 1$ and these compounds are not metabolized, differences in the AUC (e.g. $\text{AU}{\text{C}}_{\text{oral}}>\text{AU}{\text{C}}_{\text{IV}}$) are attributable to differences in route-specific excretion. For some PFAS, there is evidence of accumulation in the liver (Butenhoff et al., 2009; Conley et al., 2022) with an oral route able to deliver PFAS to the liver more readily compared to an IV route of exposure. A major contributor to this observation most likely concerns enterohepatic recirculation for PFAS (Cao et al., 2022) through transporter-mediated uptake in the liver. Furthermore, both human and rat Na⁺/taurocholate cotransporting polypeptide (NTCP) have demonstrated in vitro affinity to transport PFBS, PFHxS, PFOS, PFOA, and PFDA (Vujic et al., 2024) which are five PFAS from this study with evidence of increased oral AUC. To a lesser extent, protein binding such as liver fatty acid binding protein (L-FABP) (Yang et al., 2020) could also impact accumulation of PFAS in the liver. During the first pass for the gavage route of exposure, these liver-specific effects on PFAS may result in the formation of a depot of PFAS in the liver that is slowly released to the blood stream. This effect would be muted under an IV route of exposure where PFAS would more readily make its way to the kidney for excretion before circulation to the liver. Interestingly, there is no significant difference in terminal half-life when comparing IV vs gavage (Fig. B.3) following administration of a single dose. This again indicates a first pass effect in the liver where differences in AUC and thus systemic clearance are determined during the early time-course (distribution phase) while not impacting the terminal half-life (elimination phase).

4.5. Limitations and assumptions

One limitation of the analysis is the potential for non-linear elimination kinetics often seen with renal clearance of PFAS. Using a one- or two-compartment model still results in first-order clearance where previous studies have demonstrated utility of saturable resorption and non-linear elimination to account for dose-dependent changes in clearance (Loccisano et al., 2013; Wambaugh et al., 2013). This possibility for dose-dependent clearance might explain the larger uncertainty for some PFAS. For example, Lou et al. (2009) demonstrated dose-dependent clearance effects for female mice at larger PFOA doses. If both low and high dose time-course concentration data are pooled into a single clearance for a given PFAS in mice, this effect will not be accounted for. In addition, a dose-dependent effect on clearance might not be readily observed in the animal datasets used to parameterize the pharmacokinetic models in this study owing to the larger applied doses used across studies. Lower dose concentrations producing internal doses closer to environmentally relevant exposures in humans, coupled with a more mechanistic description of PFAS clearance would better enhance our understanding of PFAS half-lives.

Another limitation is in the animal data available for modeling. The hierarchical fitting methodology is amenable to multiple datasets measured across numerous studies where uncertainty and variability in the pharmacokinetic parameters can be more readily quantitated. However, for mice and non-human primates only one or two time-course datasets were available for many PFAS, and a hierarchical methodology could not be applied to the observed data. In these instances, the posterior probability distribution only provides a measure of the underlying variability in the study-specific data and is not representative of the larger population of studies and animal species and colonies. In addition, these models were parameterized on single-dose PFAS data. As discussed above, differences in internal dosimetry are likely to exist following repeated, low-dose administration of PFAS when compared to these single-doses. Time-course concentration datasets from multiple sources and for repeated dosing regimens are needed to truly characterize the uncertainty and variability of the PK parameters.

5. Conclusion

In this analysis, we applied a hierarchical Bayesian methodology to characterize PFAS pharmacokinetics across three laboratory animal species frequently used for chemical risk assessment: mice, rats, and non-human primates. In this partial-pooling method, each observed time-course concentration dataset is fit by sampling from a higher-level “population” distribution so that all available data are utilized without placing undue weight on a single study or two for determining the pharmacokinetic parameters needed for internal dosimetry predictions. Following parameterization of either a one- or two-compartment model, the resulting posterior distributions allow for direct comparisons of pharmacokinetics between different groups to assess possible differences. Ultimately, species- and sex-specific population-level PK values, with the resulting uncertainty, are determined for each PFAS for which time-course blood concentration data exist. These distributional (probabilistic) estimates of PFAS PK parameters provide information about uncertainty and variability in the parameters and can be propagated through PK models to determine distributional estimates of PFAS internal dose.

Using these results, routinely applying the default inter-species extrapolation approaches for clearance without considering human-specific dosimetric differences does not appear to be appropriate for these PFAS. This is due to numerous pharmacokinetic characteristics that appear unique to each species and sex. While sex-dependent differences in rat pharmacokinetics have been shown to be driven by sex hormone mediated effects, this mediator has not been replicated in humans even though there appears to also be sex-dependent differences in human pharmacokinetics. Conversely, we observe only slight (and inconsistent with human) sex-dependent effects on clearance in non-human primates which indicates clearance extrapolation from non-human primates may also not be appropriate for characterizing male vs. female human clearance. Finally, differences in clearance for different routes of exposure in animals indicate the need for inclusion of first pass effects and subsequent time-course of protein binding. A mechanistically-inspired PK model such as that used by Wambaugh et al. (2013) might have sufficient complexity to shed light on the pharmacokinetics of PFAS in a given species and sex at different dose levels via different routes of exposure. Incorporating these targeted physiological components e.g., saturable resorption and liver binding, would allow for the entire breadth of available PK data to be used to inform PFAS pharmacokinetics.

Supplementary Material

Appendix A. Supplementary data

Supplementary data to this article can be found online at https://doi.org/10.1016/j.taap.2025.117336.

Data availability

Code and underlying data use for fitting will be publicly available through Github upon publication