Predicting Human Tissue Exposures to Xenobiotics Using a Bottom-up Physiologically-Based Biokinetic Model

Advancements in physiologically-based biokinetic (PBK) modelling, in vitro-to-in vivo extrapolation (IVIVE) methodologies and development of permeability-limited biokinetic models have allowed for predictions of tissue drug concentrations without utilizing in vivo animal or human data. However, there is a lack of in vivo human tissue concentrations to validate these models. Herein, we validated the performance of our previously published bottom-up rosuvastatin (RSV) PBK model with clinical data from a recently published study that made use of positron emission tomography (PET) imaging to quantify the hepatic concentrations of [C]RSV drug-drug interaction (DDI) with cyclosporine A (CsA). Simulated RSV area under the plasma concentration-time curve (AUC0h-t) and maximum plasma concentration (Cmax) before and after DDI were within 1.5-fold of the observed data. Simulated AUC0-30min and Cmax ratios in the DDI setting matched the observed ratios closely (within 1.1-fold). To predict RSV hepatic concentrations, the model inputs were modified to account for RSV in the bile canaliculi after biliary excretion. The model recapitulated the observed hepatic concentrations before DDI and the decrease in hepatic concentrations after DDI. Simulated area under the liver concentration-time curve (AUC0-30min,liver), maximum liver concentration (Cmax,liver), AUC0-30min,liver ratio and Cmax,liver ratios were predicted within 1.5-fold of the observed data. In summary, we validated the ability of bottom-up PBK modelling to predict RSV hepatic concentrations with and without DDI with CsA. Our findings confirmed the importance to account for drug distributed within the bile canaliculi for accurate prediction of hepatic tissue drug levels when compared against in vivo liver PET scan data.


Introduction
A quantitative understanding of the free or unbound concentrations of a chemical compound within various tissues of the body is necessary to fully appreciate its pharmacodynamic or toxicodynamic potential (Chu et al., 2013). It is accepted that only the intracellular unbound fraction of a biologically active compound interacts with its molecular target, driving the potential for efficacy or toxicity. In the pharmaceutical sector where clinical studies using human subjects are frequently performed, the unbound plasma concentration (measured plasma concentration multiplied by fraction unbound (fu,p)) is frequently assumed to be a surrogate measure of unbound tissue concentrations (Ryu et al., 2020). However, this relies on the assumption of the free-drug/chemical hypothesis, which is invalid for compounds with poor passive permeability where tissue concentrations are modulated by either active uptake or efflux membrane transporters (Zhang, Donohue, et al., 2019). For certain compounds, it has been found that the steady-state ratio of unbound tissue concentrations against unbound plasma concentration (Kp,uu) can be much greater than one, indicating tissue accumulation. For example, the rosuvastatin (RSV) liver Kp,uu (Kp,uu,liver) was estimated to be 57, representing a 57-fold higher unbound RSV concentration in the liver versus plasma (Zhang, Hop, et al., 2019). Therefore, the unbound plasma concentration can be an inappropriate measure of the unbound tissue concentrations. Conventionally, intracellular unbound concentrations are assessed by harvesting the tissues of animals dosed with the compound of interest. However, with the growing shift towards non-animal testing methods for risk-assessments of chemicals, there is a need for alternative methods to obtain 2 Methods

PBK Model of RSV
The population-based ADME Simcyp ® simulator (Version 18, Release 1, Certara UK Ltd, Simcyp Division, Sheffield, UK) was used to develop all our PBK models. Compound dependent input parameters for RSV are found in Table 1. The PBK model of RSV was unchanged based on the bottom-up model we published previously (Chan et al., 2019). Briefly, the full PBK model was used to describe the perfusion-limited distribution of RSV into various organ compartments. The Rodgers and Rowland tissue composition method was used to predict the tissue-to-plasma equilibrium distribution ratios for each organ compartment (Rodgers and Rowland, 2007). The permeability-limited liver (PerL) model was incorporated into the full PBK model (Figure 1) to describe the permeability-limited distribution of RSV into the liver (Jamei et al., 2014). The PerL model divides the liver into 3 compartments: intracellular water (IW), extracellular water (EW) and vascular space (VS). It is assumed that unbound, unionized compounds within the EW and VS are in instantaneous equilibrium and the distribution between both compartments through the capillary barrier is not a rate-limiting process. In contrast, distribution between the EW and IW is governed by the compound's passive and active transport across the plasma membrane. Several transporters facilitate the saturable uptake of RSV at the basolateral membrane from the EW to IW: OATP1B1, OATP1B3, OATP2B1 and sodium-taurocholate co-transporting polypeptide (NTCP) (Chan et al., 2019). Conversely, multidrug resistance-associated protein 4 (MRP4) is responsible for the efflux of RSV back into the EW from the IW at the basolateral membrane. At the canalicular membrane, two efflux transporters are responsible for the excretion of RSV into the bile canaliculi, BCRP and possibly P-glycoprotein (P-gp). An overall canalicular efflux intrinsic clearance (CLint) was used to define the transporter-mediated biliary clearance of RSV in the model (Chan et al., 2019).  Table 2. Similar to RSV, the full PBK model and Rodgers and Rowland method were used to describe perfusion-limited tissue distribution. CsA is an inhibitor of several transporters involved in the transport of RSV. Ki values of CsA for the inhibition of OATP1B1, OATP1B3, OATP2B1, NTCP and BCRP were obtained from the literature and applied to the model (Jamei et al., 2014;Vildhede et al., 2014;Wang et al., 2017). To permit inhibition of canalicular efflux of RSV, Ki of CsA for the inhibition of BCRP was used as the input parameter.

Calculation of Hepatic RSV Concentrations
In the bottom-up PBK model we published for RSV, the PerL model was utilized to account for the effect of numerous uptake transporters that mediate the distribution of RSV into the liver. The PerL within Simcyp has been described extensively previously (Jamei et al., 2014). Since the PerL model predicts the unbound IW and EW concentrations in the liver (Cu,IW and Cu,EW) separately, there is a need to amalgamate the predicted concentrations from the PerL model into an overall hepatic concentration for comparison with the [ 11 C]PET imaging data. As a result, the overall hepatic concentration is: = ÷ (1) where amount of RSV in the liver (Aliver) is calculated as: (5) VEW-eff represents the effective EW liver volume and KEW:B is a drug dependent parameter that represents the ratio of CEW to CB,VS (Jamei et al., 2014). VEW-eff accounts for the distribution of chemical compounds found within the VS and EW of the liver (Jamei et al., 2014). Finally, to calculate the Aliver, we made use of the following equation (7) fu,EW and fu,IW represents the fraction unbound of RSV in the EW and IW of the liver, which are predicted in Simcyp to be 0.187 and 0.967 respectively. fIW, fEW and fVS represents the fraction of IW, EW and VS out of the total liver volume and is defined by Simcyp to be 0.835, 0.16 and 0.05 respectively. Hepatic concentrations from the PET imaging study were normalized against the mass of the liver and the intravenous dose of RSV given in kilobecquerels (kBq/g/kBq). For ease of comparison between simulated and measured values, the liver density value of 1.08 g/mL from Simcyp and RSV dose given were applied to convert the hepatic concentrations measured in the imaging study to ng/mL. All calculations were performed on Microsoft ® Excel ® for Office 365 (Microsoft, Redmond, WA, USA). Graphs were plotted and analyzed using GraphPad Prism 8 (GraphPad Software, La Jolla, CA, USA).
From a physiological perspective, the permeability-limited model does not fully account for the physiology of biliary excretion. Biliary excretion begins when hepatic canalicular efflux transporters in the hepatocyte excrete a compound via active transport. The excreted compound will enter the bile canaliculi, pass through the Canals of Hering into the intrahepatic ducts, followed by consolidation into the common hepatic duct before it leaves the liver via the common bile duct and drains into the gall bladder (Boyer, 2013). We expect that hepatic concentrations measured from PET images to be a composite of the concentrations found not only in the EW and IW space of liver cells but also within the bile canaliculi and possibly the intrahepatic ducts. It was ALTEX preprint published November 17, 2020 doi:10.14573/altex.2007151 8 mentioned by Billington et al. that the bile ducts were excluded from the PET scans images of the liver. However, this did not exclude RSV distributed into the bile canaliculi. As RSV is reliant on biliary excretion for its elimination, during the initial phase of RSV disposition, a substantial proportion of RSV hepatic concentration from the PET imaging study is expected to be found within the bile canaliculi. Therefore, there was a need to adapt the PerL model parameters to account for distribution into the bile canaliculi. We employed a workaround that would account for the bile canaliculi concentration by removing the biliary excretion component of RSV via changing the liver canalicular efflux intrinsic clearance (CLint) input value to 0. This had the effect of combining RSV that would normally be found in the bile canaliculi with RSV found within the IW and EW space, thus allowing us to account for the fraction of RSV that reside in the bile canaliculi in the initial phase of its disposition.

Independent Simulation of Plasma Concentrations of RSV and CsA
Validation of the PBK models of RSV and CsA were conducted by performing simulations that matched the design of the PET imaging clinical study. Using the Simcyp Healthy Volunteers population database, simulations for 2 separate trials were performed for a 0.91 µg IV bolus dose of RSV and 2.5 mg/kg/h IV infusion of CsA. Refer to Table 3 for details of the population characteristics. As a range of doses (0.91 -2.57 µg, equivalent to 309 -689 MBq) were administered to the subjects from the PET imaging study, the lowest dose of RSV 0.91 µg was chosen. Simulated plasma concentrations were compared against the plasma concentrations of RSV and CsA from the PET imaging study extracted using WebPlotDigitizer (San Francisco, California, USA).
To validate the RSV PBK model, a two-fold criterion was applied to compare the predicted against observed biokinetic parameters including maximum plasma concentration (Cmax) and area under the plasma concentration-time profile (AUC0-30min). For the CsA model, visual inspection of the predicted against observed plasma-concentration time profile was used for validation because biokinetic parameters of CsA were not reported by Billington et al.

Simulating Plasma Concentrations of RSV Post-DDI with CsA
A second level of validation was performed to ascertain that our PBK models were able to predict the DDI between RSV and CsA.
Using the same population database and trial design, a CsA 2.5 mg/kg/h IV infusion over two hours followed by a RSV 0.91 µg IV bolus dose 45 minutes after the initiation of the CsA IV infusion was simulated. Similarly, a two-fold criterion was applied to compare the predicted against observed biokinetic parameters, Cmax, AUC0-30min and Tmax for RSV after the DDI with CsA. Cmax and AUC0-30min ratios were evaluated using the quotient of the values after and before DDI.

Simulating Hepatic Concentrations of RSV Pre-and Post-DDI with CsA
Using the same trial design mentioned, we applied the bottom-up RSV PBK model to simulate RSV hepatic concentrations after a 0.91 µg RSV IV bolus dose. As mentioned previously, during initial simulations of the unchanged RSV PBK model, predictions of hepatic concentrations were suboptimal. Modification of the PerL model biliary excretion parameter was performed to account for distribution of RSV within the bile canaliculi. Comparisons of the simulations before and after this modification was done to understand the impact of this modification. Furthermore, as PET imaging scans are unable to differentiate the parent [ 11 C]RSV and its metabolite, metabolism of RSV in the PBK model was switched off to recapitulate this effect when predicting RSV hepatic concentrations. After the above optimization of the PBK model of RSV to predict hepatic concentrations, we proceeded to predict the effect of a DDI with CsA on RSV hepatic concentrations. Comparison of the simulated maximum hepatic concentration (Cmax,liver), area under the hepatic concentration-time profile (AUC0-30min,liver), time needed to reach Cmax,liver (Tmax,liver) and AUC0-30min,liver/AUC0-30min ratio against the observed data was performed. For the DDI trial, ratios of Cmax,liver, AUC0-30min,liver and AUC0-30min,liver/AUC0-30min post-DDI to pre-DDI were evaluated.

Comparison of Hepatic Tissue Concentrations Predicted using a Permeability-limited versus Perfusion-Limited Approach
To further evaluate the performance of a permeability-limited approach in predicting the transporter-mediated distribution of RSV into the liver, a simulation was performed to calculate the liver tissue:plasma partition coefficient (Kp,liver) and Kp,uu,liver of RSV using the PerL model. Using the Simcyp Healthy Volunteer population database, a 1.0 mg/kg/h IV infusion was administered for 96 hours to obtain equilibrium concentrations of RSV in the plasma and liver (Table 3). Subsequently, the ratio of AUC0-96h,liver to AUC0-96h was calculated to obtain Kp,liver. To determine Kp,uu,liver, the ratio of unbound AUC0-96h,liver of the IW component (AUC0-  96,liver,IW) to unbound AUC0-96h was calculated. Where unbound AUC0-96h,liver,IW was obtained from the product of fu,IW and AUC0-96,liver,IW, while unbound AUC0-96h was obtained from the product of fu,p and AUC0-96.

Evaluating the PK/PD Correlation of Rosuvastatin
The RSV PBPK model was utilized to perform a PK/PD correlation of RSV with the predicted plasma and hepatic concentrationtime profile. The lowest clinically used dose of 5 mg repeated once daily oral dose over a duration of 1 week was simulated using the Simcyp Healthy Volunteer population database (Table 3). The predicted RSV Cu,IW, plasma concentration (Cp) and unbound Cp (Cu,p) was compared against the reported 50% inhibitory concentration (IC50) against HMG-CoA reductase (McTaggart et al., 2001) to assess if our PBPK model was able to replicate the clinical efficacy observed at this dose.

Sensitivity Analysis of the Input Parameters within the PerL Model
Parameter sensitivity analyses were performed using the local sensitivity analysis function available within Simcyp. The objectives of our sensitivity analysis were: (1) identify key model input parameters that influenced the predicted plasma and/or hepatic biokinetic parameters, and (2) investigate our hypothesis that modification of the PerL model by removing the biliary excretion component is necessary to recapitulate the RSV hepatic concentrations from the PET imaging study. Model input parameters for the PerL model were increased and decreased by 2, 4, 8 and 16-fold. The corresponding change in output parameters such as Cmax, AUC0-30min pre-and post-DDI were investigated. As the local sensitivity analysis function only outputs the variation in Cu,IW pre-DDI, both Cmax,IW and AUC0-30min,IW were regarded as a suitable surrogate measure of the hepatic biokinetic parameters. We were unable to investigate the impact of varying the model input parameters for hepatic biokinetic parameters post-DDI due to limitations in the local sensitivity analysis function.

Model Validation of RSV and CsA
Results of our simulations for 0.91 µg IV bolus dose of RSV and 2.5 mg/kg/h IV infusion of CsA demonstrate that the independent models accurately predicted the clinical results from the PET imaging study. The plasma concentration-time profile for the RSV and CsA simulations are presented in Figure 2 and 3 respectively. It should be noted that RSV plasma concentrations from only a single subject from the PET imaging study were available for comparison. Predicted AUC0-30min and Cmax of the whole study cohort After validating the RSV and CsA models independently, we moved on to validate the DDI model between RSV and CsA. The predicted plasma concentration-time profiles before and after the DDI are presented in Figure 4. Similarly, only clinical data for the RSV plasma concentration-time profile of a single subject was available for comparison. After the DDI with CsA, the plasma concentrations of RSV increased. The predicted RSV AUC0-30min increased from 0.021 to 0.028 ng/mL with a AUC0-30min ratio of 1.372. Whereas the predicted Cmax remained unchanged at 0.304 ng/mL with a ratio of 1.002. When compared against the observed data, predicted AUC0-30min and Cmax after the DDI with CsA were within 1.5-fold of the observed data (Table 4). Importantly, the predicted AUC0-30min and Cmax ratios exhibited a fold difference of 1.088 and 0.945 when compared against the observed data. The model was able to recapitulate the extent of increase in plasma concentrations and AUC0-30min as well as the unchanged Cmax of RSV after the DDI with CsA.

Fig. 4: RSV plasma concentration-time profile of the simulated drug-drug interaction between a 0.91 µg IV bolus dose of RSV and 2.5 mg/kg/h IV infusion of CsA in both linear (A) and log10 Y-axis scale (B)
The black circles and red triangles represent the RSV clinical data before and after the DDI with CsA. The solid black and red line represents the simulated mean RSV plasma concentrations before and after the drug-drug interaction with the 95 th and 5 th percentile bounded by the grey and red shaded area respectively.

Simulations of Hepatic Concentrations of RSV
Results for the simulations of RSV hepatic concentrations with and without modifying biliary clearance to account for distribution into the bile canaliculi of the liver are illustrated in Figure 5. The predicted biokinetic parameters versus the observed values are found in Table 5. When the fraction distributed into the bile canaliculi was not accounted for, simulations for RSV hepatic concentrations predicted a gradual decrease in hepatic concentrations after 0.05 h. In this scenario, the fold difference of Cmax,liver, AUC0-30min,liver and Tmax were outside the two-fold criterion and the model was unable to recapitulate the observed increase in RSV concentrations within the liver. Cmax,liver and AUC0-30min,liver was underpredicted with a fold difference of 0.434 and 0.206. When the distribution of RSV into the bile canaliculi was included in the calculation of hepatic concentrations, the newly predicted Cmax,liver (0.273 ng/mL) and AUC0-30min,liver (0.122 ng/mL.h) closely matched the observed values (0.277 ng/mL and 0.129 ng/mL.h) with a fold difference of 0.986 and 0.951 respectively. Upon comparing the ratio of AUC0-30min,liver/AUC0-30min,blood, the predicted value of 9.514 closely matched the observed value of 12.66 ± 5.83 (mean ± SD) in the PET imaging study, with a fold difference of 0.752. The model was also able to recapitulate the observed plateau of RSV hepatic concentrations during the first 30 minutes after the IV bolus dose.

Fig. 5: RSV hepatic concentration-time profile after a 0.91 µg IV bolus dose of RSV with and without accounting for distribution within the bile canaliculi in both linear (A) and log10 Y-axis scale (B).
The circles represent the observed RSV hepatic concentrations for 6 individual subjects, each with a different color. The solid and dashed black line represents the simulated hepatic concentrations with and without accounting for distribution within the bile canaliculi and the grey shaded area bounds the 95 th and 5 th percentile of each simulation.

Simulations of Hepatic Concentrations PSV Post-DDI with CsA
Having demonstrated the ability of our PBK model to predict RSV hepatic concentration-time profiles, we proceeded to simulate the effect of a DDI between RSV and CsA on the predicted RSV hepatic profiles. Our model was able to recapitulate the observed decrease in hepatic concentrations of RSV after a DDI with CsA ( Figure 6). After the DDI, predicted Cmax,liver decreased from 0.273 ng/mL to 0.175 ng/mL with a Cmax,liver ratio of 0.640 and predicted AUC0-30min,liver decreased from 0.122 ng/mL.h to 0.079 ng/mL.h with a AUC0-30min,liver ratio of 0.645 (Table 6). Compared against the observed Cmax,liver (0.242 ng/mL) and AUC0-30min,liver (0.108 ng/mL/h) after the DDI with CsA, the predicted parameters were slightly underpredicted but still fell within 1.5-fold (0.721 and 0.733) of the observed value. Whereas the predicted Cmax,liver and AUC0-30min,liver ratio was 0.732 and 0.771 fold of the observed values respectively. While this demonstrates a slight overprediction of the impact of a DDI with CsA on RSV hepatic concentrations, the predicted biokinetic parameters were within our two-fold acceptance criteria.

Predictions of Liver Tissue:Plasma Concentration Ratio and PK/PD Correlation of Rosuvastatin
After a 1.0 mg/kg/h IV infusion administered for 96 hours, the predicted mean Kp,liver and Kp,uu,liver were 1.13 and 11.70 when the original RSV model (Chan et al., 2019) was used. This represents a significant accumulation of the unbound drug in the liver versus the plasma. Similarly, when the lowest clinical dose of RSV was simulated, the predicted RSV Cu,IW remained above the IC50 value of 2.6 ng/mL (McTaggart et al., 2001) for majority of the dosing interval (Figure 7). In contrast, the predicted Cp remained below the IC50 threshold for most of the dosing interval and the predicted Cu,p fell below the IC50 threshold for the entire dosing interval. Correlation between the PK/PD of RSV is best predicted when the predicted Cu,IW was used to compare against the IC50 threshold.

Sensitivity Analyses
Upon varying the drug input parameters of the PerL model by 2 to 16-fold from its original value, the sensitivity analysis revealed that the plasma biokinetic parameters (Cmax and AUC0-30min before and after the DDI) were insensitive to changes in the input parameters. In contrast, the predicted Cmax,IW was sensitive to changes in the OATP1B1 maximal transport rate (Jmax) and passive diffusion clearance (CLpd) input parameters ( Figure 8A). In particular, when CLpd increased by 16 fold, the resultant Cmax,IW decreased by 4-fold. A similar effect was observed for AUC0-30min,IW.  The circles and triangles represent the observed RSV hepatic concentrations before and after the drugdrug interaction respectively for 4 individual subjects. Each subject is represented by the circle and triangle of the same color. The solid black and red line represents the simulated RSV hepatic concentrations before and after the drugdrug interaction and the grey and red shaded area bounds the 95 th and 5 th percentile of each simulation.  To investigate if removing the biliary excretion component was necessary to recapitulate the hepatic concentrations from the PET imaging study, we utilized the unchanged PBK model of RSV and varied the input parameters of the PerL model by 2 to 16-fold. Other than the canalicular efflux CLint input parameter, changing the input parameters of the PerL model led to minimal change in the output CIW. The model was sensitive only to changes in the canalicular efflux CLint ( Figure 8B). However, decreasing the CLint by 16-fold was still insufficient to reach the predicted CIW obtained with the modified PBK model ( Figure 8C). In this study, we hypothesized that bottom-up PBK modelling would be able to recapitulate the hepatic concentrations of RSV as well as accurately predict the impact of CsA on the hepatic concentrations of RSV, using the recently published PET imaging study by Billington et al to validate our simulations. In doing so, we aimed to build further understanding of the ability of bottom-up PBK modelling to predict tissue concentrations. We utilized the bottom-up PBK model of RSV that we previously published and adapted a CsA PBK model from the Simcyp compound file library with modifications to the inhibitory constants. By successfully recapitulating the plasma biokinetics of a RSV IV bolus dose prospectively, before and after a DDI with CsA, we demonstrated the robustness of PBK modelling in predicting the impact of a DDI on plasma concentrations. Due to its poor passive permeability, the uptake of RSV into the liver is permeability-limited and mediated by numerous hepatic transporters such as OATP1B1, OATP1B3, OATP2B1 and NTCP. As these active transporters facilitate the uptake transport of unbound drugs against the concentration gradient, this would lead to an accumulation of unbound drug in the intracellular space of the liver. Moreover, as the rate of passive permeability is much lower than the rate of active uptake for RSV, the accumulated intracellular unbound drug would not be able to able to equilibrate with the vascular space or extracellular water. Hence, this leads to asymmetrical unbound RSV concentrations between the liver and plasma at steady state (Zhang, Hop, et al., 2019). This phenomenon is recapitulated in our predicted Kp,uu,liver values of 11.70. These values are comparable to the Kp,uu,liver values of 11.6 and 6.36 measured using suspended human hepatocytes (Yoshikado et al., 2017). Other reported values for Kp,uu,liver include 35 and 57 measured using suspended rat hepatocytes and with an in vivo rat study (Riccardi et al., 2017). Collectively, these indicate that a permeability-limited approach can recapitulate the liver accumulation of RSV. Furthermore, by utilizing the PerL model, our unchanged PBK model of RSV was able to replicate the observed clinical efficacy of the lowest clinical dose of RSV (5 mg daily dosing). This is demonstrated by the predicted Cu,IW remaining above the IC50 value for most of the dosing interval of 24 hours. This highlights the importance of assessing tissue concentration which represents the location of the biological target. Plasma concentrations which can be distant from the site of action may provide misleading information as demonstrated by our predictions of Cp and Cu,p falling below the IC50 threshold for most if not the entire dosing interval. Utilizing Cu,IW provided the most accurate PK/PD correlation for the lowest clinically used dose of RSV.

Tab. 6: Simulated versus observed hepatic biokinetic parameters for the DDI between RSV and CsA
While OATP1B1, OATP1B3, OATP2B1 and NTCP mediate the active uptake of RSV into the liver; BCRP and possibly P-gp actively excretes RSV into the bile canaliculi, facilitating its elimination into bile. CsA being a potent inhibitor of OATP1B1, OATP1B3 and BCRP, would lead to an increase in plasma concentrations of RSV as the hepatic uptake and excretion of RSV is limited and clearance is reduced. This DDI has been observed not only in the PET imaging study but also clinically in heart transplant patients (Simonson et al., 2004). A dose reduction of RSV is recommended in the Crestor ® product label as well when co-administering RSV with CsA (Astra Zeneca, 2003). While the changes in plasma concentrations after a DDI with CsA is clear, it is crucial to understand how a DDI with CsA will impact the unbound tissue concentrations of RSV. The change in unbound tissue concentrations, rather than the total or unbound plasma concentration (Chu et al., 2013) is the key determinant of the efficacy and toxicity of RSV. As the Kp,uu,liver of RSV is much greater than 1, the unbound plasma concentration of RSV is not a reliable surrogate measure for the unbound hepatic concentration of RSV. In other words, an increase in unbound plasma concentrations of RSV after a DDI with CsA may not necessarily represent an increase in unbound hepatic concentration of RSV. This is because CsA inhibits both the hepatic uptake and biliary efflux of RSV, rendering the change in hepatic concentrations of RSV dependent on the relative magnitudes of inhibition of hepatic uptake (liver input) and biliary efflux (liver output). In the PET imaging study, a decrease in overall hepatic RSV concentrations was observed and we recapitulated the same results with our PBK model predictions after we modified the biliary excretion input parameter to account for distribution within the bile ducts. The latter point highlights a limitation of in vivo tissue imaging which lacks sufficient resolution to further discriminate between RSV found within tissue extracellular (such as bile canaliculi) and intracellular spaces (Guo et al., 2018).
In addition to the above, the PerL model is constructed such that any biliary excreted compound is transferred from the intracellular liver into the enterohepatic compartment immediately and the predicted liver concentrations will not account for the presence of RSV within the bile canaliculi. Hence, a discrepancy between model outputs and observed data could arise from (1) an inability of the imaging approach to discriminate between biliary and intracellular RSV content, and/or (2) the absence of a bile canalicular compartment within the PerL model. To resolve this conundrum, we modified the input parameters of the PerL model by switching off biliary excretion in order to retain RSV within the IW and EW liver compartments. We acknowledge that this may be an unconventional approach, as this results in the inclusion not just of canalicular RSV, but also RSV accumulated in the gallbladder. In the analysis of [ 11 C]RSV concentrations, Billington et al. excluded the gallbladder content (observed as a bright spot within the PET image), which indicates our approach may overestimate RSV levels. Nevertheless, we judged that our approach is an acceptable compromise for the following reasons. Firstly, the fasting volume of the gallbladder is around 21.9 mL (Loreno et al., 2009), while the volume of the liver in a healthy adult reported in Simcyp is roughly 1650 mL. This suggests that the RSV content within the gallbladder is a small fraction of that found within total liver spaces. Secondly, the observed concentration of [ 11 C]RSV remained constant throughout the dosing interval, which could be recapitulated by the simulation only when biliary excretion was set to zero, while a rapid decline is observed with biliary excretion activated. This is supported by our sensitivity analysis which revealed that the predicted hepatic concentrations were sensitive only to changes in the biliary excretion input parameter. In general, changes in hepatic concentrations required exaggerated changes in PerL input parameters that are unrealistic, given that these are in vitro measurements and not values predicted using in silico methods where a greater degree of variability can be expected. In other words, this is consistent with our postulation that the majority of RSV is still found within hepatocytes, interstitial spaces or bile canaliculi in the first 30 minutes and modification of the PerL model was necessary in order to recapitulate In addition to the above, our study has other limitations. For example, we were unable to account for the inhibition of biliary efflux of RSV by CsA, as we utilized an overall intrinsic biliary clearance in vitro parameter for RSV. However, we believe that the impact of this limitation is minimal during the first 30 minutes after the administration of RSV since the mean terminal elimination half-life of RSV is 20.3 -31.3 hours (Martin et al., 2002(Martin et al., , 2003. To recapitulate the whole liver concentrations obtained from the PET imaging study, a custom permeability hepatic model can be constructed to include the distribution within the bile canaliculi as well as the canalicular bile flow. As doing so would require additional model construction and validation, we believe that the use of our previously validated PBK model of RSV to predict whole liver hepatic concentrations would be sufficient in demonstrating the ability of PBK modelling to predict tissue concentrations. The value of this work is in illustrating an approach by which PBK modelling, when parameterized by relevant in vitro data pertaining to the tissue uptake and efflux of xenobiotics, is able to quantitatively describe local tissue biokinetics in humans. While this case study uses RSV as a model compound, the approach is generalizable to (1) other chemicals, and (2) other organs where transporters influence tissue concentrations. This is useful for the following reasons. Firstly, animals remain the go-to model when assessments of tissue concentrations are required; however, we show here that modelling and simulation is able to accurately reproduce the time-course of tissue levels within the liver. We anticipate that this will spur a shift towards greater adoption of PBK modelling to reduce/replace the use of animals in obtaining tissue concentrations. Secondly, the approach we have demonstrated is not bespoke or applicable only to RSV, but to any chemical that utilizes transporters for tissue penetration and clearance. The transporters studied here are well-known xenobiotic transporters that transport many exogenous organic acids. Once the relevant kinetics of uptake and efflux are characterized for a particular chemical, it is straightforward to parameterize the PBK model and estimate human tissue concentrations. Finally, this approach can be adapted for other organs with high transporter expression, such as the kidneys, provided the unique physiology of these organs are carefully accounted in the model. In summary, we hope that our study would build further confidence in the use of PBK modelling to recover tissue concentrations of xenobiotics and encourage broader exploration and adoption of this methodology in place of animal toxicokinetic studies for the risk assessments of xenobiotics (Punt et al., 2017). We anticipate that PBK modelling can be applied in parallel with chemical discovery and development where it will form part of the decision-making process when deciding whether a novel compound moves on to the next phase of development. To achieve this, further development and verification of PBK models for a broader range of xenobiotic compounds must be performed alongside robust measurements of in vivo human tissue biokinetic data for the same compound coupled with the consultancy of regulatory authorities (Paini et al., 2019). Eventually, this will help refine the design of in vivo biokinetic studies, and thus reduce the number of animals needed for efficacy and safety testing of chemicals.

Conclusion
In conclusion, our study has demonstrated the ability of bottom-up PBK modelling to accurately predict the plasma and liver concentrations of RSV before and after a DDI with CsA. We are unaware of other comparable studies that have demonstrated the ability of a well-parameterized bottom-up PBK approach to accurately predict human tissue chemical concentrations. Importantly, our work also demonstrated that it is possible to predict the impact of co-administration of interacting mixtures of chemicals, provided the points of interaction are well-characterized. We hope that our study will encourage future application of bottom-up PBK modelling in predicting both plasma and tissue concentrations during the development and risk assessments of novel chemicals in place of animal biokinetic testing. Our study has also highlighted several limitations of using PET imaging studies to predict hepatic concentrations as well as the limitation of using the PerL model to recapitulate the hepatic concentrations obtained from such PET imaging studies. Future studies should be conducted to further understand the relevance of PET imaging in obtaining tissue concentrations as well as to improve the PerL model by including a physiologically-relevant bile canaliculi compartment. Our work highlights that mechanistic PBK modelling approaches can accurately predict tissue concentrations of chemicals, provided sufficient in vitro data is available to parameterize these models. Furthermore, utilizing PBK model predicted tissue concentrations will enable better PK/PD correlation versus the use of plasma concentration. We envision that our work will spur industry to characterize their chemicals with appropriate in vitro ADME assays and utilize PBK modelling to obtain critical in vivo human tissue biokinetic predictions and perform pharmacodynamic/toxicodynamic correlations.