Estimation of Fetal-to-Maternal Unbound Steady-State Plasma Concentration Ratio of P-Glycoprotein and/or Breast Cancer Resistance Protein Substrate Drugs Using a Maternal-Fetal Physiologically Based Pharmacokinetic Model

Pregnant women are frequently prescribed drugs to treat chronic diseases such as human immunodeficiency virus infection, but little is known about the benefits and risks of these drugs to the fetus that are driven by fetal drug exposure. The latter can be estimated by fetal-to-maternal unbound plasma concentration at steady state (Kp,uu,fetal). For drugs that are substrates of placental efflux transporters [i.e., P-glycoprotein (P-gp) or breast cancer resistance protein (BCRP)], Kp,uu,fetal is expected to be <1. Here, we estimated the in vivo Kp,uu,fetal of selective P-gp and BCRP substrate drugs by maternal-fetal physiologically based pharmacokinetic (m-f-PBPK) modeling of umbilical vein (UV) plasma and maternal plasma (MP) concentrations obtained simultaneously at term from multiple maternal-fetal dyads. To do so, three drugs were selected: nelfinavir (P-gp substrate), efavirenz (BCRP substrate), and imatinib (P-gp/BCRP substrate). An m-f-PBPK model for each drug was developed and validated for the nonpregnant population and pregnant women using the Simcyp simulator (v20). Then, after incorporating placental passive diffusion clearance, the in vivo Kp,uu,fetal of the drug was estimated by adjusting the placental efflux clearance until the predicted UV/MP values best matched the observed data (Kp,uu,fetal) of nelfinavir = 0.41, efavirenz = 0.39, and imatinib = 0.35. Furthermore, Kp,uu,fetal of nelfinavir and efavirenz at gestational weeks (GWs) 25 and 15 were predicted to be 0.34 and 0.23 (GW25) and 0.33 and 0.27 (GW15). These Kp,uu,fetal values can be used to adjust dosing regimens of these drugs to optimize maternal-fetal drug therapy throughout pregnancy, to assess fetal benefits and risks of these dosing regimens, and to determine if these estimated in vivo Kp,uu,fetal values can be predicted from in vitro studies. SIGNIFICANCE STATEMENT The in vivo fetal-to-maternal unbound steady-state plasma concentration ratio (Kp,uu,fetal) of nelfinavir [P-glycoprotein (P-gp) substrate], efavirenz [breast cancer resistance protein (BCRP) substrate], and imatinib (P-gp and BCRP substrate) was successfully estimated using maternal-fetal physiologically based pharmacokinetic (m-f-PBPK) modeling. These Kp,uu,fetal values can be used to adjust dosing regimens of these drugs to optimize maternal-fetal drug therapy throughout pregnancy, to assess fetal benefits and risks of these dosing regimens, and to determine if these estimated in vivo Kp,uu,fetal values can be predicted from in vitro studies.


Introduction
Pregnant women frequently take drugs (medication) throughout their pregnancy to treat the mother for conditions such as hypertension or cancer or to treat the maternal-fetal pair for conditions such as human immunodeficiency virus (HIV) infection (McGowan and Shah, 2000;Mitchell et al., 2011;Haas et al., 2018). However, these drugs are often prescribed without knowledge of their fetal benefits and risks that are driven by fetal (and possibly by placental) drug exposure. Fetal drug exposure can be quantified only at delivery when simultaneous sampling of umbilical vein blood and maternal blood is possible. However, because these drug concentrations are time dependent, they need to be collected in multiple maternal-fetal dyads to allow the estimation of No author has an actual or perceived conflict of interest with the contents of this article.
fetal drug exposure . From these, fetal drug exposure, which is the fetal-to-maternal unbound steady-state plasma concentration ratio (K p,uu,fetal ), can be estimated (Anoshchenko et al., 2021b). For drugs that passively cross the placenta, provided there is no fetal or placental metabolism of the drug, K p,uu,fetal is easy to predict, as it will be 1.0 . However, the placenta is richly endowed with efflux transporters, such as P-glycoprotein (P-gp) and breast cancer resistance protein (BCRP) at the maternal-placenta barrier, which efflux the drug from the placenta to the maternal blood. For drugs that are a substrate of these efflux transporters, K p,uu,fetal will be <1, and its deviation from unity will depend on the fraction of the drug effluxed by the transporter(s) (f efflux ). Estimation of a drug's K p,uu,fetal at term and at earlier gestational age, especially for those that are effluxed, is important for several reasons. First, it can be used to adjust dosing regimens of these drugs to optimize maternal-fetal drug therapy throughout pregnancy, provided that the f efflux of the drug at each gestational age can be estimated. Such estimation is now possible given our quantification of placental transporters in the first and second trimesters as well as at term by quantitative targeted proteomics (Anoshchenko et al., 2020). Second, it can be used to assess fetal benefits and risks of these drug dosing regimens. Third, these K p,uu,fetal values can be used to determine if they can be predicted from in vitro studies using the proteomics-informed efflux ratio approach, as we have done before (Anoshchenko et al., 2021b). Therefore, to fulfill the above broad goals, we estimated the in vivo K p,uu,fetal of selective P-gp and/or BCRP substrate drugs by maternal-fetal physiologically based pharmacokinetic (m-f-PBPK) modeling of umbilical vein (UV) plasma and maternal plasma (MP) concentrations obtained simultaneously at term from multiple maternal-fetal dyads. Three drugs were studied: nelfinavir (P-gp substrate), efavirenz (BCRP substrate), and imatinib (P-gp/BCRP substrate). An m-f-PBPK model for each drug was developed and validated for the nonpregnant population and pregnant women using the Simcyp simulator (v20). Then, after incorporating placental passive diffusion clearance, the in vivo K p,uu,fetal of the drug was estimated by adjusting the placental efflux clearance until the predicted UV/MP values best matched the observed data.

Materials and Methods
Our search criteria for selecting the drug candidates were as follows: 1) candidate drug should be transported only by P-gp or by BCRP or by P-gp/BCRP based on extensive in vitro studies; and 2) in vivo paired UV and MP drug concentrations data should be available from a large number of maternal-fetal dyads at multiple time points over the dosing interval (or for several half-lives) after the last maternal dose. A total of three candidate drugs fulfilled these criteria: nelfinavir, which is effluxed solely by P-gp and not by BCRP (Gupta et al., 2004;Salama et al., 2005); efavirenz, which is effluxed solely by BCRP but not by Pgp (Dirson et al., 2006;Janneh et al., 2009;Peroni et al., 2011); and imatinib, which is effluxed by both BCRP and P-gp (Hamada et al., 2003;Burger et al., 2004;Oostendorp et al., 2009;Zhou et al., 2009).
PBPK Model Simulations and Criteria for Validation. PBPK simulation of the pharmacokinetic (PK) profiles of the above drugs was implemented as summarized in Fig. 1. Briefly (but detailed below), for each step of modeling, the predicted PK profiles and PK parameters (maximum plasma drug concentration [C max ] and area under the curve of total plasma concentration-time profile [AUC]) of the drug were compared with the observed data. The observed plasma concentration-time profiles in graphical format were digitized using WebPlotDigitizer (https://apps.automeris.io/wpd/). These values were reported in the publications as geometric mean, arithmetic mean, or median. Therefore, our PBPK-predicted values are also reported in the same format. The PK profiles of the drugs were simulated using 100 virtual subjects (10 trials × 10 subjects). The PBPK model was considered validated if the observed PK profile fell within the 5th and 95th percentiles of predicted data and the simulated PK parameters fell within the range of 0.80-to 1.25-fold of the observed data (Ladumor et al., 2019a,b). All of the PBPK simulations were performed with trial designs (age range, proportion of female, gestational age, and dosing regimens) that matched the corresponding in vivo study (Supplemental Table 1).
Development and Validation of Drug PBPK Models for Nonpregnant Adults. A full PBPK model was constructed for nelfinavir using the Simcyp simulator (v20). Drug-related parameters for nelfinavir were collected from the literature (Table 1). A whole-body PBPK model was applied for the distribution of nelfinavir, and tissue-to-plasma partition coefficient (K p ) values were predicted using Simcyp Method 1 (Poulin and Theil, 2009). Nelfinavir binds extensively to a1-acid glycoprotein (AAG) with a fraction unbound in human plasma (f u ) of 0.014 (Zhang et al., 2001;Motoya et al., 2006). Nelfinavir is metabolized by the cytochrome P450 (CYP450) isoforms CYP3A, CYP2C19, CYP2D6, CYP2C9, CYP1A2, and CYP2E1, and the fraction of drug metabolized (f m ) by each isoform was based on the inhibition of nelfinavir metabolism in pooled human liver microsomes (HLMs) in the presence of selective cytochrome P450 inhibitors (https://www.accessdata.fda.gov/drugsatfda_docs/nda/97/020778ap.pdf). The intrinsic hepatic clearance (CL int ) of nelfinavir by each isoform was back-calculated from the intravenous total systemic clearance (CL iv 5 37.7 l/h) using the Simcyp simulator (Sarapa et al., 2005) after correcting for renal clearance (f e 5 2%) and biliary clearance (f CL,bile 5 10%) (https://www.accessdata.fda.gov/ drugsatfda_docs/nda/97/020778ap.pdf). Our previously reported mechanism-based inhibition and induction of CYP3A by nelfinavir in HLMs and hepatocytes, respectively (Dixit et al., 2007;Kirby et al., 2011), and competitive inhibition of CYP3A, CYP2C9, and CYP1A2 by nelfinavir (Lillibridge et al., 1998) were incorporated into the PBPK model. Then, PK data after intravenous administration were simulated and validated using the observed data. Thereafter, the Advanced Dissolution, Absorption and Metabolism (ADAM) model of Simcyp, with integrated in vitro dissolution profiles in the fed and fasted state, was used to describe nelfinavir absorption (Shono et al., 2011;Chapa et al., 2020). Then, nelfinavir PK after single oral administration in the fed/fasted state, multiple doses, and coadministration with ritonavir (inhibitor of CYP3A and CYP2D6, inducer of CYP3A and CYP2C9; Simcyp default compound file) were predicted and validated. Efavirenz and imatinib PBPK models for the nonpregnant adults were reproduced without modification from previous publications (Atoyebi et al., 2019;Adiwidjaja et al., 2020) and validated with the additional published in vivo data.  1. Workflow for estimation of in vivo K p,uu,fetal using the Simcyp m-f-PBPK model. A PBPK model for each drug was developed for the nonpregnant population using the Simcyp simulator (v20), and the predicted PK profiles of these drugs were validated with data after intravenous (i.v.) and oral administration as well as drug-drug interaction studies (step 1). Systemic maternal PK of drugs in the second trimester, third trimester, and postpartum was predicted using the pregnant population of the Simcyp simulator and validated with the observed data (step 2). Then, using the estimated passive diffusion clearance (CL PD ) of the drugs, the magnitude of the placental efflux clearance (CL efflux,placenta ) and the K p,uu,fetal were estimated by adjusting the CL efflux,placenta until the predicted UV/ MP values best matched the observed data (step 3).

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Development and Validation of Drug PBPK Models for Pregnant Women. After validating the PK of the drug in the nonpregnant population, drug-specific parameters were fixed, and except for the changes in CYP450 activity, the pregnancy-induced changes in physiologic parameters specified in the Simcyp pregnancy module were implemented. The pregnancy-induced changes in hepatic CYP450 activity were based on our previously published data: CYP3A was induced 2-fold during the second and third trimesters (Ke et al., 2012;Zhang et al., 2015), CYP2D6 was induced 1.9-and 2-fold during the second and third trimesters, CYP1A2 was suppressed by 48% and 65% during the second and third trimesters (Ke et al., 2013), CYP2B6 activity was induced by 1.1-and 1.3-fold during the second and third trimesters, and CYP2C9 activity was induced by 1.5-and 1.6-fold during the second and  (Sarapa et al., 2005;Damle et al., 2006); (B) Observed (mean) and predicted plasma C-T profile of 600 mg efavirenz (once daily by mouth) at steady state in nonpregnant adults (Villani et al., 1999); and (C) Observed (median) and predicted plasma C-T profile after single dose of 100 mg imatinib in nonpregnant adults (Ostrowicz et al., 2014). The observed data (open circles) fell within the 5th and 95th percentiles (dashed lines) of the predicted data (continuous black line). The predicted PK endpoints (AUC and C max ) also fell within 0.80-to 1.25-fold of the observed data (Tables 2 and 3). lmol/l 6.50 ADAM, Advanced Dissolution, Absorption, and Metabolism model; B/P, blood-to-plasma partition ratio; CL int,bile , intrinsic biliary clearance; CL int,CYPx , intrinsic clearance via the listed CYP450 isozyme; CL iv , intravenous clearance; CL R , renal clearance; EC50 CYP3A , nelfinavir concentration that produces half-maximal induction of CYP3A; E max,CYP3A , maximal fold induction of CYP3A relative to control; f CLbile , fraction of drug excreted in the bile; f e , fraction of drug excreted in the urine; f m,CYP450 , fraction metabolized by CYP450 enzymes; f u , unbound fractions in plasma; K app,CYP3A , concentration of mechanism-based inhibitor associated with half-maximal inactivation rate of CYP3A enzymes; k i,CYPx , concentration of inhibitor that produces half-maximal inhibition of CYP450 isozyme; k inact,CYP3A , maximum inactivation rate of CYP3A; pKa, acid dissociation constant; P o:w , octanol-water partition coefficient; Vss, steadystate volume of distribution.
Estimation of K p,uu,fetal Using an M-F-PBPK Model third trimesters (Ke et al., 2014). CYP2C19 activity was suppressed by 62% and 68% during the second and third trimesters (Dickmann and Isoherranen, 2013;Ke et al., 2014). Then, nelfinavir and efavirenz PK in postpartum, second, and third trimester women was predicted and validated using the observed data. Corresponding in vivo data for imatinib are not available. We assumed physiologic parameters in postpartum women (6-12 weeks) had returned to levels in the nonpregnant women prior to pregnancy (gestational age 5 0). In addition, the gestational stage in our study was defined per U.S. Department of Health and Human Services (HHS) recommendations: 1-12 weeks for the first trimester, 13-28 weeks for the second trimester, and 29-40 weeks for the third trimester.
Estimating Human K p,uu,fetal at Term. Maternal pharmacokinetics of nelfinavir, efavirenz, and imatinib (by mouth) were predicted using pregnancy PBPK models and compared with the observed PK profiles. Then, the bidirectional placental passive diffusion clearance (CL PD,placenta ) of the drug at maternal-placental and placental-fetal barriers was estimated, as we have previously described . Briefly, we chose midazolam as an in vivo calibrator to estimate CL PD,placenta of nelfinavir, efavirenz, or imatinib. The CL PD,placenta of the drug (nelfinavir, efavirenz, or imatinib) was estimated by scaling CL PD,placenta of midazolam (CL PD,midazolam ) using eq. 1: Where P app,midazolam and CL PD,midazolam are 489.9 nm/s and 500 l/h (mean value in Caco-2 and MDR1-MDCKI cells), respectively (Yamashita et al., 2000;Mahar Doan et al., 2002;Tolle-Sander et al., 2003;Gertz et al., 2010), and P app,x is the apparent membrane permeability (P app ) values (nm/s) of nelfinavir (8.8 in LLC-PK cells; Kim et al., 1998), efavirenz (45.85, mean value of two studies in Caco-2 cells; Takano et al., 2006;Siccardi et al., 2012), and imatinib (6.36 in MDCK II mock cells; Breedveld et al., 2005). Bidirectional intrinsic placental passive diffusion clearance (CL int,PD,placenta , ll/min/ml placenta volume) at maternal-placenta and placenta-fetal barriers was obtained by dividing CL PD,placenta by placental volume. The placental volume was calculated using eq. 2 (Kapraun et al., 2019),  where AUC fetal,u is the area under the curve of the unbound umbilical vein plasma concentration-time profile, AUC m,u is the area under the curve of the unbound maternal plasma concentration-time profile, and N is the number of observed and predicted UV/MP values.
PBPK Model Prediction of K p,uu,fetal of the Drugs at an Earlier Gestational Ages (GW15 and GW25). To predict the K p,uu,fetal of nelfinavir and efavirenz at an earlier gestational age, total placental P-gp and BCRP abundance, previously quantified by us using quantitative targeted proteomics (Anoshchenko et al., 2020), was incorporated into the Simcyp pregnancy module "Sim-Pregnancy." A second-order polynomial model was fitted to the gestational agedependent relative abundance of placental P-gp and BCRP (relative to term value, which was set as 1.0), respectively (see eq. 5 and 6; R-square values of the fitted polynomials were 1.0; Supplemental Fig. 1). P À gp relative abundance ¼ 0:003 Â GW 2 ð Þ À 0:228 Â GW þ 5:010 ð5Þ BCRP À relative abundance ¼ 0:001 Â GW 2 ð Þ À 0:086 Â GW þ 2:899 ð6Þ These equations were used to interpolate the placental abundance of the transporters at GW15 and GW25. Then, these interpolated values were used to scale the above estimated (term) placental efflux clearances of nelfinavir and efavirenz (CL int,P-gp,placenta : nelfinavir; CL int,BCRP,placenta : efavirenz) and incorporated in the Simcyp pregnancy module. Within this module, the above-estimated term CL int,PD,placenta and CL int,efflux,placenta was scaled based on the mean volume of the placenta for the respective gestational age. Then, the maternal-fetal PK profiles of the drugs were predicted at GW15 and GW25 using the same trial design as . The predicted PK endpoints (AUC and C max ) also fell within 0.80-to 1.25-fold of the observed data (Table 4).
Estimation of K p,uu,fetal Using an M-F-PBPK Model for term. From these profiles, the K p,uu,fetal of nelfinavir and efavirenz was estimated. Such predictions for imatinib were not possible, as the fraction of imatinib transported by P-gp or BCRP is unknown and will need to be determined, as we have described previously (Kumar et al., 2021).

PBPK Model Predictions and Validation for the Nonpregnant Population.
Our predictions of nelfinavir PK were successfully validated after intravenous dose, single oral dose (fed and fasted), multiple oral dose administration, and coadministration with ritonavir. The observed concentration-time (C-T) profiles fell within the 5th and 95th percentiles of predicted data ( Fig. 2A; Supplemental Fig. 2), and the predicted PK parameters (AUC and C max ) also fell within 0.80-to 1.25-fold of the observed data ( Table 2). The PBPK models for efavirenz and imatinib were successfully reproduced, and except for imatinib C max after coadministration with ketoconazole, their simulated PK profiles were consistent with the reported in vivo data (Fig. 2, B and C; Supplemental Fig. 3; Table 3).

PBPK Model Predictions and Validation for Pregnant Women.
The PBPK pregnancy model for nelfinavir and efavirenz successfully predicted the PK of the drugs in postpartum, second trimester, and third trimester women (corresponding data for imatinib are not available) (Figs. 3 and 4). Also, the majority of the predicted PK endpoints (AUC and C max ) fell within 0.80-to 1.25-fold of the observed data (Table 4).
Estimated Human K p,uu,fetal at Term. Using our acceptance criteria, the predicted MP concentration-time profiles agreed well with the observed data of nelfinavir, efavirenz, and imatinib (Fig. 5, A, D, and G). The estimated CL int,PD,placenta of nelfinavir, efavirenz, and imatinib at term were 240, 1480, and 170 ll/min/ml placenta volume, respectively (Table 5). Without incorporating placental efflux clearance (CL efflux,placenta ) that is in the presence of only CL PD,placenta of the drug, the UV plasma concentration (Fig. 5, B, E, and H) and UV/MP ratio (Fig. 5, C, F, and I) were considerably overpredicted with AAFE > 1 and, as expected, the estimated K p,uu,fetal was 1.0 (Table 5).
By adjusting CL int,efflux,placenta of the drugs (nelfinavir: 350; efavirenz: 2200; imatinib: 320 ll/min/ml placenta volume), the majority of the observed UV plasma concentrations and the UV/MP ratios fell within the 5th and 95th percentiles of the model predicted data (Fig. 5). As  (Kreitchmann et al., 2019) and predicted plasma C-T profile of efavirenz (600 mg, once daily by mouth) at steady state in (A) postpartum, (B) second trimester, and (C) third trimester, respectively; observed (geometric mean) (Lamorde et al., 2018) and predicted plasma C-T profile of efavirenz (400mg, once daily by mouth) at steady state in (D) postpartum and (E) third trimester (second trimester data are not available), respectively; and observed (median) (Cressey et al., 2012) and predicted plasma C-T profile of efavirenz (600 mg, once daily by mouth) in (F) postpartum and (G) third trimester (second trimester data are not available), respectively. The observed data (open circles) fell within the 5 th and 95 th percentiles (dashed lines) of the predicted data (continuous black line). The predicted PK endpoints (AUC and C max ) also fell within 0.80-to 1.25-fold of the observed data (Table 4).

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these data are steady-state data, the predicted AUC fetal /AUC m were close to the mean observed UV/MP ratio and AAFE equaled 1.00. K p,uu,fetal values at term estimated from the UV/MP data were 0.41, 0.39, and 0.35 for nelfinavir, efavirenz, and imatinib, respectively. These data indicate that the fraction of drug transported by placental Pgp or BCRP at term (f efflux 5 1 À K p,uu,fetal ) followed the order imatinib (0.65) > efavirenz (0.61) > nelfinavir (0.59). Prediction of Nelfinavir and Efavirenz K p,uu,fetal at Earlier Gestational Ages (GW15 and GW25). The MP plasma concentrations of nelfinavir and efavirenz were marginally affected by gestational age, and the UV plasma concentration, UV/MP ratio, and K p,uu,fetal all decreased with gestational age (Fig. 6; Table 5).

Discussion
Nelfinavir and efavirenz are prescribed to prevent the transmission of HIV from the mother to her fetus (Perry et al., 2005;Vrouenraets et al., 2007). However, as we have shown here, they are prevented from distribution into the fetal compartment by extensive placental efflux, thus potentially reducing their efficacy in preventing maternal-fetal HIV transmission. In contrast, imatinib, a selective tyrosine kinase inhibitor, is used to treat cancers (Ali et al., 2009). When administered to a pregnant woman, fetal harm or abortion can occur (Ali et al., 2009). These cases illustrate the importance of estimating fetal drug exposure (K p,uu,fetal ) at all gestational ages to assess the safety and efficacy of drugs administered to pregnant women. In addition, if these safety and efficacy data dictate, these K p,uu,fetal values can be used to design alternative dosing regimens to enhance drug safety and efficacy, as we have proposed for antenatal corticosteroids (Anoshchenko et al., 2021a).
Although K p,uu,fetal can be estimated at term from UV/MP values, sampling UV blood is not possible at earlier gestational ages. Therefore, to estimate drug K p,uu,fetal at earlier gestational ages, the only recourse is PBPK modeling and simulation. For all the above reasons, we estimated K p,uu,fetal of nelfinavir, efavirenz, and imatinib at term and earlier in gestation (nelfinavir and efavirenz only). In addition, though drugs are frequently taken by pregnant women, no UV/MP data are available for the majority of these drugs. Because obtaining such data is extremely challenging, the only recourse is to estimate K p,uu,fetal for these drugs. We have previously shown that this is possible through in vitro transport studies combined with m-f-PBPK modeling and simulation and the quantitative targeted proteomics-informed relative expression factor (REF) approach (Anoshchenko et al., 2021b). However, such predictive methods need to be validated. Thus, another reason for estimating term nelfinavir, efavirenz, and imatinib K p,uu,fetal values was to use them in the future to validate predictions made by our m-f-PBPK model (Anoshchenko et al., 2021b). K p,uu,fetal is determined by several factors, namely placental transport (efflux or influx), placental metabolism, and fetal clearance of the drug. Since the placenta is not endowed with the CYP450 enzymes found in adult livers, the metabolism of most drugs within this organ is negligible . The fetal liver size is small. In addition, except for CYP3A7, it also does not express many of the CYP450 enzymes found in the adult liver until about one year after birth (Thakur et al., 2021). For both of these reasons, the fetal liver plays a miniscule role in the CYP450 clearance of drugs. Therefore, for the drugs studied here, we assumed that the placental and fetal metabolism of these drugs was negligible. Consequently, as we have shown before, K p,uu,fetal of these drugs will be determined solely by passive diffusion and transport across the placenta .
To estimate K p,uu,fetal , we deliberately used the UV/MP values as our endpoint rather than just the UV unbound plasma AUC profile. This is because the latter is determined by maternal unbound plasma concentrations that are highly variable (see Fig. 5), resulting in highly variable UV plasma concentrations (total and unbound). This high variability is Estimation of K p,uu,fetal Using an M-F-PBPK Model due to pooling UV and MP values from multiple maternal-fetal dyads.
Using UV/MP values as an endpoint mitigates the variability observed when using the UV values as endpoints.
In the present study, the PK parameters of three drugs, effluxed by the placental transporters, were successfully predicted and validated after PBPK modeling and simulation of PK data in nonpregnant adults  (1250 mg, twice daily) was administered (by mouth, fed) for at least 15 days, followed by 1250 mg (by mouth, fasted) on the day of delivery, between 31 and 41 weeks of gestation (Hirt et al., 2007); (D-F) efavirenz (600 mg, once daily) was administered between 37 and 41 weeks of gestation (Cressey et al., 2012); and (G-I) imatinib (400 mg daily) was administered between 35 and 41 weeks of gestation (Chelysheva et al., 2018). The x-axis is the time between the last dose and delivery. Dashed lines represent the 5th and 95th percentiles of the predicted data in the presence of CL efflux,placenta ; open circles represent observed data. K p,uu,fetal values for nelfinavir, efavirenz, and imatinib estimated from the UV/MP data were 0.41, 0.39, and 0.35, respectively. and pregnant women (Tables 2-4). Then, the K p,uu,fetal of these drugs at term was estimated to be 0.41, 0.39, and 0.35 for nelfinavir, efavirenz, and imatinib, respectively. The fraction of these drugs effluxed by the placenta (f efflux 5 1 À K p,uu,fetal ) was 0.59, 0.61, and 0.65, respectively, demonstrating that placental P-gp and BCRP significantly prevent their distribution into the fetal compartment. To our knowledge, this is the first time that the K p,uu,fetal of a placental BCRP substrate as well as that of a dual P-gp/BCRP substrate have been estimated. Furthermore, this is the first study to construct and validate a PBPK model for the disposition of nelfinavir in nonpregnant adults and pregnant women.
Based on the above term pregnancy data, because we have quantified the abundance of placental transporters at various gestational ages (Anoshchenko et al., 2020), we were able to predict the K p,uu,fetal of nelfinavir and efavirenz earlier in gestation (GW15 and GW25). The Simcyp pregnancy module does not allow predictions any earlier (<GW15), as physiologic data at these earlier gestational ages are not currently available. In addition, we could not make these predictions for imatinib, as the f efflux of this drug by placental P-gp and BCRP is currently not known. However, these values can be predicted in the future from in vitro transport data and REF, as we have done before for other drugs (Kumar et al., 2021). Consistent with our expectations and previous publication (Anoshchenko et al., 2021a), due to a decrease in placental size, both CL efflux,placenta and CL PD,placenta decreased with gestational age, but the decrease in the latter was greater than the former. Therefore, the K p,uu,fetal of both nelfinavir and efavirenz at GW15 (0.23, 0.27) and GW25 (0.34, 0.33) was lower than at term (0.41, 0.39). These data can inform the fetal efficacy and toxicity of these drugs at earlier gestational ages.
There are a few limitations to our study. First, the PBPK model of imatinib was not validated for pregnant women due to a lack of such in vivo data. Second, imatinib may be transported by human organic anion transporting polypeptide 1A2 (OATP1A2) and multidrug resistance protein 4 (MRP4) Yamakawa et al., 2011). However, data on pregnancy-induced changes in OATP1A2 and MRP4 activity are not available and therefore were not included in our model based on Adiwidjaja's model (Adiwidjaja et al., 2020). Third, for our nelfinavir PBPK model, f m by each CYP450 isoform was based on CYP450 inhibition of nelfinavir metabolism in HLMs, and enzyme cross-inhibition by these inhibitors was not taken into consideration (Patilea-Vrana et al., 2019). However, none of the above limitations detracts from correctly estimating K p,uu,fetal , provided that the maternal plasma concentrations are predicted well. Fourth, we assumed that nelfinavir solely binds to AAG rather than albumin (I), as the association constant of nelfinavir for AAG (7.25 × 10 7 /M) is 70 times higher than that for HSA (1.11 × 10 6 /M) (Motoya et al., 2006). Fifth, the fraction unbound of the drugs in fetal plasma was the Simcyp-predicted value (Supplemental Table 2) because the corresponding experimentally measured values are not available in the literature. Any inaccuracy in our estimate of the fraction of drug bound in the maternal and fetal compartment will result in inaccuracy in our K p,uu,fetal estimate. Sixth, the potential effects of HIV or cancer comorbidity on the placental drug permeability or transporters are unknown and were therefore not incorporated in the model. Again, this does not detract from our estimate of K p,uu,fetal , as it was based on the observed data from women who had these clinical conditions. Seventh, the Simcyp model does not allow passage of drug from the placenta directly into the amniotic fluid, which can be swallowed by the fetus. Irrespective of the route of drug passage, our K p,uu,fetal values will be unaffected, as they are based on the observed UV/MP values.
In summary, we estimated the in vivo K p,uu,fetal of nelfinavir, efavirenz, and imatinib through PBPK modeling and simulation. Prospectively, the K p,uu,fetal of these drugs could be used to design dosing regimens of these drugs for pregnant women throughout pregnancy to B C A E F D Fig. 6. Simulated steady-state (A and D) maternal plasma (MP) concentrations; (B and E) umbilical vein (UV) plasma concentrations; and (C and F) the UV/MP profiles of (A-C) nelfinavir or (D-F) efavirenz at varying gestational ages. Profiles were simulated after administration of (A-C) nelfinavir (1250 mg, twice daily in fed state for 15 days) and (D-F) efavirenz (600 mg, once daily for 15 days). K p,uu,fetal values for nelfinavir were 0.41, 0.34, and 0.23 at GWs 38, 25, and 15, respectively. K p,uu,fetal values for efavirenz were 0.39, 0.33, and 0.27 at GWs 39, 25, and 15, respectively.
Estimation of K p,uu,fetal Using an M-F-PBPK Model maximize their efficacy and minimize their fetal toxicity. Furthermore, in the future, these K p,uu,fetal could be used to validate their predictions made through in vitro studies using the proteomics-informed REF approach. Once validated, these m-f-PBPK models, in combination with in vitro studies, could be used in the future to predict fetal exposure throughout pregnancy to any drug that is actively effluxed by placental P-gp or BCRP.
Wrote or contributed to the writing of the manuscript: Peng, Ladumor, Unadkat.