Expansion of a PBPK model to predict disposition in pregnant women of drugs cleared via multiple CYP enzymes, including CYP2B6, CYP2C9 and CYP2C19

Abstract

Aim

Conducting PK studies in pregnant women is challenging. Therefore, we asked if a physiologically-based pharmacokinetic (PBPK) model could be used to predict the disposition in pregnant women of drugs cleared by multiple CYP enzymes.

Methods

We expanded and verified our previously published pregnancy PBPK model by incorporating hepatic CYP2B6 induction (based on in vitro data), CYP2C9 induction (based on phenytoin PK) and CYP2C19 suppression (based on proguanil PK), into the model. This model accounted for gestational age-dependent changes in maternal physiology and hepatic CYP3A, CYP1A2 and CYP2D6 activity. For verification, the pregnancy-related changes in the disposition of methadone (cleared by CYP2B6, 3A and 2C19) and glyburide (cleared by CYP3A, 2C9 and 2C19) were predicted.

Results

Predicted mean post-partum to second trimester (PP : T₂) ratios of methadone AUC, C_max and C_min were 1.9, 1.7 and 2.0, vs. observed values 2.0, 2.0 and 2.6, respectively. Predicted mean post-partum to third trimester (PP : T₃) ratios of methadone AUC, C_max and C_min were 2.1, 2.0 and 2.4, vs. observed values 1.7, 1.7 and 1.8, respectively. Predicted PP : T₃ ratios of glyburide AUC, C_max and C_min were 2.6, 2.2 and 7.0 vs. observed values 2.1, 2.2 and 3.2, respectively.

Conclusions

Our PBPK model integrating prior physiological knowledge, in vitro and in vivo data, allowed successful prediction of methadone and glyburide disposition during pregnancy. We propose this expanded PBPK model can be used to evaluate different dosing scenarios, during pregnancy, of drugs cleared by single or multiple CYP enzymes.

What is Already Known about this Subject

• During pregnancy, changes in physiology and absorption, distribution, metabolism and excretion (ADME) processes can significantly affect the disposition of drugs. Such changes may require adjustments in the dosing regimen of the drug.

• Since conducting pharmacokinetic (PK) studies in pregnant women is challenging, alternative approaches that can predict adjustment of drug dosing regimens (if any) are highly desirable.

What this Study Adds

• We expanded and verified a physiologically based PK model, which incorporated gestational age-dependent changes in maternal physiology and major hepatic CYP enzyme activity, to predict disposition during pregnancy of drugs cleared by multiple CYP enzymes (e.g. glyburide and methadone).

Introduction

Considerable literature data demonstrate that the pharmacokinetics (PK) of drugs can be significantly affected by pregnancy. Such changes may lead to either underdosing or overdosing of medication with the standard adult dose, with varying consequences for safety and efficacy 1. For example, in pregnant opioid-dependent women, the oral clearance (CL_oral) of methadone (METH) is induced by ∼105% during the second trimester (T₂) vs. post-partum (PP) and ∼65% during third trimester (T₃) vs. PP 2. Given the established link between plasma methadone concentration and the pharmacological effects 3, these changes during pregnancy may require careful evaluation of patient complaints of a dose ‘not holding’. Similarly, in gestational diabetic subjects, the steady-state AUC(0,12 h) and C_max of glyburide (GLB), a drug with an established plasma concentration–effect relationship at therapeutic doses 4, are 53% and 55% lower during T₃ vs. non-pregnant type 2 diabetic subjects 5. These results suggest that patients with inadequate glucose control might benefit from increased GLB dosage. Obviously, for drugs operating at the plateau phase of the plasma concentration–effect curve, the pregnancy-induced change in their PK would be of less concern.

Altered drug disposition can be attributed to pregnancy-induced changes in drug absorption (e.g. gastric pH, transporters), distribution (e.g. plasma protein binding and transporters), metabolism (e.g. cytochrome P450 (CYP) metabolism) and excretion (e.g. renal secretion via transporters) (ADME). Further, data in the literature suggest that the magnitude of change in maternal hepatic enzyme activity is CYP isoform specific and gestational age dependent 6. The underlying mechanism for the hepatic isoform-specific and gestational state specific induction during pregnancy is not fully understood. It has been postulated that the rising concentrations of various hormones in maternal blood, including placental growth hormone, progesterone, corticosteroids and estrogens, are responsible for induction of hepatic enzyme activity 7.

Since it is logistically impossible to delineate the changes in PK of all drugs administered to pregnant women, alternative approaches such as mechanistic modelling, to predict drug disposition and adjustment of drug dosing regimens (if any) are highly desirable. These approaches, in conjunction with opportunistic PK studies in pregnant women of drugs administered for therapeutic purposes, should improve our ability to adjust drug dosing regimens for pregnant women. To this end, we have focused on a systems pharmacology approach, i.e. physiologically-based pharmacokinetic (PBPK) modelling. PBPK modelling has the advantage of incorporating both physiological parameters that are important for ADME processes and drug-specific parameters (e.g. physico-chemical and drug disposition characteristics) into a quantitative predictive model 8,9. A maternal, whole-body PBPK model, incorporating prior physiological parameters as well as maternal hepatic CYP activity in each trimester was recently developed 10,11. We refined this PBPK model and showed that the PBPK model populated with CYP3A, 1A2 and 2D6 activity change, based on CL_oral of midazolam, caffeine and metoprolol, respectively, could accurately predict the disposition during pregnancy of other drugs cleared primarily by the same CYP enzyme, namely CYP3A-metabolized drugs nifedipine and indinavir (CYP3A) 12, CYP1A2-metabolized drug theophylline and CYP2D6-metabolized drugs paroxetine, dextromethorphan and clonidine 13. In the current study, we expanded and verified the established PBPK model, by incorporating CYP2B6 induction (based on in vitro data), CYP2C9 induction (based on phenytoin PK), and CYP2C19 suppression (based on proguanil PK). For model verification, the PBPK model was used to predict the disposition during pregnancy of drugs cleared via these multiple CYP pathways including methadone (METH) and glyburide (GLB).

Methods

General workflow of PBPK model development and verification criterion

A general workflow (Figure 1) of PBPK modelling and simulation of test compounds in non-pregnant subjects consisted of the following steps: (i) comparison of mean plasma concentration–time (C–T) profiles simulated using a 13-compartment full PBPK model (Simcyp® Population-based Simulator Version 12.1, Simcyp Limited, Sheffield, UK) with those obtained from in vivo studies including i.v. dosing, single and multiple oral dosing (to qualify the drug-specific parameters); (ii) refinement (hence referred to as modified model) of the drug-specific parameters (e.g. f_m) if the prediction in (i) above deviates significantly (<0.8-fold or >1.25-fold) from that observed. Such refinements were often based on changes in mean AUC and mean concentration–time profiles in the presence of inhibitors or genetic polymorphism of the enzymes clearing the drug; (iii) populating the time-varying full PBPK model constructed in Matlab v. 7.10® (2010, Mathworks®, Natick, MA) with these qualified drug-specific parameters and pregnancy-induced CYP activity changes (see below). Once the drug model was qualified in the non-pregnant population, the drug-specific parameters were fixed for simulating PK of drugs during pregnancy and post-partum. The post-partum systemic exposure to drugs was considered to represent drug exposure in the non-pregnant female population.

Figure 1.

A diagram depicting the general workflow of PBPK modeling and simulation. Our modelling approach entails a two step model validation procedure, first to demonstrate adequacy of the model for the non-pregnant population and second for the pregnant population. Simcyp was used to for the first step, i.e. to qualify the drug-specific parameters in the non-pregnant population. For the second step of model validation, these fixed drug-specific parameters were fed into the MATLAB model to predict C–T profiles in the pregnant population. The MATLAB model was populated with known pregnancy-dependent system changes, including presumed pregnancy effect on CYP enzyme activity

Verification of the established PBPK model was primarily based on AUC because achieving equivalent drug exposure in pregnant and non-pregnant women was our primary focus. The term ‘verification’ is used in place of ‘validation’ to acknowledge the complexity of the PBPK model that requires more than plasma data to accomplish proper validation. In addition, prediction of C_max and C_min was considered because achieving similar drug C_max and C_min may be important for some drugs where these measures are related to drug efficacy and/or toxicity. For model verification, mean AUC, C_max and C_min of METH and GLB during pregnancy were predicted and compared with published studies in pregnant subjects. We chose the criterion of PK bioequivalence as the criterion for successful verification of the model, namely, the predicted mean population PK parameters of the drug (as described above), should fall within 80% to 125% of the observed value, i.e. 0.80 ≤ predicted/observed ≤1.25.

General pregnancy PBPK model structure and key assumptions

The general pregnancy PBPK model structure and key assumptions were described in detail previously 10,12. Briefly, the placental-fetal unit was represented as a single lumped compartment because the focus of the current study was to predict maternal PK of drugs during pregnancy. The gestational age dependent changes in physiological parameters (e.g. cardiac output, glomerular filtrate rate, etc) were incorporated into an existing PBPK model (Jamei et al. 9). Maternal glomerular filtration rate (GFR) was assumed to increase during pregnancy by 19%, 40% and 37% during T₁, T₂ and T₃, respectively 11. The change in drug unbound fraction in plasma (f_u,p) during pregnancy, as a function of serum albumin or α₁-AGP concentrations, was accounted for in the model as described previously 12. The established PBPK model also assumed that hepatic CYP3A activity increased by 2.0-fold (measured by midazolam CL_oral) during T₃ 12. The magnitude of CYP3A during T₂ was assumed to be the same as that of T₃, as suggested by similar T₂ vs. T₃ effect on indinavir CL_oral 14. The PBPK model was further expanded to incorporate pregnancy-induced induction of CYP2B6 and CYP2C9, as well as suppression of CYP2C19 as described below. Maternal hepatic CYP2B6 was assumed to increase during pregnancy by 1.1-fold, 1.4-fold and 1.9-fold (based on in vitro to in vivo extrapolation, see results) during T₁, T₂ and T₃, respectively. Maternal CYP2C9 activity was assumed to increase by 1.4-fold, 1.5-fold and 1.6-fold (reported by phenytoin PK) during T₁, T₂ and T₃ 15,16 (see results). Maternal CYP2C19 activity, as reported by CL_oral of the anti-malarial agent proguanil 17,18, was assumed to decrease by 62% and 68% during T₂ and T₃, respectively (see below). These changes in CYP activity were considered static for each trimester. Hepatic organic anion transporter OATP1B1 or 2B1 activity was assumed to remain constant throughout pregnancy. These changes were accomplished in Matlab v7.10®.

The mass balance differential equations (except for the permeability-limited liver model) used in the model have been described previously 10,12. Briefly, all tissues except maternal liver were considered to be well-stirred compartments, i.e. that the unbound tissue concentration is at equilibrium with the unbound concentration in the emergent blood. The maternal liver was modelled as a permeability-limited tissue, incorporating scaled active uptake (PS_int,OATP) and scaled passive diffusion clearances (CL_pd) of unbound drug at the sinusoidal membrane, and scaled metabolic clearance (CL_int,u,h) of unbound drug (Equations 1 and 2). The liver compartment was subdivided into extracellular (EC) and intracellular compartments (IC). The EC combined tissue blood (11.5% of liver volume) and interstitial fluid (16.3% of liver volume). Biliary excretion of unchanged drug is negligible for the tested drugs and was therefore not considered in the current model.

1

2

For drugs that are not actively transported into the hepatocytes (such as METH and PHT), equation 3 was used. Equation 4 was used to describe the apparent intrinsic clearance. Equation 5 was used to describe the dynamic change of the enzyme amount as a result of auto-induction by drugs such as PHT.

3

4

5

where C_ab, C_h, C_vbsl, C_vbg and C_vbh represent the concentrations in the arterial blood, liver, spleen-blood, gut-blood and hepatic outlet (or liver-blood), respectively; Q_h, Q_g and Q_sl represent the blood flows of the liver, gut and spleen respectively; V_h, V_EC and V_IC represent the volume of the liver, extracellular compartment and intracellular compartment of the liver, respectively; f_u and f_u,h represents the fractions unbound in plasma and liver (f_u,h = f_u/K_p for drugs with no active uptake or efflux). CL_int,u,h, V_max and K_m represent the unbound hepatic intrinsic clearance, maximum velocity and the Michaelis-Menten constant for metabolism, respectively, and A_CYP and A_CYP,0 represent the total hepatic amount of CYP isoform at a given time and at baseline. K_deg represents the apparent first order degradation rate constant of the CYP enzyme, EC_50,u and E_max represent the unbound concentration at which 50% of maximum induction is reached, and the maximum induction potential, respectively. Pregnancy-induced change, either induction or suppression of CYP enzyme activity was reflected in unbound hepatic intrinsic clearance CL_int,u,h for drugs with linear kinetics or A_CYP,0 for drugs associated with saturable hepatic metabolism.

METH PBPK model construction

Methadone (METH), a drug used to treat opiate addiction, is mainly eliminated via hepatic metabolism by CYP2B6, CYP3A and CYP2C19, with a significant contribution from renal elimination (16–27%) 19,20. A number of studies have shown that methadone distribution and disposition are influenced by its chirality. R-METH has lower plasma protein binding level (binding to α₁-AGP), a larger volume of distribution, and higher total body clearance 21,22. Therefore, PBPK models for R-METH and S-METH were constructed, respectively, to account for the differential disposition of each enantiomer. Physiochemical and protein binding parameters (log P_o : w, pK_a, B : P ratio, f_u,p), absorption (F_a, k_a, t_lag), distribution (V_ss), elimination (CL_IV) and excretion (CL_r) were obtained from the literature (see Table 1). Initial scaling of in vitro metabolic data 19,23 did not fully recover the observed R- and S-METH metabolic clearance, CL_H. Therefore hepatic unbound intrinsic clearance CL_int,u was back-calculated from observed CL_H (= CL_IV − CL_r) using the well-stirred liver model. Because the in vitro K_m for CYP2B6, CYP3A and CYP2C19 23 is significantly greater than the therapeutic METH concentration of 1–2 μm, saturation of hepatic CYP enzymes in the clinically used dose range is unlikely. This speculation is also supported by comparable mean CL_oral following chronic dosing vs. single dosing of the racemate 20,21,24–26. For these reasons saturable metabolism was not incorporated into the model. The contribution from individual CYP to total metabolic clearance obtained in vitro is 43.4%, 45.3% and 9.1% (R-METH) and 69.2%, 37.1% and 10.4% (S-METH), for CYP2B6, 3A and 2C19, respectively 19. In vivo f_m for individual CYP was calculated by taking the product of f_m (= 1 − f_e) and the fractional contribution of individual CYP. Urine pH has a significant effect on renal clearance. When urine pH is below 6, the contribution of renal clearance becomes significant, accounting for around 16–27% of total body clearance 20,27. The average literature values for CL_r and f_e of R-METH and S-METH were used in the final model 20,21,28. The constructed drug model was verified by comparing predicted mean AUC, C_max and C_min of R-METH and S-METH following single and multiple oral dosing of the racemate in non-pregnant subjects to reported literature values. The drug-dependent parameters of METH are listed in Table 1.

Table 1.

Summary of methadone (MET) drug-dependent parameters

Parameter	Value	Methods/reference
Molecular weight	309.4	a
Log Po:w	3.93	b
pKa	9.2	a
B : P ratio	0.75	c
fu,p	R = 0.16; S = 0.12	d
Fa	0.88	e
ka (h−1)	0.59	f
Fg	R = 0.98; S = 0.99	Predicted by Qgut modelg
tlag (h)	0.295	f
Vss (l kg−1)	R = 6.2; S = 4.7	Predictedh
CLi.v. (l h−1)	R = 8.6; S = 6.8	i
CLr (l h−1)	R = 1.8; S = 1.1	j
CLint,u (μl min−1/pmol)	R: CLint,u,2B6 = 0.306 CLint,u,3A = 0.039	k
	CLint,u,2C19 = 0.078
	S: CLint,u,2B6 = 0.427 CLint,u,3A = 0.028
	CLint,u,2C19 = 0.078
fm and fe	R: fm,2B6 = 35.1% fm,3A = 36.6%fm,2C19 = 7.3% fe = 21% S: fm,2D6 = 49.8% fm,3A = 26.7% fm,2C19 = 7.5% fe = 16%	l,j

^aReported 62. ^bhttp://www.chemspider.com/Chemical-Structure.3953.html. ^cReported value 27. ^dAverage value for R-methadone (R) and S-methadone (S) in the literature 62–65. ^eBack-calculated from mean reported F_a × F_g (= 0.78 − 0.79) 26 and predicted F_g (= 0.98 − 0.99). Reported mean F is 0.82 (range 0.41–0.99) 20,26,64. ^fMean reported values 21,65. ^gQ_gut model is provided in Simcyp simulator. It retains the form of the ‘well-stirred’ liver model, but the flow term (Q_gut) is a hybrid of both permeability through the enterocyte membrane and villous blood flow 66. ^hPredicted according to Rodgers & Rowland 67. Reported V_ss following i.v. dosing is 5.9 ± 1.4 (R-METH) and 3.4 ± 0.9 (R-METH) 20 or 4.74 ± 1.94 l kg⁻¹ (racemic METH) 26. ⁱReported 20. ^jUrine pH has a significant effect on renal clearance. When urine pH is below 6, the contribution of renal clearance becomes significant, accounting for around 16–30% of total body clearance 27. Average of the literature values was used 20,21,28. ^kIn vitro HLM or recombinant CYP data 19,23 did not fully recover observed metabolic clearance. Therefore, CL_int,h,u for CYP2B6, 3A and 2C19 were back calculated from hepatic CL (= CL − CL_r), f_m for individual CYP (see below), and ‘average’ population values for liver weight and hepatic CYP enzyme abundance of 17, 137 and 14 pmol mg⁻¹ protein for CYP2B6, 3A and 2C19, respectively. ^lThe contribution from individual CYP to total metabolic clearance obtained in vitro was 43.4%, 45.3% and 9.1% (R-METH) and 69.2%, 37.1% and 10.4% (S-METH), for CYP2B6, 3A and 2C19, respectively 19. In vivo f_m for individual CYP was calculated by taking the product of f_m (= 1 − f_e) and the percent contribution from individual CYP.

In vitro to in vivo extrapolation (IVIVE) of CYP2B6 induction during pregnancy

Hepatic CYP2B6 mRNA expression and enzyme activity was shown to be induced by estradiol in a concentration-dependent manner in human hepatocytes, with EC_50,u of 1.9 ± 0.5 μm and E_max (fold-increase) of 34 ± 22 (based on CYP2B6 mRNA expression), respectively 29. The corresponding values based on CYP2B6 activity data are 4.1 ± 4.1 μm and 20 ± 21, respectively 29. Because estradiol depletion in human hepatocytes is significant with a reported half-life of 0.57 ± 0.12 h 30, the reported EC_50,u was corrected for estradiol depletion by calculating the average concentration (AUC(0,τ)/τ) during an incubation period of 24 h. In the same experiment, rifampicin and carbamazepine were included as positive controls. Since the in vivo E_max of CYP2B6 induction by rifampicin or carbamazepine is not known, the in vivo E_max for estradiol-mediated CYP2B6 induction was not calibrated. Based on meta-analysis of literature data, the average estradiol concentration in plasma is 9.3, 33.3 and 59.6 nm during T₁, T₂ and T₃ 11. The reported mean unbound fraction in plasma of estradiol is 2% (range 1–3%) in the non-pregnant population 31. Estradiol mainly binds to albumin 31 and its unbound fraction in plasma is predicted to increase from the average pre-pregnancy level of 2% to 2.1%, 2.3% and 2.9% during T₁, T₂ and T₃. These correspond to unbound estradiol concentrations of 0.20, 0.76 and 1.72 nm, respectively. The magnitude of CYP2B6 induction based on CYP2B6 mRNA data was predicted using equation 6.

6

GLB PBPK model construction

GLB has dose-proportional kinetics following single and multiple oral dosing in the clinical dose range 32. GLB is almost exclusively cleared via hepatic metabolism (f_e < 0.1%) 33. Data in the literature regarding the contribution from individual CYP, particularly CYP2C9, to the metabolic clearance of GLB are inconsistent. In one study, selective inhibition studies in human liver microsomes showed that CYP3A plays a major role in GLB metabolism (∼53%), followed by CYP2C9 (∼28%) and CYP2C19 (<20%) 34. In another study, using a similar experimental approach, the individual CYP contribution to GLB metabolism was as follows: CYP3A (∼50%)> CYP2C8 (∼33%)> CYP2C19 (∼17%) 35. In vivo studies, on the other hand, suggested a significant role for CYP2C9 in the clearance of GLB. Single and multiple coadministration of fluvastatin (40 mg), a CYP2C9 inhibitor, increased the plasma AUC of GLB by 23% 36. CYP2C9 is a highly polymorphic enzyme. Kirchheiner et al. showed that the total oral clearance of GLB in the CYP2C9 *3/*3 subjects (n = 3) was approximately 40% of that in the CYP2C9*1/*1 subjects (n = 4) 4. Niemi et al. reported that the oral clearance of GLB in individuals heterozygous for the CYP2C9*3 allele (n = 2) was 35.7% of the respective value in the CYP2C9*1/*1 subjects 37. These clinical studies suggest the contribution of CYP2C9 to GLB metabolism in vivo (f_m,2C9) falls in the range of 18.6% to 63%. Considering all the in vitro and in vivo evidence, in the final GLB model, the assigned contribution from individual CYP to total GLB metabolic clearance was 50%, 30% and 20% for CYP3A, 2C9 and 2C19, respectively. GLB has also been identified in vitro as a substrate of OTAP2B1 38 and an inhibitor of OATP1B1 39. It is likely that GLB is also a substrate of OATP1B1, although this has not been shown in literature to date. In vivo, 600 mg i.v. rifampicin over 30 min immediately followed by 1.25 mg oral GLB increased GLB plasma AUC by 118% and C_max by 81% 33. Because rifampicin is a potent pan OATP inhibitor, this significant drug–drug interaction could be attributed to the inhibition of OATP2B1 and/or OATP1B1-mediated hepatic uptake clearance of GLB. These results also indicate the fraction of transport-mediated clearance towards total hepatic uptake clearance is at least 54.5%, assuming complete inhibition of OATPs by rifampicin.

The PBPK modelling strategy for GLB was as follows: First, the metabolic clearance of GLB (= 3.6 l h⁻¹) was predicted via IVIVE from two independent in vitro studies 34,40 and similar clearance values were obtained. Definitive in vitro transport studies of GLB are not available, therefore the following parameters were estimated simultaneously using mean glyburide plasma PK data reported in subjects taking a single oral dose of 1.75–5 mg glyburide: hepatic bidirectional permeability clearance (CL_pd), and hepatic intrinsic uptake clearance by OATP (or the permeability surface area product, PS_int,OATP). As discussed above, both OATP2B1 and 1B1 could be important in mediating the uptake of the drug into hepatocytes and therefore a lumped clearance PS_int,OATP, was used. Two automated sensitivity analyses were conducted to identify the initial estimates for fitting PS_int,OATP and CL_pd (Figure S1). There are many combinations of PS_int,OATP and CL_pd values that can result in an AUC within the range of 0.46–0.73 ng ml⁻¹ h following 1.75 mg orally, which is 80–125% of the mean AUC observed in vivo (0.58 ng ml⁻¹ h). Consequently the combination with PS_int,OATP > CL_pd (PS_int,OATP 50 μl min⁻¹/10⁶ cells; CL_pd 30 μl min⁻¹/10⁶ cells) were selected and used as initial estimates for data fitting, as the fraction of transport-mediated clearance towards total hepatic uptake clearance is at least 54.5% as discussed earlier. Other drug-specific parameters, including physiochemical and protein binding parameters (log P_o:w, pK_a, f_u,p), absorption (F_a, k_a, t_lag), distribution (V_ss) and excretion (CL_r) were obtained from literature. The drug-dependent parameters of GLB are listed in Table 2. To predict the drug–drug interaction between GLB and rifampicin, a rifampicin drug model provided in Simcyp simulator was updated with an in vitro K_i of rifampicin against hepatic OATP2B1 or 1B1. The in vitro K_i sourced from the online database UCSF-FDATransPortal (http://bts.ucsf.edu/fdatransportal) ranged from 0.41–17 μm. Varma et al. showed using PBPK modelling, the in vivo K_i of rifampin to be 0.41–0.6 μM, essentially the most potent in vitro K_i values reported. These K_i values best recovered the DDI between RIF and pravastatin, a well-established substrate drug of hepatic OATP1B1 41. Hence we used in vivo K_i of 0.41 μm in our prediction.

Table 2.

Summary of glyburide (GLB) drug-dependent parameters

Parameter	Value	Methods/reference
Molecular weight	494.0	a
Log Po:w	4.79	b
pKa	5.3	c
B : P ratio	0.55	Assumed d
fu,p	0.015	e
Fa	0.84	a
ka (h−1)	0.756	f
tlag (h)	0.39–0.46	f
Fg	0.91	Predicted by Qgut model
Vss (l kg)−1	0.1	Predictedg
CLIV (l h−1)	4.4	h
CLr (l h−1)	0.001	i
CLint,CYP (μl min−1/pmol)	CLint,CYP3A4 = 0.238	j
	CLint,2C9 = 0.268
	CLint,CYP2C19 = 0.931
CLpd (μl min−1/106 cells)	24	Parameter estimationk
PSint,OATP2B1 (μl min−1/106 cells)	43.5	Parameter estimationk
fm	fm,3A = 50%	l
	fm,2C9 = 30%
	fm,2C19 = 20%

^aReported 32. ^bhttp://www.drugbank.ca/drugs/DB01016. ^cLiterature value 68. ^dThere is no evidence in the literature that glyburide partitions into erythrocytes. Therefore B : P was calculated from the equation: E : P = [B : P − (1 − Hct)]/Hct, where E : P refers to erythrocyte partition coefficient and Hct refers to haematocrit value (mean value of 0.45 used). ^eAverage of reported value in the literature 5,69. ^fOptimized in the range of 0.39–0.46 h. The reported value is 0.46 h 70. ^gPredicted V_ss according to Rodgers & Rowland is 0.61 l kg⁻¹ 67. This value was further optimized by applying a global K_p scalar of 0.1, in order to match the reported V_ss of 0.077 ± 0.013 l kg⁻¹ following i.v. infusion 59. ^hReported value is 4.4 ± 0.56 l h⁻¹ (n = 8) 59. ⁱReported value 33. ^jBack calculation from hepatic clearance, f_m for individual CYP (see below), and ‘average’ population values for liver weight and hepatic CYP enzyme abundance of 137, 73 and 14 pmol mg⁻¹ protein for CYP3A, 2C9 and 2C19, respectively. Hepatic intrinsic metabolic clearance (= 252.9 l h⁻¹) was predicted using in vitro to in vivo extrapolation. Briefly, in vitro CL_int,u determined in HLM 40 was scaled by ‘average’ population values for liver weight and microsomal protein of 1618 g and 38.9 (mg g⁻¹ liver), respectively. Alternatively, in vitro V_max and K_m determined in recombinant CYP enzyme system 34 were scaled by ‘average’ population values for liver weight and respective hepatic CYP enzyme abundance as described above. Both approaches yielded similar values and the mean hepatic intrinsic clearance was used. ^kHepatic bidirectional permeability clearance (CL_pd), and hepatic intrinsic uptake clearance by OATP (or the permeability surface area product, PS_int,OATP), were estimated simultaneously using mean glyburide plasma PK data reported in subjects taking a single oral dose of 1.75–5 mg glyburide. ^lThe contribution from individual CYP obtained using HLM with selective chemical inhibitors is 53%, 28% and 19% for 3A, 2C9 and 2C19, respectively 34. In another study, the contribution from CYP3A was approximately 50%, whereas 2C8 and 2C19 combined contribute 50% 35. However, in vivo drug–drug interaction studies using fluvastatin as the perpetrator (a 2C9 inhibitor) reported AUC % change of 23% 36. In addition, a 2.7-fold higher glyburide AUC in subjects with CYP2C9*1/*3 and CYP2C9*2/*3 vs. CYP2C9*1/*1 was observed 37. This evidence suggests that CYP2C9 plays a significant role in glyburide metabolism in vivo. Therefore, the in vitro contribution from individual CYPs was adjusted accordingly and 50%, 30% and 20% for 3A, 2C9 and 2C19, respectively, was assigned in the final model.

Back-calculation of the magnitude of CYP2C19 suppression during pregnancy based on proguanil PK

CYP2C19 mediates the biotransformation of the anti-malarial agent, proguanil, to its active metabolite cycloguanil. Proguanil is also excreted as unchanged drug in urine (f_e = 32%) 42. Proguanil is extensively absorbed from the gastrointestinal tract and exhibits linear PK over the dose range 100 mg to 400 mg 43. The drug is 75% bound to plasma proteins and highly partitions into the red blood cells (blood : plasma concentration ratio or B : P = ∼5) 44. The CL_oral of proguanil decreases by 60% during T₂ and T₃ in patients with uncomplicated P. falciparum malaria, as compared with non-pregnant healthy subjects 17. A possible disease effect on CL_oral of proguanil cannot be completely ruled out. In another study, where the plasma metabolic ratio of proguanil : cycloguanil was used as a CYP2C19 marker, this metabolic ratio was 62% higher during T₃ vs. post-partum in subjects phenotyped as CYP2C19 extensive metabolizers 18. The observed decrease in proguanil CL_oral during pregnancy, was then used to back-calculate the magnitude of decrease in 2C19 activity after accounting for other pregnancy related components of proguanil CL_oral (CL_r, B : P ratio and plasma protein binding). Specifically, F_a × F_G was assumed to be equal to unity and remain unchanged during pregnancy. The CL_r of proguanil greatly exceeds (>11-fold) the renal filtration clearance (= f_u,p × GFR), suggesting proguanil is actively transported in the kidney. Because the renal transport mechanism of proguanil is unknown and because CL_r has not been assessed in pregnant women, we assumed that only the filtration clearance was increased during pregnancy. The B : P ratio was predicted to decrease from a baseline value of 5.0 to 4.4 during T₃ following a decrease in haematocrit value. Lastly, f_u,p was predicted to increase from baseline value of 0.25 to 0.33 during T₃ as a function of plasma albumin concentration. Using the well-stirred liver model shown below, the back-calculated CL_int,h,u, i.e. CYP2C19 activity, is decreased by 62% in T₂ and 68% in T₃.

7

Results

In vitro to in vivo extrapolation (IVIVE) of CYP2B6 induction during pregnancy

Using human hepatocytes, it was recently shown that hepatic CYP2B6 mRNA expression and enzyme activity, can be induced by estradiol following a 48 h incubation period, with an EC_50,u of 1.9 ± 0.5 μm and E_max (fold-increase) of 34 ± 22 (based on CYP2B6 mRNA expression), respectively 29. The average EC_50,u was 61.4 nm after correcting for estradiol depletion (see Methods). For reasons outlined in Methods, the E_max for estradiol-mediated CYP2B6 induction was not calibrated based on positive control data including rifampicin and carbamazepine. At the unbound estradiol concentration in plasma of 0.20, 0.76 and 1.72 nm, during T₁, T₂ and T₃, respectively, the predicted magnitude of CYP2B6 induction based on CYP2B6 mRNA data was 1.1-, 1.4- and 1.9-fold, respectively. The predicted magnitude based on CYP2B6 activity data was 1.0-, 1.1- and 1.3-fold, respectively. Because the increase in the rate of enzyme translation following administration of an inducer is secondary to its effect on the rate of transcription, there may be a delay, for example, due to turnover rate of nuclear receptors mediating the increased level of protein synthesis, between the manifestation of these two processes 45. Considering these factors, the predicted magnitude of CYP2B6 induction based on CYP2B6 mRNA data, was used in subsequent PBPK modelling of methadone disposition.

Methadone (METH) PK prediction in pregnancy using PBPK model incorporating CYP2B6 induction based on in vitro data

The mean AUC, C_max and C_min of R-METH and S-METH following a single oral dose of racemic METH of 9.9 mg in non-pregnant subjects were quantitatively predicted by the constructed R-METH and S-METH models (i.e. predicted/observed in the range of 0.8–1.2, Figure 2A and Table 3). At steady-state, the mean AUC, C_max and C_min of R-METH and S-METH following chronic dosing of racemic METH of 70 mg once daily or 100 mg once daily were also quantitatively predicted, with the exception of AUC(0,τ_ss) (70 mg once daily) of S-METH and C_min,ss (70 mg once daily) of R-METH (Figure 2B and Table 3). Nevertheless, the corresponding predicted/observed of the latter was 1.26 and 0.75, respectively. Then, METH exposure in pregnant women was predicted based on the study design described 2. In this study, the disposition of racemic METH was studied in nine pregnant subjects who had been on METH maintenance therapy. R-METH and S-METH plasma concentrations following an average dose of 30 mg once daily of racemic METH were predicted respectively, and the summed concentrations of each enantiomer were compared with the observed data (Figure 3 and Table 4). The model predicted mean AUCR (PP : T₂) of 1.9, mean C_max ratio (PP : T₂) of 1.7 and mean C_min ratio (PP : T₂) of 2.0, compared with observed mean ratios 2.0, 2.0 and 2.6, respectively. The model predicted mean AUCR (PP : T₃) of 2.1, mean C_max ratio (PP : T₃) of 2.0 and mean C_min ratio (PP : T₃) of 2.4, compared with observed mean ratios 1.7, 1.7 and 1.8, respectively. The PBPK model successfully predicted racemic methadone PK during T₂, i.e. predicted/observed of mean AUC, C_max and C_min in the range of 0.80–1.11 (Table 4). T₃ AUC and C_min were slightly under-predicted, with pred./obs. of 0.79 and 0.73, respectively. R-METH and S-METH plasma unbound fraction was predicted to increase by 23% and 25% during T₂, and 27% and 29% during T₃ vs. post-partum, as a result of reduced plasma concentration of α₁-AGP, the major binding protein. The reported pregnancy effect on racemic METH plasma unbound fraction was not significant, although there was a trend towards increased unbound fraction by 19–31% during pregnancy vs. post-partum. The predicted R-METH and S-METH CL_r was 1.7-fold and 1.8-fold higher during T₃ vs. post-partum, as a result of increased GFR and plasma unbound fraction, comparable with the reported value of two-fold of the racemate.

Figure 2.

Predicted and observed plasma concentration–time profiles of the methadone (METH) enantiomers R-METH and S-METH following the administration of single oral dose of 9.9 mg (A) and multiple oral doses of 70 mg day⁻¹ (B) to non-pregnant subjects. The solid and dashed lines represent predicted mean R-METH and S-METH profile, respectively. Mean observed data are overlaid (• R-METH profile; ○ S-METH profile) 20,21. Error bars represent SDs

Table 3.

Methadone PK parameters in non-pregnant healthy volunteers

R-methadone				S-methadone
AUC(0,∞)	Observed	Predicted	Predicted/	AUC(0,∞)	Observed	Predicted	Predicted/
(ng ml−1 h)			observed	ng ml−1 h			observed
9.9 mg*	461 ± 72	463.0	1.00	9.9 mg*	639 ± 165	591.7	0.93
Cmax (ng ml−1)				Cmax (ng ml−1)
9.9 mg	13 ± 3	15.8	1.22	9.9 mg	23 ± 6	19.5	0.85
Cmin,96h (ng ml−1)				Cmin,96h (ng ml−1)
9.9 mg	1.9	1.63	0.85	9.9 mg	1.7	2.1	1.21
AUC(0,τss)				AUC(0,τss)
70 mg once daily†	3484 ± 1846	3777	1.08	70 mg once daily†	3797 ± 2088	4767	1.26
100 mg once daily‡	5540 ± 2100	5305	0.96	100 mg once daily‡	5730 ± 2580	6740	1.18
Cmax,ss (ng ml−1)				Cmax,ss (ng ml−1)
70 mg once daily	251 ± 68	217	0.86	70 mg once daily	303 ± 97	299.1	0.99
100 mgonce daily	322 ± 109	299	0.93	100 mg once daily	366 ± 128	402.6	1.10
Cmin,ss (ng ml−1)				Cmin,ss (ng ml−1)
70 mg once daily	148 ± 50	110.5	0.75	70 mg once daily	146 ± 61	140.4	0.96
100 mg once daily	184.5	163.1	0.88	100 mg once daily	177.0	215.2	1.22

*Reported mean ± SD values in subjects receiving a single oral dose of 9.9 mg racemic methadone (n = 12) 20. †Reported mean ± SD values normalized to a 70 mg racemic methadone daily dose (n = 18) 21. ‡Reported mean ± SD values normalized to a 100 mg racemic methadone daily dose (n = 16) 25.

Figure 3.

Predicted and observed plasma concentration–time profiles of racemic methadone (METH) in pregnant subjects on METH maintenance therapy of 30 mg day⁻¹. (A) The solid and dashed lines represent predicted mean METH profile during post-partum and during the second trimester (T₂), respectively. (B) The solid and dashed lines represent predicted mean METH profile during post-partum and during the third trimester (T₃), respectively. Mean observed data are overlaid (• post-partum profile; ○ T₂ or T₃ profile) 2. Error bars represent SDs

Table 4.

Methadone PK parameters (30 mgonce daily) during T₃ and post-partum

AUC(0,τ)	Observed*	Predicted	Predicted/observed
(ng ml−1 h)
Pregnancy(T2)	1607.7	1778.7	1.11
Pregnancy(T3)	1953.1	1539.0	0.79
Postpartum(PP)	3225.8	3298.1	1.02
AUCPP/AUCT2	2.0	1.9	0.92
AUCPP/AUCT3	1.7	2.1	1.30
Cmax (ng ml−1)
Pregnancy(T2)	104.3 ± 23.2	108.9	1.04
Pregnancy(T3)	117.7 ± 24.0	94.5	0.80
Postpartum(PP)	204.4 ± 17.6	190.2	0.93
Cmax,PP/Cmax,T2	2.0	1.7	0.89
Cmax,PP/Cmax,T3	1.7	2.0	1.16
Cmin,24h (ng ml−1)
Pregnancy(T2)	42.2 ± 6.7	51.6	1.04
Pregnancy(T3)	60.1 ± 16.1	43.9	0.73
Post-partum (PP)	108.3 ± 14.7	105.6	0.98
Cmin,PP/Cmax,T2	2.6	2.0	0.94
Cmin,PP/Cmax,T3	1.8	2.4	1.33

*AUC was calculated based on reported mean CL_oral and mean dose of 30 mg (n = 9) 2. C_max and C_min,24h were extracted from published dose-adjusted mean concentration–time profiles, using ‘digitize’, a MATLAB tool for digitizing images that is freely available on http://www.mathworks.com/matlabcentral/.

PHT prediction to inform CYP2C9 induction during pregnancy

The PHT model provided in the Simcyp simulator was used without modification. The major 4-hydroxy metabolite was attributed to CYP2C9 (f_m,2C9 = 72%) and CYP2C19 (f_m,2C19 = 8%) mediated clearance, whereas the non 4-hydroxy (f_m,other = 15–20%) clearance was unassigned. Furthermore, the model also accounted for saturable metabolism by CYP2C9 and 2C19, as well as auto-induction of CYP2C9 (see Table 5). To confirm in vivo f_m,2C9, we predicted the effect of fluconazole inhibition (200 mg day⁻¹ orally for 14 days) on PHT PK (250 mg day⁻¹ orally for 4 days). The fluconazole model provided in the Simcyp simulator was used without modification. The predicted PHT AUCR (AUC_inhibited/AUC_control) of 2.15 (data not shown) was comparable with the observed AUCR of 1.75 46. Furthermore, the mean AUC, C_max, C_min and C_pre-dose of PHT (300 mg once daily) in non-pregnant subjects were quantitatively predicted by the PHT model (i.e., predicted/observed in the range of 0.83–1.02, Figure 4A and Table 6). In studies conducted in the pregnant subjects, PHT plasma trough concentration (i.e. C_pre-dose) is invariably used as a marker of CYP2C9 activity. Hence the change in PHT C_pre-dose was used here to back calculate the magnitude of increase in CYP2C9 activity. In pregnant epileptic patients receiving a fixed PHT dose of 300 mg daily, PHT C_pre-dose is decreased by 43%, 51% and 61% during T₁, T₂ and T₃, respectively 15,16. Through sensitivity analysis, CYP2C9 fold-induction was 1.4-, 1.5- and 1.6-fold, during T₁, T₂ and T₃, respectively, to recover the reported changes in PHT C_pre-dose (Figure 4B). The predicted PHT plasma unbound fraction was 15%, 26% and 30% during T₁, T₂ and T₃, compared with the reported values of 14%, 16–38% and 26–40%, respectively 16,47.

Table 5.

Summary of phenytoin (PHT) drug-dependent parameters

Parameter	Value
Molecular weight	252.28
Log Po:w	2.47
pKa	8.15
B : P ratio	0.61
fu,p	0.1
Fa	0.9
ka (h−1)	0.53
Fg	1.0
Vss (l kg−1)	0.573
CLIV (l h−1)	2.07
CLr (l h−1)	0.015
Vmax (μl min−1/pmol)	Vmax,2C9 = 0.24
	Vmax,2C19 = 1.53
Km (μm)	Km,2C9 = 4.1
	Km,2C19 = 36.8
CLint,other (μl min−1 mg−1)	0.97
Emax (CYP2C9)	1.9
EC50 (μm) (CYP2C9)	15.3
fm and fe	fm,2C9 = 72%
	fm,2C19 = 8%
	fm,other = 19%
	fe = 1%

Figure 4.

Predicted and observed phenytoin (PHT) plasma concentrations following multiple oral doses of 300 mg day⁻¹. (A) Predicted (solid line) and observed (symbols) 56–58 PHT plasma concentration–time profiles following chronic dosing of 300 mg day⁻¹ (orally) in non-pregnant healthy subjects. (B) The grey bars represent predicted percent decrease in PHT trough concentration (C_pre-dose) and the white bars represent observed mean percent decrease in PHT C_pre-dose in pregnant women during pregnancy (T₁, T₂ and T₃) vs. post-partum 16. □, Lim et al. 56; ◊, Purkins et al. 58; •, Randinitis et al. 57

Table 6.

Phenytoin (300 mg Q.D.) PK parameters in non-pregnant subjects

	Observed*	Predicted	Predicted/observed
AUC(0,τss) (ng ml−1 h)	207.6 ± 25.5	201.6	0.97
Cmax,ss (ng ml−1)	10.3 ± 1.5	10.6	1.03
Cmin,ss (ng ml−1)	7.6 ± 1.5	6.3	0.83
Cpre-dose (ng ml−1)	7.3 ± 1.1	6.3	0.87

*Mean ± SD of reported values in non-pregnant, healthy subjects (n = 31 total) receiving chronic administration of 300 mg day⁻¹ 56–58. C_min,ss refers to the last plasma sample taken during the dosing interval and C_pre-dose refers to the plasma trough concentration before the daily dose.

GLB PBPK model prediction incorporating OATP uptake

The constructed GLB model, accounting for metabolism by CYP3A, CYP2C9 and 2C19, as well as hepatic OATP-mediated uptake, was verified against the disposition kinetics following the administration of a single oral dose of 1.75–5 mg to non-pregnant healthy volunteers. Model-predicted AUC(0,∞), C_max and C_min,12 h all met the verification criterion, with predicted/observed in the range of 0.87–1.25 (Figure 5A and Table 7). C_min,24 h of GLB (5 mgorally) was under-predicted, with a predicted/observed of 0.21. Following rifampicin treatment (600 mg i.v. over 30 min), the predicted GLB (1.25 mg orally) plasma AUCR and C_max ratios were 1.88 and 1.47, respectively, compared with the observed ratios of 2.2 ± 0.51 and 1.8 ± 0.28, respectively 33 (Figure S2A). The rifampicin plasma concentration–time profile was also in reasonable agreement with the observed data 48 (Figure S2B).

Figure 5.

(A) Predicted and observed plasma concentration–time profiles of glyburide (GLB) after administration of a single oral dose of 1.75–5 mg to non-pregnant subjects. The black and grey solid lines represent predicted mean profile in subjects receiving 1.75 mg and 5 mg, respectively. Mean observed data after the administration of 1.75 mg GLB (• and ○) and 5 mg GLB (◆) are overlaid [37],[71],[72]. (B) Predicted and observed plasma concentration–time profiles of glyburide (GLB) following chronic dosing of 1 mg day⁻¹ orally during the third trimester (T₃) and post-partum. The solid and dashed lines represent predicted mean GLB profile during post-partum and during T₃, respectively. Mean observed data 5 are overlaid (•: non-pregnant type 2 diabetic subjects profile or T2DM; ○: gestational diabetic subjects T₃ profile or GDM). Error bars represent SDs

Table 7.

Glyburide PK parameters after oral dosing in non-pregnant subjects

1.75 mg*	Observed	Predicted	Predicted/observed
AUC(0,∞) (ng ml−1 h)	273.9	281.0	1.03
Cmax (ng ml−1)	85.8	75.0	0.87
Cmin,12h (ng ml−1)	2.6	3.2	1.25
5 mg†
AUC(0,∞) (ng ml−1 h)	809 ± 388	800.8	0.99
Cmax (ng ml−1)	109 ± 44	104.8	0.96
Cmin,24h (ng ml−1)	5.0	1.0	0.21
Glyburide PK parameters (1 mg twice daily) during T3 and post-partum
AUC(0,τ)
(ng ml−1 h)	Obs.‡	Pred.	Pred./Obs.
Pregnancy (T3)	72 ± 27	62.4	0.87
Post-partum (PP)	153 ± 69	161.1	1.05
AUCPP/AUCT3	2.1	2.6	1.2
AUC(0,τ)	Obs.‡	Pred.	Pred./Obs.
Pregnancy (T3)	15 ± 8	14.2	0.95
Post-partum (PP)	33 ± 21	30.8	0.93
Cmax,PP/Cmax,T3	2.2	2.2	0.99
Cmin,24h (ng ml−1)
Pregnancy (T3)	1.82	0.41	0.23
Post-partum (PP)	5.85	2.87	0.49
Cmin,PP/Cmax,T3	3.2	7.0	2.17

*Reported mean values in non-pregnant, healthy subjects with CYP2C9*1/*1 or *1/*2 genotype (n = 18 total) 37,71. †Reported mean ± SD values (n = 24). The genotype of the subjects is unknown 72. ‡Reported mean ± SD values normalized to 1 mg twice daily in gestational diabetic subjects during the third trimester (n = 40) and non-pregnant type 2 diabetic subjects (n = 26) 5. CYP2C9 genotype had no impact on GLB disposition in this study.

The GLB plasma concentration–time profile following a fixed dose of 1 mg once daily in pregnant women was predicted based on the study design described 5. In this study, the steady-state GLB disposition was evaluated in gestational diabetic subjects (n = 40) during T₃ and compared with non-pregnant type 2 diabetic subjects (n = 26). Predicted mean GLB AUCR (PP : T₃), C_max ratio (PP : T₃) and C_min ratio (PP : T₃) were 2.6, 2.2 and 7.0, compared with the observed values of 2.1, 2.2 and 3.2. Model-predicted AUC(0,τ) and C_max during T₃ and post-partum met the verification criterion, with predicted/observed in the range of 0.87–1.05 (Figure 5B and Table 7). C_min,12h of GLB during T₃ and post-partum was under-predicted, with predicted/observed of 0.23 and 0.49, respectively. The GLB plasma unbound fraction was predicted to increase from 1.5% to 2.1% during T₃. In comparison, the reported GLB plasma unbound fraction in gestational diabetic subjects during T₃ (1.6 ± 0.1%) was not different from that of the non-pregnant type 2 diabetic subjects (1.5 ± 0.1%).

Discussion

Many studies in the literature have utilized model (probe) drugs that report CYP enzyme activities to delineate the magnitude of change in activity of major CYP enzymes, mostly during the third trimester (e.g. caffeine for CYP1A2, metoprolol for CYP2D6, midazolam for CYP3A, PHT for CYP2C9) 49. However, for hepatic CYP2B6 enzymes, such a probe drug study (e.g. bupropion) to delineate in vivo CYP2B6 activity during pregnancy has not been reported. Therefore, we utilized a bottom-up approach based on mechanistic studies (i.e. IVIVE). Based on the gradually rising concentration of estradiol in plasma, we predicted that hepatic CYP2B6 induction during pregnancy increased gradually and peaked during T₃ at 1.9-fold of the post-partum value. It is noteworthy that estradiol concentrations vary considerably between individuals during pregnancy 50, and, as such, the magnitude of CYP2B6 induction could vary between women during pregnancy. For example, at the highest reported estradiol plasma concentration of ∼140nm, the predicted fold-induction of CYP2B6 is 3.1-fold. We then confirmed the predicted magnitude of CYP2B6 induction in vivo by predicting METH disposition during pregnancy. To do so, a respective METH PBPK model accounting for stereo-selective disposition of R-METH and S-METH was constructed and verified against observed PK data following single or multiple oral dosing of the racemate to the non-pregnant population. The PBPK model accounting for CYP2B6 induction, as well as known pregnancy effect on other clearance pathways including CYP3A, CYP2C19, and CL_r, successfully predicted METH disposition during T₂ as compared with the observed data 2. Model prediction of METH disposition during T₃ was less robust. We suspect this is due to the fact that the reported mean T₂ CL_oral is 21% higher than mean T₃ CL_oral. This observed trend in vivo in METH CL_oral during T₂ vs. T₃, although not statistically significant, is opposite to what we predicted based on the IVIVE approach. Other clinical studies conducted in pregnant subjects on METH maintenance therapy showed a similar or greater magnitude of increment in METH CL_ORAL during pregnancy vs. post-partum (2.9–3.6 fold) 51, or vs. historical controls (∼1.6 fold) 52. However because plasma concentration–time profiles were not reported in those studies and they had a limited sample size, these data were not used for model verification. One limitation of our study is that because METH CL_oral reports the change in multiple clearance pathways, it might not be a sensitive reporter of CYP2B6 activity. As suspected, sensitivity analysis showed CYP2B6 fold-induction in the range of 1.0–3.0-fold and 1.0–2.0-fold during T₂ and T₃, respectively, could recover the observed plasma AUC of METH during pregnancy (i.e. predicted/observed within 0.80–1.25). These results also indicate that IVIVE based on CYP2B6 activity data, which predicted a smaller induction potential vs. that of mRNA data, could also recover the observed pregnancy effect on METH disposition. Future studies with probe drug bupropion during various stages of pregnancy and post-partum are highly desirable to further confirm the in vivo fold-induction of CYP2B6 predicted from in vitro data. Nevertheless, the above successful prediction of METH disposition during pregnancy shows for the first time that quantitative PK predictions of drugs cleared by multiple CYP enzymes is possible, through a PBPK model that integrates prior physiological knowledge such as CYP activity, in vitro and in vivo data.

CYP2B6 is also an important clearance pathway for the HIV drug efavirenz. In vitro, CYP2B6 has been identified as the main isoform metabolizing efavirenz, with smaller contributions from CYP2A6, CYP3A and UGT2B7. In vivo, CYP2B6 genetic variations are one of the main sources of efavirenz PK variability 53. Interestingly, the AUC and C_max of efavirenz did not differ during pregnancy and post-partum in a Thai population and only C_min,24 h was lower during T₃ 54. A possible explanation for the lack of effect of pregnancy on efavirenz PK, at least in this Thai population, could be that the PK variability introduced by the CYP2B6 genotype reduced the power of the study to detect the pregnancy effect. Auto-induction of CYP2B6 and CYP3A4 is another potential explanation. For CYP3A4, in vitro and in vivo data support an inverse correlation between the baseline enzyme activity and the fold induction of enzyme activity, that is, the magnitude of induction depends on the baseline enzyme activity 45. If the same holds true for CYP2B6, for an individual with high 2B6 activity pre-pregnancy (due to auto-induction), pregnancy-related increase in CYP2B6 activity may be smaller.

Estradiol (∼157 nm) enhanced activities of CYP2C9 (diclofenac 4'-hydroxylation) by 1.3–2.0 fold in human hepatocytes, a magnitude comparable with that of known inducers of CYP2C9 such as phenobarbital 30. Estradiol (100 nm) was shown to down-regulate CYP2C19 mRNA expression by ∼30% in human hepatocytes via activation of estrogen receptor 55. These mechanistic studies provide a potential explanation for the mechanisms by which CYP2C9 is increased and CYP2C19 activity is decreased during pregnancy. However, a concentration-dependent induction or suppression relationship (i.e. EC₅₀ and E_max) has not been established for these CYP isoforms. Therefore the IVIVE of the magnitude of CYP2C9 and 2C19 induction or suppression in each trimester is not possible.

To model the PK changes of the CYP2C9 substrate drug GLB during pregnancy, we used the probe drug PHT as the model training drug. PHT PK are complicated by two balancing factors, saturable metabolism by CYP2C9 and CYP2C19 reducing its metabolic clearance at higher concentrations and auto-induction of CYP2C9 increasing its metabolic clearance at higher concentrations. The established PHT drug model accounting for these mechanisms quantitatively predicted PHT PK, including C_pre-dose, following chronic dosing in the non-pregnant population. Numerous studies have assessed PHT C_pre-dose in epileptic patients during pregnancy 15,16,47. Although the overall trend of the change in PHT C_pre-dose during each trimester was consistent across various studies, the exact magnitude differed. For example, Yerby et al. reported that the drop in PHT total and free concentration was 37%, 49%, 49% and 32%, 41% and 38%, respectively, during T₁, T₂ and T₃ 47. PHT dose used during pregnancy was increased (453 mg day⁻¹) compared with post-partum (333 mg day⁻¹). We selected Tomson et al.'s study as the model training set because of its superior study design: a large sample size (n = 29), fixed PHT dose, monotherapy, and trough sampling. Interestingly, following the same fixed dose of 300 mg day⁻¹, PHT mean C_pre-dose during the post-partum period (10.27 ± 5.25 μg l⁻¹) reported in this study was 41% higher than the reported mean C_pre-dose in the non-pregnant, healthy population (∼7.3 μg l⁻¹, n = 31) 56–58. The difference in C_pre-dose between epileptic patients and healthy subjects may be reflective of disease-related factors on PHT disposition. As a result of this difference, the PHT model quantitatively predicted C_pre-dose in the non-pregnant healthy population (Table 6), but under-predicted C_pre-dose in the pregnant epileptic patients (data not shown). However, it is expected that at steady-state, CYP2C9 activity change is proportional to the percent change in PHT C_pre-dose. Therefore, the difference in the absolute value of baseline C_pre-dose (predicted vs. observed) should not affect the capacity of the model to recover the change in CYP2C9 activity. The modest induction of CYP2C9 recovered from in vivo data was also comparable with the magnitude observed in in vitro studies, of 1.3–2.0 fold in human hepatocytes 30.

The commonly used proton pump inhibitors including omeprazole, lansoprazole and pantoprazole, are primarily metabolized by CYP2C19. The effect of pregnancy on the PK of these drugs has not been studied. Pregnancy-induced suppression of CYP2C19 activity was back-calculated from the magnitude of decrease in CL_oral of proguanil after accounting for other pregnancy related components of proguanil CL_oral (see Methods). One caveat of this approach, however, is that renal clearance is a significant clearance pathway of proguanil, especially during pregnancy when CYP2C19 activity is suppressed. The pregnancy effect on CL_r of proguanil is unknown, therefore we assumed that only the filtration clearance (∼10% of renal clearance) was increased during pregnancy. To assess definitively the magnitude of CYP2C19 induction during pregnancy, we propose that a PK study with the 2C19 probe omeprazole be conducted during various stages of pregnancy and post-partum in the future.

GLB has long been considered as primarily metabolized by CYP2C9. Pharmacogenetic studies appear to support this and suggest that in vivo CYP2C9 contributes significantly (up to 63%) to GLB metabolism, based on a limited number of subjects with reduced catalytic activity of CYP2C9 37. However, recent in vitro studies 34,40, including from our laboratory 35, suggest that CYP3A is the major isoform metabolizing GLB, contributing ∼50% to GLB metabolism, followed by ∼30% contribution from CYP2C9 and ∼20% contribution from CYP2C19. The constructed GLB model, accounting for metabolism by these multiple CYPs, also incorporated hepatic OATP-mediated uptake in order to explain a significant drug–drug interaction caused by rifampicin treatment. Hepatic OATP-mediated uptake of the drug into hepatocytes is not likely to be the sole rate-limiting step of drug clearance from the body, since GLB i.v. clearance of 4.4 l h⁻¹ 59 can be well-estimated by metabolic clearance. Consistent with this speculation, the estimated mean GLB sinusoidal uptake clearance of 572 l h⁻¹ (Figure S2C) is greater than the hepatic intrinsic metabolic clearance of 252.9 l h⁻¹ (see footnotes to Table 2). Following rifampicin treatment (600 mg i.v. over 30 min), GLB plasma AUCR and C_max ratio were well predicted by the constructed PBPK model. It is not known whether pregnancy affects hepatic OATP expression or activity. Therefore no change in OATP activity was assumed in the current model. However, we conducted a sensitivity analysis to assess the impact of hepatic OATP activity on GLB plasma AUC during T₃. The latter was shown to be sensitive to change in hepatic OATP activity, when no pregnancy-related CYP induction or suppression was assumed (Figure S2D). Therefore, we cannot rule out the possibility that hepatic OATP activity is affected during pregnancy. The GLB plasma concentration–time profile following a fixed dose of 1 mg once daily in pregnant women was quantitatively predicted. Because C_max prediction met verification criterion, the under-prediction of GLB steady-state C_min,12 h during T₃ and post-partum could possibly be due to inadequate prediction of tissue distribution (hence the t_1/2 of drugs) which could result in inadequate prediction of C_min. The absorption of GLB was assumed to follow first order kinetics with a lag time. Under this assumption, the absorption phase of the GLB plasma profile following a single oral dose in non-pregnant subjects (Figure 4A) was adequately described. However this was not the case in pregnant subjects following multiple doses (Figure 4B). Other absorption models, such as an inverse Gaussian density function, have been used to describe GLB absorption 5. It is not clear as to what factors contribute to the apparent non-linear absorption of GLB. Saturation of intestinal transporters such as P-glycoprotein and the breast cancer resistance protein are possible explanations because GLB has been identified as a substrate for both transporters 60. However, when evaluating GLB C_max in the dose range from 0.875 mg–10 mg oral dose in the literature (University of Washington DIDB, http://www.druginteractioninfo.org/), we did not observe dose-dependent change in C_max with increasing dose. Similar to METH CL_oral, because GLB CL_oral reports the change in multiple clearance pathways, it will not be a sensitive reporter of CYP2C9 activity. CYP2C9 and CYP2C19 together contribute ∼50% of GLB metabolic clearance. We performed a sensitivity analysis by simultaneously varying CYP2C9 activity in the range of 1.0-fold to 3.0-fold induction, and a reduction in CYP2C19 activity of 0% to 80%, respectively. Multiple combinations of CYP2C9 and 2C19 activity change, for example, 2.7-fold induction of CYP2C9 activity coupled with 80% reduction of CYP2C19 activity, could recover the observed plasma AUC of GLB during T₃ (i.e. predicted/observed within 0.80–0.93). This highlights the importance of conducting PK studies in pregnant women with a well-established probe drug, to delineate definitively the change in hepatic enzyme activity during pregnancy. Nevertheless, our successful prediction of GLB AUCR (PP : T₃) during pregnancy illustrates the utility of using a PBPK model, incorporating pregnancy-dependent changes in CYP activities, to predict the disposition of a drug cleared by multiple pathways.

In summary, we have shown for the first time that our PBPK model 1) can quantitatively predict the disposition of drugs during pregnancy when they are cleared via multiple CYP pathways using prior knowledge of a pregnancy effect on various clearance pathways, 2) extrapolates in vitro data on estradiol-mediated CYP2B6 induction to its in vivo effect on the CYP2B6 substrate drug METH and 3) allows generalization beyond the model drugs studied (e.g. PHT, proguanil) to other drugs with well-characterized ADME characteristics (e.g. GLB). Previously, we have shown that such extrapolation can also be made for CYP3A 12, 1A2 and 2D6-metabolized drugs 61. Nevertheless, the magnitude of in vivo induction of hepatic CYP2B6 and suppression of hepatic CYP2C19 activity in pregnant women needs to be confirmed. Since conducting PK studies in pregnant women is challenging, our expanded PBPK model provides a valuable tool to evaluate different dosing regimens of drugs cleared primarily by single or multiple CYP enzymes during pregnancy. Future expansion of the presented PBPK model could incorporate variability in the predicted drug exposure measures when necessary data on the variability (and covariance) in the system- and drug-dependent parameters are better defined. While achieving equivalent drug (total or unbound) exposure in pregnant and non-pregnant women is often the primary focus of maternal pharmacotherapy, it is equally important to evaluate carefully fetal and neonatal safety, especially for drugs such as GLB that can cross the placenta. A comprehensive fetal model could be incorporated into this PBPK model in the future to predict fetal exposure to drugs. Using such systems a pharmacology approach can potentially allow us to identify drugs whose maternal-fetal PK, and therefore their efficacy and toxicity for the mother and/or the fetus, are likely to be affected by pregnancy. Conducting the trial in silico before its execution in vivo can be helpful in optimizing the design of a ‘first in pregnancy’ PK study including prioritizing study period (first, second or third trimester), sample size and dosage selection. The generated information or hypotheses can be rigorously tested, and the model can be further refined as data become available from such PK studies. Ultimately, the proposed approach may help support the design of rational dosing regimen for pregnant women and their offspring.

Competing Interests

All authors have completed the Unified Competing Interest form at http://www.icmje.org/coi_disclosure.pdf (available on request from the corresponding author) and declare ABK was supported by the Office of Women's Health, US Food and Drug Administration, JDU was a member of the Simcyp (now part of Certara) scientific advisory board and no other relationships or activities that could appear to have influenced the submitted work.

Supporting Information

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Figure S1

Changes in glyburide AUC (1.75 mg orally) as a function of hepatic bidirectional permeability clearance (CL_pd), and hepatic intrinsic uptake clearance by OATP (PS_int,OATP). There are many combinations of PS_int,OATP and CL_pd values that can result in AUC within the range of 0.46–0.73 ng ml⁻¹ h following 1.75 mg orally, which is 80–125% of the mean AUC observed in vivo (0.58 ng ml⁻¹ h). Consequently, PS_int,OATP > CL_pd (PS_int,OATP 50 μl min⁻¹/10⁶ cells; CL_pd 30 μl min⁻¹/10⁶ cells) were selected and used as initial estimates for data fitting

Figure S2

(A) Predicted plasma concentration–time profiles of GLB after administration of a single oral dose of 1.25 mg to non-pregnant subjects, in the presence and absence of rifampin (RIF) treatment (600 mg i.v.) (control: solid line; RIF treatment: dashed line). (B) Predicted (solid line) and observed (●) [50] plasma concentration–time profiles of rifampin (600 mg i.v. over 30 min infusion). (C) Predicted time course of GLB hepatic sinusoidal uptake clearance in the presence and absence of RIF treatment (control: solid line; RIF treatment: dashed line). (D) Change in GLB AUC (1 mg day⁻¹ orally) during T₃ as a function of hepatic OATP activity. While hepatic OATP activity was increased up to 10-fold of the value used in the final GLB model, pregnancy-induced changes in CYP activities were ignored. The dashed line represents the mean observed value