Development and Verification of a Full Physiologically Based Pharmacokinetic Model for Sublingual Buprenorphine in Healthy Adult Volunteers that Accounts for Nonlinear Bioavailability

Abstract

Sublingual buprenorphine is used for opioid use disorder and neonatal opioid withdrawal syndrome. The study aimed to develop a full physiologically based pharmacokinetic (PBPK) model that can adequately describe dose- and formulation-dependent bioavailability of buprenorphine. Simcyp (v21.0) was used for model construction. Four linear regression models (i.e., untransformed or log transformed for dose or proportion sublingually absorbed) were explored to describe sublingual absorption of buprenorphine across dose. Published clinical trial data not used in model development were used for verification. The PBPK model’s predictive performance was deemed adequate if the geometric means of ratios between predicted and observed (P/O) area under the curve (AUC), peak concentration (C_max), and time to reach C_max (T_max) fell within the 1.25-fold prediction error range. Sublingual buprenorphine absorption was best described by a regression model with logarithmically transformed dose. By integrating this nonlinear absorption profile, the PBPK model adequately predicted buprenorphine pharmacokinetics (PK) following administration of sublingual tablets and solution across a dose range of 2–32 mg, with geometric mean (95% confidence interval) P/O ratios for AUC and C_max equaling 0.99 (0.86–1.12) and 1.24 (1.09–1.40), respectively, and median (5th to 95th percentile) for T_max equaling 1.11 (0.69–1.57). A verified PBPK model was developed that adequately predicts dose- and formulation-dependent buprenorphine PK following sublingual administration.

SIGNIFICANCE STATEMENT

The physiologically based pharmacokinetic (PBPK) model developed in this study is the first to adequately predict dose- and formulation-dependent sublingual buprenorphine pharmacokinetics. Accurate prediction was facilitated by the incorporation of a novel nonlinear absorption model. The developed model will serve as the foundation for maternal-fetal PBPK modeling to predict maternal and fetal buprenorphine exposures to optimize buprenorphine treatment for neonatal opioid withdrawal syndrome.

Introduction

Buprenorphine, administered as a sublingual tablet or solution, is used in the management of opioid use disorder (OUD). Buprenorphine acts as a partial agonist at the μ opioid receptor (Martin et al., 1976), as an antagonist at δ and κ opioid receptors (Leander 1988; Negus et al., 2002), and as a full agonist at the nociceptin/orphanin FQ opioid receptor (Wnendt et al., 1999). This intricate pharmacological profile gives rise to buprenorphine’s more desirable clinical properties compared with other opioids, such as lower abuse potential and reduced likelihood of fatal respiratory depression (Pergolizzi et al., 2010). Among Medicaid enrollees diagnosed with OUD, the use of buprenorphine increased from 28.1% to 37.3% between 2014 and 2018, making it the most prescribed medication to treat OUD (Donohue et al., 2021).

Opioid use during pregnancy is not uncommon. In 2019, 6.6% of pregnant women self-reported use of prescription opioids, of which 21.2% disclosed opioid misuse (Ko et al., 2020). Newborns prenatally exposed to opioids are at risk of developing neonatal opioid withdrawal syndrome (NOWS) after birth. NOWS is characterized by gastrointestinal dysfunction and neurologic excitability (Patrick et al., 2020) and requires pharmacological treatment in those neonates whose symptoms are otherwise insufficiently controlled (Wachman et al., 2018). Sublingually administered buprenorphine is an emerging treatment of NOWS (Simon et al., 2021), but current dosing strategies have been empirically established and lack a robust pharmacokinetic (PK) and pharmacodynamic (PD) rationale (Hjelmström et al., 2020). Neonatal buprenorphine PK is highly variable (Ng et al., 2015; Mizuno et al., 2021; van Hoogdalem et al., 2021), and recent physiologically based pharmacokinetic (PBPK) modeling and simulation by our group indicated that variability is likely driven by differences in the extent of sublingual absorption, biliary clearance, and cytochrome P450 (CYP) 3A4 activity, especially early in life (van Hoogdalem et al., 2022a). Strategies to improve the treatment of NOWS with buprenorphine include further improving our understanding of the complex PK/PD relationship and subsequently adjusting the starting dose to the expected PK profile of the neonate. Additionally, initial dosing could be tailored to the anticipated NOWS severity.

The severity of NOWS differs greatly between affected neonates, but symptoms tend to be more severe in newborns born at term (Liu et al., 2010), whose mothers used tobacco during pregnancy (Choo et al., 2004; Bakstad et al., 2009), and those who had greater opioid exposure in utero (van Hoogdalem et al., 2022b). Estimating the extent of prenatal opioid exposure is challenging. Intuitively, fetal opioid exposure may strongly correlate with maternal intake, but studies have failed to demonstrate a consistent relationship between maternal OUD medication dose and postnatal NOWS severity (Dashe et al., 2002; Bakstad et al., 2009; Dryden et al., 2009; Jones et al., 2014). This may be, in part, explained by the everchanging nature of maternal opioid PK during pregnancy and the likelihood that fetuses are more vulnerable to opioid effects at certain points during gestation (van Hoogdalem et al., 2022b). Maternal-fetal PBPK modeling offers a comprehensive framework that can incorporate the kaleidoscopic interplay of maternal and fetal factors that ultimately dictate prenatal opioid exposure (van Hoogdalem et al., 2022b). This, in turn, can open the way for precision treatment of NOWS based on the prenatally modeled severity.

Accurately predicting buprenorphine PK following sublingual administration is challenging since bioavailability is dependent on the formulation (tablet versus solution) (Nath et al., 1999, Schuh and Johanson 1999; Harris et al., 2004; Strain et al., 2004; Chawarski et al., 2005) and decreases with dose (Harris et al., 2004; Ciraulo et al., 2006; Dong et al., 2019). Several PBPK models for sublingual buprenorphine have been developed to date, but none have adequately integrated nonlinear bioavailability. Kalluri et al. (2017) constructed a full PBPK model, which was later expanded to a pregnancy PBPK model (Zhang et al., 2018), but others were not able to recreate these models due to the ambiguous description of sublingual absorption (Silva et al., 2022). Our group developed a neonatal minimal PBPK model (van Hoogdalem et al., 2022a), which was based on a model developed by Johnson et al. (2016), but given the neonatal application, the model was only verified for low doses and does not accurately capture reduced bioavailability with higher doses. In line with PBPK modeling best practices, it is recommended to develop and validate the model in healthy adults before extrapolating it to special populations. Therefore, to lay a strong foundation for planned maternal-fetal PBPK modeling, the aim of the present study was to develop a full PBPK model for buprenorphine that can adequately describe dose- and formulation-dependent bioavailability following sublingual administration.

Materials and Methods

PBPK Model Development

A full PBPK model for buprenorphine was constructed and verified using Simcyp (v21.0; Simcyp Limited, Sheffield, UK). A schematic representation of the PBPK model is shown in Fig. 1. Drug physiochemical and physiologic parameters used to build the PBPK model are shown in Table 1 (Bullingham et al., 1980; Holland et al., 1989; Avdeef et al., 1996; Kuhlman et al., 1996; https://www.accessdata.fda.gov/drugsatfda_docs/nda/2002/20-733_Subutex_BioPharmr.pdf; Takahashi et al., 2001; Elkader and Sproule 2005; Picard et al., 2005; Chang and Moody 2009; Cubitt et al., 2009; Hassan et al., 2009; Moore et al., 2018; https://pubchem.ncbi.nlm.nih.gov/compound/644073). The fraction unbound in blood plasma was set to be 0.04 as reported by Elkader and Sproule (2005). The fraction absorbed was assumed to be 1. Concentration-time profiles reported by Dong et al. (2019), who administered buprenorphine sublingual tablets at doses of 2, 4, 8, 12, 16, and 24 mg to 82 opioid-naïve volunteers, were digitized using WebPlotDigitizer (v4.5, Ankit Rohatgi, Pacifica, CA). The first-order absorption rate constant from the gastrointestinal tract was optimized to accurately capture the peak concentration (C_max) using the concentration-time profile following administration of a 24-mg buprenorphine sublingual tablet reported by Dong et al. (2019). A lag time parameter was integrated into the buprenorphine population PK model developed by Moore et al. (2018), and utilizing Bayesian estimation in MWPharm++ (v2.0.4; Mediware Incorporated, Prague, Czech Republic), the population PK model was fitted to the observed concentration-time profiles reported by Dong et al. (2019) for sublingual tablet doses of 2, 4, 8, 12, 16, and 24 mg to determine mean lag time. Elimination was based on in vitro enzyme kinetics data (Michaelis-Menten constant and V_max) for CYP2C8-, CYP3A4-, UDP-glucuronosyltransferase (UGT)-1A1-, UGT1A3-, UGT2B7-, and UGT2B17-mediated metabolism, renal clearance, and biliary clearance. Renal clearance was calculated based on a mass balance study where 1% was excreted unchanged in urine (https://www.accessdata.fda.gov/drugsatfda_docs/nda/2002/20-733_Subutex_BioPharmr.pdf), with a total plasma clearance (CL) of 54.1 L/h (Bullingham et al., 1980).

TABLE 1.

Input data for the full PBPK model for buprenorphine

Parameter	Value	Reference
Physiochemical
Molecular weight (g/mol)	467.6	https://pubchem.ncbi.nlm.nih.gov/compound/644073
LogP	4.98	Avdeef et al., 1996
Compound type	Ampholyte	Avdeef et al., 1996
pKa (acid; phenol)	9.62	Avdeef et al., 1996
pKa (base; amine)	8.31	Avdeef et al., 1996
Blood binding
B/P	1	Bullingham et al., 1980
f u, plasma	0.04	Elkader and Sproule, 2005
Plasma binding components	AGP	Takahashi et al., 2001
Gastrointestinal tract absorption (first-order model)
fa	1a
ka (h−1)	0.016b
Lag time (h)	0.22c
f u, gut	0.4b
Qgut (L/h)	16.8d
Peff, man (10−4 cm/s)	6.83d
Caco-2 7.4:7.4 (10−6 cm/s)	66.7	Hassan et al., 2009
Sublinguale absorption (first-order model)
fa	1a
ka (h−1)	1b
Proportion of dose inhalede (tablet) (%)	38.1–19.7 × log(Dose)f
Proportion of dose inhalede (solution) (%)	53.3–25.6 × log(Dose)f
Distribution (full PBPK model)
Tissue-to-plasma partition coefficients (Kp)
Adiposeg	17.800	Takahashi et al., 2001
Boneh	1.603	Takahashi et al., 2001
Brainh	19.206	Takahashi et al., 2001
Guti	2.252	Takahashi et al., 2001
Hearth	1.714	Takahashi et al., 2001
Kidneyi	6.372	Takahashi et al., 2001
Liveri	8.695	Takahashi et al., 2001
Lungh	3.921	Takahashi et al., 2001
Muscleh	0.905	Takahashi et al., 2001
Pancreash	3.016	Takahashi et al., 2001
Skin	3.500	Holland et al., 1989
Spleenh	2.286	Takahashi et al., 2001
Predicted Vss (L/kg)	6.23d
Observed Vss (L/kg)	4.95	Kuhlman et al., 1996
Elimination
CYP2C8
Vmax (pmol/min per mg protein)	176.3	Picard et al., 2005
Km (μM)	12.4	Picard et al., 2005
CYP3A4
Vmax (pmol/min per mg protein)	520	Picard et al., 2005
Km (μM)	13.6	Picard et al., 2005
UGT1A1
Vmax (pmol/min per mg protein)	2870	Chang and Moody, 2009
Km (μM)	66.4	Chang and Moody, 2009
UGT1A3
Vmax (pmol/min per mg protein)	286	Chang and Moody, 2009
Km (μM)	202	Chang and Moody, 2009
UGT2B7
Vmax (pmol/min per mg protein)	173	Chang and Moody, 2009
Km (μM)	13.8	Chang and Moody, 2009
UGT2B17
Vmax (pmol/min per mg protein)	172	Chang and Moody, 2009
Km (μM)	9.6	Chang and Moody, 2009
f u, mic	0.1	Cubitt et al., 2009
CLrenal (L/h)	0.54j
CLbiliary (μl/min per million cells)	51	Johnson et al., 2016

AGP, α₁-acid glycoprotein; B/P, blood-to-plasma ratio; CL_biliary, biliary clearance; CL_renal, renal clearance; f_a, fraction absorbed; f_{u, gut}, fraction unbound in enterocytes; f_{u, mic}, fraction unbound in in vitro microsomal incubation; f_{u, plasma}, fraction unbound in blood plasma; k_a, first-order absorption rate constant; K_m, Michaelis-Menten constant; P_{eff, man}, human jejunum effective permeability; Q_gut, nominal flow in gut model; UGT, UDP-glucuronosyltransferase; V_ss, volume of distribution at steady-state.

^aAssumed value.

^bEmperically optimized to accurately capture the C_max observed following administration of a 24-mg buprenorphine sublingual tablet as reported by Dong et al. (2019).

^cDetermined through Bayesian estimation, employing concentration-time profiles reported by Dong et al. (2019) for sublingual tablet doses of 2, 4, 8, 12, 16, and 24 mg. A lag time (T_lag) parameter was integrated into the buprenorphine population PK model developed by Moore et al. (2018), and utilizing Bayesian estimation in MWPharm++, the population PK model was fitted to the observed concentration-time profiles at each dose level. Value represents the arithmetic mean of Bayesian-estimated T_lag across the 2–24-mg dose range.

^dSimcyp predicted value.

^eThe sublingual route of administration is not available in Simcyp; sublingual absorption is therefore mimicked by employing the first-order inhalation model in combination with the inhaled route of administration.

^fDose is in mg, and logarithm base is 10. The value is calculated manually, and the computed proportion is then entered into the first-order inhalation model. Note that a coefficient of variation of 33.9% is applied to the administered dose to reflect variability in bioavailability; more details are provided in this manuscript.

^gReported radioactivity at 24 h postinjection was used for calculation.

^hReported radioactivity at 8 h postinjection was used for calculation.

ⁱReported radioactivity at 1 h postinjection was used for calculation.

^jCalculated by Johnson et al. (2016) based on a mass balance study where 1% was excreted unchanged in urine (https://www.accessdata.fda.gov/drugsatfda_docs/nda/2002/20-733_Subutex_BioPharmr.pdf), with a total plasma clearance of 54.1 L/h (Bullingham et al., 1980).

Fig. 1.

Full PBPK model structure. The sublingual route of administration is not available in Simcyp; sublingual absorption is therefore mimicked by employing the first-order inhalation model in combination with the inhaled route of administration. The proportion of the dose inhaled equals the proportion sublingually absorbed. The remaining fraction of the dose is swallowed.

The present model was based on a minimal PBPK model for buprenorphine developed earlier by our group (van Hoogdalem et al., 2022a), which, in turn, was adapted from a model described by Johnson et al. (2016). The minimal PBPK model was expanded to a full PBPK model by incorporating tissue-to-plasma partition coefficients (Kp). There were no reports of Kp values for buprenorphine from human tissue data. Therefore, Kp values were estimated using tissue distribution data in rats generally measured between 1 and 144 hours following subcutaneous injection of radiolabeled buprenorphine (Holland et al., 1989; Takahashi et al., 2001). Moment-dependent distribution of buprenorphine and its metabolites was considered when determining optimal time points to calculate Kp values; e.g., Kp values for gut, kidney, and liver were obtained using distribution data measured at 1 hour postdose to minimize measuring the distribution of buprenorphine metabolites rather than buprenorphine. The volume of distribution at steady state (V_ss) was predicted in Simcyp.

As the sublingual route of administration is not available in Simcyp, sublingual absorption was simulated by employing two separate absorption models: one for lung and another for gastrointestinal absorption as described previously (van Hoogdalem et al., 2022a). In this approach, the proportion of the dose inhaled to undergo lung absorption mirrors the proportion that would be absorbed sublingually and circumvents first-pass metabolism. The remaining fraction is swallowed and is subject to the first-pass effect. Sublingual and gastrointestinal absorption was simulated based on the parameters summarized in Table 1.

Linear Regression Modeling of Sublingual Absorption

Plasma concentration-time data were extracted from dose-escalation (Schuh and Johanson 1999, Harris et al., 2004; Dong et al., 2019) studies (training data) using WebPlotDigitizer. Area under the curve [AUC; i.e., area under the curve from zero to infinity (AUC_0–∞) and area under the curve in one dosing interval (AUC_0–τ) for single and multiple dose studies, respectively] and C_max following sublingual tablet or solution administration were determined by fitting the buprenorphine population PK model reported by Moore et al. (2018) to these extracted concentration-time profiles using MWPharm++. All PK parameters were fitted with 6–20 concentration-time points for each trial. Subsequently, through multiple iterations with the PBPK model, the proportion of the dose designated for sublingual absorption in the PBPK model was determined to precisely recover the AUC and C_max observed for doses between 2 and 32 mg administered in selected dose-escalation studies (Schuh and Johanson 1999; Harris et al., 2004; Dong et al., 2019), termed as the ideal proportion. Ideal proportion determination involved continuously adjusting the sublingual absorption proportion empirically during each run until the PBPK model predicted a geometric mean AUC and C_max identical to that observed. Ideal proportions were determined separately for AUC and C_max as different sublingual absorption proportions were often necessary to accurately replicate each exposure metric. The relationship between AUC- and C_max-optimized ideal proportion and dose was explored for sublingual tablets and solution separately through linear regression modeling using the stats package (v4.1.2, R Core Team) for R (v4.1.2; R Foundation for Statistical Computing, Vienna, Austria). The following bivariate linear model was used (eq. 1):

where Proportion_i is the AUC- or C_max-optimized ideal proportion (%) for clinical study i, α is the intercept, β is the slope, and Dose is the sublingual tablet or solution dose in milligrams. Visual inspection of the data indicated a linear or inverse exponential relationship between ideal proportion and dose. Therefore, four varieties of the linear model were explored, i.e., either Dose and Proportion_i untransformed, or with Dose, Proportion_i, or both logarithmically transformed using a decimal logarithm of base 10. Thus, in total, 16 linear regression analyses were performed, namely, four linear model varieties explaining four individual relationships (i.e., AUC- and C_max-optimized ideal proportions versus sublingual tablet and solution doses, assessed as separate formulations). The linear model achieving the highest mean coefficient of determination across the four individual relationships was selected (Supplemental Table 1). AUC- and C_max-optimized linear models were subsequently averaged to capture both AUC and C_max using one equation, thereby obtaining two final linear models (one for sublingual tablets and one for sublingual solution) describing the relationship between ideal proportion and dose.

PBPK Model Verification and Evaluation

Following an extensive literature search for plasma buprenorphine PK data in healthy volunteers, the PBPK model’s predictive performance was assessed for intravenous and sublingual administration successively by determining the average-fold error (AFE) and absolute average-fold error (AAFE) between predicted and observed concentrations and the ratio between predicted and observed (P/O) AUC, CL, C_max, and, in case of sublingual administration, time to reach C_max (T_max). The following equations were used to calculate AFE and AAFE (eqs. 2 and 3, respectively):

All data used for model verification were independent (test data), i.e., not used in the development of the PBPK or sublingual absorption model.

Predicted PK parameters were obtained by running virtual trials in Simcyp and represented the geometric mean of the virtual trial’s population. Virtual trials were conducted using the Sim-Healthy Volunteers population file. The population’s age (preferably age range, but mean age if no range was reported), proportion of females (50% was assumed for studies that did not report the participants’ sex), and administered buprenorphine dose and formulation were matched to that in the clinical study. All virtual trials involving sublingual administration of buprenorphine were conducted under the fasted state. For virtual trials in which buprenorphine was sublingually administered, a coefficient of variation of 33.9% was applied to the administered dose to reflect variability in bioavailability, which is consistent with the average variation in bioavailability after sublingual administration observed by Bullingham et al. (1982). The virtual cohort consisted of 100 individuals (10 individuals × 10 trials) for each simulation. The virtual trial duration was set to the time associated with the last reported observable concentration in the clinical study. For the sampling plan, predefined uniform intervals were selected, and the number of time samples was set to 16,000.

For clinical studies in which buprenorphine was intravenously administered, observed PK parameters were defined as those reported in the trial; missing values were calculated through noncompartmental analysis using Edsim++ (v2.0.4; Mediware Incorporated, Prague, Czech Republic). Clinical studies rarely determined a true C_max following intravenous administration. Instead, C_max generally represented the first concentration measured a few minutes after completion of a bolus injection. Therefore, to match predicted and observed C_max, predicted C_max was defined as the modeled concentration at the time point associated with the first concentration measured.

For clinical studies in which buprenorphine was sublingually administered, observed PK parameters were, similar as described under Linear Regression Modeling of Sublingual Absorption, obtained through Bayesian estimation by fitting the buprenorphine population PK model reported by Moore et al. (2018) to concentration-time data extracted from publications using WebPlotDigitizer. Reported PK parameter values were not used as some studies employed sparse sampling strategies, which limited the robustness of time-associated (i.e., T_max and C_max) and exposure-dictated (i.e., AUC) PK parameters. In the interest of consistency, all concentration-time profiles of sublingually administered buprenorphine for each clinical study were digitized and used to estimate PK parameters through Bayesian estimation.

Potential bias in the PBPK model’s prediction following sublingual administration was evaluated using predicted-versus-observed AUC, C_max, and T_max and dose-versus-respective-P/O-ratio plots.

Statistical Analysis

Geometric means and 95% confidence intervals (CIs) of PK parameter P/O ratios were calculated using the DescTools package (v0.99.44; Signorell et mult. al.) for R. Normal distribution of P/O ratios was examined through the Shapiro-Wilk test. The predictive performance of the PBPK model was deemed adequate if the geometric means of PK parameter P/O ratios fell between 0.8-fold and 1.25-fold (1.25-fold prediction error range). In addition to assessing whether geometric mean PK parameter P/O ratio fell within the relatively narrow 1.25-fold prediction error range, the proportion of all AAF, AAFE, and PK parameter P/O ratios falling within the wider twofold prediction error range was determined.

Results

Verification of the PBPK Model’s Predictive Performance following Intravenous Administration

The structure of the full PBPK model was first externally verified by determining the AFE, AAFE, and P/O ratios of AUC_0–∞, CL, and C_max following intravenous administration of buprenorphine in healthy volunteers. Twelve PK studies, spanning a dose range of 0.3–16 mg and including a total of 69 subjects (aged 20–66.8 years) with 89 concentration-time profiles, were used for intravenous model verification (Table 2) (Bullingham et al., 1982; Kuhlman et al., 1996; Mendelson et al., 1997; Huestis et al., 2013; Bai et al., 2016; Lim et al., 2019). For all 12 PK studies, the AFE and AAFE, as well as the P/O ratios of AUC_0–∞, CL, and C_max, fell within the twofold prediction error range. Geometric mean (95% CI) AUC_0–∞, CL, and C_max P/O ratios were 1.01 (0.90–1.13), 0.95 (0.84–1.08), and 0.91 (0.78–1.05), respectively, indicating adequate predictive performance of these PK parameters following intravenous administration across a wide dose range in healthy volunteers. All predicted-versus-observed buprenorphine concentration-time profiles following intravenous administration are shown in Fig. 2. The relative contribution of individual metabolic and elimination pathways involved in the clearance of buprenorphine is shown in Supplemental Fig. 1, which was comparable to the minimal PBPK model reported previously (van Hoogdalem et al., 2022a).

TABLE 2.

Predicted and observed pharmacokinetic parameters of buprenorphine following intravenous administration

Clinical Trial	Dose (mg)	Route of Administration	n	Female (%)	Mean Age [range] (years)	AFE	AAFE		AUC0–∞ (ng × h/mL)		CL (L/h)	Cmax (ng/mL)
Bullingham et al., 1982	0.3	Intravenous (1 min)	5	60	66.8	0.66	1.71	Predicted Observed		5.96 5.80a	50.3 51.8b	1.390.96
								P/O ratio		1.03	0.97	1.45
Bullingham et al., 1982	0.3	Intravenous (1 min)	5	60	64.2	1.34	1.39	PredictedObserved		4.763.14a	63.095.7b	1.391.08
								P/O ratio		1.52	0.66	1.29
Bullingham et al., 1982	0.3	Intravenous (1 min)	5	60	66.0	1.09	1.62	PredictedObserved		4.653.20a	64.493.8b	1.380.95
								P/O ratio		1.45	0.69	1.45
Bai et al., 2016	0.3	Intravenous (2 min)	24	24.0	35.5 (20–53)	0.59	1.72	PredictedObserved		4.805.20	62.557.7b	1.712.32
								P/O ratio		0.92	1.08	0.74
Lim et al., 2019	0.3	Intravenous (5 min)	14	NR	25	0.87	1.36	PredictedObserved		4.534.09	66.277.7	1.932.73
								P/O ratio		1.11	0.85	0.71
Mendelson et al., 1997	1	Intravenous (30 min)	6	16.7	29 (21–38)	1.12	1.31	PredictedObserved		15.818.4	63.262.5	13.114.3
								P/O ratio		0.86	1.01	0.92
Kuhlman et al., 1996	1.2	Intravenous (1 min)	5	0.0	34.4 (27–40)	0.85	1.58	PredictedObserved		19.717.4	60.876.8	25.437.5
								P/O ratio		1.13	0.79	0.68
Huestis et al., 2013	2	Intravenous (1 min)	5	0.0	34.6 (32–39)	0.79	1.49	Predicted Observed		33.341.4	60.149.8	15.719.3
								P/O ratio		0.80	1.21	0.81
Huestis et al., 2013	4	Intravenous (1 min)	5	0.0	34.6 (32–39)	0.73	1.59	PredictedObserved		66.675.9	60.153.2	31.444.0
								P/O ratio		0.88	1.13	0.71
Huestis et al., 2013	8	Intravenous (1 min)	5	0.0	34.6 (32–39)	0.74	1.54	PredictedObserved		133.2153.3	60.152.4	62.985.7
								P/O ratio		0.87	1.15	0.73
Huestis et al., 2013	12	Intravenous (1 min)	5	0.0	34.6 (32–39)	0.73	1.46	PredictedObserved		199.8245.1	60.154.7	94.3107.9
								P/O ratio		0.82	1.10	0.87
Huestis et al., 2013	16	Intravenous (1 min)	5	0.0	34.6 (32–39)	0.85	1.43	Predicted Observed		266.4269.1	60.160.0	125.8134.0
								P/O ratio		0.99	1.00	0.94
								Geo. meanc		1.01	0.95	0.91
								(95% CI)		(0.90–1.13)	(0.84–1.08)	(0.78–1.05)

NR, not reported.

^aCalculated through noncompartmental analysis.

^bCalculated following CL = Dose/AUC_0–∞.

^cGeometric mean of P/O ratios.

Fig. 2.

PBPK model–predicted and observed concentration-time profiles of buprenorphine following intravenous administration. Blue solid line and shaded area represent the mean and 5th to 95th percentile range of the virtual population (n = 100), respectively. Open circles represent individual observations. Closed circles and whiskers represent mean and standard deviation of the observations, respectively. References for reported observations are provided in Table 2.

Integrating Nonlinear Sublingual Absorption into the PBPK Model

Linear regression models with logarithmically transformed dose best described the relationships between AUC- and C_max-optimized ideal proportions and sublingual tablet and solution doses (mean coefficient of determination, 0.756; Fig. 3 and Supplemental Table 1), which indicated that sublingual buprenorphine absorption is nonlinear across dose. By averaging the AUC- and C_max-optimized linear regression models, two final absorption equations were obtained, namely, proportion of the dose sublingually absorbed equals 38.1 – 19.7 × log(Dose) and 53.3 – 25.6 × log (Dose) for sublingual tablets and solution, respectively. These equations were integrated into the PBPK model as shown in Fig. 1.

Fig. 3.

Proportion of the dose required by the physiologically-based pharmacokinetic (PBPK) model to be sublingually absorbed to exactly recover the (A) AUC (i.e., AUC_0–∞ and AUC_0–τ for single and multiple dose studies, respectively) and (B) C_max observed in the clinical trial (i.e., ideal proportion) across dose. Blue and orange circles, triangles, and diamonds represent sublingual tablet and solution data obtained from Harris et al. (2004), Schuh and Johanson (1999), and Dong et al. (2019), respectively. Blue and orange dotted lines represent linear regression models with logarithmically transformed dose for buprenorphine tablets and solution, respectively. Respective shaded areas represent the 95% CI of the regression models. Associated linear-log equations are shown in the upper right corners (where dose is in milligrams and logarithm base is 10), with coefficients of determination (R²) shown in the lower-left corners. The final buprenorphine PBPK model uses the average of the AUC- and C_max-optimized equations, i.e., proportion sublingually absorbed equals 38.1–19.7 × log(Dose) and 53.3 – 25.6 × log(Dose) for sublingual tablets and solution, respectively.

Verification and Evaluation of the PBPK Model’s Predictive Performance following Sublingual Administration

The PBPK model with the developed description of nonlinear sublingual buprenorphine absorption was subsequently externally verified by determining the AFE and AAFE, as well as the P/O ratios of AUC, C_max, and T_max following sublingual administration of buprenorphine tablets and solution separately. For verification of the PBPK model’s predictive performance following sublingually administered tablets, 16 PK studies, spanning a dose range of 2–32 mg and including a total of 296 subjects (aged 19–54) with 419 concentration-time profiles, were used (Table 3) (Nath et al., 1999; McAleer et al., 2003; Chawarski et al., 2005; Ciraulo et al., 2006; Moody et al., 2011; Jönsson et al., 2018). For all 16 PK studies, the AFE and AAFE, as well as the P/O ratios of AUC, C_max, and T_max, fell within the twofold prediction error range. Geometric mean (95% CI) AUC and C_max P/O ratios were 0.96 (0.82–1.12) and 1.20 (1.05–1.37), respectively, and the median (5th to 95th percentile) for T_max was 1.12 (0.69–1.53).

Table 3.

Predicted and observed buprenorphine pharmacokinetic parameters following administration of sublingual tablets

Observed PK parameters were obtained through Bayesian estimation by fitting the buprenorphine population PK model reported by Moore et al. (2018) to extracted concentration-time profiles.

Clinical Trial	Dose (mg)	Route of Administration	n	Female (%)	Mean Age [range] (years)	AFE	AAFE		AUCa (ng×h/mL)	Cmax (ng/mL)	Tmax (h)
McAleer et al., 2003	2	Sublingual, tablet	27	0.0	(19–42)	0.77	1.48	Predicted	7.32	1.37	1.14
								Observed	10.3	1.47	1.48
								P/O ratio	0.71	0.93	0.77
Ciraulo et al., 2006	4	Sublingual, tablet	23	30.4	34.5	1.87	1.90	Predicted	15.9	2.67	1.12
								Observed	9.62	1.87	1.00
								P/O ratio	1.65	1.43	1.12
Jönsson et al., 2018	4	Sublingual, tablet	61	41.0	31.4 (19–54)	0.92	1.59	Predicted	13.7	2.31	1.08
								Observed	21.8	2.14	1.69
								P/O ratio	0.63	1.08	0.64
Nath et al., 1999	8	Sublingual, tablet	6	0.0	28 (23–42)	1.11	1.52	Predicted	22.6	3.52	1.15
								Observed	23.5	2.95	1.10
								P/O ratio	0.96	1.19	1.05
McAleer et al., 2003	8	Sublingual, tablet	27	0.0	(19–42)	0.82	1.32	Predicted	22.9	3.49	1.14
								Observed	29.1	3.84	1.27
								P/O ratio	0.79	0.91	0.90
Ciraulo et al., 2006	8	Sublingual, tablet	23	30.4	34.5	1.42	1.57	Predicted	27.1	4.15	1.12
								Observed	20.8	2.47	0.99
								P/O ratio	1.30	1.68	1.13
McAleer et al., 2003	12	Sublingual, tablet	27	0.0	(19–40)	0.81	1.30	Predicted	31.0	4.35	1.15
								Observed	41.0	4.81	1.12
								P/O ratio	0.76	0.90	1.03
McAleer et al., 2003	16	Sublingual, tablet	27	0.0	(19–40)	0.77	1.33	Predicted	38.2	4.98	1.15
								Observed	52.7	6.11	0.79
								P/O ratio	0.72	0.82	1.46
Chawarski et al., 2005	16	Sublingual, tablet, m.d.	18	29.5	37.8	1.71	1.71	Predicted	45.5	6.68	1.12
								Observed	31.2	3.45	0.71
								P/O ratio	1.46	1.94	1.58
Ciraulo et al., 2006	16	Sublingual, tablet	23	30.4	34.5	1.26	1.40	Predicted	45.0	5.93	1.12
								Observed	42.0	4.11	0.96
								P/O ratio	1.07	1.44	1.17
Moody et al., 2011	16	Sublingual, tablet, m.d.	11	100.0	41.5	0.92	1.24	Predicted	46.8	6.87	1.00
								Observed	57.8	6.58	0.90
								P/O ratio	0.81	1.04	1.11
Moody et al., 2011	16	Sublingual, tablet, m.d.	20	0.0	35.7	1.27	1.30	Predicted	45.3	6.58	1.17
								Observed	40.9	4.54	1.05
								P/O ratio	1.11	1.45	1.11
Jönsson et al., 2018	16	Sublingual, tablet	64	40.6	32.1 (20–51)	1.00	1.52	Predicted	39.7	5.17	1.09
								Observed	56.3	5.29	1.54
								P/O ratio	0.71	0.98	0.71
Chawarski et al., 2005	24	Sublingual, tablet, m.d.	19	29.5	37.8	1.24	1.26	Predicted	60.1	8.01	1.13
								Observed	56.8	6.86	0.91
								P/O ratio	1.06	1.17	1.24
Ciraulo et al., 2006	24	Sublingual, tablet	23	30.4	34.5	1.18	1.38	Predicted	59.5	6.81	1.13
								Observed	61.7	5.08	0.75
								P/O ratio	0.96	1.34	1.51
Chawarski et al., 2005	32	Sublingual, tablet, m.d.	20	29.5	37.8	1.51	1.51	Predicted	72.2	8.76	1.13
								Observed	55.5	6.17	0.97
								P/O ratio	1.30	1.42	1.16
								Geo. meanc	0.96	1.20	1.12c
								(95% CI)	(0.82–1.12)	(1.05–1.37)	(0.69–1.53)

m.d., multiple doses.

^aAUC_0–∞ and AUC_0–τ for single and multiple dose studies, respectively.

^bGeometric mean of P/O ratios.

^cMedian (5^th to 95th percentile) of P/O ratios.

For verification of the predictive performance following administration of sublingual solution, seven PK studies, spanning a dose range of 2–16 mg and including a total of 75 subjects (aged 21–42) with 81 concentration-time profiles, were used (Table 4) (Kuhlman et al., 1996; Mendelson et al., 1997; Nath et al., 1999; Chawarski et al., 2005). For all seven PK studies, the AFE and AAFE, as well as the P/O ratios of AUC and T_max, fell within the twofold prediction error range, except for the AAFE of the 4-mg dose in the study by Kuhlman et al. (1996). The P/O ratio for C_max fell within the twofold prediction error range in six out of seven (85.7%) PK studies. Geometric mean (95% CI) AUC and C_max P/O ratios were 1.05 (0.75–1.46) and 1.34 (0.95–1.90), respectively, and the median (5th to 95th percentile) for T_max was 1.02 (0.75–1.69). For three studies in which both intravenous and sublingual PK were reported, the P/O ratios of bioavailability were within the twofold prediction error range in all cases and 1.25-fold in two cases, and the geometric mean was also within the 1.25-fold range (Supplemental Table 2).

Table 4.

Predicted and observed buprenorphine pharmacokinetic parameters following administration of sublingual solution

Unless stated otherwise, observed PK parameters were obtained through Bayesian estimation by fitting the buprenorphine population PK model reported by Moore et al. (2018) to extracted concentration-time profiles.

Clinical Trial	Dose (mg)	Route of Administration	n	Female (%)	Mean Age [range] (years)	AFE	AAFE		AUCa (ng×h/mL)	Cmax (ng/mL)	Tmax (h)
Mendelson et al., 1997	2	Sublingual, solution (3 min hold)	6	16.7	29 (21–38)	1.59	1.78	Predicted	9.36	1.94	1.11
								Observed	14.3b	1.60b	1.25b
								P/O ratio	0.65	1.21	0.89
Mendelson et al., 1997	2	Sublingual, solution (5 min hold)	6	16.7	29 (21–38)	1.60	1.80	Predicted	9.36	1.94	1.11
								Observed	13.2b	1.72b	1.62b
								P/O ratio	0.71	1.13	0.69
Kuhlman et al., 1996	4	Sublingual, solution	6	0.0	34.4 (27–40)	0.79	2.57	Predicted	17.1	3.28	1.15
								Observed	15.0	3.22	0.60
								P/O ratio	1.14	1.02	1.92
Nath et al., 1999	8	Sublingual, solution	6	0.0	28 (23–42)	0.79	1.35	Predicted	28.9	5.19	1.14
								Observed	34.6	6.72	1.02
								P/O ratio	0.84	0.77	1.12
Chawarski et al., 2005	8	Sublingual, solution,	18	29.5	37.8	1.52	1.52	Predicted	35.0	6.38	1.12
								Observed	25.4	3.19	1.18
		m.d.						P/O ratio	1.38	2.00	0.95
Chawarski et al., 2005	12	Sublingual, solution,	19	29.5	37.8	1.59	1.59	Predicted	47.3	8.27	1.12
								Observed	33.7	4.50	0.98
		m.d.						P/O ratio	1.40	1.84	1.14
Chawarski et al., 2005	16	Sublingual, solution,	20	29.5	37.8	1.83	1.83	Predicted	58.1	9.80	1.12
								Observed	36.4	4.91	1.10
		m.d.						P/O ratio	1.60	2.00	1.02
								Geo. meanc	1.05	1.34	1.02d
								(95% CI)	(0.75–1.46)	(0.95–1.90)	(0.75–1.69)

m.d., multiple doses.

^aAUC_0–∞ and AUC_0–τ for single and multiple dose studies, respectively.

^bValue as reported in the original study, i.e., not obtained through Bayesian estimation.

^cGeometric mean of P/O ratios.

^dMedian (5th to 95th percentile) of P/O ratios.

On average for tablet and solution formulations, the geometric mean (95% CI) AUC and C_max P/O ratios were 0.99 (0.86–1.12) and 1.24 (1.09–1.40), respectively, and the median (5th to 95th percentile) for T_max was 1.11 (0.69–1.57). All predicted-versus-observed buprenorphine concentration-time profiles following sublingual administration are shown in Fig. 4. Predicted-versus-observed plots for AUC and T_max did not reveal a bias as data points were symmetrically distributed across the line of equality (Fig. 5). Similarly, dose-versus-P/O-ratio plots suggested an unbiased prediction of AUC and T_max across dose (Fig. 6), although clinical studies in which participants received sublingual solution were relatively few, and the dose range was smaller. Although comparison plots indicated a modest trend toward overpredicting C_max, especially for high doses, the PBPK model’s predictive performance of buprenorphine PK following sublingual administration seemed to overall be adequate for both formulations across a wide dose range in healthy volunteers.

Fig. 4.

PBPK model–predicted and observed concentration-time profiles of buprenorphine following sublingual (s.l.) administration. Blue solid line and shaded area represent the mean and 5th to 95th percentile range of the virtual population (n = 100), respectively. Open circles represent individual observations. Closed circles and whiskers represent mean and standard deviation of the observations, respectively. References for reported observations are provided in Tables 3 and 4. m.d., multiple doses.

Fig. 5.

Comparison plots between predicted and observed for the final sublingual buprenorphine PBPK model, showing PBPK model–based predicted versus observed (A) AUC (i.e., AUC_0–∞ and AUC_0–τ for single and multiple dose studies, respectively), (B) C_max, and (C) T_max. In each panel, the solid black line represents the line of equality, where grayscale dashed, dot-and-dash, and dotted lines represent 1.25-, 1.5-, and twofold prediction error ranges, respectively. Curved blue solid lines represent locally estimated scatterplot smoothing curves.

Fig. 6.

Comparison plots between dose and P/O ratio for the final sublingual buprenorphine PBPK model, showing dose versus the P/O ratio (A) AUC (i.e., AUC_0–∞ and AUC_0–τ for single and multiple dose studies, respectively), (B) C_max, and (C) T_max as listed in Tables 3 and 4. Sublingual tablet and solution doses are represented by diamonds and circles, respectively. In each panel, the solid black line represents the line of equality, where descending shades of blue filled areas represent 1.25-, 1.5-, and twofold prediction error ranges, respectively. Curved black dashed lines represent locally estimated scatterplot smoothing curves.

Discussion

This is the first study to describe dose- and formulation-dependent sublingual buprenorphine absorption across a wide dose range through PBPK modeling. The developed model will serve as a foundation to build a maternal-fetal PBPK model for buprenorphine, which can be used to explore the relationship between fetal buprenorphine exposure and the severity of NOWS postnatally. By integrating a novel description of nonlinear sublingual buprenorphine absorption, the model adequately predicted PK following administration of sublingual tablets and solution. First, the full PBPK model structure was successfully externally verified using published intravenous PK data. Subsequently, a total of 23 published PK studies not used for model development, in which 371 healthy volunteers received buprenorphine as either sublingual tablet or solution across a dose range of 2–32 mg, were used to verify the final PBPK model. Geometric mean P/O ratios of AUC, C_max, and T_max were close to unity and fell within the 1.25-fold prediction error range. Comparison plots between dose and P/O ratio indicated unbiased prediction of all PK parameters, except for C_max, which suggested a moderate trend toward overprediction, especially for high doses.

Previous studies have demonstrated nonlinear PK of sublingually administered buprenorphine (either as tablet or solution) across the entire dose range used for the management of OUD (Harris et al., 2004; Ciraulo et al., 2006; Dong et al., 2019). PK following intravenous administration, in contrast, is linear (Huestis et al., 2013), which strongly suggests that nonlinearity observed under sublingual dosing is driven by varying bioavailability rather than by changes in clearance. Various mechanisms have been proposed to explain nonlinear bioavailability, including varying dissolution degrees and times between tablet strengths (Harris et al., 2004), where high-dosed formulations may need to be kept in situ longer to allow maximal absorption, thereby increasing the risk of swallowing relatively more of the dose. In addition, buprenorphine sequesters in oral tissues (Cone et al., 1990), which decreases the concentration gradient that drives sublingual absorption of buprenorphine. The absorption model proposed in this study captures nonlinear bioavailability observed clinically. It is, however, important to note that the model was developed using PK data across a dose range of 2–32 mg (Schuh and Johanson, 1999; Harris et al., 2004; Dong et al., 2019). We caution against applying the absorption model outside this dose interval.

The developed PBPK model assumed the same lag time for both the tablet and solution. We investigated the lag time for the tablet and solution formulations by estimating it using concentration-time data from the 11 published PK studies. The results indicated no significant difference in estimated lag time between the formulations (tablet, 0.20 ± 0.09; solution, 0.17 ± 0.08; P = 0.37), indicating that using the same lag time for both tablet and solution is reasonable.

The developed PBPK model tended to underpredict the buprenorphine concentrations in the terminal elimination phase, where the discrepancy is particularly noticeable following intravenous administration (Fig. 2), which was consistent with the previous buprenorphine PBPK model reported by Kalluri et al. (2017). One possible explanation is the model's lack of consideration for enterohepatic recirculation, which is a significant limitation, particularly as buprenorphine is partially metabolized by UGTs, and its glucuronide conjugate can be reabsorbed after deconjugation by intestinal bacteria (McAleer et al., 2003). In addition, low observed concentrations might be influenced by assay variability as assay error is typically large near the lower limit of quantitation.

The developed model has a few limitations. First, Kp values used to describe the buprenorphine tissue distribution were obtained from rat data as there are no reports of buprenorphine Kp values for human tissues. More importantly, distribution in rats was not measured under strict steady-state conditions (Holland et al., 1989; Takahashi et al., 2001), which limits the robustness of the Kp values estimated in this study. Nevertheless, using these Kp values, observed concentrations were well captured by the PBPK model, and V_ss was furthermore calculated at 6.23 L/kg in Simcyp, which approximates 4.95 L/kg observed clinically (Kuhlman et al., 1996). It is important to acknowledge that in this clinical study, V_ss was derived from clearance multiplied by the mean residence time following an intravenous bolus injection, which may not accurately represent steady-state conditions, suggesting that the observed V_ss could be an estimate rather than a precise measurement. We explored using the Rodgers and Rowland (2006) method as an alternative to predict tissue distribution (method 2 in Simcyp), but this resulted in an estimated V_ss of 23.0 L/kg, which would necessitate the application of an empirically identified Kp scalar to recover the observed V_ss. Instead, we deemed distribution estimated from rat data to be more in line with the physiologic rationale of PBPK modeling. Furthermore, Takahashi et al. (2001) reported degrees of in vitro plasma protein binding in rats and humans of 88.9%–95.3% and 94.4%–96.7%, respectively, suggesting no interspecies differences. The buprenorphine concentrations in tissues were not verified in the present model as there were no available concentration-time data in human tissues, other than placenta, following sublingual administration of buprenorphine. Further clinical study investigating the buprenorphine tissue distribution in humans is warranted to verify the prediction of tissue concentrations, although the extensive verification in this study indicated the adequate prediction of the plasma concentration.

Another limitation is that the present model overestimates C_max modestly following sublingual administration of buprenorphine tablets and solution (geometric mean P/O ratios of 1.20 and 1.34, respectively). Manual parameter estimation of ideal proportion would preferably have yielded one and the same value to recover both observed AUC and C_max simultaneously for each dose, but ideal proportion values for AUC and C_max diverged, especially at the lower and upper limits of the dose spectrum (Fig. 3). This indicates an oversimplification of sublingual absorption in the current PBPK model. The model accounts for differences in the total transfer of buprenorphine across oral mucosa, but the rate of this process is likely variable across dose and formulation. Absorption rate differences were not integrated into the PBPK model, and AUC- and C_max-optimized nonlinear absorption models were instead averaged, leading to a modest overestimation of C_max overall. To understand the implication of this overestimation, it is worthwhile to briefly review the PK/PD relationship of buprenorphine and, specifically, the degree by which its PD effect is explained by C_max compared with AUC. Yassen et al. (2007) characterized the PK/PD relationship of buprenorphine in healthy volunteers with respect to its respiratory depressant effect, which is an unambiguous marker for buprenorphine’s penetration into the central nervous system and its receptor association/dissociation kinetics at the μ opioid receptor (Boom et al., 2012). They estimated the time required for concentration at the effect site to reach 50% of the plasma concentration for buprenorphine at 75.3 minutes (Yassen et al., 2007), which, relative to other opioids, indicates a slow onset of action but a longer duration, where its effect is only marginally driven by C_max (Upton et al., 1997). Since the developed PBPK model adequately predicts AUC following sublingual administration of buprenorphine, we believe the implications of modestly overestimating C_max are therefore limited. It is important to note, though, that we are not discounting the significance of C_max altogether, particularly as the primary determinants of buprenorphine-induced NOWS in the fetus remain unclear. Consequently, it is essential for the PBPK model to adequately predict all PK parameters and exposure metrics, enabling a thorough investigation into their association with NOWS severity.

In conclusion, the full PBPK model developed in this study is the first to adequately capture buprenorphine PK following sublingual administration (either as tablet or solution) across a wide dose range. The model provides valuable insights into the mechanisms that underly complex sublingual buprenorphine PK. Potential applications of the model include using it to optimize the treatment of OUD with buprenorphine, but for our group specifically, the model forms the basis for planned maternal-fetal PBPK modeling endeavors (van Hoogdalem et al., 2024). Improving the treatment of NOWS requires tailoring of pharmacotherapy based on the expected severity of withdrawal symptoms. Predicting fetal drug exposure prior to birth might better inform the severity of NOWS after birth than the maternal dose. Maternal-fetal PBPK modeling of buprenorphine facilitates estimation of prenatal buprenorphine exposure throughout gestation based on maternal intake, which opens the way for examining the likely link it has with postnatal withdrawal severity. This, in turn, could enable maternal-fetal PBPK model–informed precision dosing of buprenorphine, which is expected to improve the clinical outcomes of neonates affected by NOWS. The thoroughly verified PBPK model for buprenorphine developed in this study forms the fundament for this task.

Abbreviations

AAFE

absolute average-fold error

AFE

average-fold error

AUC

area under the curve

AUC_0–τ

area under the curve in one dosing interval

AUC_0–∞

area under the curve from zero to infinity

CI

confidence interval

CL

clearance

C_max

peak concentration

CYP

cytochrome P450

Kp

tissue-to-plasma partition coefficients

NOWS

neonatal opioid withdrawal syndrome

OUD

opioid use disorder

P/O

predicted and observed

PBPK

physiologically based pharmacokinetic

PD

pharmacodynamic

PK

pharmacokinetic

T_max

time to reach C_max

UGT

UDP-glucuronosyltransferase

V_ss

volume of distribution at steady state

Authorship Contributions

Participated in research design: van Hoogdalem, Vinks, Mizuno.

Conducted experiments: van Hoogdalem, Tanaka, Johnson, Mizuno.

Performed data analysis: van Hoogdalem, Tanaka, Johnson, Vinks, Mizuno.

Wrote or contributed to the writing of the manuscript: van Hoogdalem, Tanaka.