3.3 Validation 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 validated by
determining P/O ratios of AUC, CL/F, Cmax, and
Tmax following sublingual administration of
buprenorphine tablets and solution separately. For validation 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 to 54) with 419 concentration-time
profiles, were used (Table 3 ).25,27,29,52-54For all 16 PK studies, the P/O ratios of AUC, CL/F,
Cmax, and Tmax fell within the 2-fold
prediction error range. Geometric mean (95% CI) AUC, CL/F,
Cmax, and Tmax P/O ratios were 0.96
(0.82–1.12), 1.07 (0.92–1.24), 1.20 (1.05–1.37), and 1.07
(0.94–1.23), respectively.
For validation 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 to 42) with 81
concentration-time profiles, were used (Table
4 ).25,27,41,50 For all seven PK studies, the P/O
ratios of AUC, CL/F, and Tmax fell within the 2-fold
prediction error range. The P/O ratio for Cmax fell
within the 2-fold prediction error range in six out of seven (85.7%) PK
studies. Geometric mean (95% CI) AUC, CL/F, Cmax, and
Tmax P/O ratios were 1.05 (0.75–1.46), 0.98
(0.72–1.33), 1.34 (0.95–1.90), and 1.06 (0.79–1.41), respectively.
On average for tablet and solution formulations, the geometric mean
(95% CI) AUC, CL/F, Cmax, and Tmax P/O
ratios were 0.99 (0.86–1.12), 1.04 (0.92–1.18), 1.24 (1.09–1.40), and
1.07 (0.95–1.20), respectively. All predicted vs . observed
buprenorphine concentration-time profiles following sublingual
administration are shown in Supplementary Figure 2 . Predictedvs . observed goodness-of-fit plots for AUC, CL/F, and
Tmax did not reveal a bias, as data points were
symmetrically distributed across the line of equality (Figure
3 ). Similarly, dose vs . P/O ratio goodness-of-fit plots
suggested an unbiased prediction of AUC, CL/F, and Tmaxacross dose (Figure 4 ), although clinical studies in which
participants received sublingual solution were relatively few and the
dose range was smaller. Although goodness-of-fit plots indicated a
modest trend towards overpredicting Cmax, 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.
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
fetomaternal PBPK model for buprenorphine on, 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 validated 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
validate the final PBPK model. Geometric mean P/O ratios of AUC, CL/F,
Cmax, and Tmax were close to unity and
fell within the 1.25-fold prediction error range. Goodness-of-fits plots
indicated unbiased prediction of all PK parameters, except for
Cmax, which suggested a moderate trend towards
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.26,28,29 PK following intravenous administration,
in contrast, is linear,51 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,26 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,55which 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.23,26,28 We caution against
applying the absorption model outside this dose interval.
The developed model has a few limitations. Kp values used to describe
distribution of buprenorphine across various organs were obtained from
rat data38,40 and may therefore not capture human
physiology in all respects. More importantly, distribution in rats was
not measured under strict steady-state
conditions,38,40 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 the
volume of distribution at steady-state (Vss) was
furthermore calculated at 6.23 L/kg in Simcyp, which approximates 4.95
L/kg observed clinically.41 We explored using the
Rodgers and Rowland method as an alternative to predict tissue
distribution (method 2 in Simcyp),56 but this resulted
in an estimated Vss of 23.0 L/h, which would necessitate
the application of an empirically identified Kp scalar to recover the
observed Vss. Instead, we deemed distribution estimated
from rat data, albeit not measured under ideal steady-state conditions,
to be more in line with the physiological rationale of PBPK modeling.
Another limitation is that the present model overestimates
Cmax 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 Cmax simultaneously for each dose, but
ideal proportion values for AUC and Cmax diverged,
especially at the lower and upper limits of the dose spectrum
(Figure 2 ). 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 Cmax-optimized nonlinear absorption models were
instead averaged, leading to a modest overestimation of
Cmax 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 Cmax compared to AUC.
Yassen et al . characterized the PK/PD relationship of
buprenorphine in healthy volunteers with respect to its respiratory
depressant effect,57 which is an unambiguous marker
for buprenorphine’s penetration into the central nervous system (CNS)
and its receptor association/dissociation kinetics at the μ-opioid
receptor.58 They estimated the time required for
concentration at the effect site to reach 50% of the plasma
concentration (t1/2,ke0) for buprenorphine at 75.3
minutes,57 which, relative to other opioids, indicates
a slow onset of action, but a longer duration, where its effect is only
marginally driven by Cmax.59 Since the
developed PBPK model adequately predicts AUC following sublingual
administration of buprenorphine, we believe the implications of modestly
overestimating Cmax are therefore limited.
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 fetomaternal PBPK
modeling endeavors. Improving the treatment of NOWS requires tailoring
of pharmacotherapy based on the expected severity of withdrawal
symptoms. Fetomaternal PBPK modeling of buprenorphine facilitates
estimation of prenatal buprenorphine exposure throughout gestation based
on the maternal intake, which opens the way for examining the likely
link it has with postnatal withdrawal severity. This, in turn, could
enable fetomaternal PBPK model-informed precision dosing of
buprenorphine, which is expected to improve the clinical outcomes of
neonates affected by NOWS. The thoroughly validated PBPK model for
buprenorphine developed in this study forms the fundament for this task.