The present model was based on a minimal PBPK model for buprenorphine developed earlier by our group [15], which, in turn, was adapted from a model described by Johnson et al. [33]. The minimal PBPK model was expanded to a full PBPK model by incorporating tissue-to-plasma partition coefficients (Kp). Kp values were estimated using tissue distribution data in rats generally measured between 1 and 144 hours following subcutaneous injection of radiolabeled buprenorphine [38, 40]. 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.
Following expansion to a full PBPK model, first-order absorption models were optimized using buprenorphine concentration-time profiles reported by Dong et al. [28] to describe sublingual absorption of buprenorphine. As the sublingual route of administration is not available in Simcyp, sublingual absorption was mimicked by employing the first-order inhalation model in combination with the inhaled route of administration as described previously [15]. In this inhalation model, the proportion of the dose inhaled equals the proportion sublingually absorbed. The remaining fraction is swallowed.
Linear regression modeling of sublingual absorption
Concentration-time data were extracted from dose-escalation [23, 26] and dose-linearity [28] studies (training data) using WebPlotDigitizer (v4.5, Ankit Rohatgi, Pacifica, CA). Area under the curve (AUC; i.e., AUC0– ∞ and AUC0–τ for single and multiple dose studies, respectively) and peak concentration (Cmax) following sublingual tablet or solution administration were determined through Bayesian estimation by fitting the buprenorphine population PK model reported by Moore et al. [46] to these extracted concentration-time profiles using MWPharm++ (v2.0.4; Mediware Incorporated, Prague, Czech Republic). Subsequently, the proportion of the dose to be sublingually absorbed in the PBPK model to exactly recover the AUC and Cmax observed in the clinical trial (i.e., ideal proportion) was determined by reviewing PBPK model-based predicted geometric mean AUC and Cmax under various degrees of sublingual absorption. The relationship between AUC- and Cmax-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 (Equation 1):
1) Proportioni = α + β × Dose
where Proportioni is the AUC- or Cmax-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 untransformed or with Dose, Proportioni, 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 Cmax-optimized ideal proportions vs. sublingual tablet and solution doses). The linear model achieving the highest mean coefficient of determination (R2) across the four individual relationships was selected. AUC- and Cmax‑optimized linear models were subsequently averaged, 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 validation and evaluation
Following an extensive literature search for buprenorphine PK data in healthy volunteers, the PBPK model’s predictive performance was assessed for intravenous and sublingual administration successively by determining the ratio between predicted and observed (P/O ratio) AUC, clearance (CL) or apparent clearance (CL/F), Cmax, and, in case of sublingual administration, time to reach Cmax (Tmax). All data used for model validation 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. 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. For virtual trials in which buprenorphine was sublingually administered, a coefficient of variation (CV) of 33.9% was applied to the administered dose to reflect variability in bioavailability, which is consistent with the average variation observed by Bullingham et al. [47]. 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 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 Cmax following intravenous administration. Instead, Cmax generally represented the first concentration (Cfirst) measured few minutes after completion of a bolus injection (Tfirst). Therefore, to match predicted and observed Cmax, predicted Cmax was defined as the modeled concentration at Tfirst.
For clinical studies in which buprenorphine was sublingually administered, observed PK parameters were, similarly to described for linear regression modeling, obtained through Bayesian estimation by fitting the buprenorphine population PK model reported by Moore et al. [46] to concentration-time data extracted from publications using WebPlotDigitizer. Reported PK parameter values were not used, as some studies employed limited sampling strategies, which limited the robustness of time-associated (i.e., Tmax and Cmax) and exposure-dictated (i.e., AUC and CL/F) 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 vs. observed AUC, CL/F, Cmax, and Tmax and dose vs. respective P/O ratio goodness-of-fit 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 PK parameter P/O ratios falling within the wider 2-fold prediction error range was determined.
RESULTS
Validation of the PBPK model’s predictive performance following intravenous administration
The structure of the full PBPK model was first externally validated by determining P/O ratios of AUC0–∞, CL, and Cmax 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 to 66.8 years) with 89 concentration-time profiles, were used for intravenous model validation (Table 2) [41, 47-51]. For all 12 PK studies, the P/O ratios of AUC0–∞, CL, and Cmax, fell within the 2-fold prediction error range. Geometric mean (95% CI) AUC0–∞, CL, and Cmax 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 vs. observed buprenorphine concentration-time profiles following intravenous administration are shown in Figure 2.