DataBOW-001 (Ranolazine)

The details of the BOW-001 study have been previously described [7]. Briefly, this was a phase 1, open-label, crossover study to evaluate the effect of posaconazole on the pharmacokinetics of ranolazine in 27 subjects with normal-weight (N = 14) and obesity (N = 13). Posaconazole was administered with a continental breakfast of at least 350 cal as a 300 mg delayed-release tablet twice on study day 2, and once a day on the mornings of study days 3–15. The CYP3A victim drug, ranolazine, was administered as a 500 mg extended-release tablet on the mornings of study days 1, 15, 18, 22, 25, and 29. Pharmacokinetic (PK) samples were taken for posaconazole pre-dose on study days 2, 5, 8, 12, and 15, and prior to the administration of ranolazine on study days 18, 22, 25, and 29. One additional posaconazole sample was taken 5 h after the posaconazole dose on study day 15 for approximate determination of the maximum plasma concentration (Cmax) of posaconazole. Ranolazine PK samples were taken pre-dose and at 1, 2, 4, 6, 8, 12, 18, 24, and 32 h post-dose on study days 1, 15, 18, 22, 25, and 29. The study included healthy volunteers of 18–50 years (inclusive) and body mass index (BMI) of 35 kg/m2 or greater for the obesity cohort and 18.5–24.9 kg/m2 (inclusive) for the normal-weight cohort. In total, the study included 14 subjects with BMI 18–24.9 kg/m2 (50% male/female) and 13 subjects with obesity (4 male, 9 female).

BOW-002 (Lurasidone)

The details of the BOW-002 study have also been previously described [8]. Briefly, this trial was a phase 1, open-label, crossover study to evaluate the effect of posaconazole on the pharmacokinetics of lurasidone in 24 subjects with normal-weight (N = 11) and obesity (N = 13). Posaconazole was administered with a continental breakfast of at least 350 cal as a 300 mg DRT twice on study day 4, and once daily on the mornings of study days 5–17. The CYP3A victim drug, lurasidone, was administered as a 20 mg tablet with food on the mornings of study days 1, 14, 20, 23, 26, and 30. Posaconazole PK samples were taken pre-dose on study days 4, 7, and 11, and prior to the administration of lurasidone on study days 14, 20, 23, 26, and 30. Additional posaconazole PK samples were taken 5 h after posaconazole administration on study day 17 and on study day 33. Lurasidone PK samples were taken pre-dose and at 1, 2, 3, 4, 8, 12, 18, 24, 48, and 72 h post-dose on study days 1, 14, 20, 23, 26, and 30. The study inclusion criteria were identical to BOW-001, with healthy volunteers ages 18–50 (inclusive) and BMI of 35 kg/m2 or greater for the obesity cohort or 18.5–24.9 kg/m2 (inclusive) for the normal-weight cohort. In total, the study included 11 subjects with BMI 18–24.9 kg/m2 (6 male, 5 female) and 13 subjects with obesity (6 male, 7 female).

Data handling

Data from the BOW trials were evaluated for consistency with the dataset and potentially excluded for the following reasons: 1) the value was inconsistent, either with other values for the individual or with the chronological sequence of study procedures, and could not be resolved through the query resolution process, 2) values without adequate identifying information to allow reasonable and unique assignment as a subject observation and 3) values associated with a documented error in drug administration, specimen collection, specimen handling, or bioanalytical procedures, if the error(s) were reasonably expected to result in spurious data. Plasma concentrations below the lower limit of quantification (LLOQ) were treated as missing values for the purposes of pharmacokinetic analyses; the LLOQ values for posaconazole, ranolazine, and lurasidone were 1 ng/mL, 5 ng/mL, and 0.25 ng/mL, respectively. For some graphical representations of plasma concentrations at corresponding times, values below the LLOQ were entered as the LLOQ.

Individual, clinical, and demographic covariate factors were included in the population data set. Wherever possible and necessary, missing covariates were imputed using established methods.

Data for submodel verification and validation

In the absence of additional clinical data beyond BOW-001 and BOW-002 to support the development of the PBPK submodels for posaconazole, lurasidone, and ranolazine, data were digitized from published literature using WebPlotDigitizer [13]. For posaconazole, IV data from Kersemaekers et al. [14] were digitized and used to inform estimates for intrinsic clearance. For ranolazine submodel verification, IV and oral data were digitized from Moss et al. [15] and Tan et al. [16], respectively. For lurasidone submodel verification, oral data from Hu et al. [17] and Findling et al. [18] were used.

Chemical data

A minimal set of physicochemical and biochemical data were required for PBPK modeling of all compounds analyzed. This included the following information: molecular weight, log of octanol:water partition coefficient (logP), blood:plasma concentration ratio (BP), and a measure of clearance. Physicochemical values were found in the literature or available online resources [19,20,21,22,23,24,25,26,27,28,29], and used to estimate partition coefficients (Kps) using published in silico prediction methods by either Poulin and Theil [30, 31] or Berezhkovskiy [32].

Physiological data and virtual population

Individual anthropometric data and mean physiological parameters are often used to scale individual physiological parameters informing PBPK modeling. Mean physiological parameters and estimates of variability in tissue volumes, blood flows, tissue composition, and regional enzyme expression were curated from publicly available sources [21, 22, 33,34,35,36,37,38,39,40].

For modeling purposes, a virtual population of 1000 individuals was generated by repeatedly generating individuals described by a target range of ages, body weights, heights, and BMIs, and a specified percentage of females and males (i.e., 50% each). To avoid sampling subjects with unrealistic physiological parameters, boundaries around individual covariates were set based on the observed extrema of the BOW studies. Briefly, age- and sex-specific physiological parameters (e.g., tissue volumes and blood flows) for standard individuals were generated, and then a target body weight, height, and BMI were used to select appropriate individuals from the National Health and Nutrition Examination Survey (NHANES) dataset [33]. Based on the selected sex, baseline physiological parameters were obtained from the International Commission on Radiological Protection (ICRP) references values. The values were then scaled using linear interpolation of target anthropometric values using height against mean values obtained in the NHANES data to obtain the final subject-specific physiological parameters. A summary of the demographic information (age, weight, height, BMI, sex) for the virtual population used for simulations is provided in the Supplementary Table 1.

Software and optimization

Data manipulation and visualization were conducted in using version 4.2.2 of R [41], a data analysis language suitable for use in regulated environments. Model development and simulation were executed using the mrgsolve package for R [42]. All code was maintained using the version control system Subversion (http://subversion.apache.org/). All analyses were conducted on a computer grid with multiple computer nodes. Each node ran the linux operating system that utilized the Intel® Fotran compiler (version 12.0.4 for linux).

Parameter estimation was performed using the new unconstrained optimization with quadratic approximation (newuoa) function from the nloptr [43] package in R using an extended least squares objective function. Parameters that were optimized using digitized data from the literature were done so by fitting the parameters to a single “typical” individual matching the study demographic parameters (i.e. height, weight, age, sex) wherever available. In the absence of such data, a “typical” individual was assumed to be a 30-year-old male with a height of 1.76 m and weight of 73 kg. Parameter uncertainty was assessed either based on the Hessian matrix from parameter fitting or by bootstrapped analysis using 200 randomly sampled replicant populations generated from resampling the original BOW study data (with replacement) in the normal weight and obesity cohorts, refitting the parameters to the selected populations, and estimating the coefficient of variation (CV%) across the replicate populations.

Submodel developmentGeneral model structure

Individual whole-body PBPK submodels describing the PK of posaconazole and CYP3A victim drugs were adapted from a voriconazole model described in Elmokadem et al. [44]. Discrete compartments describing adipose, bone, brain, large intestine, small intestine, heart, kidney, liver, lung, muscle, spleen, stomach, and skin tissues, as well as venous and arterial blood were included. Absorption into tissue compartments assumed perfusion-limited kinetics, and first-pass clearance effect were included in using correct representation of vasculature connection between the gastrointestinal tract organs and the liver. A compartment for intestinal lumen was included, and biliary excretion into the small intestine from the liver was included as either as a discrete or continuous process. Clinical profiles for all drugs were better predicted when a specialized compartment representing a peripheral sampling site was included in the model and subsequently all parameter estimation and model predictions reference the plasma concentrations in the peripheral sampling site as opposed to venous blood concentration.

Since the goal of the final model is to create a unified structure capable of describing posaconazole, lurasidone, and ranolazine, some compound-specific extensions were added to the general model. These extensions include saturable metabolic pathways and proper representation of formulation-dependent absorption mechanisms (ranolazine). A schematic of the unified PBPK model structure, modeling workflow, and description of the model equations are provided in the Supplementary Information.

DDI kinetics

After validating the individual submodels, a single model consisting of duplicate whole-body PBPK compartments for tracking posaconazole and an interchangeable victim substrate (i.e., ranolazine or lurasidone) was created. Initial attempts to capture the inhibition of CYP3A metabolism for the victim substrates assumed simple competitive (i.e., reversible) inhibition in the liver and the gut in response to posaconazole concentrations in the respective tissues. These assumptions led to consistent over-predictions of the recovery of CYP3A metabolism in the victim substrates after posaconazole was discontinued. As a result, a time-dependent inhibition (TDI) model was incorporated, which required additional equations tracking CYP3A enzyme abundance. Synthesis and degradation parameters for CYP3A were available in the literature [23,24,25,26,27, 29, 45], and the parameters for inactivation of CYP3A by posaconazole (kinact) and the dissociation constant between posaconazole and CYP3A (Ki) were estimated using a two-step approach. First, a coarse two-dimensional grid representing a range of values for kinact and Ki was created (0.3–3 µg/mL), and simulations corresponding to the study protocols was used while scanning over points in this grid. The geometric mean-fold error (GMFE, calculated as \(^\left(\frac\right)\right|)}\)) for the predicted and observed area under the concentration–time curve extrapolated to infinity (AUCinf) was computed for each timepoint, and the kinact and Ki associated with the minimum fold error was identified. Second, the estimated Ki value was fixed and a finer grid search for kinact (0.1–0.15 h−1) was performed to further fine-tune the estimate. It is important to note that the parameters for kinact and Ki are not victim-drug specific, but were optimized to capture the observed DDIs as perpetrated by posaconazole.

Verification and validation

For the drug submodels and unified DDI model, verification and validation (V&V) activities were performed in a manner consistent with the risk-informed credibility framework described in Kuemmel et al. [46]. Given the contexts of use for this model to 1) characterize the duration and magnitude of potential DDIs stemming from posaconazole washout and 2) characterize the relative duration and extent of washout DDIs in patients with obesity (PwO) compared to normal-weight controls, the model V&V was conducted assuming a high value of model influence and decision consequence. As such, the verification (e.g., correctness of implementation of model code and accuracy of underlying software and algorithms) and validation (e.g., accuracy of the overall model and assumptions, and ability to answer the specific questions of interest) were conducted to high degrees of rigor. Model performances were validated quantitatively using GMFE and qualitatively using visual predictive checks comparing the virtual cohorts to the clinical data observed in the BOW studies. Individual drug PBPK submodels were further qualified via box plots of the GMFE distributions to support adequacy of the underlying models.

To demonstrate consistency between the model predictions and observations, the GMFE was calculated for AUC, Cmax, and Tmax with a conservative GMFE between 1 and 2 indicating acceptable model performance in both the model calibration and validation phases for both victim drugs (e.g. lurasidone and ranolazine). For posaconazole, as the clinical data from BOW-001 and BOW-002 were sparsely sampled and given the purpose of the model to capture DDIs with or after stopping posaconazole, the submodel was calibrated and validated by demonstrating a GMFE between 1 and 2 for AUC and half-life. Given the role of posaconazole as the perpetrator drug at steady-state and during washout, properly characterizing AUC and half-life was deemed fit for the purposes of the current model.

The integrated PBPK model characterizing interactions between posaconazole and ranolazine or lurasidone was also validated using strict criteria for GMFE between 1 and 2 for the predicted vs. observed AUCinf and Cmax of the victim drug in the normal-weight and obesity cohorts on BOW-001 study days 15, 18, 22, 25, and 29 for ranolazine and BOW-002 study days 14, 20, 23, 26, and 30 for lurasidone. GMFE values grouped by weight cohort and PK measurement for each drug were plotted against the unity line with a twofold error band to qualitatively demonstrate the validity of the model.