Methods
Study design
The PBPK modeling was conducted in PK-Sim® (version 11.0, part of the Open Systems Pharmacology suite), which has a system- and drug-dependent component. The simulated trials were conducted in virtual healthy adult and pediatric population groups. For adults, healthy volunteers between 18 and 60 years were selected. Virtual pediatric subjects were aged 0-18 years and divided into 5 groups: 0-1 years, 1-3 years, 5-8 years, 8-12years, 12-18 years. All simulations were performed with virtual population of 100 individuals. The proportion of female was the default 0.5 in each simulation. Both p.o. and i.v. administration of VRCZ were simulated in healthy adults and pediatrics.
PBPK model establishment and validation of TAC
General physiochemical properties (molecular weight, LogP, compound type, pKa) of TAC and in vitro data from blood, plasma protein were utilized for building the PBPK model [13-15]. System-dependent physiological parameters (organ volumes, blood flow rates, hematocrit, etc.) were provided in PK‐Sim® with the small molecule model. The input parameters for specific intestinal permeability were optimized using the PK profiles of single 5mg TAC in healthy subjects. According to the clinical routine drug regimens, a simulation of TAC was performed at a single dosage of 2 mg for adults. The predictive performance was evaluated by visually comparing predicted concentration-time data with the observed data from the literature for initial verification
[16]. Predicted concentration-time profiles were obtained using the developed PBPK model of TAC. Observed concentration–time data were obtained in graphical form using GetData Graph Digitizer version 2.25.0.32. The ratio of predicted to observed pharmacokinetics (PK) values was used to evaluate model performance. Next, the quantitative assessment was conducted by calculating the mean fold error (MFE) of PK parameters such as the area under the plasma concentration-time curve (AUC) and maximum concentrations (Cmax), expressed as the ratio of predicted to observed mean values. The model was acceptable if it met the 0.5- to 2.0-fold limit. After model validation, the adult PBPK model was scaled to children (pediatric PBPK model). Drug-specific parameters defined in the adult PK data were kept constant for the pediatric PBPK model. The physiological parameter values for pediatric individuals were taken from the PK-Sim population database. The PBPK model performance in pediatrics was evaluated using the quantitative verification described in adult model verification[17].
PBPK model establishment and validation of VRCZ
Drug-specific physicochemical properties were obtained from the literature [18, 19]. Organ-plasma partition coefficients were determined using Poulin and Theil’s method based on the literature [20]. The model was verified with clinical data of adults and pediatrics in different formulations[21, 22]. The PBPK model performance in children was evaluated using the quantitative verification described in TAC model verification.
DDI simulations of TAC and VRCZ in adults and pediatrics
The DDI of TAC combined with VRCZ in different formulations and different dosing regimens were simulated in adults and pediatrics. Verified PBPK models were used to predict the DDI using PK-Sim®. The dosage and dosing interval of TAC and VRCZ were prescribed on the basis of the clinical routine drug regimens. The detailed dosage regimens are shown in Table 1. DDI simulations were performed in turn following these dosing schedules.
Sensitivity Analysis
Sensitivity of the DDI between TAC and oral VRCZ to single parameters (local sensitivity analysis) was calculated as relative change of AUC using the Sensitivity Analysis tool implemented in PK-Sim®. Sensitivity analysis was performed applying a relative perturbation of 1000 % (variation range 10.0, maximum number of 9 steps). Parameters selected for the sensitivity analysis fulfilled one of the
following criteria: (1) optimized; (2) related to optimized parameters; (3) a strong influence in the model. Sensitivity to a parameter was calculated as the ratio of the relative change of the simulated AUC to the relative variation of the parameter around its value used in the final model according to the Eq. (1):
\begin{equation} S=\frac{AUC}{\text{AUC}}\bullet\frac{P}{P}\nonumber \\ \end{equation}
where S = sensitivity of the simulated AUC0–24 to the examined model parameter value, ∆AUC= change of the simulated AUC0–24, AUC = simulated AUC0–24 with the original parameter value, ∆p = change of the examined parameter value, p = original parameter value. A sensitivity value of +1.0 means that a 10% change in the examined parameter causes a 10% alteration of the predicted AUC.