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Clinical Evaluation of Acetaminophen–Galgeuntang Interaction Based on Population Approaches

Galgeuntang (GGT), a traditional herbal medicine, is widely co-administered with acetaminophen (AAP) for treatment of the common cold, but this combination has not been the subject of investigation. Therefore, we investigated the herb–drug interaction between GGT and AAP by population pharmacokinetics (PKs) modeling and simulation studies. To quantify PK parameters and identify drug interactions, an open label, three-treatment, three-period, one-sequence (AAP alone, GGT alone, and AAP and GGT in combination) clinical trial involving 12 male healthy volunteers was conducted. Ephedrine (EPD), the only GGT component detected, was identified using a one-compartment model. The PKs of AAP were described well by a one-compartment model and exhibited two-phase absorption (rapid followed by slow) and first-order elimination. The model showed that EPD significantly influenced the PKs of AAP. The simulation results showed that at an AAP dose of 1000 mg × 4 times daily, the area under the concentration versus time curve of AAP increased by 16.4% in the presence of GGT compared to AAP only. In conclusion, the PKs of AAP were affected by co-administration of GGT. Therefore, when AAP is combined with GGT, adverse effects related to overdose of AAP could be induced possibly.


Introduction
Herbal medicines are widely used alone or in combination with synthetic drugs. Co-administration of herbal medicines and synthetic drugs may result in drug interactions, which could affect efficacy of treatment [1]. Indeed, a large number of over-the-counter combinations of synthetic and herbal drugs is used to treat mild conditions, despite the dearth of data on their interactions.

Participants
Twelve male healthy volunteers who met the inclusion and exclusion criteria participated in this study. The inclusion and exclusion criteria were provided in the Supplementary Material Table S1. All participants gave their informed consent before participating the study. The study was performed in accordance with the Declaration of Helsinki, and the protocol was approved by the Ethics Committee of Daejeon Korean Hospital of Daejeon University (Project identification no. DCDC_18_01, approved on 3 January 2018).

Clinical Trial
This open-label, three-treatment, three-period, one-sequence clinical trial involved 12 male healthy volunteers. Each participant received three treatments with a 7 ± 1-day washout period in-between. The treatment schedule was as follows: period 1, (G1) single-dose AAP 500 mg (2 tablets); period 2, (G2) combination of AAP 500 mg (2 tablets) and GGT 640 mg (12 tablets); and period 3, (G3) single-dose GGT 640 mg (12 tablets). A dose of 1000 mg AAP (equal to 2 tablets) was used in this study because in clinical practice, AAP is recommended at 1000 mg for the treatment of the common cold. To enhance efficacy of AAP, GGT is suggested in combination with AAP, and the maximum recommended dose of GGT is 12 tablets per day. Therefore, we applied this dose of GGT in our study.
After screening (days −28 to −1), participants underwent a baseline assessment (day 0). All participants fasted from 10 p.m. on the night prior to the day of drug administration. During period 1, participants were given the drug at 8 a.m. and resided in the study center for at least 7 h for sample collection. In periods 2 and 3, the subjects stayed in the center for at least 30 h for PK analysis. The study design is shown in Figure 1.

Participants
Twelve male healthy volunteers who met the inclusion and exclusion criteria participated in this study. The inclusion and exclusion criteria were provided in the Supplementary Material Table  S1. All participants gave their informed consent before participating the study. The study was performed in accordance with the Declaration of Helsinki, and the protocol was approved by the Ethics Committee of Daejeon Korean Hospital of Daejeon University (Project identification no. DCDC_18_01, approved on 3 January 2018).

Clinical Trial
This open-label, three-treatment, three-period, one-sequence clinical trial involved 12 male healthy volunteers. Each participant received three treatments with a 7 ± 1-day washout period in-between. The treatment schedule was as follows: period 1, (G1) single-dose AAP 500 mg (2 tablets); period 2, (G2) combination of AAP 500 mg (2 tablets) and GGT 640 mg (12 tablets); and period 3, (G3) single-dose GGT 640 mg (12 tablets). A dose of 1000 mg AAP (equal to 2 tablets) was used in this study because in clinical practice, AAP is recommended at 1000 mg for the treatment of the common cold. To enhance efficacy of AAP, GGT is suggested in combination with AAP, and the maximum recommended dose of GGT is 12 tablets per day. Therefore, we applied this dose of GGT in our study.
After screening (days −28 to −1), participants underwent a baseline assessment (day 0). All participants fasted from 10 p.m. on the night prior to the day of drug administration. During period 1, participants were given the drug at 8 a.m. and resided in the study center for at least 7 h for sample collection. In periods 2 and 3, the subjects stayed in the center for at least 30 h for PK analysis. The study design is shown in Figure 1.

Drug Quantification
Blood samples were analyzed by high-performance liquid chromatography-tandem mass spectrometry (Agilent 1100 HPLC; AB Science API2000). Analytes were detected by multiple reaction monitoring at 152. product m/z) for AAP, glycyrrhetic acid, (6)-shogaol, paeoniflorin, EPD, puerarin, and domperidone (internal standard), respectively. The calibration curves for AAP and EPD were linear at 50 to 10,000 ng/mL and 50 to 2500 ng/mL, respectively (R 2 > 0.99). If concentrations of AAP or EPD were measured outside of linear range, they would be diluted and re-measured to fit the calibration curves. The intra-day and inter-day accuracies and precisions of AAP and EPD was provided in Supplementary Materials Table S2. The analytical methods for (6)-shogaol and puerarin were developed with linear range of 100 ~ 2500 ng/mL and 50 ~ 2500ng/mL, respectively. However, both of components in GGT were detected under Limit of quantitation in whole plasma samples. Two remaining components, glycyrrhetic acid and paeoniflorin, were not detected in our plasma samples. The analytical column was a Gemini-C18 (5 µ m, 50 × 4.6 mm). The compounds were separated using a stationary mobile phase consisting of 0.5% formic acid and

Drug Quantification
Blood samples were analyzed by high-performance liquid chromatography-tandem mass spectrometry (Agilent 1100 HPLC; AB Science API2000). Analytes were detected by multiple reaction monitoring at 152. product m/z) for AAP, glycyrrhetic acid, (6)-shogaol, paeoniflorin, EPD, puerarin, and domperidone (internal standard), respectively. The calibration curves for AAP and EPD were linear at 50 to 10,000 ng/mL and 50 to 2500 ng/mL, respectively (R 2 > 0.99). If concentrations of AAP or EPD were measured outside of linear range, they would be diluted and re-measured to fit the calibration curves. The intra-day and inter-day accuracies and precisions of AAP and EPD was provided in Supplementary Materials Table S2. The analytical methods for (6)-shogaol and puerarin were developed with linear range of 100~2500 ng/mL and 50~2500ng/mL, respectively. However, both of components in GGT were detected under Limit of quantitation in whole plasma samples. Two remaining components, glycyrrhetic acid and paeoniflorin, were not detected in our plasma samples. The analytical column was a Gemini-C18 (5 µm, 50 × 4.6 mm). The compounds were separated using a stationary mobile phase consisting of 0.5% formic acid and methanol at a ratio of 20:80 v/v and a flow rate of 0.4 mL/min. Representative chromatograms of blank plasma, blank plasma Pharmaceutics 2020, 12, 1182 4 of 14 sample spiked with internal standard, standard samples of AAP and EPD, and a real plasma sample of AAP and EPD were provided in Supplementary Materials Figure S2.

Non-Compartmental PK Analysis
Non-compartmental PK analysis was performed using Phoenix WinNonlin (version 8.2.0.4383, Certera LP). The PK parameters were compared between the two groups by Mann-Whitney U-test (IBM SPSS Statistics Version 24). The level of statistical significance was set at α = 0.05 for all tests. The area under the concentration-time profile curve from zero to the last time point (AUC 0-t ) was calculated by the linear log trapezoidal method. Terminal rate constant (λ z ) was calculated by performing a set of linear regressions of the log(concentration)-time data using at least three sample points from the terminal portion of the curve. Terminal elimination half-life (t 1/2 ) was calculated as t 1/2 = ln(2)/λ z . The AUC from zero to infinity (AUC inf ) was derived as total AUC extrapolated to infinity using the terminal rate constant, AUC inf = AUC 0-t + C last /λ z , where C last is the last observed concentration. CL/F was calculated as dose ÷ AUC inf . The V/F was calculated as CL/F/λ z , where F is bioavailability.

Population PK Analysis
A population PK analysis was conducted by nonlinear mixed-effects modeling (NONMEM, version 7.4.1). PK parameters and interindividual and residual variabilities were estimated using first order conditional estimation with interaction. The model was modified in a sequential manner to identify that which best fit the data. The model was chosen based on the OFV and plots of goodness of fit. IIV was described using an exponential error model (Equation (1)): where P i represents estimate value of parameter P for ith individual, P pop represents typical value of parameter P at the population level, and η i is the IIV which describes the difference between individual and population value. η i was assumed to be normally distributed with mean of 0 and variance of ω 2 . Additive, proportional, and combination of additive and proportional error models were explored for residual variability and the proportional error model was chosen as the final residual variability model, since the other models were statistically insignificant (objective function value (OFV) increased 99.3 for additive model and combined-error model showed same OFV even though one more degree of freedom in comparison with proportional error model). Therefore, proportional error model was adopted in our study to describe the difference between observed and predicted values as below (Equation (2)): where C ij and C are the jth measured observation and prediction for the ith subject, respectively; E pij is the proportional random error which was assumed to have normal distribution with a mean of zero and a variance of σ 2 . After development of optimal AAP model, a covariate analysis was conducted to assess additional variables as determinants of the variability in the PK estimate. The co-administered drug (GGT) was considered a covariate. Covariate was tested using forward selection (p < 0.05) and backward elimination (p < 0.01) processes with likelihood ratio test to determine whether GGT affects the PKs of AAP. The effect of GGT on PKs of AAP was tested by linear, exponential, and power function models. The differences between OFV of each model and the base model were calculated. During forward selection, a covariate was selected if it showed at least a decrease of 3.84 in OFV. In backward elimination, an increase of at least 6.64 unit of OFV was set as criteria for retaining a covariate.
The final model was validated by VPC and nonparametric bootstrapping. The parameter estimates of the bootstrap samples were re-estimated and the median and 95% confidence intervals were compared with those estimated using the final model. For VPCs, the estimated parameter and Pharmaceutics 2020, 12, 1182 5 of 14 the final model were used to simulate 1000 data sets, and the observed data were overlaid on the simulated median and 90% prediction intervals.

Simulation Scenarios
To mimic the recommended dose based on the status of patients, AAP dose is suggested from 1000 mg to the maximum dose of 1000 mg × 4 times (8 tablets) per day for treatment of the common cold [22,23]. Twelve tablets of GGT 640 mg per day is the maximum recommended dose. Therefore, two simulation scenarios were used to evaluate the magnitude of any interaction, (AAP 1000 mg once daily + GGT 7680 mg once daily) and (AAP 1000 mg × 4 times daily + GGT 7680 mg once daily) in a week. The effect of GGT on the PKs of AAP was assessed by monitoring the AUC t , C max , and t 1/2 of AAP in the presence and absence of GGT. The median plasma concentration of AAP over time was plotted. The AUC t of one dose on day 7 was estimated using the linear log trapezoidal method. The magnitude of the influence of GGT on AAP was evaluated by calculating the ratio of AUC t of AAP when co-administered GGT to AUC t of AAP administered alone on day 7.

Non-Compartmental PK Analysis
Among the components of GGT, only EPD (Ephedra sinica) was detected under our analysis. Therefore, we investigated the interaction between AAP and EPD. Figure 2 shows the mean plasma concentration versus (vs.) time profiles of AAP administered alone (group 1, G1) and AAP co-administered with GGT (group 2, G2). Table 2 summaries PK parameters of AAP in the presence or absence of GGT according to non-compartmental analysis (NCA) results. The area under the concentration-time curve from time zero to infinity (AUC inf ), the maximum plasma concentration (C max ), the half-life (t 1/2 ), and volume of distribution (V/F) of AAP significantly decreased in G2 in comparison to those in G1 (p < 0.001).
Pharmaceutics 2020, 12, x FOR PEER REVIEW 5 of 15 were compared with those estimated using the final model. For VPCs, the estimated parameter and the final model were used to simulate 1000 data sets, and the observed data were overlaid on the simulated median and 90% prediction intervals.

Simulation Scenarios
To mimic the recommended dose based on the status of patients, AAP dose is suggested from 1000 mg to the maximum dose of 1000 mg × 4 times (8 tablets) per day for treatment of the common cold [22,23]. Twelve tablets of GGT 640 mg per day is the maximum recommended dose. Therefore, two simulation scenarios were used to evaluate the magnitude of any interaction, (AAP 1000 mg once daily + GGT 7680 mg once daily) and (AAP 1000 mg × 4 times daily + GGT 7680 mg once daily) in a week. The effect of GGT on the PKs of AAP was assessed by monitoring the AUCt, Cmax, and t1/2 of AAP in the presence and absence of GGT. The median plasma concentration of AAP over time was plotted. The AUCt of one dose on day 7 was estimated using the linear log trapezoidal method. The magnitude of the influence of GGT on AAP was evaluated by calculating the ratio of AUCt of AAP when co-administered GGT to AUCt of AAP administered alone on day 7.

Non-Compartmental PK Analysis
Among the components of GGT, only EPD (Ephedra sinica) was detected under our analysis. Therefore, we investigated the interaction between AAP and EPD. Figure 2 shows the mean plasma concentration versus (vs.) time profiles of AAP administered alone (group 1, G1) and AAP co-administered with GGT (group 2, G2). Table 2 summaries PK parameters of AAP in the presence or absence of GGT according to non-compartmental analysis (NCA) results. The area under the concentration-time curve from time zero to infinity (AUCinf), the maximum plasma concentration (Cmax), the half-life (t1/2), and volume of distribution (V/F) of AAP significantly decreased in G2 in comparison to those in G1 (p < 0.001).

Base Model
One-and two-compartment with first-order elimination and absorption were initially tested in development AAP model. The objective function values (OFV) of those models are listed in Table 3. One-compartment model gave an OFV of 1493. When two-compartment was applied, the OFV Pharmaceutics 2020, 12, 1182 6 of 14 increased by 34.6 units comparing to one-compartment model. Therefore, one-compartment was used in the next step.  Variety of absorption models was tested to describe absorption process of AAP. Gastric emptying (GE) was firstly modelled in absorption phase of AAP owing to the dependence of AAP absorption on rate of GE [24]. Another simple GE model was also taken into consideration due to sparse absorption data. In which, absorption phase was modelled with two periods, initially rapid absorbed (represented by k a-fast ) and followed by absorbed slowly (represented by k a-slow ). Results show that the greatest decrease of OFV was shown in the model with two periods of absorption phase. Therefore, this model was used in the covariate step and was considered the base model. Scheme of the base model is provided in Figure 3.

Base Model
One-and two-compartment with first-order elimination and absorption were initially tested in development AAP model. The objective function values (OFV) of those models are listed in Table 3. One-compartment model gave an OFV of 1493. When two-compartment was applied, the OFV increased by 34.6 units comparing to one-compartment model. Therefore, one-compartment was used in the next step.
Variety of absorption models was tested to describe absorption process of AAP. Gastric emptying (GE) was firstly modelled in absorption phase of AAP owing to the dependence of AAP absorption on rate of GE [24]. Another simple GE model was also taken into consideration due to sparse absorption data. In which, absorption phase was modelled with two periods, initially rapid absorbed (represented by ka-fast) and followed by absorbed slowly (represented by ka-slow). Results show that the greatest decrease of OFV was shown in the model with two periods of absorption phase. Therefore, this model was used in the covariate step and was considered the base model. Scheme of the base model is provided in Figure 3. One-compartment, first-order elimination, first-order absorption 1493 2 Two-compartment, first-order elimination, first-order absorption 1527 +34.6 1 3 One-compartment, first-order elimination + Gastric emptying pattern 1487 −5.73 1 4 One-compartment, first-order elimination + two-phase absorption (ka-fast + ka-slow) 1485 −7.94 1 ΔOFV, change in objective function value.

Covariate Model and Drug Interactions
In the covariate analysis, the effect of co-administration EPD on the principal PK parameters (apparent clearance (CL/F), absorption rate (k a-slow and k a-fast ), and volume of distribution (V/F)) of AAP  Table 4. EPD was identified as a significant covariate for V/F, k a-slow , and k a-fast of AAP. Linear equations were used to describe the effect of EPD on PKs of AAP as below (Equations (3)-(5)): where TVV, TVK a-fast , and TVK a-slow are the typical value of V/F, k a-fast , and k a-slow of AAP in the population without concomitant, respectively. COV V/F , COV Ka-fast , and COV Ka-slow represent the covariate on V/F, k a-fast , and k a-slow of AAP, respectively. Incorporation of EPD significantly reduced the interindividual variability (IIV) and OFV (p < 0.05). IIV of V/F and k a-slow was expressed as coefficient of variation, decreased from 16.9 to 0% and 22.9 to 0%, respectively. The final estimated parameters are listed in Table 5, and goodness of fit plots for the final AAP model are shown in Figure 4. Plots of population predicted concentrations (PRED) vs. observed concentration and individual predicted concentrations (IPRED) vs. observed concentration showed a symmetric distribution. In addition, in plots of conditional weight residual (CWRES) vs. PRED and CWRES vs. time, the plasma concentration showed a symmetry about CWRES = 0. Therefore, the model adequately described the observed plasma concentration.

Covariate Model and Drug Interactions
In the covariate analysis, the effect of co-administration EPD on the principal PK parameters (apparent clearance (CL/F), absorption rate (ka-slow and ka-fast), and volume of distribution (V/F)) of AAP was investigated. The criteria for selecting the final model are listed in Table 4. EPD was identified as a significant covariate for V/F, ka-slow, and ka-fast of AAP. Linear equations were used to describe the effect of EPD on PKs of AAP as below (Equations (3)-(5)): where TVV, TVKa-fast, and TVKa-slow are the typical value of V/F, ka-fast, and ka-slow of AAP in the population without concomitant, respectively. COVV/F, COVKa-fast, and COVKa-slow represent the covariate on V/F, ka-fast, and ka-slow of AAP, respectively. Incorporation of EPD significantly reduced the interindividual variability (IIV) and OFV (p < 0.05). IIV of V/F and ka-slow was expressed as coefficient of variation, decreased from 16.9 to 0% and 22.9 to 0%, respectively. The final estimated parameters are listed in Table 5, and goodness of fit plots for the final AAP model are shown in Figure 4. Plots of population predicted concentrations (PRED) vs. observed concentration and individual predicted concentrations (IPRED) vs. observed concentration showed a symmetric distribution. In addition, in plots of conditional weight residual (CWRES) vs. PRED and CWRES vs. time, the plasma concentration showed a symmetry about CWRES = 0. Therefore, the model adequately described the observed plasma concentration.

Model Evaluation
The parameter estimates and 95% confidence intervals for the parameters were calculated ( Table 5). All estimates obtained from the final model were comparable to the bootstrap estimates (n = 1000) and were within the 95% bootstrap confidence intervals. Figure 5 shows the result of visual predictive check (VPC) (n = 1000) for AAP. Overall, the VPC suggested that the final model adequately describes the distribution of AAP concentration. The simulated median represented the trend of the observed concentration. In addition, the majority of the observed values fell within the 90% prediction intervals.
Pharmaceutics 2020, 12, x FOR PEER REVIEW 9 of 15 = 1000) and were within the 95% bootstrap confidence intervals. Figure 5 shows the result of visual predictive check (VPC) (n = 1000) for AAP. Overall, the VPC suggested that the final model adequately describes the distribution of AAP concentration. The simulated median represented the trend of the observed concentration. In addition, the majority of the observed values fell within the 90% prediction intervals.

Simulation of Drug Interaction
Simulations were performed 1000 times using the developed model to assess the effect of GGT on PKs of AAP. AAP at 1000 once a day or 1000 mg × 4 times a day was administered in the presence Figure 5. Visual predictive check (VPC) plot of the final model for AAP observations. Empty circles: observed AAP concentration; pink area: 95% confidence intervals of median predicted concentration; gray areas: 95% confidence intervals of 5th and 95th percentile predicted concentration.

Simulation of Drug Interaction
Simulations were performed 1000 times using the developed model to assess the effect of GGT on PKs of AAP. AAP at 1000 once a day or 1000 mg × 4 times a day was administered in the presence or absence of GGT (7680 mg) daily. The drugs were given consecutively over 1 week. The result was provided in the Table 6. The median predicted AAP plasma concentrations are shown in Figures 6 and 7. AAP administered alone (1000 mg; Figure 6A) resulted in the following PK parameters: AUC t = 43,606 ng/mL h, C max = 10,872 ng/mL, and t 1/2 = 2.17 h. In the presence of GGT ( Figure 6B), the steady-state PK parameters of AAP were as follows: AUC t = 43,024 ng/mL h, C max = 9474 ng/mL, and t 1/2 = 4.69 h. The AUC of AAP in combination with GGT is comparable to that in group of AAP administered alone, which was unlikely to be clinically significant. Simulation of 1000 mg × 4 times per day of AAP administered alone yielded the following steady state PK parameters: AUC t = 40,940 ng/mL h, C max = 13,679 ng/mL, and t 1/2 = 2.17 h ( Figure 7A). When co-administered with GGT, the AUC t and t 1/2 increased to 42,854 ng/mL h and 2.8 h, respectively ( Figure 7B), while the predicted C max decreased to 13,149 ng/mL, comparing to AAP administered alone. PK parameters of AAP were as follows: AUCt = 43,024 ng/mL h, Cmax = 9474 ng/mL, and t1/2 = 4.69 h.
The AUC of AAP in combination with GGT is comparable to that in group of AAP administered alone, which was unlikely to be clinically significant. Simulation of 1000 mg × 4 times per day of AAP administered alone yielded the following steady state PK parameters: AUCt = 40,940 ng/mL h, Cmax = 13,679 ng/mL, and t1/2 = 2.17 h ( Figure 7A). When co-administered with GGT, the AUCt and t1/2 increased to 42,854 ng/mL h and 2.8 h, respectively ( Figure 7B), while the predicted Cmax decreased to 13,149 ng/mL, comparing to AAP administered alone.

Discussion
We investigated the effect of GGT on PKs of AAP in 12 healthy males using a population PK modeling approach. The PKs of AAP were best described by a one-compartment and first-order elimination and two-period absorption phases. EPD, the only component of GGT detected, was identified as a covariate in the model. The CL/F, V/F, ka-fast, and ka-slow of AAP were estimated to be 22.5 L/h, 16.3 L, 0.970 L/h, and 0.320 L/h when administered alone, and 22.5 L/h, 84.6 L, 7.60 L/h, and 0.0901 L/h when administered with GGT, respectively.
In our study, GE was applied to describe absorption process of AAP due to the dependence of AAP absorption on the rate of GE [24]. A biphasic GE pattern was modelled, in which a fraction of total administered drug (f1) rapidly reaches the systemic circulation (SC) in a short time (around 10-15 min), and later, the remaining fraction (f2) releases from the stomach to the small intestine and enters SC followed by mono-exponential model [25]. Therefore, we described the pattern in the model using MTIME options to make it simple (two periods of absorption phase). In which, f1 is quickly absorbed into SC with rapid absorption rate (ka-fast), and after the amount of time (MTIME), f2 enters SC with lower absorption rate (ka-slow). This model was confirmed to well describe absorption process of AAP than the others (e.g., transit absorption mode, lag time) in our study.
Since the dependence of AAP absorption on GE rate [24], absorption of AAP is susceptible to factors which can change GE rate, such as food or concomitant intake. In this study, for GGT 7680 mg, a total of 12 tablets were co-administered with AAP. Those of tablet intake was enough to stimulate gastro-intestinal (GI) mobility under fasting condition, so the ka-fast of AAP could be increased; however, it was not a clinically meaningful change because the absorption process effected by ka-fast would be ended in MTIME (=0.294 h) after drug administration. The ka-slow was decreased since the absorption process could be prolonged for GI stimulation by GGT intake [26]. It meant the residence time of drugs from the stomach to the small intestine was increased, so when AAP was co-administered with GGT, the absorption rate constant of AAP could be smaller by a prolonged absorption process than AAP administered alone.

Discussion
We investigated the effect of GGT on PKs of AAP in 12 healthy males using a population PK modeling approach. The PKs of AAP were best described by a one-compartment and first-order elimination and two-period absorption phases. EPD, the only component of GGT detected, was identified as a covariate in the model. The CL/F, V/F, k a-fast , and k a-slow of AAP were estimated to be 22.5 L/h, 16.3 L, 0.970 L/h, and 0.320 L/h when administered alone, and 22.5 L/h, 84.6 L, 7.60 L/h, and 0.0901 L/h when administered with GGT, respectively.
In our study, GE was applied to describe absorption process of AAP due to the dependence of AAP absorption on the rate of GE [24]. A biphasic GE pattern was modelled, in which a fraction of total administered drug (f 1 ) rapidly reaches the systemic circulation (SC) in a short time (around 10-15 min), and later, the remaining fraction (f 2 ) releases from the stomach to the small intestine and enters SC followed by mono-exponential model [25]. Therefore, we described the pattern in the model using MTIME options to make it simple (two periods of absorption phase). In which, f 1 is quickly absorbed into SC with rapid absorption rate (k a-fast ), and after the amount of time (MTIME), f 2 enters SC with lower absorption rate (k a-slow ). This model was confirmed to well describe absorption process of AAP than the others (e.g., transit absorption mode, lag time) in our study.
Since the dependence of AAP absorption on GE rate [24], absorption of AAP is susceptible to factors which can change GE rate, such as food or concomitant intake. In this study, for GGT 7680 mg, a total of 12 tablets were co-administered with AAP. Those of tablet intake was enough to stimulate gastro-intestinal (GI) mobility under fasting condition, so the k a-fast of AAP could be increased; however, it was not a clinically meaningful change because the absorption process effected by k a-fast would be ended in MTIME (=0.294 h) after drug administration. The k a-slow was decreased since the absorption process could be prolonged for GI stimulation by GGT intake [26]. It meant the residence time of drugs from the stomach to the small intestine was increased, so when AAP was co-administered with GGT, the absorption rate constant of AAP could be smaller by a prolonged absorption process than AAP administered alone.
In our population PK result, GGT increased V/F while it had no effect on CL/F of AAP, and sequentially resulted in an increase in t 1/2 of AAP. Our result about no effect on CL/F also confirmed with previous reports that GGT may have no effect on AAP hepatic metabolism. This result is likely consistent with the study of Lee et al. [27], in which the authors reported that GGT at 0-300 ug/mL had no effect on AAP metabolic enzymes (CYP3A4, CYP 1A2, CYP 2A6, CYP 2D6, CYP2E1). The increment of V/F by GGT could be explained by the fact that GE was increased by a prolonged absorption process. In addition, no effect on hepatic metabolism did not mean that no interactions in GI metabolism, the potential interaction between AAP and GGT in GI metabolism could be in GI metabolism. However, the limitation of knowledge of GGT or EPD on GI metabolism was we could not conclude about the potential interaction in GI. This would be promised future work to figure out exact mechanisms of interaction.
An increase in t 1/2 will lead to an increase in accumulation of plasma level if accumulation occurs after multiple dose regimen. If the successive dosage is administered before the previous doses are completely eliminated, plasma concentration will be accumulated. A drug is considered completely eliminated (around 97% of a drug) from body after five half-life [28]. In our simulation scenario of AAP 4000 mg per day (1000 mg × 4 times), dosing interval (6-h) is lesser than five times of t 1/2 of AAP in both G1 and G2, therefore accumulation occurs in both groups. The extent of drug accumulation is calculated as the following Equation (6) [29]: where AR is accumulation ratio, k is the terminal elimination rate constant, and tau is the dosing interval. According to this equation, AR is 1.18 and 1.63 in AAP alone group and combined group (AAP + GGT), respectively. The extent of drug accumulation in AAP alone group is lower than that of combined group. It results in an increase in AUC of AAP in combined group comparing to that in AAP alone group at dose of 1000 mg × 4 times per day with an increase of approximately 116.4% of AUC inf . This indicates an enhancement of efficacy and a greater risk of side effects as well. If > 4000 mg/day, severe liver injury can result [30], possibly because of saturation of sulfation and glucuronidation pathway in the liver. This increases hepatic NAPQI production and depletes NAPQI detoxification capacity [21], and eventually results in AAP-induced hepatotoxicity. Therefore, when co-administered with GGT, adverse effects related to overdose of AAP could be induced possibly.
A total of 1000 mg × 4 times per day of AAP was applied in the simulation scenario because it is the highest recommended dose of AAP for treatment of the common cold [22,23]. As reference, patients can use 1000 mg AAP every 6 h, and should not take more than 4000 mg in 24 h. In addition, AAP was reported to follow linear pharmacokinetics for doses of less or equal to 18 mg/kg [31]. Therefore, it is appropriate to extrapolate PKs of AAP 1000 mg × 4 times per day from AAP 1000 mg.
In addition to investigating the effect of EPD on PKs of AAP, we also checked the impact of AAP on PKs of EPD, in which AAP as perpetrator and EPD as victim. The NCA results and plot of concentration vs. time profile of EPD with/without AAP was provided in Supplementary Materials Table S3 and Figure S1, respectively. NCA results showed that there was no statistically significant difference between two groups, (EPD alone) and (EPD + AAP) (p > 0.05). Therefore, AAP was concluded to have no effect on PKs of EPD.
Pseudoephedrine (P-EPD), a stereoisomer of EPD, is widely combined with AAP in a fixed dose of many commercial products for treatment common cold, headache, fever, etc. [32]. P-EPD and EPD show a relatively similar in physiochemical properties, such as same solubility (8.26 mg/mL for both) [33,34], similar lipophilicity (logP = 1.13 for EPD [35], 0.89 for P-EPD [36]), etc. As physiochemical properties mainly govern PK properties of drugs in the body [37], PKs of P-EPD are comparable to PKs of EPD. As EPD has effects on PKs of AAP, P-EPD could have an interaction with AAP. Therefore, caution should be necessary when taking a combination of P-EPD and AAP, especially in multiple dosage regimen.
This study had several limitations. Movement of AAP from the stomach to the small intestine is a determinant of its absorption. In our study, subjects were fasted to exclude any effect of food on AAP absorption. However, food is typically consumed when a medicine is taken and the impact of food on AAP absorption should be taken into consideration. Moore et al. [38] reported that food delays the absorption of AAP. In the fed condition, the T max was 1.32-fold longer than in the fasted condition. In addition, the fed C max was 58% of the fasted C max . Further work is needed to investigate the influence of food on the absorption of AAP co-administered with GGT.

Conclusions
This study is the first study to describe the herb-drug interaction between GGT and AAP. The developed model is adequately described the PKs of AAP in presence or absence of GGT. Co-administered with GGT decreased k a-slow approximately 3.5 times and increased V/F and k a-fast approximately 5 and 8 times, respectively, comparing to AAP administered alone. Simulation results suggested that in the presence of GGT, the change in PKs of AAP was is unlikely to be clinically significant at AAP 1000 mg, however, at high doses (≥4000 mg AAP per day) the interaction will become worse and caution should be taken. Further study should be carried out to investigate such interactions in diverse populations and different conditions (for example, fed condition), to broaden representation.

Supplementary Materials:
The following are available online at http://www.mdpi.com/1999-4923/12/12/1182/s1, Figure S1: Comparison of plasma concentration-time profiles of ephedrine after administration alone or co-administration with acetaminophen (AAP). Each point represents the mean and standard deviation. EPD, ephedrine, Figure S2: Representative chromatogram of blank plasma (A), blank plasma spiked with internal standard (B), standard sample of AAP at dose of 2 µg/mL (C), standard sample of EPD at dose of 0.5 µg/mL (D), real sample of AAP at 3 h after administration combination of AAP and Galgeuntang (GGT) (E), real sample of EPD at 3 h after administration combination of AAP and GGT (F), Table S1: Inclusion and exclusion of participants enrolling clinical trial, Table S2: Intra-day and inter-day of accuracies and precisions of AAP and EPD, Table S3: NCA results of PK parameters of EPD.