Population pharmacokinetic modeling
Figure S1 illustrates the time-plasma concentration profiles of morniflumate, which served as the input data for modeling. Oral absorption of morniflumate occurred rapidly within 0.5 h after administration, with multiple absorption steps occurring over the course of approximately 2 h. Table S2 shows the pharmacokinetic parameters of morniflumate obtained through NCA. The mean Tmax of morniflumate was 1.33 h, indicating fast absorption, whereas T1/2 and MRT were relatively short at 4.04 and 4.91 h, respectively. Additionally, a large V/F of 1412.77 L suggested extensive in vivo distribution of morniflumate, whereas the large CL/F of 289.64 L/h suggested that the in vivo elimination of morniflumate was quite high.
The structure of the morniflumate population pharmacokinetic model could be described as a two-compartment model with five sequential first-order absorption. A significant improvement in model fit (reduction of \(-\)2LL; p < 0.05 and/or 0.01) was observed in the two-compartment model versus the one-compartment as the primary compartment. However, in the models with three compartments or more, an increase in the total number of parameters resulted in higher \(-\)2LL values. Consequently, the plasma morniflumate concentration profiles could be explained by the distribution in the central and peripheral compartments of the body with two velocity phases. Several structural absorption compartment models such as the Tlag reflection, the non-sequential two absorption model (applying two or more absorption points and accounting for bioavailability), and the sequential absorption model (applying two or more absorption rate constant parameters between successive absorption compartments) have been used to describe multiple absorption patterns. The application of the Tlag reflection and non-sequential two absorption model was limited to account for the multiple absorption patterns of morniflumate and increased \(-\)2LL compared to the basic model, which has only one absorption rate constant parameter for oral absorption. On the other hand, the application of the sequential absorption model significantly improved GOF plots with significant model improvement (reduction of \(-\)2LL; p < 0.05 and/or 0.01). A total of five sequential absorption compartments were incorporated, and further increases in compartment number did not yield significant model improvements. For the residual error model, a log additive error model was found to be suitable, resulting in a substantial reduction in \(-\)2LL of approximately 90% while maintaining the total number of parameters. Other residual error models such as additive, power, and mixed models led to significant increases in \(-\)2LL compared to the proportional error model used in the basic model. The IIVs in the pharmacokinetic parameters of morniflumate were assessed using an exponential error model, as shown in the following equation: Pi = Ptv · exp(ŋi), where ŋi is the random variable for the ith individual, which was normally distributed with a mean of 0 and a variance ω2, Pi is the parameter value of the ith individual, and Ptv is the typical value of the population parameter. Through step-by-step validation of the need to consider each parameter IIV related to model improvement (i.e., reduction of model complexity), IIV was considered only for Vp/F, CLp/F, Ka1, Ka2, Ka3, Ka4, and Ka5. The inclusion of IIVs in Vc/F and CLc/F did not result in significant model improvement with changes in the number of parameters (changes of \(-\)2LL; p > 0.05 and/or 0.01). Here, Vc and Vp represent the volumes of distribution of morniflumate in the central and peripheral compartments, respectively, whereas CLc and CLp represent the morniflumate clearance in the central and peripheral compartments, respectively. Ka1, Ka2, Ka3, Ka4, and Ka5 were the absorption rate constants between each absorption compartment (dosing depot-to-depot 2, depot 2-to-depot 3, depot 3-to-depot 4, depot 4-to-depot 5, depot 5-to-central compartment) in the multiple oral absorption of morniflumate, with F denoting the bioavailability upon oral administration. Figure 1 illustrates the pharmacokinetic model structure of morniflumate established in this study, and Table S3 summarizes the steps taken for establishing the morniflumate pharmacokinetic model structure. Several physiological and biochemical parameters measured during clinical trials were considered as candidate covariates to explain the IIV in the pharmacokinetics of morniflumate. Effective covariates were identified through a stepwise covariate exploration approach. This approach consisted of sequentially applying or removing candidate covariates to the model parameters with IIV and assessing the significance of objective function value (OFV) changes. Significant correlations were confirmed through forward selection and backward elimination of covariates for model parameters, and the standard p values were set at 0.05 and 0.01, respectively. Finally, BMI variability was considered as an effective covariate related to Vp/F in the description of morniflumate pharmacokinetic IIVs. Although BSA diversity also showed a significant correlation (reduction of OFV; p < 0.05 and/or 0.01) with Vp/F, the impact of BMI was relatively more influential in reducing the OFV. Moreover, simultaneous covariate reflection of BMI and BSA on Vp/F was not significant when the reduction in OFV (p > 0.05 and/or 0.01) was taken into account as the number of parameters increased, and the GOF plots did not confirm the visual improvement of the model. The reflection of the candidate covariates explored in this study for the CLp/F, Ka1, Ka2, Ka3, Ka4, and Ka5 parameters did not result in significant model improvement (changes of OFV; p > 0.05 and/or 0.01). Particularly, although BMI and GFR were suitable when applied as forward selection criteria (reduction of OFV; p < 0.05) when included as covariates for CLp/F, they were not significant in the backward elimination process (increase of OFV; p > 0.01). The steps taken to incorporate potential covariates into the established morniflumate basic population pharmacokinetic model parameters and associated results are summarized in Table S4. The formula for the final established population pharmacokinetic model parameters of morniflumate is as follows:
$$\frac{\text{V}\text{c}}{\text{F}} = \text{t}\text{v} \frac{\text{V}\text{c}}{\text{F}}$$
$$\frac{\text{C}\text{L}\text{c}}{\text{F}} = \text{t}\text{v} \frac{\text{C}\text{L}\text{c}}{\text{F}}$$
\(\frac{\text{V}\text{p}}{\text{F}}\) = tv \(\frac{\text{V}\text{p}}{\text{F}}\) · (BMI/median BMI)^dVp/FdBMI · exp(ŋVp/F)
\(\frac{\text{C}\text{L}\text{p}}{\text{F}}\) = tv \(\frac{\text{C}\text{L}\text{p}}{\text{F}}\) · exp(ŋCLp/F)
Ka1 = tv Ka1 · exp(ŋKa1)
Ka2 = tv Ka2 · exp(ŋKa2)
Ka3 = tv Ka3 · exp(ŋKa3)
Ka4 = tv Ka4 · exp(ŋKa4)
Ka5 = tv Ka5 · exp(ŋKa5)
where tv represents the typical values and dVp/FdBMI is the degree of correlation between Vp/F and BMI. The parameter values of the final population pharmacokinetic model of morniflumate are summarized in Table 1.
Table 1
Parameter values of the established population pharmacokinetic model for morniflumate.
Parameter | Estimate | Standard error | Relative standard error (%) | Shrinkage (%) | Interindividual variability (%) |
tvVc/F (L) | 110.88 | 26.98 | 24.33 | | |
tvCLc/F (mL/h) | 10.38 | 6.26 | 60.37 | | |
tvVp/F (L) | 10033.78 | 908.82 | 9.06 | | |
tvCLp/F (L/h) | 378.36 | 39.61 | 10.47 | | |
tvKa1 (1/h) | 9.89 | 3.08 | 31.10 | | |
tvKa2 (1/h) | 22.79 | 3.00 | 13.16 | | |
tvKa3 (1/h) | 23.71 | 2.83 | 11.94 | | |
tvKa4 (1/h) | 4.72 | 1.18 | 25.13 | | |
tvKa5 (1/h) | 0.68 | 0.07 | 10.46 | | |
dVp/FdBMI | 2.37 | 0.62 | 26.00 | | |
ε | 0.30 | 0.02 | 6.45 | | |
ω2Vp/F | 0.01 | 0.01 | 36.43 | 30.01 | 11.74 |
ω2CLp/F | 0.35 | 0.12 | 32.94 | 1.28 | 59.55 |
ω2Ka1 | 0.00 | 0.00 | 8.43 | 49.57 | 1.87 |
ω2Ka2 | 0.86 | 0.04 | 4.57 | 26.92 | 92.60 |
ω2Ka3 | 0.87 | 0.04 | 4.02 | 26.98 | 93.35 |
ω2Ka4 | 0.92 | 0.32 | 34.43 | 17.39 | 96.13 |
ω2Ka5 | 0.02 | 0.01 | 50.13 | 24.65 | 13.13 |
tv: typical value. |
dVp/FdBMI: correlation between the body mass index and the distribution volume of the peripheral compartment. |
Vc/F, distribution volume of the central compartment; CLc/F, clearance from the central compartment; Vp/F, distribution volume of the peripheral compartment; CLp/F, movement rate between the central and peripheral compartments; Ka1, absorption rate constant from morniflumate dosing depot to depot 2; Ka2, absorption rate constant from depot 2 to depot 3; Ka3, absorption rate constant from depot 3 to depot 4; Ka4, absorption rate constant from depot 4 to depot 5; Ka5, absorption rate constant from depot 5 to central compartment. |
Model qualification
Figure S2 illustrates the GOF plot results of the morniflumate population pharmacokinetic model established in this study. The morniflumate concentration values predicted by the population pharmacokinetic model of morniflumate at both the population or individual levels showed relatively good agreement with the experimentally obtained observations. The conditional weighted residuals (CWRES) were symmetrically distributed with respect to zero. That is, CWRES were well distributed at random without any visible bias. Moreover, the CWRES values across all points of predicted concentration or time in the population did not deviate from ± 4. Quantile–quantile (QQ) plots of the components of CWRES and weighted residuals (WRES) exhibited a close approximation to a straight line where the X- and Y-axes were symmetrical (within ± 6 ranges). Therefore, the GOF plot results (Figure S2) confirmed that the final population pharmacokinetic model of morniflumate had no graphically significant problems. The bootstrapping results for the established morniflumate population pharmacokinetic model are summarized in Table S5. All of the parameter values estimated in the final morniflumate model were within the 95% confidence interval of the bootstrap analysis results (1000 replicates). The model parameter estimates closely matched the median estimated by bootstrap analysis, with differences remaining within 10%. This confirmed the robustness and reproducibility of the final morniflumate population pharmacokinetic model established herein. The NPDE analysis results are presented in Fig.S3. The assumption of a normal distribution for the differences between predictions and observations of morniflumate pharmacokinetics was acceptable. The QQ plots and histogram further confirmed the normality of the NPDE. Moreover, the NPDE results over time and the predicted values were relatively symmetric with respect to zero (within ± 4 ranges). Figure 2 illustrates the VPC results of the morniflumate population pharmacokinetic model. The majority of the observation values (> 90% of all data) for morniflumate pharmacokinetics were well within the 95% confidence intervals of the prediction values. These findings suggested that the population pharmacokinetic model adequately described the overall experimental data. Furthermore, the established model was externally validated using an additional dataset (Cho et al., 2013) of morniflumate administration and the VPC results are presented in Fig. S4. Our findings confirmed that all mean observations reported (Cho et al., 2013) not only overlapped within the 95% confidence interval of the predicted values but were also relatively well distributed within the 50% predicted region. This suggested that the established population pharmacokinetic model of morniflumate reasonably described not only the internal dataset but also the external pharmacokinetic dataset (Cho et al., 2013) without bias. Moreover, our results indirectly demonstrated the versatility of the morniflumate population pharmacokinetic model established in this study and its potential for extended clinical applications. Overall, the final established population pharmacokinetic model of morniflumate exhibited an acceptable level of performance without any major issues.
Expansion to the pharmacometrics model of niflumic acid
The established and validated population pharmacokinetic model structure and parameter values of morniflumate were fixed as representative values of the population, after which they were expanded into models for predicting the pharmacokinetics-pharmacodynamics of niflumic acid. The model was extended using previously reported mean plasma concentration profiles of niflumic acid according to exposure to morniflumate (Cho et al., 2013) and LTB4 synthesis inhibition data (Civelli et al., 1991) according to plasma concentration of niflumic acid. This was an effective approach that could be used to expand the model to niflumic acid, as only the plasma concentration of morniflumate was measured for each subject in the morniflumate bioequivalence test. Figure 1 illustrates the extended structure from the morniflumate population pharmacokinetic model to the pharmacokinetic-pharmacodynamic model for niflumic acid. Some of the substances cleared from the central compartment to the metabolite compartment are transformed into niflumic acid, and the niflumic acid concentrations in the metabolite compartment are structured to lead to the effect compartment (for simulating inhibition of LTB4 synthesis). The differential equation of the metabolite compartment was as follows:
\(\frac{\text{d}{\text{C}}_{\text{m}}}{\text{d}\text{t}}=(\frac{\text{C}\text{L}\text{c}}{\text{F}}\bullet {\text{C}}_{\text{c}}\) )/\({\text{V}}_{\text{m}}-{\text{K}}_{\text{e}}\bullet {\text{C}}_{\text{m}}\)
where Cm and Vm represent the concentration and the apparent volume of distribution of niflumic acid in the metabolite compartment, respectively, Cc is the concentration of morniflumate in the central compartment, Ke is the rate constant for excretion from the metabolite compartment as various metabolite forms, including morniflumate and/or niflumic acid.
Figure 3 shows the population-level mean morniflumate and niflumic acid plasma concentration profiles predicted using the extended morniflumate-niflumic acid pharmacokinetic model and the fitting results with the observed values (following oral exposure to 700 mg morniflumate). The observed mean plasma concentrations (Cho et al., 2013) of morniflumate and niflumic acid aligned reasonably well with the model-predicted population means. Additionally, in the case of niflumic acid, most of the observations fell within the 95% confidence interval for the mean value predicted by the model. This suggested that the extended pharmacokinetic model of morniflumate-niflumic acid developed in this study could accurately predict the mean population pharmacokinetic profiles of morniflumate and niflumic acid (according to morniflumate exposure) at relatively acceptable levels.
To combine the response in the effect compartment with the concentration of niflumic acid in the metabolite compartment, we applied a sigmoid Emax model with baseline (Dutta et al., 1996, Knechtle et al., 2021). The formula is as follows:
\(\text{E}={\text{E}}_{0}+(\frac{{\text{E}}_{\text{m}\text{a}\text{x}}\bullet {{\text{C}}_{\text{m}}}^{{\gamma }}}{{{\text{E}\text{C}}_{50}}^{{\gamma }}+ {{\text{C}}_{\text{m}}}^{{\gamma }}}\) )
where E represents the percent (%) of LTB4 synthesis inhibition, E0 is the basal LTB4 synthesis inhibitory effect percent (%) without niflumic acid, Emax represents the maximal effect percent (%) of inhibition of LTB4 synthesis by niflumic acid in plasma, EC50 is the concentration of niflumic acid in plasma required to achieve half of the Emax, and γ represents the sigmoidicity factor related to the steepness of the profile. When selecting the pharmacodynamics model, several direct and indirect response models were sequentially applied to explain the niflumic acid mean plasma concentration and LTB4 synthesis inhibition data to ensure reasonable interpretation and optimal data fitting. During model fitting, the quantitative indicators of AIC and \(-\)2LL served as the basis for assessing the suitability of the pharmacodynamics model. The optimized typical values of the pharmacodynamic model parameters E0, Emax, EC50, and γ were 0.06%, 58.45%, 20.08 µg/mL, and 5.38, respectively. Figure 4 illustrates the LTB4 synthesis inhibition according to plasma niflumic acid concentration predicted by the model and the fitting results of the observed values. All of the observations (Civelli et al., 1991) aligned well with the mean values of the model predictions and fell within the 95% confidence interval. These findings suggested that the sigmoid Emax model with baseline established in this study could accurately explain the inhibition of LTB4 synthesis in response to changes in plasma niflumic acid concentration. Fig. S5 shows the inhibition profile of LTB4 synthesis in the population mean over time after oral exposure to 700 mg of morniflumate, which was predicted using the established morniflumate-niflumic acid pharmacometrics model. After a single oral exposure to morniflumate, the maximum inhibitory effect on LTB4 synthesis was observed at approximately 2–4 h, and rapidly decreased thereafter, with almost no effects observed at 6–8 h.
Model simulation and quantitative prediction
Model simulations were conducted to assess the impact of the selected effective covariates on the final established morniflumate population pharmacokinetic model based on numerical changes and reflections. BMI was identified as a covariate of Vp/F and model simulations were performed using the mean, median, maximum, and minimum values of the observed BMI data within the group. This comprehensive evaluation aimed to validate the pharmacokinetic-pharmacodynamic outcomes of morniflumate and niflumic acid, which were predicted according to changes in covariates explored with our newly developed morniflumate population pharmacokinetic model. The mean, median, maximum, and minimum values of observed BMI within the group were 22.26, 21.89, 28.41, and 17.36 kg/m2, respectively. Fig. S6 shows the simulation results of the population pharmacokinetic model of single oral administration of morniflumate (700 mg) according to the variations in BMI. As the BMI value increased, the plasma morniflumate concentrations of the population decreased, whereas as the BMI value decreased, the plasma morniflumate concentrations of the population increased. Figure 5 shows the comparison of the pharmacokinetic profiles of morniflumate and niflumic acid with group means after a single oral exposure to 700 mg of morniflumate according to BMI values. Higher BMI values were associated with lower plasma concentrations of morniflumate and niflumic acid, as well as a reduction in the inhibition of LTB4 synthesis and a shorter drug effect duration. This suggests that morniflumate may be less effective in individuals with high BMI compared to those with normal BMI (BMI, 1998).
Furthermore, multiple oral exposure simulations of morniflumate (based on the assumption of linear kinetics) revealed differences in the mean plasma concentrations of morniflumate at steady-state according to changes in BMI values. Figure 6 shows a comparison of the pharmacokinetic profiles of morniflumate and niflumic acid with group means after multiple oral exposures to 700 mg of morniflumate according to BMI values. Higher BMI levels were associated with lower plasma concentrations of morniflumate and niflumic acid, reduced inhibition of LTB4 synthesis, and shorter duration of drug effect compared to relatively lower BMI groups. Additionally, the variability in the pharmacokinetic-pharmacodynamic profiles of morniflumate and niflumic acid tended to increase with higher BMI values. These findings suggest that individuals with lower BMI may achieve stable therapeutic concentrations and maintain the drug effect for a longer duration after oral exposure to morniflumate.
Figure 7 compares the steady-state plasma concentrations of morniflumate and niflumic acid and the inhibition of LTB4 synthesis after multiple oral exposures to morniflumate in response to changes in BMI. There were no significant differences (p > 0.05) in the steady-state plasma concentrations of morniflumate and niflumic acid, as well as the inhibition of LTB4 synthesis between groups with mean and median BMI values. This may be because the mean and median BMI values established during the model simulation were 22.26 and 21.89 kg/m2, respectively, and there was no large difference between the two values. However, the mean plasma concentrations of morniflumate and niflumic acid between the two groups with mean and median BMI were 1.06 and 1.09 µg/mL and 72.71 and 75.20 µg/mL, respectively, which were higher in the group with median BMI. The differences in the steady-state plasma concentrations of morniflumate and niflumic acid and the inhibition of LTB4 synthesis between the groups with maximum and minimum BMI values were significant (p < 0.05). The plasma concentrations of morniflumate and niflumic acid at steady-state in the two groups with the maximum and minimum BMI values were 0.66 and 1.77 µg/mL and 45.63 and 121.58 µg/mL, respectively, which represented a 2.66–2.68-fold difference. A 57.15% and 58.50% difference in the mean inhibition of LTB4 synthesis in steady-state was observed between the two groups with the maximum and minimum BMI values, respectively, and the variability between the maximum and minimum effects was 6.06 and 0.01%, respectively, which translated to an extremely large 606-fold difference. Table 2 compares the plasma concentrations of morniflumate and niflumic acid according in response to changes in BMI values at steady-state after multiple oral exposures to morniflumate, as well as the distribution of the predicted LTB4 synthesis inhibition results. Our findings suggested that lower BMI values significantly increased the mean plasma levels of morniflumate and niflumic acid in a steady-state could, whereas LTB4 synthesis remained strongly inhibited with low variability.
Table 2
Comparison of morniflumate and niflumic acid plasma concentrations and leukotriene B4 (LTB4) synthesis inhibitory values at steady-state (156–168 h; following multiple oral exposures to 700 mg morniflumate at 12 h intervals) according to body mass index (BMI) predicted using the proposed morniflumate-niflumic acid pharmacometrics model.
Covariate application | Morniflumate concentrations | Morniflumate concentration fluctuation a | Niflumic acid concentrations | Niflumic acid concentration fluctuation a | Inhibition of LTB4 synthesis | LTB4 synthesis inhibition fluctuation a |
Mean BMI | 0.85–1.64 µg/mL (1.06 µg/mL) | 47.96% | 58.96–96.05 µg/mL (72.71 µg/mL) | 38.61% | 58.33–58.49% (58.44%) | 0.28% |
Median BMI | 0.89–1.67 µg/mL (1.09 µg/mL) | 46.99% | 61.32–98.45 µg/mL (75.20 µg/mL) | 37.72% | 58.36–58.49% (58.44%) | 0.23% |
Max BMI | 0.48–1.26 µg/mL (0.66 µg/mL) | 61.92% | 33.28–69.91 µg/mL (45.63 µg/mL) | 52.40% | 54.89–58.44% (57.15%) | 6.06% |
Min BMI | 1.52–2.31 µg/mL (1.77 µg/mL) | 34.25% | 105.30–143.26 µg/mL (121.58 µg/mL) | 26.50% | 58.50–58.50% (58.50%) | 0.01% |
a Fluctuation was calculated as the ratio of the maximum value to the difference between the maximum and minimum values in each distribution. |
The mean, median, max, and min BMI were 22.26, 21.89, 28.41, and 17.36 kg/m2, respectively. |
The values in parentheses in the table represent the mean values in each distribution. |