Introduction

Piroxicam is a non-steroidal anti-inflammatory drug used to alleviate symptoms of osteoarthritis and rheumatoid arthritis (Weintraub et al. 1977; Dessain et al. 1979). Piroxicam reduces the synthesis of prostaglandins via inhibition of both cyclooxygenase-1 (COX-1) and cyclooxygenase-2 (COX-2) (Berg et al. 1999; Blanco et al. 1999). The most common adverse events of piroxicam are nausea, constipation, flatulence, abdominal pain, and diarrhea (Pfizer 2016). The risk of serious cardiovascular adverse events, including myocardial infarction and stroke, and serious gastrointestinal adverse events such as bleeding, ulceration, and perforation are increased by piroxicam (Dean 2019). It should be used for the shortest possible duration at the lowest effective dose (Pfizer 2016).

Piroxicam is primarily metabolized to 5’-hydroxypiroxicam by cytochrome P450 2C9 (CYP2C9) (Brogden et al. 1981). CYP2C9 is involved in the metabolism of various clinically used drugs, including glipizide (Kim et al. 2022), losartan (Bae et al. 2011b, 2012), meloxicam (Bae et al. 2011a; Lee et al. 2014), and S-enantiomer of warfarin (Rettie et al. 1992). CYP2C9 is genetically polymorphic and approximately 85 allele variants for CYP2C9 (CYP2C9*1B to CYP2C9*85) have been identified to date (https://www.pharmvar.org/gene/CYP2C9). Among them, CYP2C9*2 (rs1799853, c.430C > T, p.Cys144Arg) and *3 (rs1057910, c.1075A > C, p.Ile359Leu) alleles are the most common variants with overall frequency of 9.14% and 6.37% worldwide, respectively (Daly et al. 2017). These allele variants show impaired enzyme activity toward a number of substrates both in vitro and in vivo (Tang et al. 2001; Kirchheiner et al. 2004; Choi et al. 2012; Lee et al. 2015; Wang et al. 2015; Kim et al. 2017). Tracy et al. (2002) demonstrated that the CYP2C9*3 allele variant reduces enzyme activity for 5’-hydroxylation of piroxicam in vitro. Perini et al. (2005) reported significantly higher exposures and lower clearances for piroxicam in individuals carrying CYP2C9*2 or CYP2C9*3 alleles compared to homozygous CYP2C9*1 allele in vivo. Especially, exposure and half-life (t1/2) in the CYP2C9*3/*3 genotype were increased by 5.31- and 8.75-fold compared to the CYP2C9*1/*1 genotype, respectively (Perini and Suarez-Kurtz 2006). In vivo studies presented notable differences not only in the pharmacokinetics but also pharmacodynamics of piroxicam according to CYP2C9 genetic polymorphism (Perini et al. 2005; Perini and Suarez-Kurtz 2006). The drug label for piroxicam recommends the dose reduction in CYP2C9 poor metabolizers (CYP2C9PM) because they may have abnormally high plasma levels (Pfizer 2016). These studies suggest that responses of piroxicam could be varied according to the genetic polymorphism of CYP2C9.

Physiologically based pharmacokinetic (PBPK) modeling is a mechanistic approach for the prediction of the pharmacokinetics of drugs (Zhuang and Lu 2016; Kim et al. 2018). It is a useful tool to guide dose adjustment in various clinical scenarios such as pediatric populations (Yellepeddi et al. 2019; Verscheijden et al. 2020), pregnancy (Abduljalil and Badhan 2020; Coppola et al. 2021), organ impairments (Suri et al. 2015; Heimbach et al. 2021), and the effects of genetic polymorphisms (Rüdesheim et al. 2020; Cho et al. 2021a; Jung et al. 2021; Xu et al. 2021). Previously, PBPK models for several NSAIDs including celecoxib (Kim et al. 2021), flurbiprofen (Loisios-Konstantinidis et al. 2020), and meloxicam (Cho et al. 2021b) were established in different CYP2C9 genotypes. However, the piroxicam PBPK model related to CYP2C9 genetic polymorphism has not been reported. In this study, we developed and validated the PBPK model for piroxicam in the populations carrying the most two common CYP2C9 allele variants.

Methods

Software and data source

PBPK model of piroxicam was developed and validated using PK-Sim® version 10.0 (Bayer AG, Leverkusen, Germany). Previously published concentration–time profiles were digitized with Engauge Digitizer® version 12.1 (https://markummitchell.github.io/engauge-digitizer/) according to the proposed digitization algorithm in Wojtyniak et al. (2020). Pharmacokinetic parameters which were not obtained from the publications were estimated via non-compartmental analysis (NCA) with the BA Calc 2007 analysis program (MFDS, Cheongju, Republic of Korea).

Previous publications were extensively investigated to obtain information on the absorption, distribution, metabolism, and excretion (ADME) process, physicochemical characteristics, and clinical pharmacokinetic data for piroxicam. In this study, we only gathered the clinical studies in which the administration of piroxicam was an oral route. Among the collected clinical pharmacokinetic data, only two articles contain pharmacogenomic data (Perini et al. 2005; Perini and Suarez-Kurtz 2006). The data of the two articles were used for model development and the others were used for model validation. Information on the collected clinical data for the development and validation of the PBPK model is presented in Table 1.

Table 1 Clinical studies used for the development and validation of the piroxicam PBPK model
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Model building

The “middle-out” strategy was used for the PBPK model building. The physicochemical parameters were obtained from drug databases or previous studies. The specific intestinal and organ permeabilities were calculated in the software (Thelen et al. 2011, 2012; Hindmarsh et al. 2021). Fraction metabolized by CYP2C9 (fm, CYP2C9) was estimated as 81.1% using the area under the plasma concentration–time curve from 0 to infinity (AUCinf ) values in CYP2C9*1/*1 and CYP2C9*3/*3 genotypes (Perini and Suarez-Kurtz 2006) based on previously reported methods (Ito et al. 2005; Huang et al. 2017). In the estimation, it was assumed that CYP2C9*1/*1 and CYP2C9*3/*3 genotypes are translated into CYP2C9 extensive metabolizer (CYP2C9EM) and CYP2C9PM phenotypes, respectively. The turnover number (kcat) was optimized to capture the estimated fm, CYP2C9 value and Michaelis–Menten constant (Km) obtained from Tracy et al. (2002) was used. The reference concentration of CYP2C9 was 3.84 μmol/L (Rodrigues 1999). Relative expression values in each organ were obtained from the reverse transcription-polymerase chain reaction (RT-PCR) data (Nishimura et al. 2003; Nishimura and Naito 2005, 2006). Renal clearance value was determined to capture the profile of cumulative excretion as unchanged form in urine within the ranges presented in Ishizaki et al. (1979). Dissolution times (80% dissolved) were adjusted based on dissolution profiles in biorelevant media (Li et al. 2019). Partition coefficients and cellular permeabilities were estimated as Schmitt and PK-Sim® standard methods, respectively (Schmitt 2008; Hindmarsh et al. 2021). kcat values were optimized in different CYP2C9 genotypes based on the previous pharmacogenetic studies (Perini et al. 2005; Perini and Suarez-Kurtz 2006). Parameter optimization was performed as the Levenberg–Marquardt algorithm in the PK-Sim® software. The PBPK model was developed for the different populations and dose regimens in the development dataset and verified using the validation dataset. Clinical studies without information on CYP2C9 genotype were assumed that all subjects of the studies were carrying homozygous CYP2C9*1 allele.

Sensitivity analysis

Sensitivity analysis was performed in the PK-Sim® software. In the analysis, a total of 861 parameters were assessed for AUCinf and maximum plasma concentration (Cmax). The sensitivity was calculated by the following Eq. 1.

$${\text{S}} = \frac{{\Delta {\text{PK}}}}{{{\text{PK}}}} \div \frac{{\Delta {\text{ p}}}}{{\text{p}}}$$
(1)

where \(S\) is the sensitivity, \(PK\) is the initial values of the pharmacokinetic parameter, \(\Delta PK\) is the change of the pharmacokinetic parameters from initial values, \(p\) is the initial values of the assessed input parameter, and ∆p is the change of assessed input parameters from initial values, respectively. A sensitivity of + 1.0 indicates that + 10% change of an assessed input parameter causes + 10% change of the predicted pharmacokinetic parameters.

Model evaluation

The PBPK model was evaluated using visual and numerical methods. Observed plasma concentration–time profiles were graphically compared with the predicted profiles by plotting the geometric mean and 5th to 95th percentiles for a virtual population (n = 100). Demographic ranges for virtual populations were adjusted to be similar to those of the observed population. If the age and proportion of female (%) range had not been obtained from the clinical studies, it was assumed as 19 to 65 years and 50%, respectively. Others were generated via the implemented algorithm in the PK-Sim® software. The standard deviation for the reference concentration of CYP2C9 was assigned as 1.15 μmol/L to reflect moderate variability (30% of the mean). The PBPK model was numerically evaluated by comparing observed and predicted AUC, Cmax, and t1/2 values. A two-fold error range was used as the acceptance criterion for the model. In other words, the PBPK model could be justified if the fold error (predicted value divided into observed value) is within the 0.5–2 range. Geometric mean values for virtual populations were used as predicted values and reported values in clinical studies or estimated values based on the NCA were used as observed values. Lastly, the overall performance of the PBPK model was evaluated via a goodness-of-fit plot for the predicted versus observed plasma concentrations. Average fold error (AFE), absolute average fold error (AAFE), and root mean square error (RMSE) were used to evaluate the prediction accuracy and precision, respectively. AFE, AAFE, and RMSE were calculated according to Eqs. (2–4).

$${\text{AFE}} = { }10^{{\frac{1}{{\text{N}}}\sum {\text{log}}\left( {\frac{{{\text{Predicted}}}}{{{\text{Observed}}}}} \right)}}$$
(2)
$${\text{AAFE}} = { }10^{{\frac{1}{{\text{N}}}\sum \left| {{\text{log}}\left( {\frac{{{\text{Predicted}}}}{{{\text{Observed}}}}} \right)} \right|}}$$
(3)
$${\text{RMSE}} = { }\sqrt {\frac{{\sum \left( {{\text{Predicted}} - {\text{Observed}}} \right)^{2} }}{{\text{N}}}}$$
(4)

Results

A total 54 of clinical data were collected. Clinical trial data of various doses, administration period, and age of subjects were included. Most of the clinical studies recruited healthy subjects, but several clinical studies targeted patients with osteoarthritis or rheumatoid arthritis. Data of two pharmacogenomic studies (Perini et al. 2005; Perini and Suarez-Kurtz 2006) were used for development of PBPK model.

The summary of input parameters for the PBPK model is presented in Table 2. The fraction unbound (fu) value was adjusted to be 0.01% lower value than the minimum value of Blocka et al. (1988) to capture the plasma-concentration time profiles more accurately. Simulation for the individual PBPK model after the administration of 20 mg single oral dose properly captured not only the plasma concentration–time profiles but also the metabolized and excreted fractions (Fig. 1). The estimated volume of distribution (Vd) was 0.15 L/kg which is almost consistent with the previously reported value (0.14 L/kg) (Pfizer 2016).

Table 2 Summary of input parameters used in the piroxicam PBPK model
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Fig. 1
figure 1

Predicted and observed plasma concentration–time profiles of piroxicam after a single oral dose of piroxicam 20 mg. Solid, dashed, and dotted lines indicate predicted plasma concentration, fraction excreted to urine, and fraction metabolized by CYP2C9, respectively. The open circles and error bars indicated observed mean and standard deviation (or standard error), respectively. Observed plasma concentration and fraction excreted to urine data were obtained from Perini et al. (2005) and Ishizaki et al. (1979), respectively. Fraction metabolized by CYP2C9 data was estimated based on Perini and Suarez-Kurtz (2006)

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Predicted plasma concentration–time profiles in different CYP2C9 genotypes were visually similar to the observed profiles (Fig. 2). Predicted AUCinf in CYP2C9*1/*2, CYP2C9*1/*3, and CYP2C9*3/*3 genotypes were 1.83-, 2.07-, and 6.43-fold higher than CYP2C9*1/*1 genotype, respectively, and significant differences for predicted Cmax in different CYP2C9 genotypes were not identified (1.89–1.96 μg/mL) (Table 3) (Fig. 3). In addition, PBPK model overall accurately described and predicted the plasma concentration–time profiles in pediatric, adult, and geriatric populations who received a single or multiple-dose regimens (Fig. 4). All fold error values for AUC, Cmax, and t1/2 were included in the acceptance criterion with the ranges of 0.57–1.59, 0.63–1.39, and 0.65–1.51, respectively (Table 3).

Fig. 2
figure 2

Predicted and observed plasma concentration–time profiles of piroxicam after a single oral dose of piroxicam 20 mg in different CYP2C9 genotypes. Solid and dashed lines indicate geometric mean and 5th to 95th percentiles, respectively. Open circles and error bars indicate observed mean and standard deviation (or standard error), respectively. Observed plasma concentration data except CYP2C9*3/*3 genotype was obtained from Perini et al. (2005) and CYP2C9*3/*3 genotype was obtained from Perini and Suarez-Kurtz (2006). Plasma concentration–time profiles are expressed using linear and semi-logarithmic plots

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Table 3 Results for the development and validation of the piroxicam PBPK model
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Fig. 3
figure 3

Results of sensitivity analysis toward AUCinf A and Cmax B. x-axis and y-axis indicate sensitivity and lists of sensitive parameters, respectively

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Fig. 4
figure 4

Representative predicted and observed plasma concentration–time profiles of piroxicam for different populations and dose regimens. Solid and dashed lines indicate geometric mean and 5th to 95th percentiles, respectively. Open circles and error bars indicate observed mean and standard deviation (or standard error), respectively. Observed data in Mäkelä et al. (1991) are depicted as individual values

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Sensitivity analysis shown in Fig. 3 presented that dose had an equal impact on AUCinf and Cmax (1.00). Lipophilicity which had the highest impact in Cmax (− 1.82) was identified as having a relatively low impact in AUCinf (0.03). The parameters related to the enzymatic pathway of CYP2C9, including kcat, Km, reference concentration, and ontogeny factor, had an impact on the AUCinf and Cmax with higher influences for AUCinf than Cmax. Several organ volumes were identified as sensitive physiological characteristics.

Among the collected articles, except for the two papers used for model establishment, all other papers did not include pharmacogenomic data, so model validation for each genotype using PK data not used for model establishment could not be performed. Therefore, model validation was performed using PK data without pharmacogenomic information. The goodness-of-fit plot for a total 674 of predicted versus observed plasma concentration data is illustrated in Fig. 5. The range of fold error values for plasma concentrations was 0.11–3.13. 93.9% of fold error values were within the two-fold range. AFE, AAFE, and RMSE were 0.93, 1.27, and 0.72, respectively.

Fig. 5
figure 5

Goodness-of-fit plot of predicted versus observed plasma concentrations. Solid and dashed lines indicate line of unity and two-fold range, respectively

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Discussion

Genetic polymorphisms of drug metabolizing enzymes and transporters cause the inter-individual variations in drug response to varying degrees (Byeon et al. 2019; Bae et al. 2020; Jung et al. 2020a; Shin et al. 2020; Kim et al. 2022). Also, drug interactions significantly influence the pharmacokinetics of clinically used drugs (Byeon et al. 2018; Lee et al. 2019; Jung et al. 2020b). According to the advance in computational technology, a personalized dose administration strategy considering physiological characteristics of individuals or populations, genetic polymorphisms of drug metabolizing enzymes or transporters, and drug interactions has been proposed via the PBPK modeling approach (Li et al. 2020; Rüdesheim et al. 2020; Cho et al. 2021a, 2021b; Jung et al. 2021; Wojtyniak et al. 2021; Xu et al. 2021).

CYP2C9 is primarily responsible for the metabolism of a number of NSAIDs including ibuprofen, lornoxicam, meloxicam, flurbiprofen, and celecoxib and significant effects of CYP2C9 genetic polymorphism on the pharmacokinetics or pharmacodynamics of these drugs have been reported (Bae et al. 2011a; Choi et al. 2011; Lee et al. 2014, 2015; Ochoa et al. 2015; Kim et al. 2017). Like these NSAIDs, piroxicam is mainly metabolized by CYP2C9 and the influences of CYP2C9 genetic polymorphism on the piroxicam actions are known (Perini et al. 2005; Perini and Suarez-Kurtz 2006; Calvo et al. 2017). CYP2C9 genotype is potentially involved in the adverse events given the relationship between exposure and toxicity of the NSAIDs (Smith et al. 2022). Piroxicam has a longer t1/2 than other NSAIDs metabolized by CYP2C9 such as celecoxib, flurbiprofen, and meloxicam (Theken et al. 2020). This amplifies the potential risks in the patients with reduced CYP2C9 metabolism and hampers dose titration due to lack of data (Theken et al. 2020). Drug label and Clinical Pharmacogenetics Implementation Consortium (CPIC) guidelines for piroxicam recommend the consideration of dose reduction or the alteration to other NSAIDs which are not metabolized by CYP2C9 or metabolized by CYP2C9 with short half-life in CYP2C9PM group, respectively (Pfizer 2016; Theken et al. 2020).

To overcome the potential risk in patients carrying CYP2C9 allele variants and fulfill the lack of data related to piroxicam and CYP2C9 genotype to some extent, we developed and validated the first PBPK model for piroxicam according to CYP2C9 genetic polymorphism. In the model development, physicochemical and ADME properties for piroxicam were incorporated. In vitro enzyme kinetic data (Tracy et al. 2002) significantly under-estimated in vivo clearance of piroxicam in CYP2C9*1/*1 genotype. Hence, we estimated the fraction metabolized by CYP2C9 based on the previously reported pharmacogenetic study (Perini and Suarez‐Kurtz 2006). CPIC assigned CYP2C9*1/*1 genotype as CYP2C9EM phenotype and CYP2C9*3/*3 genotype as CYP2C9PM phenotype, respectively (Theken et al. 2020). Accordingly, the fraction was calculated based on the ratio of AUCinf in CYP2C9*1/*1 and CYP2C9*3/*3 genotypes (Ito et al. 2005; Perini and Suarez‐Kurtz 2006; Huang et al. 2017). Minor enzymatic pathways such as dealkylation and glucuronidation of piroxicam were identified, but it is not well reported and no candidate genes have been published (Brogden et al. 1981; Milligan et al. 1993). Thus, only the 5’-hydroxylation of piroxicam, the principal metabolic pathway mediated by CYP2C9, was applied in our model.

Our model successfully captured the pharmacokinetic alterations according to CYP2C9 genetic polymorphism. Especially, the pharmacokinetics of piroxicam in the CYP2C9*3/*3 genotype which had been traced for an extremely long period (120 days), were properly captured in this model. Furthermore, the range of fold error values for the pharmacokinetic parameters (AUC 0.57–1.59, Cmax 0.63–1.39, and t1/2 0.65–1.51) was within the acceptance criterion (Table 3) and the goodness-of-fit plot showed that the predicted data were overall in agreement with the observed data (AFE 0.93, AAFE 1.27, and RMSE 0.72). It suggests the present model was properly established for single and multiple doses of 0.4 or 1.0 mg/kg in children and 20–60 mg in adults, including the elderly, in both fasting and eating conditions. Although the sample size used for the modeling of the CYP2C9*3/*3 genotype was very small (n = 1), the present model could provide an insight for grasping the pharmacokinetics of piroxicam, simultaneous considering genetic and non-genetic factors.

Several modeling studies for the pharmacokinetics of piroxicam in humans have been reported (Wang et al. 2000; Tvrdonova et al. 2009; Li et al. 2019). Wang et al. (2000) reported population pharmacokinetic and pharmacodynamic model for piroxicam and piroxicam-β-cyclodextrin to investigate the pharmacokinetic-pharmacodynamic relationship of piroxicam. In their model, the physiological and anatomical characteristics of human were not incorporated because it was conducted as a “top-down” approach based on clinical data. Tvrdonova et al. (2009) showed a physiologically motivated time-delay model. This study accurately captured the multiple peak phenomenon of piroxicam, but in vitro data of piroxicam was not considered. Li et al. (2019) developed the PBPK model to predict the pharmacokinetics of piroxicam in beagle dogs and performed interspecies extrapolation to humans. Albeit a successful model, the application of the PBPK model to pediatric or geriatric populations could not be certain since it was only verified with clinical data on an adult population. In the present study, we developed the PBPK model for piroxicam by incorporating in vitro and in vivo data, robustly validated using a number of clinical studies, and demonstrated the applicability of the PBPK model for almost the entire age populations.

In this study, the PBPK model for only the two most common CYP2C9 allele variants (*2 and *3) was developed because of the lack of available pharmacogenetic studies. Two pharmacogenetic studies used for the PBPK modeling were performed in the Brazilian population (Perini et al. 2005; Perini and Suarez‐Kurtz 2006). CYP2C9*13 (rs72558187, c.269 T > C, p.Leu90Pro) allele variant, found only in East Asians with a frequency of 0.5% (Bae et al. 2011b), significantly influences the plasma exposures for various CYP2C9 substrates (Bae et al. 2011a, 2012; Choi et al. 2011, 2012). Previous studies reported the PBPK models related to CYP2C9*13 allele variants for celecoxib (Kim et al. 2021), meloxicam (Cho et al. 2021b), and candesartan (Jung et al. 2021) based on the clinical trials performed in the healthy Korean population. Further pharmacogenetic and modeling studies would be needed for the proper prescription of piroxicam in the East Asian population carrying the CYP2C9*13 allele.

There were several limitations in the present study. First, physiological differences between healthy volunteers and subjects with arthritis were not considered. Several studies were performed on the subjects with osteoarthritis or rheumatoid arthritis (Darragh et al. 1985; Blocka et al. 1988; Mäkelä et al. 1991; Caldwell 1994), but we developed and validated the PBPK model based on the parameters used in healthy volunteers without any modifications for these diseases. Second, in most clinical studies, all subjects were assumed to be carrying homozygous CYP2C9*1 allele due to the low frequencies of CYP2C9*2 or *3 allele variants (Daly et al. 2017). Nevertheless, a few of the subjects in the clinical data could be carrying allele variants and it could be one of the causes for the discrepancies between the predicted and observed data. Third, digitized plasma concentration–time profiles could be discrepant with the raw data. Wojtyniak et al. (2020) reported the greatest pitfall for the data digitizing comes from the pre-existing errors and they recommended making published data available as raw values. However, raw data for the pharmacokinetics of piroxicam were not available and the resolution of the piroxicam profiles was relatively low since the most of clinical studies used in this study were reported a long time ago. It would be better to interpret the results of the modeling under the consideration of these potential limitations.

In conclusion, the PBPK model for piroxicam related to CYP2C9 genetic polymorphism was properly established and described the pharmacokinetics of piroxicam in different CYP2C9 genotypes. It could be used as a cornerstone to predict the pharmacokinetics of piroxicam in a number of clinical scenarios. We expect the present model could contribute to personalized pharmacotherapy for patients treated with piroxicam.