Development of population PK model with enterohepatic circulation for mycophenolic acid in patients with childhood-onset systemic lupus erythematosus

Abstract

AIM

This study aimed to develop a population pharmacokinetic (PK) enterohepatic recycling model for MPA in patients with childhood-onset systemic lupus erythematosus (cSLE).

METHODS

MPA concentration–time data were from outpatients on stable oral mycophenolate mofetil (MMF) and collected under fasting conditions, with standardized meals (1 and 4 h post-dose). Sampling times were pre-dose, 20, 40 min, 1, 1.5, 2, 3, 4, 6 and 9 h, post dose. The population PK analysis simultaneously modelled MPA and 7-O-MPA-β-glucuronide (MPAG) concentrations using nonlinear mixed effect modelling.

RESULTS

PK analysis included 186 MPA and MPAG concentrations (mg l^–1) from 19 patients. cSLE patients, age range 10–28 years, median 16.5 years were included. Mean ± SD disease duration was 3.8 ± 3.7 years. The final PK model included a gallbladder compartment for enterohepatic recycling and bile release time related to meal times, with first order absorption and single series of transit compartments. The PK estimates for MPA were CL₁/F 25.3 l h^–1, V₃/F 20.9 l, V₄/F 234 l and CL₂/F 19.8 l h^–1.

CONCLUSION

The final model fitted the complex processes of absorption and enterohepatic circulation (EHC) in those treated with MMF for cSLE and could be applied in Bayesian dose optimization algorithms.

WHAT IS ALREADY KNOWN ABOUT THIS SUBJECT

• Despite its increased use, the pharmacokinetics (PK) of mycophenolic acid (MPA) and the relationship between dose, plasma concentration and exposure are poorly understood, especially in children.

• The PK of MPA are associated with high inter- and intra-individual variability.

• MPA and its metabolites, like the inactive 7-O-MPA-β-glucuronide (MPAG) undergo enterohepatic circulation (EHC), which can contribute to an increase in exposure to MPA of 40% (range 10–60%).

WHAT THIS STUDY ADDS

• Thisis the first report of MPA PK in adolescents with childhood-onset systemic lupus erythematosus (cSLE).

• The proposed final population PK model successfully incorporates the physiological aspects associated with MPA disposition, which includes MPA and its main metabolite MPAG, and adequately reflects the complex processes of absorption and enterohepatic circulation associated with mycophenolate mofetil (MMF) oral dosing in patients with cSLE.

• This model provides a basis for further development of a model-based Bayesian estimator for individualized MPA dosing in paediatric patients treated for cSLE.

Introduction

Mycophenolate mofetil (MMF), a prodrug rapidly converted to the active moiety mycophenolic acid (MPA) has been found to be of significant benefit to renal transplant patients [1]. Additional studies have demonstrated a variety of anti-inflammatory effects associated with MMF which have lead to its use in treating autoimmune diseases such as childhood-onset systemic lupus erythematosus (cSLE) [2]. SLE is a severe disease, which significantly affects more women in the adult population. Younger children have a lower incidence of the disease, where the gender predilection is less obvious, with earlier and more severe disease seen in males [3]. MMF is considered a good therapeutic choice for SLE patients because of its lower incidence of toxicity, decreased expression of adhesion molecules and reduced endothelial injury [4], [5]. Despite its increased off label use [6], [7], the pharmacokinetics (PK) of MPA and the relationship between dose, plasma concentration and exposure are poorly understood, especially in children [8]. The pharmacokinetics of MPA are associated with high inter- and intra-individual variability [9]. Unlike renal transplant patients, cSLE patients generally do not receive concurrent therapy with calcineurin inhibitors such as ciclosporin, which have been reported to influence the pharmacokinetics of MPA [10]. Additional factors associated with variability include differences in albumin concentrations, impaired renal and hepatic function and genetic polymorphisms in drug metabolizing enzymes and transporters [8], [11].

To date, most published population PK studies of mycophenolate have been analyses involving renal transplant recipients [12]–[15], the exceptions being studies undertaken by Jiao et al. [16] in healthy subjects, de Winter et al. [17] in adult patients with autoimmune disease and Zahr et al. [18] in adult patients with SLE. Zahr et al. [18] developed a PK model which allowed use as part of a Bayesian estimator for MPA exposure. Both Jiao et al. [16] and de Winter et al. [17] characterized the role of enterohepatic recycling of MPA in the PK model. MPA and its metabolites, like the inactive 7-O-MPA-β-glucuronide (MPAG) undergo enterohepatic circulation (EHC), which can contribute to an increase in exposure to MPA of 40% (range 10–60%) [12]. Enterohepatic recycling is affected by several processes including the activity and expression of various transporters and enzymes [19]. The influence of co-medication, genetic variability and patient characteristics can result in an increase or decrease of enterohepatic recycling of MPA. Enterohepatic recycling also influences drug pharmacokinetics by increasing drug bioavailability and by influencing plasma concentration profiles of the drug often characterized by secondary peaks [20].

The objective of this study was to investigate and develop a population PK model to explain the pharmacokinetics and influence of enterohepatic recycling of MPA in subjects with cSLE.

Methods

Subjects and study design

The study was conducted as an open-label outpatient study in subjects with cSLE (diagnosis prior to or at age 16 years) [21] who had been on a stable oral regimen of MMF (Cellcept®) for >3 weeks and had received therapy for at least 2 months. Typically, when prescribing MMF to children and adolescents with SLE the dose is 600 mg m^–2 orally twice daily [22]–[24]. The study was undertaken at Cincinnati Children's Hospital Medical Center, Ohio and Children's Memorial Hospital, Chicago, Illinois and recruited eligible subjects who were receiving MMF therapy. The study was approved by the participating centres' Institutional Review Boards. Parent and child written informed consent and assent were obtained before study enrolment. Method and design has previously been described by Sagcal-Gironella et al. [25].

Inclusion criteria included male or non-pregnant female subjects who met the American College of Rheumatology (ACR) revised classification criteria for cSLE [26]. Renal function and serum albumin were assessed during the study. Part of the inclusion criteria required that the subjects had stable renal function. Subjects were excluded from the study if they had any medical condition (active or chronic) or prior surgery that could potentially interfere with the pharmacokinetic behaviour of MMF (absorption, distribution and elimination). Exclusion criteria also excluded those subjects showing any signs of acute illness (e.g. infection) within 5 days of the study visits), a history of substance or alcohol abuse and signs or symptoms of autoimmune hepatitis/severe SLE hepatitis causing liver function test elevation >2.5 of normal since commencement of MMF. Those with a history of hepatitis B or C virus infection could be included in the study. Those not currently treated with MMF for signs and symptoms of SLE and with a body weight of <30 kg were also excluded. Concurrent use of antacids containing magnesium hydroxide and aluminum hydroxide, cholestyramine (Questran®, Prevalite®) or iron supplements was prohibited during the study. Subjects were ineligible if they had a change in dosing regimen of MMF within 30 days and/or other immunosuppressive maintenance medication 15 days prior to the study visit. Those with a history of allergies or adverse drug events to MMF were also excluded.

MPA and MPAG concentration−time data were collected during an outpatient visit under fasting conditions, with standardized meals (1 and 4 h post dose). Sampling times were pre dose (1 h prior to morning MMF dose), 20, 40 min, 1, 1.5, 2, 3, 4, 6 and 9 h post dose. Study subjects completed a drug diary for 3 days prior to the study visits, recording MMF dosing history and co-medications. PK blood samples were obtained from an indwelling peripheral line or by direct venipuncture (using a gauge 23 catheter or needle, respectively). Institutional standard operating procedures were followed for drawing blood from an indwelling catheter. The indwelling i.v. line was flushed with heparin in between blood draws according to institutional standard operating procedures. The total amount of blood drawn for research purposes during the study visit could not exceed 50 ml, as based on a minimal body weight of 30 kg, which does not exceed 5% of the total blood volume. Blood samples were placed within 1 h after collection in a centrifuge at 2000 g (approximately 4000 rev min^–1) for 10 min at 4°C. The sample was stored within 1 h of centrifuging at −70°C. MPA measurement occurred at the PPRU laboratory of Cincinnati Children's Hospital Medical Center (CCHMC).

Laboratory analysis

MPA and MPAG were analyzed in plasma using a validated HPLC (high performance liquid chromatography) assay according to a modification of a previously described method [27], [28]. The lower limit of quantification (LLOQ) was 0.25 mg l^–1 for MPA and 1.0 mg l^–1 for MPAG, respectively. Intra- and inter-day precision and accuracy for QC samples was always <5%.

Pharmacokinetic analysis

The population PK analysis of MPA and MPAG was simultaneously performed using nonlinear mixed effect modelling (NONMEM, version 7.1, ICON Dev. Soln., Ellicott City, MD) with PDx-Pop® (version 4.0, 2009 ICON Dev. Soln., Ellicott City, MD) interfaced with Xpose® (version 4.3.2) and R® (version 2.12.2, 2011). The PK parameters of MPA were calculated by converting MMF doses to the equivalent MPA dose by multiplying MMF by 0.739.

All compartment models were parameterized in terms of values of apparent oral clearance (CL/F) and apparent volume of distribution (V/F). Models were evaluated and selected based on goodness of fit. The PK parameters were assessed to determine reasonable physiological plausibility; a model producing a negative clearance was excluded. Unstable models were also excluded from the model building process. Stability was assessed by changing the number of significant digits and subsequently the initial estimates for the model parameters. Further assessment and comparison used the likelihood ratio test and reviewed changes in the objective function value (OFV) between models. Improvement in model fit was determined using chi-squared distribution with one degree of freedom (ΔOFV <3.84 =P < 0.05).

Models were also compared using the Akaike information criterion (AIC) and Schwarz information criterion (SIC) to discriminate between non-hierarchical models in the selection of a structural model [29]. During model development the following diagnostic plots were used to assess visually model fit, observed (DV) vs. population predicted (PRED) or individual predicted (IPRED) values. Plots of residuals and conditional weighted residuals (CWRES) vs. time or PRED were also examined.

The modelling added random effects for the PK parameters to account for differences and similarities between individuals and observations for MPA and MPAG. The terms for variability in the model included intra- and inter-individual variability and residual (unexplained) variability (RUV). Estimations of inter-individual and residual variability were assessed for evidence of model over-parameterization [30]. Inter-individual variability was assessed using exponential (equation 1) variability models.

1

where CL_i is MPA clearance of the ith individual, θ_pop is the population value for MPA clearance and η in the inter-individual random effect with mean 0 and variance ω².

The RUV error models were evaluated using a combined additive and constant coefficient of variation error model for MPA and MPAG (equation 2).

2

where Y is the observed and IPRED is the individual predicted plasma concentrations. ε_addX, and ε_propX are the residual unexplained variability terms for the additive and proportional error models.

Base model development

Preliminary model building used an empirical approach and focused on analyzing various structural models. An evaluation was undertaken to determine how well various types of absorption models could describe the absorption profiles in the existing data set. Tested absorption models used either a first order absorption or zero order absorption model to explain the complex mechanisms associated with oral absorption of MPA [19]. Inclusion of lag time and absorption rate constants (K_a) were also assessed for improvement of estimations of the absorption processes.

Other absorption-type models were also assessed for their ability to describe the atypical absorption profiles including parallel first order absorption, mixed first order and zero order absorption and single and double gamma Weibull-type absorption models. Inclusion of an Erlang distribution model was used to describe the absorption phase, with a constant transfer rate between two absorption compartments. The principle approach in the Erlang distribution model used an analytical solution for a chain of ‘n’ compartments between the depot and central compartment [31]. The number of serial ‘n’ compartments was estimated by interposing an increasing number of compartments between the depot and central compartment until there was no further statistical improvement seen [32].

A two-compartment model with first order elimination with transit compartments was also tested for use in describing the absorption phase. The transit compartment model was used to describe drug absorption as a multiple step process and replaces the use of a lag time. A chain of presystemic compartments was used to account for any delay in the passage of a drug into the circulation. In this model, the number of transit compartments leading to the depot is estimated by the model [33].

Enterohepatic recycling models

Several methods have previously been published proposing models able to characterize the secondary absorption related to MPA enterohepatic recycling [14]–[16], [19], [34]–[36]. This study investigated several mechanisms in relation to development of a PK model able to characterize adequately MPA enterohepatic recycling. Three main approaches were applied to the data and extensively evaluated. A simultaneous modelling approach was taken to include the parent drug, MPA and the metabolite, MPAG. The first method used a similar structural model to that outlined by Petricoul et al. [37], which was a model describing enterohepatic recycling. The coding was modified in relation to times for release from the gallbladder compartment, using meal time (MTIME) to model start and end of meal times, at 1 h and 4 h respectively. Initially, a two compartment approach was used to describe the absorption phase and was assessed using lag time and duration. EHC was described by including a gallbladder compartment for accumulation of the drug. Gallbladder emptying was modelled to simulate two release times, 1 and 4 h post dose, to be consistent with the meal times during the study. Gallbladder emptying was ‘turned off’ at 2 h and 6 h post dose.

A different approach to modelling the EHC of MPA used a single series of transit compartments to describe the absorption of the MMF dose into a gut compartment. The model then used a series of chain compartments which included gastrointestinal (gut), central (MPA), peripheral compartment (MPA), central compartment for the metabolite (MPAG) and gallbladder compartment. The last approach explored the use of a double parallel mixed first and zero order absorption and transit compartments. The principles of the model structure were similar to that previously outlined by de Winter et al. [35].

Covariate analysis

Patient characteristics investigated included patient age, gender, race, ethnicity, disease duration and bodyweight. Serum albumin, aspartate aminotransferase (AST), alanine aminotransferase (ALT) and serum creatinine were assessed during subject screening (visit 1) but not at the same time as the blood draws related to the PK profile (visit 2). Therefore they were not included in the PK model as variables. An exploratory analysis was used to look for relationships between the PK parameters and covariates by visually inspecting plots of the empirical Bayesian (post hoc) estimates of individual parameters from the base model against covariate values. Allometic scaling was applied to apparent oral clearance (CL/F) and apparent volume of distribution (V/F), also investigated as a priori, and standardized to a body weight of 70 kg [38]. Following the initial analysis, covariates were included into the model using a forward stepwise inclusion approach and added into the model until there was no further decrease in OFV. Covariates were subsequently removed from the model using a backward stepwise approach.

Model evaluation

The population PK model was evaluated using a non-parametric resampling bootstrap method to assess model accuracy and stability [39]. PDx-Pop® was used to generate 200 bootstrap runs generated by random sampling using the original dataset. Standard errors for the estimated population parameters and random effects error models were also assessed. Empirical Bayesian estimates for the predicted concentrations were obtained using the post hoc option in NONMEM. The final model was further evaluated by generating visual predictive checks.

Results

Subjects and pharmacokinetics

The final data set included 19 subjects meeting the ACR classification criteria for SLE prior to age 16 years. The age range of the subjects was 10–28 years, with a mean ± SD of 16.9 ± 4 years. For the purpose of the study we defined the paediatric subpopulations as follows: child (2 to 12 years of age) and adolescent (12 to 21 years of age). The upper age limit to define paediatric populations varies, but including adolescents up to the age of 21 years is consistent with the literature [40]–[42]. The population included the following age categories, children (2–12 years) n = 2, adolescents (12–21 years) n = 14 and adults (>21 years) n = 3. There was a wide age distribution within the data with the youngest child in the population being 10 years old and the oldest adult being 28 years old. Therefore, the model was assessed to determine if there were any statistically significant effects on the PK parameters of MPA and MPAG with removal of the children and adults from the model. Age was tested as a continuous covariate and by using the categories defined above, there were no statistically significant differences related to age identified in the model. Given the dominance of data from the adolescent group (73.7%) no potential influence was seen from including the two children (10.5%) and three adults (15.8%) in the model. It was determined that due to their limited contribution to the data no influence could be elucidated and therefore these data were included in the final model.

The mean + SD dose of MMF was 1973 ± 634 mg day^–1, range 1000–3000 mg day^–1[25]. Subjects had mean ± SD disease duration with SLE of 3.3 ± 3 years. Eighteen subjects were also receiving oral prednisone therapy, 17.2 ± 10.4 mg day^–1. Three subjects were receiving high dose i.v. methylprednisolone, which has been suggested to induce UGTs [43]. However, this was not explored in this study due to a lack of available data. Further data collection to address this issue is currently being carried out by the research group. The demographic details of patients with cSLE included in the population analysis are outlined in Table 1.

Table 1.

Demographic details of patients with childhood-onset systemic lupus erythematosus (cSLE) included in the population pharmacokinetic analysis

Parameter	Mean ± SD	Range (%)
Subject age (years) (n = 19)	16.9 ± 4	10.6–28.2
Children (2–12 years) (n = 2)		(10.5%)
Adolescents (12–21 years) (n = 14)		(73.7%)
>21 years (n = 3)		(15.8%)
Weight (kg)	66.6 ± 15	43.4–103
SLE disease duration (years)	3.3 ± 3	0.2–12.8
Duration of treatment with MMF (years)	1.5 ± 1.3	0.14–6.4
Mycophenolate mofetil (mg day–1)	1973 ± 634	1000–3000
Serum albumin (g dl–1) (n = 17)*	3.5 ± 0.26	3.3–3.8
AST (units l–1) (n = 13)*	47 ± 59	16–253
ALT (units l–1) (n = 13)*	28 ± 29	10–129
Serum creatinine (mg dl–1) (n = 17)*	0.69 ± 0.17	0.5–1.0
Urine protein : creatinine ratio (n = 13)*	0.33 ± 0.34	0.03–1.16

	n = 19	% of total
Gender
Male	1	5
Female	18	95
Race:
African American	11	58
Caucasian	8	42
Ethnicity:
Hispanic	4	21
Non-Hispanic	15	79
Current medications:
Mycophenolate mofetil	19	100
Prednisone	18	95
Methylprednisolone	3	16
Hydroxychloroquine	17	89
NSAIDs	11	58
Antihypertensives	8	42

^*Assessed during visit 1 (baseline), not assessed during visit 2 (PK profile).

The initial exploratory analysis of the data revealed typical concentration–time profiles of MPA and MPAG for all subjects. The graphs display mean concentration data with standard deviation (SD) at each sample time (Figures 1, 2). The analysis showed evidence of a lag time in drug absorption and the existence of complex absorption processes in subject profiles. Figure 1, MPA vs. time (h) profile displayed a sharp initial peak around 0.5–1 h and in some profiles a smaller secondary peak occurring 4–9 h post dose. This was considered attributable to enterohepatic recycling. Overall, subject profiles varied with some showing an initial lag time followed by a rapid increase in MPA concentration during the absorption phase, then a complex distribution phase and finally elimination phase. The proposed gallbladder emptying times tested in the model were based on food intake at 1 and 4 h post dose and appeared to correspond approximately with the multiple peaks observed at 1 and 4 h post dose. In Figure 2, MPAG vs. time (h), there was some similarity in the distribution of the plasma concentrations to MPA. However, there was a delay in the peak concentrations, which occurred 1.5–2 h post dose compared with MPA.

Figure 1.

Mean ± SD mycophenolic acid, MPA (mg l^–1) plasma concentrations vs. time (h) for (n = 19) PK profiles. Mean ± SD MPA (mg l^–1) plasma concentrations vs. time (h) for each sampling time (20, 40 min, 1, 1.5, 2, 3, 4, 6 and 9 h post dose)

Figure 2.

Mean ± SD 7-O-MPA-β-glucuronide, MPAG (mg l^–1) plasma concentrations vs. time (h) for (n = 19) PK profiles. Mean ± SD MPAG (mg l^–1) plasma concentrations vs. time (h) for each sampling time (20, 40 min, 1, 1.5, 2, 3, 4, 6 and 9 h post dose)

Development of a population PK model

The population PK analysis included a total of 372 observations, 186 MPA and 186 MPAG concentrations (mg l^–1). A summary of models considered in model development is outlined in Table 2. The best preliminary PK model was a two compartment model with first order absorption and lag time, which adequately describe the data, based on OFV, AIC and SIC. This was considered the initial base model. Subsequent modelling led to the development of a more physiologically accurate model to characterize enterohepatic recycling.

Table 2.

Summary of model building used in development of a PK model for MPA and MPAG in subjects with cSLE

Model	Model descriptions	OFV	AIC	SIC
	Absorption models
1	Two compartment model with first order absorption and without lag time	433.8	453.8	486.2
2	Two compartment model with duration and lag time*	393.6	417.6	456.4
3	Two compartment model with first order absorption and Erlang distribution (serial compartments n = 5)	436.4	460.3	499.2
4	Single gamma absorption model	618.5	630.8	669.6
5	Double gamma absorption model	531.6	555.6	594.4
6	Two compartment model with first order absorption and single series of transit compartments	545.9	569.9	608.7
7	Two compartment model with two parallel first order absorption phases using transit compartments	411.3	447.3	505.4
	Enterohepatic recycling structural models
8	Two compartment model with first order absorption and lag time, additional gallbladder compartment Enterohepatic recycling, bile release meal times (1 and 4 h post dose)	1728.5	1745.5	1782.3
9	Multi-compartment model (gut, peripheral, central, gallbladder compartments) with first order absorption and single series of transit compartments. Enterohepatic recycling, bile release meal times (1 and 4 h post dose)	1941.6	1985.6	2072.3
10	Multi-compartment model (gut, central (MPA) peripheral, central (MPAG), gallbladder compartments) with first order absorption and single series of transit compartments. Enterohepatic recycling, bile release meal times (1 and 4 h postdose)†	1788.1	1805.2	1812.6
11	Multi-compartment model (gut, peripheral, central, gallbladder compartments) with two parallel first-order absorption phases and Transit compartments. Enterohepatic recycling, bile release meal times (1 and 4 h post dose)	2235.1	2283.1	2377.7
12	Multi-compartment model (gut, central (MPA) peripheral, central (MPAG), gallbladder compartments) with two parallel first-order absorption phases and transit compartments. Enterohepatic recycling, bile release meal times (1 and 4 h post dose)	2885.3	2891.3	2903.1

^*Initial base model.

^†Final population EHC PK model. MPA, mycophenolic acid; MPAG, 7-O-MPA-β-glucuronide; cSLE, childhood systemic lupus erythematosus; AIC, Akaike information criterion; SIC, Schwarz information criterion.

Other absorption models were investigated including an Erlang distribution model, which did not provide a significant improvement in the model fit (OFV increased compared with the two compartment first order absorption models). The current study also investigated the use of single and double gamma absorption models [44] finding that a double gamma absorption model was best able to fit the data as shown in Table 2.

Bodyweight was determined to have a significant influence when included in the two compartment model with first order absorption and lag time. Inclusion of bodyweight in the initial covariate analysis determined allometric-scaled bodyweight influenced apparent oral clearance (CL/F), apparent volume of distribution of MPA and CL/F of MPAG. However, inclusion of bodyweight and other covariates (age, gender, race, ethnicity and disease duration) in later more complex models, specifically those which modelled enterohepatic recycling, did not produce a significant influence and generally failed to minimize successfully. This may be associated with over parameterization of the model.

PK model with enterohepatic recycling of MPA and MPAG

The final model included a gallbladder compartment for enterohepatic recycling and meal times using a linear chain model structure. Meal times were standardized based on the study protocol of 1 and 4 h post MMF dose. The gallbladder release times were simulated to coincide with the time of the secondary peak and the intake of food relative to the dose. It was assumed that the gallbladder emptied into the gut compartment at these times.

The first enterohepatic model evaluated (Table 2, model 6) was found to be limited in its ability to describe the complex distribution phase of MPA and the model was unable to minimize successfully with the inclusion of MPAG. Subsequent models used a single series of transit compartments to describe the absorption of the MMF dose into a gut compartment. This model structure was determined to be the most adequate for describing the EHC of MPA based on successful minimization of OFV and visual inspection of the diagnostic plots. Additional model development investigated the application of a double parallel mixed first and zero order absorption and transit compartments (Table 2, model 7) that were able to fit to the data. However, the model was over-parameterized and the PK parameters were associated with very large standard errors.

The final PK model described MMF administered orally and distributed via a multi-compartment model that included a gallbladder compartment for EHC, using first order absorption and a single series of transit compartments (Figure 3). The final model was comprised of the following compartments: transit compartments (T0; Tn – 1; Tn) (1). The model included a series of a transit compartments, where n was the estimated number of transit compartments prior to the gut compartment. Additional compartments included the gut (2), a central compartment for MPA (3), peripheral for MPA (4), central for MPAG (5) and a gallbladder compartment (6). The rate constants between the compartments were described by Ktr = (N – 1)/MTT, where MTT was mean transit time into first depot compartment (h) and N was number of transit compartments prior to first depot compartment.

Figure 3.

Schematic diagram of final PK model. Compartments: transit compartments (1), gut (2), central compartment for MPA (3), peripheral for MPA (4), central for MPAG (5) and a gallbladder compartment (6). T0 = start of transit compartments Tn– 1 = transit compartments; MTT = mean transit time into first depot compartment (h); N = number of transit compartments prior to first depot compartment; K_a= absorption rate constant (h). Defining the model where Ktr = (N– 1)/MTT, k₃₀= renal eliminated MPA (FM ×k₃₅) = fraction of MPA metabolized to MPAG, FM fixed at 85%, assuming remaining 15% is metabolism of MPA to AcMPAG (not contained in model), k₃₄ and k₄₃= intercompartmental clearance of MPA (1 – FMPAG) ×k₅₀= fraction of renal eliminated MPAG, fixed to 65% (FMPAG ×k₅₆) = assuming 65% excretion of transferred MPAG from central compartment to gall bladder, with 35% accumulation in the gallbladder, EHC = biliary recirculation of MPAG into gut was fixed at 35%. Meal times were used to trigger timing of gall bladder emptying

Following transit into the gut, MPA was absorbed into the central compartment (3), using the absorption rate constant, K_a. From the central compartment, k₃₀ was estimated as renal eliminated MPA. From here, MPA is distributed to the peripheral compartment (4). k₃₄ and k₄₃ described inter-compartmental clearance of MPA from the peripheral compartment. Several assumptions were made to aid in producing a model that would successfully minimize. From the MPA central compartment [fraction metabolite (FM) ×k₃₅] was the fraction of MPA metabolized to MPAG. The model assumes that 85% of MPA (FM was fixed at 85%) is metabolized to MPAG as defined by FM in the model, assuming the remaining 15% to be related to metabolism of MPA to AcMPAG. AcMPAG concentrations were not available to include in the model. The fixed value was determined by using simulation, various assumptions and values were made and tested in the model. The fixed value of 85% provided the best model performance. The model then describes compartments estimating MPAG (5), a fraction of renal elimination for MPAG is estimated (1 – FMPAG) ×k₅₀. It was assumed that approximately 65% of MPAG is excreted unchanged by renal elimination. These elimination rates were unidentifiable by the model due to a lack of data and estimations were based on previously reported values in the literature [45]. Transfer of MPAG to the gallbladder compartment from the central MPAG compartment (FMPAG ×k₅₆) assumed 65% excretion of transferred MPAG from central to gall bladder, with the remaining portion accumulated into the gallbladder compartment, approximately 35% as defined in the model. EHC of MPAG into gut was fixed at 35%. Meal times (1 and 4 h post dose) were used to trigger timing of gall bladder emptying. Gallbladder emptying was ‘turned off’ at 2 h and 6 h post dose.

With the inclusion of gallbladder emptying in the model, it was assumed that all MPAG was released from the gallbladder compartment into the gut compartment and reconverted to MPA and subsequently reabsorbed into the system. Large inter-individual variability was estimated for the model PK parameters and large unexplained residual error remained in the final model. Inclusion of covariates did not improve the OFV in the final model. This may be due to the model being highly parameterized and blocking any signal rather than a lack of any covariate relationship. Overall, the model (Figures 4 and 5) was able to describe adequately the mechanisms associated with the pharmacokinetics of MMF. The estimates of the model are outlined in Table 3.

Figure 4.

A) Observed vs. population predicted MPA concentration, B) observed vs. individual predicted MPA concentration, C) MPA conditional weighted residuals vs. time and D) MPA conditional weighted residuals vs. population predicted MPA concentration. In plots (A, B) the solid line is the line of identity; In plots (C, D) dashed line is line of regression. MPA, mycophenolic acid, DV, dependent or observed concentration, IPRED, individual predicted concentration, CWRES, conditional weighted residual, PRED, predicted concentration

Table 3.

Summary of parameter estimates for the final enterohepatic recycling pharmacokinetic model of MPA and MPAG

Parameter	Final model Estimate	Bootstrap n = 200 Median	95% CI
CL1MPA (l h–1)	25.3	24.3	17.2, 32.4
V3 MPA (l)	20.9	22.4	13.7, 31.2
CL2 MPA (l h–1)	19.8	25.3	19.2, 31.6
V4 MPA (l)	234	239	230.2, 247.8
CLMMPAG (l h–1)	2.5	2.6	0.3, 4.9
VM = V3MPA	–	–	–
FM – fixed	85%	–	–
FMPAG – fixed	65%	–	–
KA (h−1) – fixed	1.5	–	–
MTT (h)	1.1	1.2	0.4, 1.9
n	8.2	7.5	3.8, 11.2
EHC – fixed	35%	–	–
Inter-individual variability	CV%
CL1MPA	48.6	46.5	33.9, 59.1
V3 MPA	59.2	57.6	49.8, 65.4
CL2 MPA	42.9	41.1	30.1, 52.1
V4 MPA	60.0	56.2	52.4, 67.6
CLMMPAG	55.9	54.1	42.2, 65.9
Residual variability
MPA error CV%	41.2	39.5	35.8, 43.2
MPAG error CV%	45.4	42.3	35.7, 48.9

CL1_MPA, apparent oral CL/F for MPA in the central compartment; V3_MPA, apparent volume of distribution V/F of MPA in the central compartment; CL2_MPA, apparent intercompartmental CL/F in the peripheral compartment; V4_MPA, apparent V/F of MPA in the peripheral compartment; CLM_MPA, apparent renal CL/F of MPAG. VM =V3 _MPA, MTT, mean transit time into first depot compartment (h); n, number of transit compartments prior to first depot compartment. Enterohepatic recycling parameters, EHC biliary recirculation of MPAG and meal times (1–2 h and 4–6 h) post dose_, used to trigger times of gall bladder emptying.

Evaluation of final PK model

Graphs generated for MPA and MPAG individually included CWRES vs. PRED, DV vs. IPRED and CWRES vs. time (Figures 4 and 5). Figure 4, MPA DV vs. IPRED, showed some discrepancy between the predicted and observed concentrations. Overall, the plots indicated improvement in the fit of the model to the data between the base and final model. Figure 5, MPAG DV vs. IPRED, showed good fit of the model. The predictive performance of the final models was reasonable when comparing predicted with observed MPA serum concentrations. However, due to the paucity of data available the models were limited in their ability to describe every aspect of the complex process associated with MPA and MPAG absorption. The DV vs. IPRED plots showed no obvious structural bias. However, there was some evidence of under-prediction of the maximum MPA concentrations. CWRES vs. time plots were distributed more homogenously in the MPAG compared with MPA plots.

Figure 5.

A) Observed vs. population predicted MPAG concentration, B) observed vs. individual predicted MPAG concentration, C) MPAG conditional weighted residuals vs. time and D) MPAG conditional weighted residuals vs. population predicted MPAG concentration. In plot (A, B) the solid line is the line of identity; In plots (C, D) dashed line is line of regression. MPAG, 7-O-MPA-β-glucuronide, DV, dependent or observed concentration, IPRED, individual predicted concentration, CWRES, conditional weighted residual, PRED, predicted concentration

The results of the bootstrap analyses are presented in Table 3. The mean estimates from the 200 bootstrap runs are similar to the population estimates determined from the final model. There was a success rate for the bootstrap runs was 96.5% and the 95% CI were estimated parameters based on the successful runs. The final model displayed reasonable stability and accuracy in relation to the estimates for fixed and random effects. The final model was evaluated using a visual predictive check for MPA (Figure 6) and MPAG (Figure 7). There was reasonable agreement between the observed data and the simulated data in the predictive checks for MPA and MPAG.

Figure 6.

Visual predictive check, mycophenolic acid observed data compared with the 95^th, 50^th and 5^th percentiles for 100 simulated data sets. Observed data binned according to sampling times 20, 40 min, 1, 1.5, 2, 3, 4, 6 and 9 h post dose. Comparison of median (dashed line) and 5–95^th percentile interval (solid black lines). The mean + SD dose of MMF was 1973 ± 634 mg day^–1, range 1000–3000 mg day^–1. 50^th quantities (); 10^th–90^th quantities (); 5^th–95^th quantities ()

Figure 7.

Visual predictive check, 7-O-MPA-β-glucuronide (MPAG) observed data compared with the 95^th, 50^th, and 5^th percentiles for 100 simulated data sets. Observed data binned according to sampling times 20, 40 min, 1, 1.5, 2, 3, 4, 6 and 9 h post dose. Comparison of median (dashed line) and 5–95^th percentile interval (solid black lines). The mean + SD dose of MMF was 1973 ± 634 mg day^–1, range 1000–3000 mg day^–1. 50^th quantities (); 10^th–90^th quantities (); 5^th–95^th quantities ()

Discussion

This is one of the first attempts to develop a population PK model with EHC for MPA and MPAG in patients with SLE with the inclusion of paediatric and adolescent patients. The proposed final population PK model incorporates the physiological aspects associated with MPA disposition which include MPA and its main metabolite MPAG and adequately reflects the complex processes of absorption and EHC associated with MMF oral dosing in patients with SLE. The proposed model provides a basis for further development of a model-based Bayesian estimator for individualized MPA dosing in paediatric and adolescent patients treated for SLE. The most appropriate enterohepatic recycling model able to fit the available data was a multi-compartment model with first order absorption and single series of transit compartments. The model included a series of compartments: gut, central (MPA), peripheral, central (MPAG) and a gallbladder compartment for inclusion of enterohepatic recycling with bile release triggered by meal times.

Most previous published population PK studies have been undertaken in adults receiving MMF post-renal transplantation [13], [15], [46], [47]. Conventional empirical models can be limited in their use to describe data that have multiple peaks and the varying effects of EHC. Generally, the published studies have had difficulty modelling MPA EHC or have not had datasets (i.e. no obvious secondary peaks due to EHC) able to support such a model [12]. Some population PK studies of MPA, such as studies conducted by Sam et al. and Sam & Joy [15], [48] have had multiple sampling points per subjects and have described EHC of MPA in the adult transplant population and recently in adult patients with glomerulonephritis. Studies have typically reported a lack of fit of either the complex absorption or eliminations phases or failure to characterize all identifiable peaks [12], [14], [34].

The study by Zahr et al. [18] is the only other published PK study in patients with SLE, but it only included adults. The study describes application of a Bayesian estimator using in-house software MMF® and a limited sampling strategy approach. A one compartment model with first order elimination convoluted with a triple gamma distribution input was proposed as the final model. Similar to the current study, during collection of the PK concentration–time profiles, standard meals were given 1, 5 and 10 h post dose. Peaks attributable to the absorption characteristics of MMF/MPA were observed in the absorption phase and were unlikely to be due to enterohepatic recycling. However, despite good overall predictive performance in describing the absorption profile of MPA, it is difficult to make a direct comparison between the model proposed in the current study and the more empirical method outlined by Zahr et al. [18].

A recent publication by Sam & Joy [48] outlines the development of a population PK model of MPA in adult renal autoimmune disease patients with glomerulonephritis secondary to SLE and small vessel vasculitis. The model includes MPA, MPAG and AcMPAG plasma and urine concentrations with renal and non-renal clearance assessments. The population PK model demonstrates the influence of estimated creatinine clearance and serum albumin on renal and non-renal clearance of MPA. The model demonstrates that MPA exposure is highly altered in this group of patients and is proposed for use in simulating AUC when the patient has altered serum creatinine and/or serum albumin.

Recently, de Winter et al. [35] developed a population PK model to describe MPA concentrations in adult patients with autoimmune disease. A two compartment model with first order absorption and elimination was proposed which included an extra gallbladder compartment to simulate EHC. A combination of mechanisms utilizing rate and duration defined the recycling of MPA from the gallbladder into the gastrointestinal compartment. The PK model proposed in the present study has combined some of the concepts outlined previously by Zahr et al. [18] and de Winter et al. [35] to develop a mechanism-based approach, which reflects the physiological process associated with gastric emptying.

Although there are similarities between the current model and that outlined by de Winter et al. [35] there are some fundamental differences. CL/F for MPA was reported as 8.27 l h^–1[35] in comparison with 25.3 l h^–1 estimated in this final PK model which is not allometrically scaled. Other studies [19] have reported CL/F at 16.0 l h^–1[49] and 14.7 l h^–1[50], whereas Zahr et al. [18] reported CL/F as 40.3 l h^–1. In the de Winter et al. [35] study, some subjects received concomitant treatment with ciclosporin and corticosteroids. Only MPA was modelled and estimations of the fraction of dose transported through the short and long absorption compartments were used to describe absorption into the gastrointestinal compartment. de Winter et al. [35] estimated a short lag time of 0.29 h and a long lag time of 0.64 h. The present study used a transit compartment approach to describe for the absorption time between deport and the gastrointestinal compartment and estimated a mean transit time of 1.1 h.

During model development, models estimating the fraction of MPA excreted into the bile and time of gallbladder emptying were investigated. These models required several assumptions. In the process of development of an EHC model it was assumed the release of bile occurred as a bolus from the gall bladder, using a lag time to model the expulsion of bile. This is not physiologically accurate, as bile is continuously secreted. The other limitation of this type of model is that there is only one recirculation process undertaken or the model can only be applied to a single dose study. The estimation used for the fraction of MPA found in the gallbladder and that which is excreted is assumed constant. Rates determined for MPA moving back into the intestine following recirculation are also assumed to occur at the same rate as absorption from the intestine. Due to the complexity of MPA absorption and the enterohepatic recirculation of MPAG, it is difficult to characterize and define an exclusive physiological approach [12], [20].

There are limited data available in the paediatric and adolescent populations who have SLE, and subsequently difficulty in developing a PK model for MMF that can incorporate all potential variables, e.g. UGT's. The model was used to investigate potential influences from age, gender, race, ethnicity, disease duration and bodyweight. However, none of these covariates provided a significant improvement to the EHC model. Serum albumin, aspartate aminotransferase (AST), alanine aminotransferase (ALT) and serum creatinine were taken at an initial visit and not at the time when the PK concentrations were collected. The model is potentially limited by not including serum albumin, AST and ALT as covariates in the analysis as other studies have shown them to have an influence on MPA PK [48]. However, these values as stated above were not collected in this study at the same time as the PK samples, making it inappropriate to include these data within the PK model. Including pre-existing data not directly related to the PK samples could provide values that potentially could be very different (either better or worse) due to the intervening time between the initial visit and when the PK data were obtained. Furthermore, it still to be determined if many of the assumptions shown in MPA PK models containing these covariates such as those undertaken in renal transplant patients and those with glomerulonephritis are associated with influencing MPA PK in SLE patients.

Few studies have investigated the PK of MPA in patients with autoimmune disease or SLE and data are limited. Assumptions based on the PK of MPA in renal transplant patients cannot readily be assumed in SLE patients as transplant patients are concomitantly administered calcineurin inhibitors such as tacrolimus and ciclosporin. Studies have demonstrated that the AUC of MPA is decreased when administered concomitantly with ciclosporin [14]. It is proposed that this is due to an inhibitory effect on the multidrug resistance-associated protein-2 transporter (MRP2) that controls MPAG active transport into bile [51], [52]. More recently, evidence has also suggested that inhibition may also affect the organic anion transporting polypeptide, OATP1B3 [53]. Another drug–drug interaction, which may influence the PK of MPA, particularly in SLE patients, is the concomitant use of corticosteroids. Corticosteroids have been suggested to induce MPA metabolism through the glucuronosyltransferases (UGT) pathway [43]. In the current study, 18 of the 19 subjects were receiving corticosteroid therapy. There is some evidence that tapering of steroids may result in increased MPA exposure [54]. There remains debate regarding the impact corticosteroids have on MPA and data predicting or quantifying the influence of prednisone on MPA PK are limited. Zahr et al. [18] also investigated the possible interaction of corticosteroids and MPA in patients with SLE. However, they were unable to conclude there was no interaction between corticosteroids and MPA pharmacokinetics.

In conjunction, with previously published work [25] by this group which found that weight-adjusted MMF dosing alone was not reliable for the prediction of exposure to biologically active MPA in SLE and with the development of the EHC PK model outlined here, it is proposed that the model provides a basis for further development of a model-based Bayesian estimator for individualized MPA dosing in paediatric and adolescent patients treated for SLE. Previously we have demonstrated that individualized dosing, which uses MPA PK, appears warranted as this allows for better estimation of immunologic suppression (IMPDH activity).

In the present study, both MPA and MPAG plasma concentrations were simultaneously modelled. Few published studies have included MPAG into the PK modelling [14]–[16], [55]. It has been suggested that to describe the complex metabolism and absorption of mycophenolates, all available pharmacokinetic information should be used in a model [14]. Not including such information could lead to biased models describing the PK of MMF. A future application of this study is to adapt the proposed final model for multiple dose situations. It is envisaged that by using modelling and simulation, this mechanism-based model can eventually be used in a model-based algorithm that can be used in routine clinical practice to target one specific or a range of AUC values for patients.

In conclusion, the proposed model was able to incorporate successfully physiological aspects associated with MPA disposition. The final population PK model included MPA and its main metabolite MPAG and adequately reflected the complex processes of absorption and enterohepatic recirculation associated with MMF oral dosing in patients with cSLE. This may further describe the relationship between MPA and MPAG enterohepatic recirculation leading to optimally individualized MMF therapy. This model will provide a basis for further development of individualized MPA dosing strategies in paediatric and adolescent patients treated for cSLE and will be applied and evaluated in the development of a Bayesian dose optimization algorithm.

Competing Interests

There are no competing interests to declare.