Introduction

Attention-deficit/hyperactivity disorder (ADHD) is one of the most common neurobehavioural disorders experienced in childhood, with estimated prevalence rates per 100,000 school-aged children ranging from 4,000–9,000 [1]. The persistence of ADHD symptoms into adolescence and adulthood has been increasingly observed in up to 50% or more of those diagnosed with ADHD in childhood. Pharmacotherapy remains the first line treatment option for ADHD, of which methylphenidate (MPH) is one of the most commonly prescribed stimulant medications. MPH works by inhibiting the presynaptic dopamine transporter [2], and the conventional, immediate release (IR) formulation of MPH became a mainstay of treatment for ADHD since 1955 when ADHD was termed Minimal Brain Dysfunction (MBD) [3]. Due to the short duration of action of IR MPH formulations, twice-daily or three-times-daily administration is required to maintain therapeutic effects during the normal school day and after-school hours. However, such a dosing schedule can be problematic due to the issues of inconvenience, security, and privacy at school, which may compromise treatment outcomes.

To address these issues, once-daily extended release (ER) MPH formulations have been designed to achive the desired continuous behavior improvements throughout the day with a single dose. Per FDA, “extended-release drug products are dosage forms that allow a reduction in dosing frequency as compared to when the drug is present in an immediate-release dosage form. These drug products can also be developed to reduce fluctuations in plasma concentrations” [4]. Various oral ER MPH formulations have been developed, such as Concerta using OROS technology (osmotic controlled-release oral system tablets comprising of 22% IR and 78% ER MPH), Metadate CD and Equasym XL using Diffucaps technology (containing 30% IR and 70% ER beads), Ritalin LA using SODAS technology (spheroidal oral drug absorption system delivering 50% IR and 50% enteric-coated ER beads), Medikinet retard (comprising 50% IR and 50% enteric coated ER pellets), as well as the newly approved Aptensio XR (using a novel multilayer release bead formulation, MLR-MPH, containing 40% IR/60% ER beads) [2, 5], and other fomulation products.

In general, many of the ER MPH formulations were designed to provide a fast onset of action, followed by a prolonged duration of action [6], except for some formulations, e.g. Metadate-ER nor Ritalin-SR. The initial rapid onset might be attributed to the “ramp” effect associated with the quick dissolution of the IR component within each of the ER formulations [7, 8]; whereas the ER component is intended to attain a lowered drug concentration at noon with a second peak in drug concentraiton occurring 6–8 hours following dosing with a gradual decline afterwards. Such an ideal formulation design ensures a regular appetite during lunch and dinner and a usual sleep pattern, while allowing for symptom control during morning and afternoon activities [6, 9]. However, the lowered drug concentration at noon is only apparent for Ritalin LA, but otherwise is not espounsed by other product labeling nor prominently seem in PK profiles of other products.

With different delivery technologies and variable ratios between the IR and ER components, these approved ER oral dosage forms of MPH exhibit diverse profiles of absorption phases and varied patterns of action over the course of the day [10, 11]. The peak plasma concentrations, the time to reach the peak concentrations, and the rate of plasma concentrations increase and decrease differ among these formulations. A potential positive correlation between plasma MPH concentrations and the extent of ADHD sympton reduction has been proposed [1, 2, 12], suggesting that the temporal clinical responses of MPH follow its plasma concentration versus time profiles. Therefore, a quantitative understanding and characterization of the diverse pharmacokinetic profiles may help inform the magnitude of clinical effects throughout the day for different formulations. Such knowledge might be valuable for clinicians in terms of optimizing treatment regimens to ensure temporal symptom controls suited to individual patient’s needs.

Physiological absorption models, with the integration of anatomy and physiology of human gastrointestinal (GI) tract as well as physicochemical properties of chemicals, have been widely utilized as a useful approach to describe oral absorption and disposition of various modified release formulations [13–15]. However, to the best of our knowledge, no such model exists for ER MPH dosage forms. In the current study, a previously developed physiologically based pharmacokinetic (PBPK) model for IR MPH [16] was modified to describe the pharmacokinetic behaviors of multiple ER MPH formulations in adult humans, where ER MPH products containing multi-particulate beads/pellets with different release characteristics were considered. Instead of describing the oral uptake with an empirical first order process as described in the original model [16], various events occurring in the GI tract were described in a mechanistic framework to account for the physiology of the GI tract, physiochemical properties of MPH, and formulation related information. This mechanistic description of the GI tract provides some insight into the diversity of the absorption profiles observed among different ER MPH formulations.

Materials and Methods

The oral absorption PBPK model

The schematic of the whole body PBPK model incorporated with the oral absorption model is depicted in Fig 1. Model parameters for the whole body PBPK model presented in the original paper [16] were used in the current model, except that hepatic metabolic constants representing hydrolysis were derived directly from in vitro studies and model parameters describing hepatic oxidation, as well as non-specific loss in the GI tract were recalibrated as described below.

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Fig 1. Schematic depicting the physiological absorption model for immediate release (IR) and extended release (ER) MPH formulations.

The oral absorption model is composed of nine compartments, representing the stomach, duodenum, jejunum divided into two compartments, ileum divided into three compartments, cecum, and ascending colon. Dissolution of the IR component occurs throughout the GI tract, primarily in the stomach, whereas the release/dissolution of the ER component takes place only in the intestine accompanied by a delay time. M, metabolism; Loss, non-specific loss, IR immediate release.

https://doi.org/10.1371/journal.pone.0164641.g001

Consistent with the original model, the hydrolysis of MPH enantiomers in the liver was described with a Michaelis-Menten equation integrating the competitive binding to the hCES1A1 enzyme between d- and l-MPH [16]. The Michaelis constants for d- and l-MPH (Kmliverd and Kmliverl, μg/L) were set equal to the reported Km values, and the maximum hepatic reaction velocity (VmaxliverdC and VmaxliverlC, μg/h/kg^0.75) were derived based on the reported in vitro catalytic constant values (Kcat, 0.165 min^-1 and 0.335 min^-1) experimentally determined using the recombinant human CES1A1 enzyme [29] as described in the original paper [16] without any adjustment. Accordingly, the clearance terms (KmetdC and KmetlC, L/h/kg^0.75) representing the oxidation of MPH enantiomers in the liver were determined to ensure that 20% of the total dose metabolized in the liver undergoes this pathway [30].

The oral absorption model, similar to what has been proposed in the ACAT model in the Gastroplus program (Simulations Plus, Inc.), is composed of nine compartments representing the stomach, duodenum, jejunum divided into two compartments, ileum divided into three compartments, cecum, and ascending colon. Physiological characteristics (e.g. pH, volume, surface area, transit time, permeability) of each section and MPH-specific input data (e.g. solubility, permeability, logP, pKa) were either obtained from the literature, derived based on available data, or estimated using the ADMET Predictor (Simulations Plus, Inc.) (Tables 1 and 2). The IR component of MPH formulations undergoes dissolution quickly in GI fluids, primarily in the stomach, while the ER beads are assumed subject to release/dissolution in the intestine due to the engineered delayed delivery systems (Fig 1). Both solid and dissolved forms of MPH are emptied from the stomach and transit along the GI tract, which is described as a first-order process governed by transit time between each section (Table 1). The dissolved drug from both IR and ER components within the luminal fluids of the intestine undergoes passive diffusion into the enterocytes, where the MPH is either taken up into the portal vein and the liver or subjected to non-specific loss in the GI tract. The key equations are described below.

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Table 1. Physiological model parameters for the gastrointestinal tract [31, 32].

https://doi.org/10.1371/journal.pone.0164641.t001

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Table 2. Physiochemical and biochemical model parameters for IR and ER MPH.

https://doi.org/10.1371/journal.pone.0164641.t002

Release/dissolution.

The rate of dissolution of IR MPH formulation in the luminal fluid (dAdiss_i/dt, μg/h) was accounted for using the diffusion layer model based on the Noyes-Whitney equation for spherical particles [36] with parameters set to default values [37]. (1) where Adiss_i (μg) is the dissolved amount of IR MPH in the luminal fluid of the ith compartment at time t, Diffcoeff is the diffusion coefficient set to 1×10⁻⁴ cm²/min, rho is the density of drug particle set to 1 g/mL, rparticle is the current spherical radius set to 5 μm, DLT is the diffusion layer thickness set to 30 μm, Vlumen_i is the volume (mL) of the lumen of the ith compartment Csolid_i is the concentration (μg/mL) of undissolved IR MPH in the luminal fluid of the ith compartment, Solif_i is the solubility (mg/L) of MPH in the luminal fluid of the ith compartment, and Cdiss_i is the concentration (μg/mL) of dissolved MPH in the luminal fluid of the ith compartment.

The dissolution of IR beads/pellets within the ER MPH formulations was described as that for IR MPH formulations, whereas the release/dissolution of the ER component was described using a general empirical Weibull function: (2) where Release (μg) is the amount of MPH released/dissolved from ER beads/pellets at time t, Max (μg) is the amount of MPH embedded in ER beads/pellets available for release at time t, A is the scale parameter which delineates the time scale of the process, the shape parameter b defines the shape of the curve (b = 1 exponential; b>1 sigmoid; and b < 1 parabolic), and the lag time, T_lag, represents the time (h) prior to the start of drug release. The value of T_lag was set to 4 hours for different ER formulations, which was estimated by visual fitting to achieve agreement with the onset of the second peak of plasma MPH concentration time courses for Ritalin LA and substantially ascending plasma concentration profiles across all the other data sets. The values of A and b were set to describe in vivo dissolution versus time profiles that best fit the time courses of plasma concentrations for MPH following oral dosing of ER MPH in adult subjects.

Solubility.

In addition to the dissolution kinetics of IR and ER components of ER MPH formulations, the solubility of MPH in the luminal fluid along the GI tract was described using the following equation with the incorporation of local pH, ionization, and bile salt concentrations [38]: (3) where Solif_i (mg/L) is the solubility of MPH in the luminal fluid of the ith compartment, accounting for the impact of ionization at local luminal pH (Solwater_i) and effect of bile salt concentrations on MPH solubility (SolBile_i).

Solwater_i (mg/L) is the solubility of MPH in the luminal fluid of the ith compartment in the absence of bile salt, which was derived based on the Henderson-Hasselbalch equation for a monoprotic weak base [39] using the following equation: (4) where S₀ is the intrinsic solubility (9,109 mg/L) calculated based on the estimated solubility of 9,250 mg/L at pH 10.58 using the ADMET Predictor (Simulations Plus, Inc.), pH is the pH value of the luminal fluid of the ith compartment and the reported pKa for MPH is 8.77 [34] (Table 1).

SolBile_i (mg/L) represents the effect of bile salt on the solubility of MPH in the luminal fluid of the ith compartment [38] (5) where MW (233.31 g/mol) is the molecular weight of MPH, Bile_i is the concentration of bile in the ith compartment (mM), which is obtained from the Gastroplus program (Simulation Plus, Inc.) (Table 1). SR is the ratio of the solubilization capacity of the bile salt to the solubilization capacity of water, calculated as SR = 10^{0.606×LogP+2.234} where the experimentally determined LogP of MPH is 0.20 [34], and SCaq is aqueous solubilization capacity, calculated as SCaq = Solwater_i×(MW_water/MW)×10⁻⁶.

Absorption.

The rate (, μg/h) of absorption of dissolved MPH across intestinal mucosa is described as a passive diffusion process, since no information on the active transport of MPH could be located: (6) where HPeff_est is the estimated human effective permeability (cm/s) derived based on the relationship established between in vitro apparent permeability across Madin-Darby canine kidney (MDCK)-low efflux cells (P_app) and in situ human effective permeability (LogHPeff_est = 0.86+0.92×LogP_app) [40]. In vitro apparent permeability (P_app) experimentally determined using the transwell assay with MDCK cells was 24.7 × 10⁻⁶ cm/s for MPH [35].

ESA_i (cm²) is the estimated surface area for the ith compartment, which is calculated using the equations developed by Helander and Fandriks (2014) incorporating the surface enlargements due to plicae circulares, villi and microvillie in the small intestine (A_i = Length_i×Diameter_i×π×1.57×6.5×13) and large intestine (A_i = Length_i×Diameter_i×π×1×1×6.5) [41], for which the length and diameter for each compartment was obtained from [31] (Table 1); NI_i is the unionized fraction of MPH in the ith compartment; Cdiss_i (μg/mL) is the concentration of dissolved MPH in the luminal fluid of the ith compartment and Cmem_i (μg/L) is the concentration of MPH within enterocytes for the ith compartment, for which the mass (volume, L) of the wall for each compartment is determined based on the ICRP Publication 89 [32] (Table 1).

Systemic uptake and non-specific loss in the GI tract.

The uptake of MPH into the portal blood is described as a flow-limited process, where fractional blood flow to the GI tract is estimated as the difference between fractional total liver blood flow (0.255 of cardiac output for males and 0.27 of cardiac output for females) and fractional arterial blood flow to the liver (0.065 of cardiac output for both males and females) [32]. Fractional blood flow to each section of the intestine is assumed to be equal and calculated as fractional blood flow to the GI tract divided by 8, yielding a value of 0.024 of cardiac output for males and 0.026 of cardiac output for females.

With the calibration of model parameters describing hepatic hydrolysis and oxidation, non-specific loss of MPH in the GI tract was introduced to achieve agreement with observed plasma concentration profiles of MPH following oral dosing of IR MPH [17–19], which was described as a first-order process (K5dC and K5lC, 1/h/kg^0.75). The values of K5dC and K5lC, along with the derived human effective permeability (HPeff_est) were determined by optimization against time courses of plasma concentrations of d- and l-MPH following oral dosing of IR MPH in adult humans [17–19].

Results

Model Calibration for IR MPH

With the Michaelis affinity constants (Kmliverd and Kmliverl) and the maximum hepatic reaction velocities (VmaxliverdC and VmaxliverlC) describing d- and l-MPH hydrolysis in the liver set directly to the in vitro derived values (Table 2), clearance terms representing hepatic oxidation of MPH enantiomers, KmetdC and KmetlC, were set to a value of 0.43 L/h/kg^0.75, yielding 20% of the total MPH metabolized in the liver undergoing the oxidation pathway [30]. The optimized gut non-specific loss constants (K5dC and K5lC) and effective human permeability (HPeff_est) were 0.79 1/h/kg^0.75, 37.8 1/h/kg^0.75, and 9.63×10⁻⁵ cm/s, respectively (Table 2).

Model predicted mean plasma d- and l-MPH concentration time courses were in good agreement with observations across all the data sets, with predicted mean concentrations within a factor of two of the observed values [17–19] (Fig 2A–2F), except that the mean concentrations for d-MPH at 18 h and l-MPH at 1.5 and 2 h were slightly overestimated in subjects receiving 40 mg IR MPH [19] by a factor of 2.1–2.7 (Fig 2C and 2F). The model-predicted mean pharmacokinetic model parameters C_max and AUC_last were consistently within twofold of the experimental values (Fig 2G and 2H) for all three data sets, except that the estimated mean AUC_last and C_max values were somewhat lower compared with observations for l-MPH in one study [19] (S2 Table). Of note, the reported mean C_max and AUC_last values in Table II for l-MPH for the study of [19] were not consistent with those shown in Figure 2 of the same paper [19]. The recalculated mean C_max and AUC_last values derived by digitalized concentration time course data from Fig 2 [19] were in good agreement with model predictions (S2 Table). In addition, the model-predicted T_max for d- and l- MPH in general agreed with observations for all three data sets except for l-MPH for the study of [19], for which the predicted median time to reach peak plasma l-MPH concentration was delayed compared with experimental data by more than 2 fold (S2 Table).

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Fig 2. Model simulated versus observed d- MPH (A, B, C) and l-MPH (D, E, F) plasma concentration profiles in adults receiving a single oral dose of IR MPH at 0.3 μg/kg [17, 18] and 40 mg [19] under fasted conditions as well as model predictability of the pharmacokinetic parameters AUC (G) and C_max (H).

Solid lines in A-F represent simulated mean plasma concentration-time profiles, whereas dashed lines represent the 5^th and 95^th percentiles for the predicted values. The observed data points (●) are shown as mean ± SD (error bars) or means only. The solid lines in G and H illustrate unity as well as a twofold deviation from unity; whereas the data points represent observed mean ± SD values with respective to the simulated mean ± SD values for AUC (G) and C_max (H). In the study of Patrick, Straughn et al. (2007), AUC and C_max values only reported for d-MPH.

https://doi.org/10.1371/journal.pone.0164641.g002

Model Evaluation for ER MPH

To fit the extended release MPH formulations, parameters of the Weibull equation (Eq 2) were adjusted except for the lag time, which was set to 4 hr. For MLR-MPH, a value of 6 (hr^b) for A and a value of 4 (unitless) for b (Table 2) were visually fitted to achieve better agreement with observed plasma MPH concentration-time profiles in adults received 20 mg [21] and 80 mg [6] MLR-MPH capsule under fasting conditions. As shown in Fig 3A and 3B, model-simulated mean plasma MPH concentration time profiles were in good agreement with observations for both data sets, except for the 0.5 h time point in the study of [21] where observed mean plasma total MPH concentration was overestimated by 5-fold.

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Fig 3. Model simulated versus observed total MPH plasma concentration profiles in adults receiving a single oral dose of MLR-MPH at (A) 20 mg [21] and (B) 80 mg [76] under fasting conditions, as well as model predictability of the pharmacokinetic parameters AUC (C) and C_max (D).

Solid lines in A and B represent simulated mean plasma concentration-time profiles, whereas dashed lines represent the 5^th and 95^th percentiles for the predicted values. The observed data points (●) are shown as mean ± SD (error bars) for the study of Adjei et al (2014), while for Reiz et al. (2008), the observed data points are expressed as mean ± SE. The solid lines in C and D illustrates unity, as well as a twofold deviation from unity; whereas the data points represent observed mean ± SD values with respective to the simulated mean ± SD values for AUC (C) and C_max (D).

https://doi.org/10.1371/journal.pone.0164641.g003

The adequate description of experimental mean plasma profiles in subjects receiving MLR-MPH was further supported by the good estimation of pharmacokinetic parameters. Model predicted AUC and C_max values all met the evaluation criterion for both studies, with predicted/observed mean values in the range of 0.6–0.95 (Fig 3C and 3D and S3 Table). Also, the observed T_max values were tracked very well by the current model (S3 Table).

For Ritalin LA, a value of 0.5 (hr^b) for A and a value of 2 (unitless) for b (Table 2) were utilized to predict plasma MPH concentration-time profiles in adults received 40 mg [22, 23] and 20 mg [9] Ritalin LA capsule under fasting conditions (Fig 4). Model-simulated and observed mean plasma concentration profiles of MPH contained within the IR beads, corresponding to the time course from 0 to 4 h, were in good agreement for all the data sets, except that the first time point for the study of [9] was largely overestimated (Fig 4A–4C). For the time course concentration profiles associated with the ER component, i.e. from 4 h to 24 h, observed peak plasma concentrations were somewhat under-predicted across all the data sets by 2 to 2.6-fold (Fig 4A–4C). In addition, model-predicted mean plasma MPH concentrations at 16 and 24 h for the study of [22] were approximately 2.2 and 3.3-fold of the observed values. Consistent with the discrepancy between model-predicted and observed mean plasma concentration time profiles, some degree of inaccuracy was noticed for the predicted pharmacokinetic model parameters. The current model properly predicted the average dose metrics of C_max over the time period from 0 to 4 h [9, 22, 23]; while model predictions of C_max from 4 h to 8 h [22] and 4 h to 10 h [23] were not considered adequate, with an error greater than two fold. In spite of inaccurate predictions of the second C_max, model predictions of AUC met the evaluation criterion for all three data sets, with the predicted/observed mean values in the range of 0.55 to 0.84 (S3 Table, Fig 4D and 4E). For the T_max, though the model-predicted average times to reach the first peak (T_max1) [9, 22] and the second peak (T_max2) [22] were consistent with observations, because of the failure to track the second peak concentrations, which were greater compared with the first one, the model predicted average T_max over a period of 24 h was imprecise compared with those found in the experimental data (2.6 versus 4.22 h and 2.6 versus 5.5 h) [9, 22] (S4 Table).

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Fig 4. Model simulated versus observed total MPH plasma concentration profiles in adults receiving a single oral dose of Ritalin LA at (A, C) 40 mg [22, 23] and (B) 20 mg [9] under fasting conditions, as well as model predictability of the pharmacokinetic parameters AUC (D) and C_max (E).

Solid lines in A-C represent simulated mean plasma concentration-time profiles, whereas dashed lines represent the 5^th and 95^th percentiles for the predicted values. The observed data points (●) are shown as mean ± SD or mean only. The solid lines in D and E illustrates unity, as well as a twofold deviation from unity; whereas the data points represent observed mean ± SD values with respective to the simulated mean ± SD values for AUC (D) and C_max (E).

https://doi.org/10.1371/journal.pone.0164641.g004

For Metadate CD (Fig 5), a value of 0.5 (hr^b) for A and a value of 2 (unitless) for b (Table 2) were visually fitted to achieve better agreement with observed plasma MPH concentration-time profiles in adults received a 20 mg Metadate CD capsule under fasting conditions [24, 25]. The model was capable of simulating plasma MPH concentration profiles resulting from exposure to oral Metadate CD for both data sets, with the difference of predicted and observed mean values within a factor of two, except that mean plasma MPH concentrations at 0.5 h in both studies were somehow overestimated by two to three-fold (Fig 5A and 5B). Consistent with the adequate description of the experimental plasma MPH concentration profiles, model-predicted pharmacokinetic parameters (T_max, C_max, AUC) for both studies were in excellent agreement with observations indicated by the ratio of predicted/observed mean values within a twofold error range (S5 Table, Fig 5C and 5D). Of note, the lag time of 4 hours used in the current model is obtained by achieving agreement between model simulations and experimental data across all the ER formulations. This is somehow inconsistent with empirical evidences for Metadate CD, for which the ER component of Metadate CD was shown to release over 3–4 hours in vivo [1] and 1 hour after placement in an aqueous medium in vitro [57].

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Fig 5. Model simulated versus observed total MPH plasma concentration profiles in adults receiving a single oral dose of Metadate CD at 20 mg [24, 25] under fasting conditions (A and B), as well as model predictability of the pharmacokinetic parameters AUC (C) and C_max (D).

Solid lines in A-B represent simulated mean plasma concentration-time profiles, whereas dashed lines represent the 5^th and 95^th percentiles for the predicted values. The observed data points (●) are shown as mean ± SD. The solid lines in C and D illustrates unity, as well as a twofold deviation from unity; whereas the data points represent observed mean ± SD values with respective to the simulated mean ± SD values for AUC (C) and C_max (D).

https://doi.org/10.1371/journal.pone.0164641.g005

For Medikinet Retard (Fig 6), a value of 0.5 (hr^b) for A and a value of 2 (unitless) for b (Table 2) were visually fitted to achieve better agreement with observed plasma MPH concentration-time profiles in adults received with 20 mg [27, 28] and 40 mg [23] Medikinet Retard capsule under fed conditions. For the study of [23], observed mean plasma MPH concentrations were underestimated from time 0 to 4 hour by 2.3 to 4.5 fold [23], while for the remainder of the time course concentration profile, model simulations adequately reproduced collected kinetic data (Fig 6A). For the studies of [27] and [28], at earlier time points (0.5–1.5 h) observed mean plasma MPH concentrations were underestimated; while at later time points (12–24 h), mean plasma MPH concentrations were over-predicted compared with observations by approximately 2 to 3-fold (Fig 6B and 6C). Systemic clearance of MPH after approximately 8 hours appears faster than model-predicted across all the three data sets (Fig 6A–6C). Accordingly, some degrees of disparity between model-forcasted and experimental pharmacokinetic parameters (T_max, C_max, AUC) were observed (S6 Table). The observed average dose metrics of C_max and AUC_0-4h for the study of [58] were underestimated, with an error fold in the range of 0.3–0.4; while for the studies of [27] and [28], model predictions of pharmacokinetic parameters were considered adequate, with ratios of predicted/observed mean values for AUC and C_max within a factor of two (Fig 6D and 6E), except that the predicted T_max for the study of [28] was approxiamately 3 hours late compared with observations (2 h versus 5 h) (S6 Table).

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Fig 6. Model simulated versus observed total MPH plasma concentration profiles in adults receiving a single oral dose of Medikinet Retard at (A) 40 mg [23] and 20 mg [27, 28] (B and C) under fed conditions, as well as model predictability of the pharmacokinetic parameters AUC (D) and C_max (E).

Solid lines in A-C represent simulated mean plasma concentration-time profiles, whereas dashed lines represent the 5^th and 95^th percentiles for the predicted values. The observed data points (●) are shown as mean except for Schutz et al (2009) where the observed data points are expressed as geometric mean. The solid lines in D and E illustrates unity, as well as a twofold deviation from unity; whereas the data points represent observed mean ± SD values (geometric mean ± SD values for the study of Schutz et al., 2009) with respective to the simulated mean ± SD values (geometric mean ± SD values for the study of Schutz et al., 2009) for AUC (D) and C_max (E).

https://doi.org/10.1371/journal.pone.0164641.g006

Sensitivity Analysis

Fig 7 shows sensitive model parameters with absolute NSC values greater than 0.1 based on the time course of MPH plasma concentration profiles over a period of 24 hour as model output. The definitions of model parameters are presented in Tables 1 and 2 and S1 Table.

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Fig 7. Sensitivity analysis.

Model parameters with absolute normalized sensitivity coefficient (NSC) values greater than 0.1 are listed in the Figure.

https://doi.org/10.1371/journal.pone.0164641.g007

For IR MPH, in addition to those model parameters identified to be sensitive in the original PBPK model [16], parameters representing the anatomy and physiology of the gastrointestinal tract also impact model predicted MPH plasma concentrations. Of these, the pH values of each small intestine section as well as the partition coefficient of the enterocytes, along with cardiac output, body weight, volume of slowly perfused tissues, partition coefficients of slowly and richly perfused tissues, appear to influence model output to a greater extent.

The sensitivity pattern was in general similar across different ER formulations, though the extent of the influence of model parameter perturbation on predicted MPH plasma concentrations as well as the correlations between model parameters and model output may vary. Compared with IR MPH, some model parameters associated with the cecum and ascending colon were found to be sensitive as well for the ER formulations but not for IR MPH. This suggests that the absorption of IR MPH predominantly occurs in the upper region of the small intestine, while for ER MPH, the cecum and ascending colon also contribute to a great extent to the absorption of MPH, primarily for the ER component. In addition, model parameters describing the Weibull function were found to influence model-predicted MPH plasma concentrations, of which the lag time significantly affect model output in an inverse manner.

Of note, the values shown in Fig 7 are the maximum absolute values over a period of 24 hours. The time course patterns of the influence of model parameters on model output vary across all the sensitive model parameters; some model parameters impact only a small portion of the time course, while others have a continuous effect throughout the period of 24 hours. In addition, the association of one specific model parameter with estimated MPH plasma concentrations may vary with time, i.e. positively correlated at some time points while negatively related at other time points (data not shown).

Discussion

This work presents the extension of a recently published whole-body PBPK model for IR MPH [16] and delineates the pharmacokinetics of multiparticulate ER MPH formulations in humans with the integration of mechanistic description of the kinetic behaviors of MPH in the GI tract. Compared with a simple conventional approach, namely using the known i.v. profiles and bioavailability of the drug to implement a dual absorption model with one fraction absorbed fast and the second fraction absorbed more slowly, the utilization of highly sophisticated modeling of GI absorption to produce the oral dose profiles for products with rapidly absorbed and slowly absorbed components exhibits several advantages. First, the sophisticated description of the GI tract provides a mechanistic framework to account for the physiology of the different sections of the GI tract, physiochemical properties of MPH, and formulation related information. Second, in contrast to the empirical description of the oral absorption in the conventional approach, the absorption of MPH across the GI tract is accounted for by the physiology of the GI tract (e.g. pH, volume, surface area of each section, etc) and physiochemical properties of ER MPH (e.g. release kinetics, ionization, permeability, etc). This allows for the quantitative track of the kinetics of IR and ER components across the GI tract to account for the release, permeability and loss occurring in each section of the GI tract, which can be different across different sections. Therefore, this sophisticated approach could provide more insights into the diversity of the absorption profiles observed among different ER MPH formulations, from both physiological and formulation-related perspectives. Third, with the integration of inter-individual viabilities in those model parameters representing the physiology of the GI tract, the current model can be used to assess population variability of internal dose metrics of MPH following oral dosing of ER MPH. In addition, the mechanistic description of the GI tract allows for the evaluation of ER MPH kinetics under different physiological/pathological (e.g. some diseases affecting the physiology of the GI tract) and dosing conditions (e.g. fed conditions, co-administration of drugs mediating the pH of the GI tract).

Due to different model calibration strategies used in the current model and the previous one [59], i.e. the direct use of in vitro to in vivo extrapolation (IVIVE)-derived model parameters describing hepatic hydrolysis (VmaxliverdC and VmaxliverlC) in the current model versus the adjustment of these derived model parameters based on i.v. dosing data sets in the previous exercise [59], model parameters describing hepatic hydrolysis, and accordingly those representing hepatic oxidation as well as intestinal non-specific loss used in the current model differ substantially from those used in the previous model. However, the use of different physicochemical and pharmacokinetic parameters in these two exercises does not mean that the kinetics of MPH (e.g hepatic metabolism), except for oral absorption, should differ between IR and ER formulations. Such apparent dissimilarity is solely because of the different strategies used for model calibration. In addition, the renal clearance terms included in the previous model were used for the description of the systemic clearance of the metabolite ritalinic acid (RA) from the volume of distribution compartment, which was derived based on available urinary excretion and plasma concentration profiles of RA after IR MPH dosing. These clearance terms for RA after dosing of ER MPH in the current model are assumed to be the same as those determined in the previous model [59]. Since there is no available RA kinetic data after oral dosing of ER MPH to evaluate these renal clearance terms, these parameters were not reported in the current model.

In the current model, whole blood flow instead of plasma flow was utilized given that simulating whole blood flow to organs provides a physiologically realistic description of blood perfusion to tissue. Then calculating plasma concentration versus whole blood concentration can easily be carried out. To simulate plasma MPH concentrations, a plasma compartment was included as shown in Fig 1 and the volume of plasma was utilized. Due to the lack of raw data, observed mean plasma concentrations versus time profiles were compared with model predictions. To avoid the potential bias in comparing mean concentrations only, scatterplot visual prediction check (VPC) would be a highly useful tool to evaluate how well the model predictions overlay with original array of plasma concentrations if raw data sets are available.

Of note, in the current model, intestinal non-specific loss of MPH was introduced to achieve agreement with observed plasma MPH concentration profiles following oral dosing of IR MPH after the calibration of hepatic metabolic constants. The underlying mechanisms responsible for the non-specific loss in the GI tract remain unclear. One possibility is that MPH might undergo metabolism in the GI tract. While no direct information is available regarding the metabolism of MPH in the GI tract, the expression of hCES1A1 mRNA, the predominant human CES1 enzyme responsible for MPH hydrolysis as identified in human livers, has been observed in both small intestine and large intestine tissues (cecum and ascending colon) [60, 61]. Also, the observation of the hydrolysis of flurbiprofen derivatives [62], which are excellent substrates for hCES1 but not for hCES2, in human intestinal microsomes also suggests the existence of hCES1 enzyme in the GI tract. Moreover, as stated in the original paper [16], route-dependent discrepancies were found for plasma and urine profiles of d- and l-MPH as well as d- and l-RA in the first two hours following i.v. and oral administration [63, 64]. Higher plasma d-MPH concentrations compared with l-MPH concentrations appeared immediately following oral dosing, while after i.v. dosing such difference was not observed until 1.5 h. In addition, higher l-RA concentrations compared with d-RA concentrations in both human plasma and urine samples were noticed in the first 2 hours after oral dosing but not after i.v. dosing. These route-dependent discrepancies could imply potential enantioselective presystemic metabolism of MPH in the GI tract. However, such assumption could be misleading and bears uncertainties as well given that there exist controversial studies showing that there is no expression of CES1 in the GI tract [65]. Also CYP3A4 is the predominant gut oxidative CYP enzyme and does not appear to metabolize MPH [66]. Therefore, more studies are warranted to better understand the kinetic behaviors of MPH in the GI tract, e.g. metabolic stability studies with human intestinal preparations.

With some exceptions, plasma concentration profiles following a single oral dose of these ER MPH dosage forms in adult humans were reasonably well predicted using the established physiological absorption model for the first time. The current model describes the dosage forms containing multiple beads/pellets that are readily dispersed throughout the GI tract; while for Concerta^® using the OROS^® technology to deliver MPH by osmotic pressure, the tablet moves along the GI tract as a whole. Therefore, pharmacokinetic studies in adults with Concerta^® were not utilized for current model evaluation.

The present physiological absorption model predicted that the IR MPH is rapidly dissolved in the GI fluid, primarily in the stomach. The dissolved MPH moves along the GI tract and gets completely absorbed into enterocytes, with the majority of absorption occurring in the proximal portion of small intestine, predominantly in the jejunum perhaps due to the relative longer transit time, and only a very small portion absorbed in the cecum and the ascending colon (Table 3). Consistent with the IR formulation, the majority of the IR component in the ER formulations was also absorbed in the jejunum under fasting conditions, with fraction absorbed in each section varying along with the ratio of IR/ER component across different ER formulations; while under fed conditions, the absorption of the majority of the IR component occurred in the ileum, which was in part due to the decreased pH in the proximal portion (duodenum and jejunum) of small intestine under fed conditions, resulting in greater ionization for the basic MPH and herein decreased absorption across the intestinal epithelial cell membranes. In accordance with this, pH values of each section of the small intestine were determined to be sensitive in terms of impacting MPH plasma concentrations (Fig 7). In contrast to the IR component, because of the delay due to the engineered formulation technology, the model indicated that the release of ER component takes place primarily in cecum and ascending colon, with the majority of absorption occurring in the ascending colon (Table 3), which has been suggested previously as well [67]. In spite of the complete absorption of the IR component, the fraction of total MPH absorbed among different ER MPH formulations varied from 65–75%. The current model suggests that about 25–35% of the total dose moves to the distal portion of the colon and undergoes fecal excretion either as unreleased solid forms (19–27%) or dissolved forms (6–9%). Therefore, the low absolute oral bioavailability of ER MPH, which found to be comparable with that of IR MPH, i.e. approximately 30% for d-MPH and 1% for l-MPH [6, 20, 63, 68], could be in part due to the incomplete absorption of ER MPH [18, 69].

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Table 3. Fraction of ER component released and total MPH absorbed in each section.

https://doi.org/10.1371/journal.pone.0164641.t003

The disparate formulation technologies, along with the variable ratio of IR MPH to ER MPH components among different ER products, yield each a unique plasma concentration profile for each preparation. For MLR-MPH, the MPH is placed in different layers in each bead, where the IR component resides in the outermost bead layer and the ER component is situated in the innermost layer and surrounded by a delayed release and a controlled release coating [70]. There is a rapid initial release provided by the IR component, which accounts for 40% of the total dose, followed by a break and subsequent release of the ER part, with the second peak comparable to the first one, creating a bimodal plasma concentration profile [21]. For Ritalin LA with the SODAS technology, the delayed release beads that contain 50% of the total dose are polymer coated, which intervals the contact of the gastrointestinal fluid with the interior drug core of the beads [71, 72]. The latency of the release of the ER component depends on the penetration of the gastrointestinal fluid into the interior core of the beads and the erosion of the polymer coating [73]. There is also a double-peak plasma concentration profile similar to that of twice-daily IR MPH, for which the ER component (50% of total dose) provides a higher peak plasma concentration compared with the IR component [5]. For Metadate CD utilizing the Diffucaps technology, the neutral core is covered by active drug layer, followed by one or more functional membranes controlling the release rate of ER MPH [27]. Metadate CD produces a biphasic plasma concentration profile, during which a rapid initial absorption is followed by a gradual escalation of plasma MPH concentrations with a higher peak concentration accounting for 70% of the total dose observed. No evidence of a plateau in plasma concentration over the lunchtime period was observed [5]. Distinct from these formulations, Medikinet Retard, consisting of IR beads and enteric coated ER beads, needs to be administered with or after breakfast to achieve the biphasic profiles, where the second peak attributed to the 50% of the total dose is comparable or slightly lower compared with the first peak [6].

Unlike the IR MPH, for which the gastric emptying time primarily controls the absorption of MPH, the absorption of MPH from various ER dosage forms depends mostly on the programmed drug release and dissolution profiles [1]. The current model integrated a Weibull function to describe the release processes of MPH across different ER MPH formulations, allowing for the depiction of diverse absorption profiles resembling multiple doses of IR MPH to varying degrees. A lag time of 4 hour was introduced to account for the different mechanisms of delay before the drug is released, along with a visually fitted A and b parameters to designate the time course of release profiles. In general, the established physiological absorption model tracked the kinetic behaviors of plasma MPH concentrations following oral dosing of MLR-MPH and Metadate CD; while some improvements are needed to reproduce accurately the time courses of MPH plasma concentrations in adults receiving Ritalin LA and Medikinet Retard. The peak concentrations associated with the ER component were underestimated for adults received Ritalin LA, for which the rate and extent of MPH release from the inner core of the beads appear greater than model predictions using the Weibull function; while for Medikinet Retard, plasma clearance were underestimated to some extent following the second peak, perhaps implying the effect of food on the clearance of MPH. Therefore, the utilization of more complex mathematical models might be needed to account for the exact mechanisms underlying these different engineered release technologies and to track the diverse plasma kinetic profiles across different formulations [74].

In addition, instead of employing mathematical models to describe the in vivo release/dissolution profiles, an alternative approach to describe the in vivo release/dissolution rate is importing dissolution profiles obtained in vitro using bio-relevant media into the physiological absorption model. However, to the best of our knowledge, such information is not available in literature for different ER MPH formulations. One study examined the in vitro dissolution profiles for three different Ritalin LA formulations with different release rates, however, plasma concentration profiles as well as in vivo absorption were not significantly correlated with in vitro dissolution profiles observed in the same study [67]. Therefore, more studies to investigate the in vitro dissolution profiles of each ER MPH formulation using bio-relevant media may be helpful. Such information may potentially be integrated into the current model for better model performance.

There are several potential applications for the current adult physiological absorption model. One important application is to predict plasma MPH concentration profiles in children following oral administration of different ER MPH formulations. Considering the high prevalence rate of ADHD in school-aged children and the particular issues pertinent to MPH use at school, e.g. security and privacy, current clinical practices favor the prescription of the ER formulations. Thus, a better understanding of the pharmacokinetic profiles of different ER MPH products in children may assist clinicians with the development of optimized therapeutic regimens. Many PBPK models have been developed to investigate the exposure of children to chemicals or drugs, where adult models were scaled to children with the integration of age-specific physiological and biochemical differences [75], including the anatomy and physiology of the gastrointestinal tract. For MPH, although age-related physiological changes (e.g. blood flow and tissue volumes) have been extensively studied, chemical specific parameters, e.g. hydrolysis and oxidation of MPH in the liver and potentially in the small intestine, as a function of age, have not been characterized fully in a quantitative manner. In particular, because of the lack of knowledge on the specific enzymes involved in MPH oxidation, inferring age-specific oxidation constants for MPH from adults to young children involves more uncertainties. In addition, although efforts have been made to estimate the age-dependent anatomy and physiology of the GI tract, many assumptions need to be tested and verified. Therefore, in order to reduce the uncertainty for the estimation of internal dose metrics of MPH in young children, further studies are needed when extrapolating adult human models to children. Of particular importance are metabolic studies with MPH using various in vitro systems, e.g. microsomes and hepatocytes, from different age groups to derive age-dependent hepatic and gastrointestinal hydrolysis and oxidation metabolic constants, along with the quantitative characterization of the anatomy and physiology of the GI tract across different developmental stages.

Another potential extension of the current model is to evaluate the food effect on the pharmacokinetics of different ER MPH formulations. It has been observed that following a high-fat meal, there is a possibility that the time to reach the peak concentrations (T_max) may be delayed probably due to the delayed gastric emptying (e.g. Metadate CD), along with potential inconsistent changes in peak concentrations (C_max), suggesting a potential temporal association with high fat intake [1]; while for some dosage forms (e.g Ritalin LA), such correlation was not observed [22]. In addition, soft food, such as applesauce, was found to have no impact on the bioavailability and kinetic profiles of some dosage forms (e.g. Metadate CD, Ritalin LA, MLR-MPH) given as applesauce/sprinkle mix [6, 22, 24], implying that the effect of food on the extent and rate of absorption for ER MPH formulations may vary depending on the of composition the food as well as the formulation itself. Further, some studies have indicated that in addition to the impact on T_max and C_max, administration of ER MPH dosage forms under different fed conditions (e.g. high fat versus standard breakfast) could result in altered biphasic plasma MPH concentration profiles (e.g. MLR-MPH) [76], indicating that the food itself, along with their effects on the physiology of the GI tract, may influence the programmed release and dissolution patterns of some ER formulations. Therefore, additional studies are needed to understand fully the kinetics of different ER formulations under fed conditions, allowing for the integration of such knowledge into the current model for the assessment of plasma MPH concentration time courses under various fed conditions with more confidence.

Last, but not the least, it has been suggested that the magnitude of symptom reduction by MPH follows its plasma concentration profiles [11, 77], in addition to the association between clinical response with the rate of rise in blood drug concentrations (the “ramp” effect) being proposed [1]. That is, a potential positive association is observed between blood MPH concentrations and clinical responses [2, 12], unless adverse effects exceed the efficacies [21]. The formulation with the highest plasma MPH concentrations at any specific time points usually yields better control of ADHD symptoms compared with other formulations [2]. Therefore, the prediction of the time courses of plasma MPH concentrations using the current model with the integration of patient-specific physiological conditions can help estimate the extent of the clinical effects throughout the day [2]. Such knowledge may assist the clinicians in the process of selecting appropriate MPH formulations to best fit the patient’s individual needs, ensuring symptom controls during the particular circumstances throughout the day. Moreover, understanding the potential differences in the plasma concentration time courses of MPH among various ER MPH formulations can help with the dose adjustment when converting a patient from one MPH ER formulation to another [21]. For example, Ritalin LA had a higher initial C_max compared with MLR-MPH, so it may be appropriate to start with a relatively higher dose when converting a patient from Ritalin LA to MLR MPH. In addition, the establishment of the association between dose and clinic effects with the incorporation of the pharmacodynamic model [78] into the current model would provide valuable insights into the time course profiles of the clinical outcome and possible side effects, offering guidance on individualized optimum treatment for ADHD for maximum efficacy [11].

In addition, the modeling approaches, e.g. the mathematical description of the dissolution, permeability, metabolism, distribution, etc, developed in the current study can be used for other drug products, including both immediate release and extended release formulations. With the integration of drug-specific information (physicochemical properties, such as solubility, Log P, pKa, and partition coefficient, etc; and metabolism kinetics) and formulation-related information (release characteristics described using Weibull function or in vitro dissolution profiles in bio-relevant media) into the current model, the absorption profile and disposition of the drug can be described in a quantitative manner. As discussed previously, compared with non-compartmental or compartmental classic pharmacokinetic modeling, the mechanistic platform established in the current model can better assist the understanding of the kinetic behaviors of other drugs in the GI tract, as well as their distribution and disposition in the system.

Conclusion

In the current study, a physiological absorption model was developed to characterize the pharmacokinetics of MPH in adults following oral dosing of both IR and ER MPH dosage forms. With the integration of information on the anatomy and physiology of the GI tract as well as MPH physicochemical properties and formulation related information, the current model provides a mechanistic description of the kinetic behaviors of ER MPH in the GI tract, instead of an empirical first-order absorption rate constant as in the original model. The model performs well compared with observed data, with excellent fit to plasma concentration profiles of MPH in adult humans receiving IR MPH, suggesting the success of the model for the description of MPH absorption and disposition in the body. For ER MPH, the model, in general, tracked the kinetic behavior of plasma MPH in adults dosed with MLR-MPH and Metadate CD; while for Ritalin LA and Medikinet Retard, some discrepancy between model predictions and observations were observed, implying the necessity of employing more complicated mathematical approaches to describe the release of MPH from these formulations. The establishment of the current model provides a valuable basis for the evaluation of ER MPH kinetics in children, as well as the assessment of food effect; it also offers assistance for the clinician in choosing the optimized dosage regimens to best fit the patient’s individual needs. In addition, the practice of the current model development provides some insights into the potential factors responsible for the observed diversity of MPH plasma concentration profiles among different ER formulations: 1) the ratio of IR/ER components across different ER formulations; 2) fasting/fed condition, for which gastric emptying and intestinal absorption rates vary; 3) engineered release profiles.

Supporting Information

Acknowledgments

The authors would like to acknowledge Drs. Annie Lumen, Luisa Camacho, and Frederick Beland for their critical review of our manuscript. The views presented in the current paper do not necessarily represent the views of the FDA.