The widespread usage of methylphenidate (MPH) in the pediatric population has received considerable attention due to its potential effect on child development. For the first time a physiologically based pharmacokinetic (PBPK) model has been developed in juvenile and adult humans and nonhuman primates to quantitatively evaluate species- and age-dependent enantiomer specific pharmacokinetics of MPH and its primary metabolite ritalinic acid. The PBPK model was first calibrated in adult humans using in vitro enzyme kinetic data of MPH enantiomers, together with plasma and urine pharmacokinetic data with MPH in adult humans. Metabolism of MPH in the small intestine was assumed to account for the low oral bioavailability of MPH. Due to lack of information, model development for children and juvenile and adult nonhuman primates primarily relied on intra- and interspecies extrapolation using allometric scaling. The juvenile monkeys appear to metabolize MPH more rapidly than adult monkeys and humans, both adults and children. Model prediction performance is comparable between juvenile monkeys and children, with average root mean squared error values of 4.1 and 2.1, providing scientific basis for interspecies extrapolation of toxicity findings. Model estimated human equivalent doses in children that achieve similar internal dose metrics to those associated with pubertal delays in juvenile monkeys were found to be close to the therapeutic doses of MPH used in pediatric patients. This computational analysis suggests that continued pharmacovigilance assessment is prudent for the safe use of MPH.

Competing interests: Dr. Donald R. Mattison has worked as a consulting expert in litigation against other pharmaceutical companies brought by government entities and private plaintiffs. Dr. Mattison is an officer of Risk Sciences International, a firm whose clients include Health Canada and the FDA. This does not alter the authors’ adherence to PLOS ONE policies on sharing data and materials.

Funding: This work was supported by NCTR/FDA and the FDA Commissioner’s Program. These sponsors had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. The views presented here do not necessarily reflect the position or opinions of the FDA/NIH nor does mention of trade names or commercial products constitute endorsement or recommendation for use. The findings and conclusions in this manuscript are those of the authors and do not necessarily represent the views of the FDA/NIH.

This is an open-access article, free of all copyright, and may be freely reproduced, distributed, transmitted, modified, built upon, or otherwise used by anyone for any lawful purpose. The work is made available under the Creative Commons CC0 public domain dedication.

To extrapolate the MPH toxicity findings reported in juvenile monkeys to children, a physiologically based pharmacokinetic (PBPK) model was constructed for MPH and its major metabolite RA for the first time. The model structure accounted for both the d- and l- enantiomers of MPH and RA in adult and young humans and non-human primates. The MPH PBPK model provided a computational methodology to evaluate and compare the pharmacokinetics of pharmacological doses of MPH in children with MPH doses used in the toxicity studies with juvenile rhesus monkeys. The metabolism and pharmacokinetics of MPH in young and adult humans have been evaluated for both immediate-release and extended-release MPH formulations. For juvenile and adult rhesus monkeys experiments conducted at the National Center for Toxicological Research (NCTR) in Jefferson, AR, only an immediate-release MPH formulation was used. Hence, to allow for cross-species comparison and extrapolation of MPH internal doses, only data obtained after the administration of immediate-release MPH are considered in the current manuscript.

Some health concerns exist for children and adults who are treated chronically with MPH. In a pediatric study to evaluate diurnal changes in salivary hormones of children taking psychotropic medications, those taking MPH tablets exhibited diminished diurnal rhythms of testosterone, while children taking extended-release MPH tablets had significantly higher testosterone levels [25] . In MPH toxicity studies in monkeys, juvenile male rhesus monkeys exhibited transient delays in puberty, lower serum testosterone levels, impaired testicular descent, and reduced testicular volume [26] . In another study, increases in blood testosterone levels were observed in peri-adolescent male rhesus monkeys [27] .

The metabolism and disposition of MPH has been investigated in a variety of laboratory animals including rats, mice, and dogs [18] , [21] . In contrast to humans, both microsomal oxidation and hydrolysis are important metabolic pathways for rats, mice, and dogs [18] , [21] . In monkeys, RA (hydrolysis) has been shown to be a major metabolite of MPH [22] , [23] and the oral bioavailability for total MPH was reported to be 22% in young monkeys [24] .

In humans, MPH is metabolized predominantly by hydrolysis (de-esterification) to the pharmacologically inactive ritalinic acid (RA), with pronounced enantioselectivity in favor of the l-enantiomer [4] , [10] , [13] – [15] ( Figure 1 ). Human carboxylesterase (CES) 1A1 has been shown to be the major enzyme responsible for the stereoselective hydrolysis of MPH [16] . In addition, other minor metabolites produced through oxidation and subsequent conjugation or hydrolysis, including the pharmacologically active metabolite para-hydroxymethylphenidate [17] , have also been identified in humans [18] . Extensive first-pass metabolism of total MPH (d-and l-MPH) results in low absolute oral bioavailability of the racemic drug. In healthy adult humans, only 22±8% and 5±3% of the d- and l-MPH, respectively, reach the systemic circulation [4] . In children diagnosed with hyperactivity, the systemic bioavailability of total MPH ranges from 11 to 52%, with an average of 31±16% [19] . The majority of MPH administered orally or by intravenous (iv) injection is excreted in urine, accounting for 80% [18] and 78–97% [20] of the administered dose within 48 h and 96 h, respectively. Only 3% of the administered MPH dose is recovered in feces over a 48 h period [18] . The major metabolite of MPH identified in urine is the hydrolytic metabolite RA, accounting for 80% of the total urinary excretion, following both oral and iv administration, while unmetabolized MPH accounted for less than 1% [13] , [18] .

Attention deficit hyperactivity disorder (ADHD) is one of the most common childhood disorders and its frequent persistence into adulthood has been increasingly recognized [1] . According to a recent survey, the number of children in the U.S. diagnosed with ADHD continues to increase. Nearly 2 million additional U.S. children/adolescents aged 4 to 17 years were diagnosed with ADHD in 2011, compared to 2003 [2] . The point prevalence of ADHD is estimated to be 5–10% in children and about 3% in adults [1] . Methylphenidate (MPH), a blocker of the monoamine transporter that inhibits reuptake of dopamine and norepinephrine, remains a mainstay of treatment for ADHD [3] . Most MPH formulations contain a racemic mixture (1∶1) of the threo pair of MPH isomers (d, l-threo MPH), which is more potent pharmacologically than its corresponding erythro pair [4] – [6] . In addition, the d-threo-MPH (d-MPH) enantiomer exhibits a greater pharmacological potency than the l-enantiomer, and there is no evidence of interconversion between these two enantiomers [7] – [10] . Starting in 1960s, conventional, immediate-release MPH became the primary stimulant used to treat ADHD symptoms. Due to its short-term action (typically only lasting for 4 hours), IR MPH is typically given two to three times a day to cover normal school and after-school hours [11] . However, under such a dosing schedule, children may experience inattention during the trough in MPH levels, e.g. during late morning classes. Other problems associated with multiple dose regimens are compliance, confidentiality, and drug security issues at school. Given the dosing limitations of immediate-release MPH, several extended-release MPH formulations with longer effective durations of action have been introduced into the market [3] , [12] , [13] .

Materials and Methods

Ethics Statement All animal procedures were approved by the NCTR Institutional Animal Care and Use Committee.

Key pharmacokinetic studies in humans Given that d-MPH and l-MPH exhibit distinct pharmacokinetic profiles [4], [10], [14], [15] and pharmacological activities [7]–[10], simultaneous PBPK model predictions of both enantiomers are clinically relevant. Therefore, therapeutic drug monitoring studies utilizing enantiospecific assays were preferentially selected for human model development. In addition, pharmacokinetic studies with parallel measurements of MPH and its major metabolite RA concentrations were also considered important for tracking the mass balance of MPH and the fraction of MPH metabolized by the hydrolytic pathway. Pharmacokinetic data sets used for model calibration and evaluation for healthy adult humans and children with ADHD are briefly summarized below (Table S1 and Table S2). MPH used in these studies is assumed to consist of a 1∶1 racemic mixture of d- and l-enantiomers [4]–[6], [13], unless the use of d-MPH is indicated. In addition, unless specified otherwise, MPH and RA concentrations mentioned hereinafter refer to total (d- plus l-) MPH and total (d- plus l-) RA concentrations. Pharmacokinetic data sets used to calibrate the adult human model were from iv and oral dosing studies [4], [24], [28]–[33]. For iv dosing, the first data set used to calibrate the model was time course of plasma d- and l-MPH concentrations following a single iv dose of 10 mg MPH in healthy adult men (n = 13) [4]. The second iv study used to calibrate the model was urinary excretion time course data for d- and l-RA in healthy adult men administered a single iv dose of 10 mg MPH (n = 9) [28]. For oral dosing, a total of six data sets were used for model calibration [24], [29]–[33], of which, three data sets provided time courses of plasma d- and l-MPH concentrations in healthy adults following a single oral dose of MPH at 0.3 mg/kg (n = 24) [29], 0.3 mg/kg (n = 19) [30], and 40 mg (n = 21) [31]; the other three studies reported time courses of plasma MPH and RA concentrations in healthy adult men following a single oral dose of MPH at 20 mg (n = 5) [32], 20 mg (n = 8) [33], and 0.15 and 0.3 mg/kg (n = 10) [24]. Pharmacokinetic data sets used to evaluate the adult human model were oral dosing studies [20], [28], [34]–[37]. The first kinetic studies used for testing the model were time courses of plasma d-MPH concentrations in healthy adults following a single oral dose of 50 or 90 mg MPH (n = 49) [34] and repeated oral doses of 30 mg MPH (n = 28) [35]. The second kinetic studies used for model evaluation were time courses of plasma MPH concentrations in healthy adults given a single oral dose of 20 mg MPH (n = 20) [36] and repeated oral doses of 5 mg MPH (n = 35), for which plasma RA concentrations were also determined [37]. The third kinetic studies used for model evaluation were urinary excretion time courses in healthy adult men for d- and l-RA following a single oral dose of 40 mg MPH (n = 9) [28] and for RA after a single oral dose of 20 mg MPH (n = 3) [20]. Additional plasma pharmacokinetic data sets in healthy adults administered either a single oral dose or repeated oral doses of MPH or d-MPH were also used for adult human model evaluation [38]–[43] (Text S1). For children, one study reported serum MPH kinetics in boys administered 10–20 mg MPH intravenously (n = 6) [44] and another study reported serum peak RA levels in boys administered 10–15 mg MPH intravenously (n = 5) [19]. However, attempts to use these data sets for pediatric model development were not successful. Systemic clearance of MPH for children in the study of [44] is dramatically different from adult humans [4]. Hepatic metabolic constants describing MPH hydrolysis by human carboxylesterase 1 (hCES1) (see below for model description) need to be increased to approximately 50 fold of adult values to capture the rapid clearance of MPH observed for these children [44] while maintaining the appropriate estimation of serum RA levels [19]. Accordingly, the resultant scaled hepatic hydrolysis rate (µg/h) in children is 22–36 fold of adult human values. This is inconsistent with the finding that children show similar hepatic expression and activity of hCES1 enzyme compared to adult humans [45]. Further, plasma concentrations of MPH enantiomers following oral administration of 10 mg MPH in children [7], [46]–[51] are under estimated to a great extent using these large hepatic metabolic constants derived from these two studies [19], [44], even if assuming a rapid oral uptake and no gut metabolism. Eventually these two studies were excluded from data sets used for model development and evaluation because of their inconsistency with respect to several other MPH pharmacokinetic data sets in children [7], [46]–[51]. Hence, the pediatric MPH model was developed using MPH pharmacokinetic data sets following oral dosing in children [7], [19], [46]: of which, two studies provided plasma concentration time courses of d- and l-MPH following a single oral dose of 10 mg MPH in 5 boys with attention deficit disorder (ADD) [46] and 9 boys with ADHD [7]; and in another study, Chan et al. [19] reported peak serum RA levels in boys administered 10–15 mg MPH orally (n = 5). Several additional pharmacokinetic data sets in children orally administered MPH were used for model evaluation [47]–[51]. The first data sets used for testing the model were plasma d-MPH concentration time courses in 14 preschool (4–5 years) and 9 school-aged (6–8 years) children with ADHD administered a single oral dose of 2.5–10 mg MPH [49] and in 31 boys with ADHD given a single oral dose of 5–20 mg MPH [50]. The second data sets used for model evaluation were plasma MPH concentration time courses in boys with ADD administered a single oral dose of MPH at 0.34 and 0.65 mg/kg (n = 14) [47], and in children with ADHD given repeated oral doses of MPH at 5–15 mg (normalized to a 5 mg dose, n = 14) [48] and 10–40 mg (normalized to a 20 mg dose, n = 14) [51].

Key pharmacokinetic studies in nonhuman primates The monkey MPH pharmacokinetic study reported by Wargin et al. [24] was used for model calibration. In this study, 5 young monkeys, aged 2.5 years, were dosed intravenously with 3 mg/kg of MPH and blood samples were collected over 9 hours [24]. Accordingly, MPH used for monkey studies is assumed to consist of a 1∶1 racemic mixture of d- and l-enantiomers [4]–[6], [13] as well. Unreported pharmacokinetic data collected from a chronic MPH toxicity study at NCTR with juvenile rhesus monkeys [22], [23], [26] were also used to calibrate the monkey MPH PBPK model. The experimental design is briefly described below. In a preliminary study conducted to determine the most appropriate vehicle for MPH, 4 adult female rhesus monkeys (6.5–9.8 kg) were dosed with 0.3 mg/kg of MPH (USP grade, Mallinckrodt, St. Louis, MO) by oral bolus gavage (solution in Prang, Bio-Serv, Frenchtown, NJ) and via iv administration. Blood samples were collected at 13 time points after iv dosing and 9 time points after oral dosing over a 24 h period and plasma levels of both MPH and RA were determined by HPLC-MS/MS [52]. Based on plasma level data obtained from these studies in adult monkeys, a chronic toxicity study was performed with MPH and juvenile male rhesus monkeys [22], [23], [26]. Twenty male rhesus monkeys, approximately 2.5 years old at the beginning of the experiment (an age approximately equivalent to 7.5 year old boys, estimated based on maximum life-span of 122 and 40 years in humans and rhesus monkeys [53], [54]), were treated orally with MPH. The details of the study design and toxicity findings have been published in Morris et al. [23] and Mattison et al. [26]. Each lot of MPH (USP grade, Mallinckrodt, St. Louis, MO) was examined for purity prior to use in the study. All lots were determined to be structurally consistent with the NIST standard for MPH, with purity ≥99.0%. MPH was dissolved in Prang (Bio-Serv, Frenchtown, NJ), an oral rehydration solution commonly used as a vehicle in non-human primate experiments. Test article preparation occurred weekly and each dose preparation was analyzed by HPLC-MS/MS [52] for dose accuracy. Only dose preparations that were within ±10% of the target dose were used. The test subjects were dosed twice a day (with a 4 hour interval), 5 days a week (Monday to Friday) via an oral dosing syringe. Both low dose (0.15 mg/kg of MPH, n = 10) and high doses (1.5 mg/kg of MPH, n = 10) were increased to final doses of 2.5 and 12.5 mg/kg [26]. These dose adjustments were required to achieve clinically relevant pediatric blood concentrations of MPH (2–10 ng/mL) [26], [55]. During the chronic MPH toxicity study, blood samples were collected after administration of MPH on a quarterly basis for about a 1-year period. On the days of blood collection (Monday to Thursday), the monkeys only received the first (morning) dose of MPH and blood samples were collected at eight time points from pre-dose to 24 h post-dose: samples were collected from 1–4 monkeys per time point. The monkeys underwent preliminary training for blood collection and were not anesthetized during the pharmacokinetic experiments. Plasma MPH and RA concentrations were determined for each monkey using an HPLC-MS/MS method [52]. Measurements of plasma MPH concentrations pre-dose and at 24 h post-dose were excluded due to quantitation limitations. Kinetic profiles of MPH and RA for each individual monkey were followed on the same day of the week when quarterly blood sampling occurred over the 1-year period. Another nonhuman primate toxicity study with MPH [27], and limited plasma measurements of MPH, were used for evaluation of the monkey model. In this study, 8 male rhesus monkeys from Johns Hopkins University, approximately 3–4 years old, weighing 3.1–10.2 kg, were orally dosed with MPH in Tang solution via a 15-min self-dosing procedure, twice a day (at 0900 and 1200 hours), 7 days a week [27]. The average consumed MPH doses were 10.7 (8.89–13.1) and 16.5 (15.5–18.7) mg/kg, with the target intake determined to be 12–16 mg/kg, which produced the therapeutic blood levels of 15–25 ng/ml [27]. Blood sampling occurred periodically at 1000 and 1300 hours, and MPH plasma concentrations were quantified using a GC-MS method.

Model Development: Adult Humans MPH: hepatic metabolism. In adult human livers, the majority (approximately 80%) of MPH is metabolized by hydrolysis resulting in the formation of RA [18], while the remaining is subject to oxidation [13], [18]. The stereoselective hydrolysis (Rmet_liver, µg/h) of d- and l-MPH was described using a Michaelis-Menten equation representing the competitive binding to the hCES1A1 enzyme between d- and l-MPH [16], [29]: (3) The Michaelis constants for d- and l-MPH (Kmliverd and Kmliverl, µg/L) were set equal to the reported Km values of 27,600 and 10,172 µg/L, experimentally determined using the recombinant human CES1A1 enzyme [16] (Table 3). CVliver is the venous plasma concentration leaving the liver for one isomer (CVliverd and CVliverl, µg/L) and CVliver inhibitor is the venous plasma concentration leaving the liver for the inhibiting isomer (CVliverl and CVliverd, µg/L). Kmliver inhibitor represents the dissociation constant for the inhibiting isomer, set to the Kmliver value of that isomer (Kmliverl and Kmliverd, µg/L). Vmaxliver (µg/h) is a scaled maximum hepatic reaction velocity, described as the product of the maximum hepatic reaction velocity constant (VmaxliverdC and VmaxliverlC, µg/h/kg0.75, for d- and l-MPH) and the body weight (BW)0.75. VmaxliverdC and VmaxliverlC (µg/h/kg0.75) were initially derived from the calculated in vitro maximal velocity of 38,496 and 78,111 ng/h/mg protein, which were obtained based on the reported in vitro catalytic constant values (Kcat, 0.165 min−1 and 0.335 min−1 for d- and l-MPH) using the recombinant human CES1A1 enzyme [16]. The in-vitro in-vivo extrapolations (IVIVE) were performed by accounting for microsomal protein content of the liver (39.19 mg microsomal protein/g liver [70]) and model predicted average liver weight (2.06 kg) for healthy men 18–30 years old [4], and estimated body weight of 74.8–84.02 kg [38]. A relative activity factor of 0.22, determined as the ratios of the imidapril hydrolase activity in human liver microsomes to the value for recombinant human CES1A1 enzyme [71], was considered to bridge the gap between the recombinant enzyme and native liver microsomes. Optimization of IVIVE derived VmaxliverdC and VmaxliverlC values was attempted using the NelderMead algorithm by simultaneous fitting to plasma concentration time courses of d- and l-MPH following iv dosing of 10 mg MPH in healthy adult men over a period of 16 h [4]. A convergence of values for VmaxliverdC and VmaxliverlC could not be achieved. Hence, the derived initial VmaxliverC values for d- and l-MPH were eventually adjusted manually (1.5 fold) to attain the best agreement between prediction and observed plasma d- and l-MPH concentrations (Table S1). PPT PowerPoint slide

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larger image TIFF original image Download: Table 3. Chemical specific model parameters. https://doi.org/10.1371/journal.pone.0106101.t003 The oxidation metabolic pathways for the MPH enantiomers in the liver were described using clearance terms (KmetdC and KmetlC, L/h/kg0.75). This metabolic pathway for each enantiomer was constrained to yield an upper bound equal to 20% of the total dose metabolized in the liver [18]. The enzymes responsible for the hepatic oxidation of MPH have not yet been identified. CYP2D6 is known not to be involved [72]. MPH: Oral uptake and gastrointestinal (GI) tract metabolism. The use of the hepatic metabolic constants derived from iv dosing of adult humans consistently overestimated the plasma levels of MPH following oral administration, even with a small first order oral uptake constant. The metabolism of MPH in the GI tract by hydrolysis and oxidation was introduced into the human PBPK MPH model to achieve better predictions of observed plasma MPH concentrations following oral administration [24], [29]–[33]. The rationales for the inclusion of GI tract metabolism are as follows. Though the predominant human CES1 enzyme identified for the hydrolysis of MPH was found primarily in human livers, expression of CES1 is also present in the human GI tract as identified by Northern blots [73], [74]. In addition, hydrolysis of flurbiprofen derivatives (flurbiprofen hydroxyethyl ester and hydroxypropyl ester), which are excellent substrates for hCES1 but not for hCES2, has been reported in human small intestine microsomes [75]. Other interesting observations suggest that the pharmacokinetics of the orally administered MPH is much less straightforward than iv administration. Higher plasma levels of d-MPH compared to l-MPH were observed immediately after oral administration (0.5 h), but not apparent until 1.5 h after iv administration [4]. Also, a distortion of the enantiomeric ratio for RA (l>>d) was observed in both human plasma and urine samples in the first 2 h after oral but not iv administration [28], [58]. Such route-dependent discrepancies found in the first 2 hours after dosing suggested the potential enantioselective presystemic metabolism of orally administered MPH in the GI tract. Expression of CYP enzymes has also been reported in human small intestines [76], although the enzymes responsible for the oxidation of MPH have not been identified [72], [77]. As such, metabolism of MPH in the GI tract by hydrolysis and oxidation was considered in the model, which was crucial to improving model performance. Following oral administration of MPH, gastric emptying of d- and l-MPH into the small intestine was described using first order gastric emptying constants (GEdC and GElC, 1/h/kg−0.25) set to a value of 3.5 1/h/kg−0.25 [63], [78]. The majority (80%) of orally administered MPH was excreted in urine. RA accounted for 80% of total urinary metabolites, and feces accounted for 3.3% [18]. MPH emptied from the stomach lumen into the small intestine lumen was assumed to be immediately available within enterocytes, where MPH is either rapidly absorbed into the portal blood supply [13] or metabolized in the GI tract as discussed above. The oral uptake of d- and l-MPH was described as a first order process (K3dC and K3lC, 1/h/kg−0.25), with no evidence for the stereospecific absorption [16]. To account for the metabolic degradation of d- and l-MPH in the gut, first-order terms (K5dC and K5lC, 1/h/kg0.75) were employed, of which, a fraction (F = 0.80, 80%) was assumed to undergo hydrolysis to form RA, and be immediately absorbed into the systemic circulation. The remaining fraction (1-F) was assumed subject to oxidation. Optimized oral uptake constants (K3dC and K3lC, 1/h/kg−0.25) and metabolism constants (K5dC and K5lC, 1/h/kg0.75) for d- and l-MPH were obtained by simultaneous fitting to plasma concentrations of d- and l-MPH in adult humans orally dosed with MPH at 0.3 mg/kg [29], [30] and 40 mg [31], as well as plasma concentrations of MPH and RA in adult men orally dosed with MPH at 20 mg [32], [33] and 0.15 and 0.3 mg/kg [24] (Table S1). Optimization was carried out using the NelderMead algorithm. RA: formation, distribution and systemic clearance. The rate of MPH hydrolysis in the liver and the GI tract was set equal to the rate of RA formation. Given that RA is highly soluble in the aqueous medium [79], the volume of distribution for RA was set to the value of total body water volume (0.6 L/kg) in adult humans [80]. Optimized systemic clearance terms for d- and l-RA (Ku_RAdC and Ku_RAlC, L/h/kg0.75) were obtained by simultaneous fitting to the urinary excretion of d- and l-RA over a period of 16 h after iv dosing of 10 mg MPH in healthy adult men [28] (Table S1). Optimization was performed using the NelderMead algorithm.

Model Development: Children Stereoselective metabolism of MPH (l>>d) has been documented in children [7], [46]. Also the expression and activity of hCES1 toward MPH in liver S9 fractions did not differ between children (aged 6–18 years old) and the pooled adult human samples [45]. Thus, the maximum velocity constants for hepatic metabolism (hydrolysis) of l- and d- MPH (VmaxliverdC and VmaxliverlC, µg/h/kg0.75) in children were set to the adult values. With no information to assume otherwise, hepatic oxidation of l- and d-MPH was also assumed to occur in children. Though the predominant enzymes responsible for the oxidation of MPH have not yet been identified, studies have demonstrated that the CPY3A subfamily is the most important subfamily among the total P450 enzymes responsible for the biotransformation of drugs in the human liver, with CYP3A4 as the most abundant isoform [81], [82]. As such, the age-dependent oxidation of MPH in the liver was assumed to be represented by the ontogeny of CYP3A4 enzymes. Hepatic RNA and protein contents of CYP3A4 as well as its activity, characterized by 6β hydroxylation of testosterone, reached adult values after 1 year of age [83]. For this reason, the clearance terms describing the metabolism of l- and d-MPH via oxidation (KmetdC and KmetlC, L/h/kg0.75) in the liver of children were assumed to be the same as adults. Since no data are available to describe the age-dependent oral uptake and metabolism of MPH in the gut, model parameters specific for oral dosing describing oral uptake (K3dC and K3lC, 1/h/kg−0.25) and gut metabolism (K5dC and K5lC, 1/h/kg0.75) for children were assumed to be the same as adult humans. Scaling of adult MPH-specific model parameters performed well for the prediction of plasma d-MPH levels, but consistently underestimated plasma l-MPH levels in boys administered 10 mg MPH orally [7], [46], even with a large oral uptake rate constant for l-MPH, suggesting that systemic clearance of l-MPH is slower in children compared with adults after oral dosing. Optimization of oral uptake and hepatic and gut metabolic parameters for MPH enantiomers was conducted using the NelderMead algorithm by simultaneous fitting to the plasma concentration time courses of d- and l-MPH in these children [7], [46], but consistent convergence of parameter values could not be achieved. Thus, with other MPH-specific parameters fixed to adult values, the first order constant (K5lC, 1/h/kg0.75) describing gut metabolism for l-MPH was decreased by approximately 14 fold to achieve better agreement between model predictions and observed plasma concentration time courses of l-MPH in these children [7], [46] (Table S2). The scaled clearance terms representing urinary excretion of l- and d-RA (Ku_RAdC and Ku_RAlC, L/h/kg0.75) were set to the adult values because of a lack of the time course RA concentrations in plasma or urine of children. The volume of distribution for RA was set to the body water volume of 0.572 L/kg in children [84], [85]. As a consequence of uncertainty in model parameter specificity, this MPH PBPK model is fit for purpose. That is, model parameters were fitted to provide agreement between observation and prediction; other factors may be important, but are unknown and not described in the model.

Model Development: Adult Monkeys Due to the lack of experimental data to determine model parameters in adult monkeys, the development of the monkey PBPK model relied primarily on cross species extrapolation using allometric scaling, as demonstrated in other PBPK models [62], [63]. The model parameters for the adult human intravenously dosed with MPH were used for the adult monkey intravenously dosed with 0.3 mg/kg MPH (NCTR data). The volume of distribution (VbodyC, L/kg) for RA was set to the total body water volume of the adult monkey (0.693 L/kg) [80]. Adult human values for parameters describing hepatic hydrolysis (VmaxliverdC and VmaxliverlC, µg/h/kg0.75) and oxidation (KmetdC and KmetlC, L/h/kg0.75) were used to describe plasma MPH concentration time course in adult monkeys. Model parameters (Ku_RAdC and Ku_RAlC, L/h/kg0.75) representing the systemic excretion of l- and d-RA in adult monkeys were assumed to be the same as adult humans. Describing the kinetics of MPH after oral administration of MPH in the adult monkey was not possible using adult human model parameters describing oral uptake and adult monkey model parameters derived from intravenous dosing of the adult monkey with MPH. To improve predictions, the first order constants describing the gut metabolism of d- and l-MPH (K5dC and K5lC, 1/h/kg0.75) were increased proportionally by 25 fold to visually fit the plasma MPH concentrations from 1 to 8 h (clearance phase) following a single oral dose of 0.3 mg/kg MPH in adult monkeys (NCTR data). The rationale for this re-parameterization was based on reports of more abundant intestinal expression of the CES1 enzyme [75], [86], [87] in monkeys than humans and more rapid hydrolysis of the CES1 substrates flurbiprofen derivatives (2 to 55 fold) [75] in monkey small intestines than humans.

Model Development: Young Monkeys Because of the lack of information on MPH disposition in young monkeys, the calibrated adult monkey model was extrapolated to describe MPH kinetics in young monkeys, as other PBPK models did [63], [88]. In sharp contrast to adult monkeys, plasma MPH was cleared more rapidly in young monkeys following iv administration [24]. To account for the observed rapid clearance of MPH in young monkeys, both maximum hepatic reaction velocity (VmaxliverdC and VmaxliverdC, µg/h/kg0.75) describing the hydrolysis and the clearance term (KmetdC and KmetlC, L/h/kg0.75) describing the oxidation in the liver derived from the adult monkey model were simultaneously increased by 10- and 100-fold to fit the plasma concentrations of MPH and RA following a single iv dose of 3 mg/kg MPH in young monkeys [24]. Due to the lack of information on urinary excretion of RA in young monkeys, parameters describing urinary excretion (Ku_RAdC and Ku_RAlC, L/h/kg0.75) and volume of distribution (VbodyC, L/kg) for young monkeys were set to adult monkeys values. With hepatic metabolic constants for MPH and parameters describing systemic distribution and clearance for RA determined by iv dosing, plasma concentration time courses of MPH and RA after repeated oral doses of 2.5 and 12.5 mg/kg of MPH in juvenile monkeys (NCTR study) were predicted using gastric emptying (GEdC and GElC, 1/h/kg−0.25) and oral uptake (K3dC and K3lC, 1/h/kg−0.25) parameters derived from the adult monkey model. The metabolism of MPH in the gut was not considered necessary in young monkeys with respect to maintaining reasonable prediction of time course kinetics of MPH and RA in plasma. Research is needed to fully understand the metabolic pathways of MPH in the liver and the GI tract for both adult and young monkeys.

Assessment of Model Performance Because of the concern for children only the juvenile monkey and child MPH models were evaluated for their ability to predict measured plasma pharmacokinetic data sets for MPH and d- and l-MPH following oral administration of immediate-release MPH. To access model performance, the Root Mean Squared Error (RMSE) was calculated for data sets in the juvenile monkey reported in this paper (NCTR data) and from Johns Hopkins University [27] and for pediatric data sets reported by [7], [46]–[51]. Model performance was calculated as following: (4)where predicted is the model predicted plasma concentration and observed is the reported plasma concentration. N represents number of predictions and observations.

Interspecies Extrapolation (Monkey to Human) Juvenile male rhesus monkeys, 5 years of age, experienced a temporary decrease in circulating testosterone levels after chronic oral exposure to 2.5 mg/kg MPH and for 12.5 mg/kg MPH, a decrease in circulating testosterone levels along with impaired testicular descent, and reduced testicular volume [26]. Boys are more frequently diagnosed with ADHD than girls [89]. MPH is approved by the FDA for use in patients 6 years of age and older [13]. Given that the juvenile monkey toxicity data was in males, the developmental toxicity of MPH was extrapolated from male juvenile monkeys to boys between approximately 6 and 15 years of age. The model performance (RMSE) for the 12.5 mg/kg juvenile monkey dose group was judged inadequate for model predictions in humans (see Results). PBPK derived oral human equivalent doses (HEDs) were only derived for the 2.5 mg/kg MPH juvenile monkey dose group. MPH HED values were calculated for the dosimetrics, maximum plasma concentration (Cmax, ng/mL) and daily area under the plasma MPH concentration curve (daily AUC, ng/mL*h per day). Preliminary simulations revealed no plasma accumulation of MPH in juvenile monkeys following a child’s therapeutic dosing schedule; while for children, a slight accumulation of plasma MPH levels was noticed with periodicity reached within 3 days. Thus, repeated daily oral dosing of MPH was simulated for 3–7 days to ensure steady state of MPH for both juvenile monkeys and children. Briefly, for juvenile monkeys, a one-week exposure for oral ingestion of MPH (2.5 mg/kg) occurred twice with a 4-h interval/day, 5 days a week, a dosing schedule utilized in the juvenile monkey toxicity study with MPH [26]. The dose metrics, Cmax and daily AUC calculated as the total AUC obtained from 1 week divided by 7 days (referred to as adjusted daily AUC, see Table S3), were recorded for MPH. Then simulations for children with repeated oral dosing of MPH twice a day, 7 days a week, with doses 4 h apart, were conducted with varying doses of MPH. The doses producing the equivalent internal dosimetrics (Cmax and daily AUC) of MPH at steady state (from day 4 to day 7) for children as those derived in the juvenile monkeys were determined as MPH HEDs. In addition, model-predicted internal dose metrics (Cmax and daily AUC) in boys 6 and 15 years of age administered clinically recommended doses by the American Academy of Pediatrics (AAP) (0.3–0.8 mg/kg twice daily, taken 4 h apart) [90] for 1 week were compared with those obtained in juvenile rhesus monkeys experiencing delayed puberty as described above. PBPK model code is contained in supplementary data (Text S2 and Text S3) and m files are available upon request.