Novel extended in vitro-in vivo correlation model for the development of extended-release formulations for baclofen: From formulation composition to in vivo pharmacokinetics

Accepted Manuscript Novel Extended In Vitro-In Vivo Correlation Model for the Development of Extended-Release Formulations for Baclofen: from Formulation Composition to in vivo Pharmacokinetics Tae Hwan Kim, Jürgen B. Bulitta, Do-Hyung Kim, Soyoung Shin, Beom Soo Shin PII: DOI: Reference:

S0378-5173(18)30912-8 https://doi.org/10.1016/j.ijpharm.2018.12.007 IJP 17975

To appear in:

International Journal of Pharmaceutics

Received Date: Revised Date: Accepted Date:

16 July 2018 7 November 2018 2 December 2018

Please cite this article as: T. Hwan Kim, J.B. Bulitta, D-H. Kim, S. Shin, B. Soo Shin, Novel Extended In Vitro-In Vivo Correlation Model for the Development of Extended-Release Formulations for Baclofen: from Formulation Composition to in vivo Pharmacokinetics, International Journal of Pharmaceutics (2018), doi: https://doi.org/ 10.1016/j.ijpharm.2018.12.007

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Novel Extended In Vitro-In Vivo Correlation Model for the Development of Extended-Release Formulations for Baclofen: from Formulation Composition to in vivo Pharmacokinetics Tae Hwan Kima, Jürgen B. Bulittab, Do-Hyung Kimc, Soyoung Shind,*,+, and Beom Soo Shine,*,+

a College

of Pharmacy, Catholic University of Daegu, Gyeongsan, Gyeongbuk 38430, Korea

b College

of Pharmacy, University of Florida, Orlando, FL 32827, USA

c KNOTUS d College e

Co., Ltd. Research center, Guri, Gyeonggi 11910, Korea

of Pharmacy, Wonkwang University, Iksan, Jeonbuk 54538, Korea

School of Pharmacy, Sungkyunkwan University, Suwon, Gyeonggi 16419, Korea

* Corresponding Authors: Beom Soo Shin, Ph.D. School of Pharmacy, Sungkyunkwan University 2066 Seobu-ro, Jangan-gu, Suwon, Gyeonggi-do 16419, Republic of Korea Tel: +82-31-290-7705, Fax: +82-31-292-8800, E-mail: [email protected] Soyoung Shin, Ph.D. College of Pharmacy, Wonkwang University 460 Iksan-daero, Iksan-city, Jeonbuk 54538, Republic of Korea Tel: +82-63-850-6816, Fax: +82-63-850-7309, E-mail: [email protected] +

Beom Soo Shin and Soyoung Shin contributed equally to this work.

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ABSTRACT In vitro-in vivo correlation (IVIVC), a predictive mathematical model between the in vitro dissolution and the in vivo pharmacokinetics has been utilized for the development of new extended release (ER) formulations. The aim of the present study was to extend the IVIVC approach, which correlates among the formulation composition, the in vitro dissolution, and the plasma drug concentration, to predict plasma drug concentrations from a given composition of the formulation, and vice versa, using baclofen as a model drug. Baclofen ER tablets with different dissolution rates were prepared by varying the composition of hydroxypropyl methylcellulose (HPMC). First, the HPMC compositions and the corresponding in vitro dissolutions parameters were correlated, and then the in vitro dissolution parameters were correlated with the in vivo dissolution parameters extracted from the pharmacokinetic profiles of the baclofen ER formulations via population pharmacokinetic modeling. The final extended IVIVC model linked the composition of the formulation, the in vitro dissolution, and the in vivo plasma concentration profile and was successfully applied for the prediction of in vivo pharmacokinetics from the amount of HPMC in baclofen ER formulations. The present approach holds great promise for designing optimal compositions of ER formulations to present desired plasma concentration profile.

KEYWORDS: extended-release formulation; in vitro-in vivo correlation; population pharmacokinetic model; hydroxypropylmethyl cellulose; baclofen.

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1. Introduction The extended-release (ER) oral dosage formulation is designed to make the drug available over an extended period of time after administration, lowering the frequency of doses, minimizing unwanted side effects, and improving patient compliance, thereby enhancing the therapeutic effects on the whole. Nevertheless, the process of development of the ER formulations usually takes time and is costly. The major difficulty in the development of ER formulations is repeating the in vivo experiments for proving the pharmacokinetic similarity of the ER formulation with a reference immediate-release (IR) formulation, which usually requires repeated clinical and nonclinical studies (Gomez-Mantilla et al., 2014). Since the extent and period of systemic drug exposures are controlled by the dissolution rate of the ER formulation, a good understanding of the in vitro dissolution profile and the in vivo plasma drug concentration profile of the dosage forms is integral to the successful development of new ER formulations. The in vitro-in vivo correlation (IVIVC), a predictive mathematical model describing the relationship between an in vitro property of an ER formulation and a relevant in vivo response (FDA, 1997), has been known as the best approach for the development of new ER formulations. Once IVIVC is established, the in vitro dissolution properties can serve as a surrogate for the in vivo pharmacokinetics (PK) study, which can accelerate the formulation development process, thereby saving time and cost (Cardot and Davit, 2012; Kim et al., 2017b). One of the critical steps in establishing IVIVC is the characterization of the in vivo dissolution profiles of the dosage forms. Various mathematical approaches have been used to estimate the in vivo dissolution profiles from the plasma concentration-time data. Conventional IVIVC approaches utilize mathematical methods such as the Wagner-Nelson (Wagner and Nelson, 1963) and the Loo-Riegelman (Loo and Riegelman, 1968) methods, or use numerical deconvolution

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(Cutler, 1978). While these conventional approaches are applicable only to highly permeable drugs such as the class I or class II drugs of the Biopharmaceutics Classification System (BCS) (Park, 2013, 2014), recent population pharmacokinetic modeling approaches can extend their application to drugs with complex physiological absorption processes (Abuhelwa et al., 2016; Kim et al., 2017a). Despite various ER oral formulations in the market, there are only a few mechanisms that are employed to control drug release rates. The major mechanisms employed include dissolution, diffusion, osmosis, and ion exchange, and most ER formulations are designed based on one or more combinations of these mechanisms (Wen and Park, 2010). The matrix dissolution system is the most commonly used system for controlled oral drug delivery in the pharmaceutical industry. In the matrix system, a drug that is homogeneously distributed throughout the polymer matrix is released as the matrix dissolves after hydration, gel formation, and swelling in aqueous media (Nokhodchi et al., 2012). Thus, the drug release is usually dependent on the properties of the polymer. A cellulose derivative, hydroxypropylmethyl cellulose (HPMC) is one of the most widely used polymers in matrix-type ER formulations. HPMC is considered an excellent drug release modifier due to its nontoxic property, ease of handling, ease of compression, ability to accommodate a large percent of drug, minimal influence of the processing variables on drug release rates, and relatively simple tablet manufacturing technology (Nokhodchi et al., 2012). It has been shown that the release rate is significantly dependent on the HPMC content, that is, the drug release rate decreased as the HPMC content was increased (Xu and Sunada, 1995). Thus, if any mathematical model that correlates the HPMC content to the drug release rate can be developed, the changes in drug release rate can be predicted from the levels of HPMC in the ER formulation.

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Therefore, this study aimed to develop a novel extended IVIVC model by extending the IVIVC concept to the composition of the formulation, and correlating among the composition of the formulation, the in vitro dissolution, and the in vivo pharmacokinetics. While the conventional IVIVC model allows the prediction of in vivo pharmacokinetics from the in vitro dissolution profiles, the present extended IVIVC model would allow the prediction of in vivo pharmacokinetics as well as the in vitro dissolution from the composition of the formulation. A mathematical relationship between the composition of the formulation and the drug release rate could predict in vitro dissolution parameters based on the composition of the ER formulation, that is, the HPMC content, without the requirement for in vitro dissolution tests. Then, instead of experimentally determining the in vitro dissolution, the in vitro dissolution parameters predicted from the HPMC content can be converted to in vivo behavior to establish IVIVC. To establish the extended IVIVC, a BCS class III drug, baclofen, was used as the model drug, and HPMC2208100 cps was used as a drug release-modifying polymer to develop the ER formulation.

2. Material and methods 2.1 Materials Lioresal® 5 mg was purchased from Novartis (Seoul, Korea). Baclofen was purchased from Whawon Pharm. Co. (Seoul, Korea). Hydroxypropyl methyl cellulose (HPMC) 2208-100 cps was obtained from Shin-Etsu Chemical Co., Ltd. (Tokyo, Japan). Magnesium stearate was purchased from Faci Asia Pacific Pte Ltd. (Jurong Island, Singapore). Sodium hydroxide and sodium chloride were purchased from Samchun Chemical Co., Ltd. (Seoul, Korea). Gabapentin (internal standard for LC-MS/MS assay), acetic acid, and formic acid were purchased from Sigma-Aldrich Co. (St. Louis, MO, USA). High performance liquid chromatography (HPLC) grade acetonitrile and water

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were purchased from J.T. Baker Co. (Philipsburg, NJ, USA). Ethanol (HPLC grade), hydrochloric acid, and potassium dihydrogen phosphate were purchased from Merck Co. (Darmstadt, Germany).

2.2 Formulation Eight different types of ER tablets containing 15 mg or 30 mg of baclofen were prepared with 2% to 60% HPMC and used in the development and validation of the extended IVIVC approach. The HPMC range of 2% – 60% was selected to cover a broad range of HPMC levels in tablets and to investigate its effect on drug release. It has been also reported that ER formulations could be successfully prepared by using these levels of HPMC (Jun et al., 2018; Mohamed et al., 2013; Prasanthi et al., 2017). To prepare the ER formulations, HPMC, lactose, and magnesium stearate were used as the drug release modifier, diluent, and lubricant, respectively. The compositions of the baclofen ER tablets are shown in Table 1. The ER granules were prepared by the wet granulation method. After mixing the baclofen with lactose and kneading with HPMC dissolved in ethanol, the dampened mixture was passed through a size 20-mesh screen. The wet granules were dried in an oven at 60˚C and again passed through a size 20-mesh screen. Prior to using the tablet press, the lubricant (1%) was added to the dried granules and mixed. Then, the mixture was compressed at a force of 20 kN by a hydraulic tablet press (Carver, Inc., Wabash, IN, USA) with a round-shaped punch (diameter: 11.7 mm).

2.3 In vitro dissolution test To evaluate the in vitro dissolution of baclofen from the reference IR (Lioresal® 5 mg) and ER tablets, the paddle method was employed, using the Distek Dissolution System 2500 coupled with

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the Evolution Dissolution Sampler 4300 (North Brunswick, NJ, USA). Two dissolution media consisting of 0.1 N HCl buffer (pH 1.2) and phosphate buffer (pH 6.8) were used and the temperature was maintained at 37 ± 0.5 °C during the release test. The dissolution test was conducted on four different vessels for each tablet using 900 mL of dissolution media. The paddle stirring speed was fixed at 100 rpm. The samples were collected by an auto sampler at 0, 0.17, 0.25, 0.33, 0.5, 0.75 and 1 h for IR tablet and 0, 0.25, 0.5 1, 2, 3, 4, 6, 8, 10, 12 and 15 h for SR tablet. After the samples were collected, the medium was refilled with fresh medium at each point of time. All the collected samples were filtered through a 45 μm polyethylene syringe filter (Distek) and immediately analyzed by the HPLC method.

2.4 Pharmacokinetic study 2.4.1

Animal study

The animal study was approved by the Institutional Animal Care and Use Committee at KNOTUS Co., Ltd (KAMSI IACUC 15-KE-054). All methods were carried out in accordance with relevant guidelines and regulations. Beagle dogs (11–12 months) were purchased from Orient Bio (Seongnam, Korea). The dogs were randomly divided into five groups, pertaining to the administration of the reference IR formulation and four different types of ER formulations, namely, ER5%, ER10%, ER15%, and ER30% (n=18, in total). After overnight fasting, the animals were fed on a canned diet (Cesar®, Mars, Inc.) and water, 30 min prior to drug administration. The tablets were orally administered to the dogs along with 10 mL of water to ensure that the dogs swallowed the tablets. The reference baclofen 5 mg IR tablets were administered twice (τ = 8 h), while the ER tablets were administered once. Food was re-supplied at 4 h after the administration of the first dose.

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Blood samples (3 mL) were collected from the jugular vein into a heparinized (5 IU/mL) tube at 0, 0.17, 0.33, 0.5, 1, 1.5, 2, 4, 6, 8, 8.17, 8.33, 8.5, 9, 9.5, 10, 12, 14, and 24 h, following the administration of the reference drug; at 0, 0.5, 1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5, 6, 8, 10, 12, and 24 h following the administration of ER5% and ER15% tablets; and at 0, 0.17, 0.33, 0.5, 1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 6, 8, 12, and 24 h following the administration of ER10% and ER30% tablets. The plasma samples were harvested by centrifugation of the collected blood at 4,000 × g at 4 ˚C for 10 min and stored at -20˚C until analysis. 2.4.2

Non-compartmental analysis

The pharmacokinetic parameters of baclofen were determined by non-compartmental analysis using the Phoenix® WinNonlin® software (Certara, L.P., Princeton, NJ, USA). These parameters included the terminal half-life (t1/2), the area under the plasma concentration–time curve from time zero to the last observation time point (AUC0-24h) and to infinity (AUCinfinity), apparent clearance (CL/F), and apparent volume of distribution (Vz/F). The maximum plasma concentration (Cmax) and the time to reach Cmax (Tmax) were obtained directly from the observed data. The relative bioavailability (BA) was estimated using the ratio of the dose-normalized AUCinfinity of the ER formulation to that of the reference IR formulation.

2.5 Drug analysis 2.5.1

HPLC

Baclofen concentrations in the dissolution medium were determined by HPLC using a Waters Alliance 2695 separation module coupled with the Waters 2487 dual absorbance detector (Waters, Milford, MA, USA). Baclofen was separated on a Kinetex C18 column (50 × 2.1 mm, i.d., 2.6 μm, Phenomenex, Torrance, CA, USA) with a KrundKatcher ultra column inline filter (Phenomenex).

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An isocratic solvent system consisting of methanol with 0.1% (v/v) aqueous triethylamine (pH 2.5, modified by the addition of phosphoric acid) (15:85 v/v %) was used as the mobile phase at a flow rate of 0.2 mL/min. The column oven temperature was set at 30 °C and the total run time was 4.5 min. The sample injection volume was 10 μL and baclofen was detected at 219 nm. The working standard solutions for HPLC analyses were prepared by serial dilutions of the stock solution in the mobile phase at concentrations of 0.5, 1, 2.5, 5, 10, 25, 50, and 100 μg/mL. 2.5.2

LC-MS/MS

Baclofen concentrations in dog plasma were determined by liquid chromatography-tandem mass spectrometry (LC-MS/MS) by using gabapentin as an internal standard. The LC-MS/MS comprised of an Agilent 6430 triple-quadrupole mass spectrometer coupled with an Agilent 1200 HPLC (Agilent Technologies, Santa Clara, CA, USA). Baclofen was separated on a Kinetex C18 column (50 × 2.1 mm, i.d., 2.6 μm, Phenomenex) with a KrundKatcher ultra column inline filter (Phenomenex). An isocratic solvent system consisting of acetonitrile and 0.05% (v/v) aqueous formic acid (10:90 v/v %) with a flow rate of 0.2 mL/min was used as the mobile phase. The column oven temperature was 30 °C and the total run time was 3.5 min. The mass spectrometer was operated using electron spray ionization (ESI) in the positive ion mode with mass transitions of 214.0→151.0 for baclofen and 172.1→14.1 for gabapentin. The plasma samples were prepared by the protein precipitation method using methanol. The lower limit of quantification was 5 ng/mL and the assay was validated by using quality control (QC) samples. The intra- and inter-day accuracy ranged from 93.6% to 105.5% and the precision was within 5.7%.

2.6 Mathematical modeling

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To establish the extended IVIVC, we developed a mathematical model for correlating between the composition of the formulation and the in vitro dissolution (Step 1). We then extracted the in vivo dissolution from the in vivo pharmacokinetic profiles via population pharmacokinetic (POP-PK) modeling (Step 2), and finally developed a model to correlate among the composition of the formulation, the in vitro dissolution, and the in vivo pharmacokinetics (Step 3). The final extended IVIVC, that is, the formulation composition-in vitro dissolution-in vivo pharmacokinetics model, was validated and utilized to predict the in vivo pharmacokinetics from the composition of the formulation, and vice versa (Step 4). Step 1: Correlation between the composition of the formulation and the in vitro dissolution To correlate the composition of the formulation, that is, the HPMC level, to the in vitro dissolution, the dissolution parameter, Vmax,in vitro, corresponding to the changes of the HPMC levels in the ER formulations, were estimated. The dissolution parameter, Vmax,in vitro, representing the maximum drug release rate, was estimated by fitting the in vitro dissolution profiles of the ER formulations at pH 1.2 and 6.8 to the Michaelis-Menten equation. The differential equation for the amount of undissolved baclofen in the dissolution medium was:

dX Tablet, in vitro Vmax, in vitro    X Tablet, in vitro dt AM50, in vitro  XTablet, in vitro

(Eq. 1)

Where, XTablet,in vitro represents the amount of baclofen in the ER formulation, Vmax,in vitro represents the maximum rate of drug release in the dissolution tester, and AM50, in vitro is the amount of drug at which the dissolution rate is half of Vmax,

in vitro.

Although AM50,

in vitro

can also affect the

dissolution profiles, dissolution profiles were more sensitive to Vmax, in vitro. Thus, we estimated Vmax, in vitro as a representing dissolution parameter to compare dissolution rates of different ER tablets.

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The dissolution data were fitted to the model by using the S-ADAPT software (version 1.57). After Vmax,in

vitro

was estimated from the in vitro dissolution profiles, the 1/Vmax,in

vitro

values were

correlated with the corresponding HPMC levels of the ER formulations by the Hill equation to predict the in vitro dissolution from the HPMC levels of the formulation. The dissolution profiles obtained from ER2%, ER10%, ER25%, ER30%, and ER60% in media at pH 1.2 and 6.8 were used for model development and parameter estimation, while those of ER5%, ER15%, and ER40% were used for the external validation of the model. Step 2: Extraction of in vivo dissolution profile from the in vivo pharmacokinetic profiles The plasma concentration-time data obtained after the oral administration of the baclofen tablets were simultaneously fitted to the POP-PK model to extract the in vivo dissolution profiles of the different ER formulations. The structural model for the pharmacokinetics of baclofen is depicted in Figure 1. Similar to the in vitro dissolution modeling (Step 1), the in vivo dissolution of baclofen from the reference and ER formulations was described via Michaelis-Menten kinetics. The differential equation for the amount of undissolved baclofen in the gastrointestinal tract was given by: dX Tablet,in vivo dt

 

Vmax, in vivo  X Tablet,in vivo AM50, in vivo  XTablet, in vivo

(Eq. 2)

Where, XTablet,in vivo represents the amount of undissolved baclofen in the gastrointestinal tract after the oral administration of the reference and ER tablets, Vmax,in vivo represents the maximum rate of drug release in the gastrointestinal tract, and AM50,in dissolution rate is half of Vmax,in

vivo.

vivo

is the amount of drug at which the

Initially, two maximum release rates (Vmax,IR1

in vivo

and

Vmax,IR2 in vivo) were applied to evaluate the intra-individual variability between the first and second doses of the reference IR formulation. However, the estimated Vmax,IR1 in vivo and Vmax,IR2 in vivo were

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close to each other, indicating the intra-individual variability is minimal, therefore one Vmax,IR in vivo

was used in the final model to simplify the model. Consequently, the two in vivo dissolution

profiles of the reference formulation and the three in vivo dissolution profiles of the ER formulations, i.e., ER5%, ER10%, and ER30% were simultaneously modeled with respective Vmax,in vivo and common AM50,in vivo values. The Vmax,in vivo and AM50,in vivo were normalized by the amount of baclofen in the formulation in order to correct the influence of the dose on the dissolution rate. The absorption of dissolved baclofen from the gut to the central compartment was described by the first-order rate constant ka. The differential equation for the dissolved amount of baclofen in the gut compartment that is available for in vivo absorption was given by: dXGut Vmax, in vivo  ka  XGut  FAbs   XTablet, in vivo dt AM50, in vivo  XTablet, in vivo

(Eq. 3)

Since baclofen is known to exhibit regional absorption after oral administration (Balerio and Rubio, 1996; Merino et al., 1989), the absorbed fraction of the dissolved drug (FAbs) was incorporated in the formula, which could change over time. Since FAbs was multiplied to the input of the drug in the gut compartment, i.e., dissolved drug amount after in vivo dissolution, FAbs could limit the amount of drug to be absorbed into the systemic compartment. The equation for FAbs was given by: FAbs  1 

Time10 TAbs5010  Time10

(Eq. 4)

Where Time refers to the time accumulated after drug administration, and TAbs50 is the time associated with a half-maximal change of FAbs. Therefore, the FAbs decreases over time, representing a reduced bioavailability due to a reduction in the expression of influx transporters passing through the gastrointestinal tract. 12

The systemic disposition of baclofen was described by the two-compartment model. The baclofen in the central compartment (amount, Xc) was assumed to be distributed to the peripheral compartment (amounts, Xp) and eliminated from the central compartment. The differential equations for the amounts of baclofen in the central and peripheral compartments were: dXC  ka  XGut  CLD  C1  CLD  C2  CL  C1 dt

(Eq. 5)

dXP  CLD  C1  CLD  C2 dt

(Eq. 6)

Where, C1 and C2 represent baclofen concentrations in their respective compartments, CLD represents the distribution clearances to the peripheral compartment, and CL is the systemic clearance. The observed data were fitted to the POP-PK model using the Monte Carlo Parametric Expectation Maximization (MC-PEM) algorithm in the parallelized S-ADAPT software (version 1.57). An importance sampling MC-PEM method (pmethod=4 in S-ADAPT) was used for population parameter estimation. Between-subject variability (BSV) was estimated using an exponential parameter variability model. The predictive performance of the POP-PK model was evaluated by visual predictive checks. Simulations were performed by using the Berkeley Madonna software (version 8.3.18). Step 3: Correlation of formulation composition-in vitro dissolution-in vivo pharmacokinetics Finally, the composition of the formulation (HPMC %), the in vitro drug release (Vmax,in vitro), and the in vivo drug release (Vmax,in

vivo)

were correlated in order to predict the in vivo plasma

concentration-time profiles from the composition of the formulation. While the HPMC% of the ER formulations was correlated with the in vitro drug release parameter Vmax,in vitro by the Hill

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equation (Step 1), the Vmax,in vitro was correlated with the estimated Vmax,in vivo (Step 2) via linear regression analysis using SigmaPlot (version 12.0, Systat Software, Inc., San Jose, CA, USA). Step 4: Model validation The final extended IVIVC model connecting formulation composition (HPMC%)-in vitro dissolution-in vivo pharmacokinetics was validated internally by using the data of the ER5%, ER10%, and ER30% tablets, and externally by using the data of the ER15% tablet. The predicted mean Cmax and AUC0-24h were calculated from the individual predicted plasma concentration-time profiles obtained after 500 Monte Carlo simulations using the Berkeley Madonna software (version 8.3.18). The predictive performance of the final extended IVIVC model was evaluated by comparing the predicted and observed values. The absolute percentage of prediction error (%PE) was calculated as:

%PE 

Predicted  Observed Observed

 100

(Eq. 7)

3. Results 3.1 The in vitro dissolution of baclofen from ER formulations The in vitro release profiles of the eight baclofen ER tablets with different HPMC compositions in the media at pH 1.2 and 6.8 are shown in Figure 2. While the overall dissolution was slightly faster at pH 1.2 than at pH 6.8, the dissolution rate significantly decreased as the HPMC level in the ER tablets was increased from 2% to 60%. For the reference IR tablet, drug release was completed within 15 min regardless of the pH of the medium. These dissolution characteristics of each of the baclofen ER tablets were reflected on their respective maximum rates of in vitro drug release, Vmax,in vitro.

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During the initial model development process, several models including Michaelis-Menten kinetics, simple zero-, or first-order kinetics were compared to describe the dissolution profiles. As a result, Michaelis-Menten kinetic model could best describe the dissolution profiles at both pH 1.2 and 6.8. The Vmax,in vitro was estimated by fitting the in vitro dissolution profiles to the Michaelis-Menten kinetic model. Sixteen in vitro dissolution profiles were simultaneously fitted with the respective Vmax,in vitro values. As indicated by the plots of the observed and fitted values (Figure 2), the in vitro dissolution model was well able to describe the overall dissolution profiles from the ER formulations. The estimated mean AM50,in vitro/dose at pH 1.2 and pH 6.8 was 1.41 and 0.60, respectively. The estimates of the in vitro dissolution parameter, Vmax,in baclofen ER tablets are presented in Table 2. The Vmax,in

vitro

vitro,

of the

decreased as the HPMC levels

increased from 2% to 60%, and the overall Vmax,in vitro values were lower at pH 6.8 than at pH 1.2.

3.2 The in vivo pharmacokinetics of baclofen The mean plasma concentration-time profiles of baclofen obtained after the oral administration of the reference and the three ER (ER5%, ER10%, and ER30%) tablets to the beagle dogs are depicted in Supplementary Figure S1. The pharmacokinetic parameters from non-compartmental analysis are summarized in Table 3. Following oral administration of the reference tablets, baclofen was rapidly absorbed with Cmax being observed within 30 min. Compared to the reference formulation, the ER tablets presented prolonged Tmax values and lower dose-normalized Cmax and AUC values. With the increase in HPMC content, the Tmax increased, and the Tmax of ER30% was the most delayed among all the ER formulations. The dose-normalized Cmax of ER30% tablet was the lowest, followed by ER10% and ER5%. The lowest dose-normalized AUC was also observed for the ER30% tablet. As Tmax and Cmax reflect on the drug absorption rate, these results indicate

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that the systemic absorption of baclofen was delayed after administration of the ER formulations in vivo, consistent with the in vitro dissolution rates. After reaching Cmax, the plasma concentrations of baclofen declined bi-exponentially with the average t1/2 ranging from 3.0 ± 0.7 h to 4.3 ± 2.6 h. There were no significant differences in t1/2 among the different formulations. The relative bioavailability, representing the extent of absorption, was significantly reduced in the ER tablets compared to the reference tablet, with the lowest relative bioavailability observed for ER30%.

3.3 Development of the extended IVIVC model 3.3.1

Correlation between the composition of the formulation and in vitro dissolution (Step 1)

In the first step of the development of the extended IVIVC model, an attempt was made to correlate the composition of the formulation with the in vitro dissolution. The composition of the formulation was represented by the HPMC level, and the in vitro dissolution was represented by the dissolution parameter, Vmax,in vitro, obtained from the in vitro dissolution model (Eq. 1). The relationship between the HPMC level and the dissolution parameter is shown in Figure 3. A mathematical relationship between the HPMC levels of the ER formulations and the reciprocal of the dissolution parameter, 1/Vmax,in

vitro,

at pH 1.2 and pH 6.8 was derived by using the Hill

equation: For a medium of pH 1.2, 1/Vmax, in vitro at pH1.2  0.149  1.968 

HPMC%1.775 28.7  HPMC%1.775 1.775

(Eq. 8)

For a medium of pH 6.8, 1/Vmax, in vitro at pH6.8  0.206  6.140 

HPMC%1.407 41.41.407  HPMC%1.407

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(Eq. 9)

The equation reasonably described the correlation between the HPMC levels and the in vitro dissolution parameters of ER2%, ER10%, ER25%, ER30%, and ER60% (Figure 3, circles). The predictive performance of the model was evaluated by an external validation, by comparing the observed Vmax,in vitro and the Vmax,in vitro predicted by the model, for ER 5%, ER15%, and ER40%, obtained from different formulation batches (Figure 3, triangles). While the predicted values from both the models in media of pH 1.2 and pH 6.8 showed good agreements with the observed values (the standard error of the regression (S) = 0.1279 and 0.0844, respectively), the model showed slightly superior predictability in a medium of pH 1.2 in the external validation. These equations (Eqs. 8 and 9) allowed interconversions between the HPMC level of the formulation and the in vitro dissolution parameter, Vmax,in vitro. Furthermore, these equations can predict the in vitro dissolution profile from the HPMC level of the ER formulation, and vice versa by combining with the in vitro dissolution model (Eq. 1). Thus, it is also possible to predict the optimal HPMC level based on the desired dissolution profile. The in vitro dissolution profiles predicted from the HPMC levels of the ER formulation were compared with the observed values and are shown in Figure 4. The predicted profiles were in good agreement with the observed in vitro dissolution profiles for both models at pH 1.2 and pH 6.8. However, a better prediction was achieved by the model for the medium at pH 1.2 in the external validation, which is consistent with the correlation between the HPMC level and 1/Vmax,in vitro (Figure 3). While the observed dissolution profiles for all ER formulations were well-predicted by the pH 1.2 model, the dissolution was over-predicted for ER40% by the pH 6.8 model (Figure 4). 3.3.2

Estimation of in vivo dissolution by the POP-PK model (Step 2)

The population pharmacokinetic (POP-PK) model was developed to estimate the in vivo baclofen dissolution from the plasma concentration-time profiles to establish the final extended IVIVC. The

17

POP-PK model consisted of two disposition compartments, and the drug dissolution and absorption were separately described by Michaelis-Menten kinetics and first-order kinetics, respectively. Since the relative bioavailability decreased as the dissolution rates of the ER tablets become slower, the POP-PK model also incorporated site-dependent absorption. The sitedependent-absorption, that is, the decrease of permeability along the gastrointestinal tract, was incorporated in the model by applying the absorbed fraction after dissolution (FAbs), which allowed changes over time. The estimated FAbs values over time, corresponding to the in vivo dissolution profiles of the baclofen ER tablets, is shown in Supplementary Figure S2. Figure 5A shows the observed and the POP-PK model-predicted plasma concentration-time profiles for ER5%, ER10%, and ER30%. The overall plasma concentration-time data were well described by the POP-PK model. The observed vs. fitted plasma concentrations of baclofen and the normalized prediction distribution errors (NPDEs) of the POP-PK model are shown in Supplementary Figures S3 and S4, respectively, and indicate a good predictive performance of the final POP-PK model. The in vivo dissolution profiles extracted from the plasma concentrationtime profiles by the POP-PK model (solid lines) compared with in observed in vitro dissolution profiles (closed circles) are presented in Figures 5B and 5C. It was observed that the predicted in vivo dissolution rates were faster than the observed in vitro dissolution rates for all the ER tablets in both the media at pH 1.2 and 6.8. The population pharmacokinetic parameter estimates for baclofen are presented in Table 4. The dose-normalized Vmax,in vivo decreased as the HPMC contents increased from 8.254 h-1 for ER5% to 4.564 h-1 for ER10%, and 1.391 h-1 for ER30%. The decrease in the in vivo dissolution rate, Vmax,in vivo, combined with the increase in the HPMC level was consistent with the in vitro dissolution rate, Vmax,in vitro (Table 2).

18

3.3.3

Correlation of formulation composition-in vitro dissolution-in vivo pharmacokinetics (Step 3)

The final extended IVIVC model was developed by establishing a correlation between the composition of the formulation (HPMC %) and the in vitro drug release (Vmax,in vitro) (Step 1), and the in vivo drug release (Vmax,in vivo) extracted from the plasma concentration-time profiles (Step 2) of the baclofen ER formulations. Comparing the observed in vitro dissolution and the estimated in vivo dissolution profiles (Figures 5B and 5C), it was found that the in vitro dissolution rates were slower than the in vivo dissolution rates. To develop a direct one-to-one relationship between the in vitro and in vivo dissolution rates, linear correlation equations were introduced. The parameter estimates for the in vitro Vmax,in vitro for the media at pH 1.2 and pH 6.8 were correlated with the estimated in vivo Vmax,in vivo by the following equations:

Vmax, in vivo  2.039  Vmax, in vitro, pH1.2 - 0.232

(Eq. 10)

Vmax, in vivo  3.609  Vmax, in vitro, pH6.8  0.231

(Eq. 11)

The correlation between the in vivo Vmax,in vivo and the in vitro Vmax,in vitro at pH 1.2 and pH 6.8 are shown in Supplementary Figure S5. Although both the in vitro Vmax,in vitro at pH 1.2 and pH 6.8 were reasonably correlated with the in vivo Vmax,in vivo by linear regressions, a superior correlation was observed with Vmax,in vitro at pH 1.2 (r2= 0.9999) than at pH 6.8 (r2= 0.9871). The correlation between the in vivo Vmax,in vivo and the in vitro Vmax,in vitro at pH 6.8 was closer to the Hill function rather than to the linear equation. By using the aforementioned linear equations (Eqs. 10 and 11), the in vivo dissolution profiles extracted from the plasma concentration vs. time profiles using POP-PK modeling could be converted to the in vitro dissolution profiles, and vice versa. The dotted lines in Figures 5B and 19

5C represent the converted in vitro dissolution profiles at pH 1.2. and pH 6.8 from the extracted in vivo dissolution profiles by using Eqs. 10 and 11, respectively. While the predicted in vivo dissolution (solid lines) were faster, a good correlation was obtained between the converted in vitro dissolution profiles (dotted lines) and the observed in vitro dissolution data (symbols) at both pH 1.2 and pH 6.8 (Figures 5B and 5C). However, the converted in vitro dissolution profiles were lower than the observed values for the ER30% tablets at pH 6.8 (Figure 5C), which may be caused by an underestimation of the Vmax,in vitro by the linear equation for the medium at pH 6.8. The superior predictability of the pH 1.2 model was also consistent with its better prediction of the in vitro dissolution profiles from the HPMC composition, in comparison to the pH 6.8 model (Figure 4). Since the better correlations between the composition of the formulation (HPMC %) and the in vitro dissolution (Vmax,in vitro), and between the in vitro dissolution (Vmax,in vitro) and the in vivo dissolution (Vmax,in vivo) were achieved by the pH 1.2 model, the model developed on the basis of the results at pH 1.2 was selected as the final extended IVIVC model. 3.3.4

Prediction of in vivo pharmacokinetics from the composition of the formulation (Step 4)

Figure 6 shows the plasma concentration-time profiles predicted from the HPMC composition, by using the final extended IVIVC model. The model predictions were in great agreement with the observed data following the oral administration of baclofen ER5%, ER10%, and ER30% tablets, suggesting the establishment of level A IVIVC. The observed and predicted Cmax and AUC0-24h values and their respective absolute percentages of prediction error (%PE) for the extended IVIVC model are summarized in Table 5. The predicted Cmax and AUC0-24h values were in excellent agreement with the observed values for all the baclofen ER formulations with the %PE within 5.87% and 5.72%, respectively, which perfectly met the criteria of the FDA guidelines.

20

Finally, the predictability of the final extended IVIVC model was further externally validated by comparing the predicted plasma concentration-time profiles of the ER formulation containing 15% HPMC, with the corresponding observed data following oral administration. As shown in Figure 6, the predicted plasma concentration-time profile of baclofen ER15% was in good agreement with the observed data. Excellent predictions of the Cmax and AUC were obtained (Table 5) which suggested the excellent predictability of the final extended IVIVC model.

4. Discussion The repeated preparation of formulations, in vitro dissolution studies, and in vivo pharmacokinetic studies due to the improper design of formulations is a major factor that delays the development of ER formulations. Although several IVIVC studies have been conducted for determining the optimal in vitro drug release profiles, there are limited attempts that apply the IVIVC concept to design the compositions of formulations. In the present study, the IVIVC concept was extended to design the compositions of formulations and this novel extended IVIVC model allows the prediction of in vivo pharmacokinetics as well as the in vitro dissolution from the composition of the formulation, and vice versa. Thus, the present approach systematizes the entire formulation development process by connecting from the formulation to the in vitro dissolution and in vivo pharmacokinetics, which has been separated so far. With the systematized approach, the formulation design could be rationalized, which would lead to a reduction of trial and errors during the optimal formulation development to achieve the desired therapeutic outcome. Therefore, the extended IVIVC approach would make the formulation development process more efficient and save a lot of time and costs.

21

In this study, baclofen was used as a model drug to develop the extended IVIVC model. Baclofen is a BCS class III drug (Fasinu et al., 2011) for which establishing level A IVIVC is challenging by using conventional IVIVC approaches. Moreover, our results indicate site-specific absorption of baclofen in the gastrointestinal tract. The lower bioavailability combined with a slower drug release rate of baclofen ER formulations was observed (Table 3). The slowly released baclofen from the ER formulations may bypass the major absorption window where the influx transporters are distributed, resulting in the lower bioavailability. These results are in good agreement with the reported pharmacokinetic properties of baclofen. Carrier-mediated transport of baclofen in the gastrointestinal tract has been reported in several in vitro and in vivo studies (Cejudo-Ferragud et al., 1996; Merino et al., 1989; Polache et al., 1993). Since the absorption of baclofen was competitively inhibited by the presence of phenylalanine during its intestinal absorption, it has been suggested that baclofen has the same uptake transporter of phenylalanine (Cejudo-Ferragud et al., 1996). In addition, the large amino acid transporter 1 (LAT-1) has been proposed as a carrier responsible for baclofen uptake (Zhang et al., 2011). However, it has been also reported the concentration-independent transport of baclofen across mouse duodenal sacs, suggesting the regional differences in the expression of transporters capable of baclofen uptake across the gastrointestinal mucosa (Balerio and Rubio, 1996). Therefore, a POP-PK model that can account for various complex physiological factors contributing the in vivo absorption was applied (Kim et al., 2017a). The site-dependent absorption of baclofen in the gastrointestinal tract was incorporated into the model by using the absorbed fraction of the dissolved drug (FAbs) that could change over time. The model predicted that the FAbs decreases over time, representing a reduced bioavailability due to a reduction in the expression of influx transporters as the drug pass through the gastrointestinal tract (Supplementary Figure S2) and resulted in the successful estimation of the in

22

vivo dissolution of baclofen. Therefore, this study provides a good example to overcome limitations of the conventional IVIVC approaches and extend the coverage of IVIVC to BCS class III drugs. In this study, in vitro dissolution was evaluated at two different pH conditions at 1.2 and 6.8, resulting in different dissolution profiles. Thus, the two structurally identical models with different model parameters were separately developed using the in vitro dissolution results at pH 1.2 and pH 6.8. The better correlations between the composition of the formulation (HPMC %) and the in vitro dissolution (Vmax,in vitro), and between the in vitro dissolution (Vmax,in vitro) and the in vivo dissolution (Vmax,in vivo) were achieved by the pH 1.2 model (Figures 3 and 5). Therefore, the model developed on the basis of the results at pH 1.2 was selected as the final extended IVIVC model. The final extended IVIVC model correlated among the HPMC composition, the in vitro dissolution, and the in vivo pharmacokinetics, establishing level A IVIVC. The validity of the final extended IVIVC model was evaluated by comparing the in vivo plasma concentration profiles predicted based on the HPMC compositions with the corresponding observed data. Once a specific HPMC composition was decided upon, the developed model allowed the prediction of the in vitro dissolution parameter (Vmax,in

vitro)

from the HPMC levels. The in vitro dissolution parameter

(Vmax,in vitro) was then converted to the in vivo dissolution parameter (Vmax,in vivo), leading to the prediction of the complete plasma concentration-time profiles (Figure 7). Conversely, this model could also be used to determine the optimal composition of HPMC in the ER formulation to achieve the desired plasma concentrations, by converting the plasma concentration-time data to predict in vivo dissolution, in vitro dissolution, and finally the level of HPMC. Upon the internal and external validation, the predicted plasma concentration-time profiles of baclofen ER formulations were in good agreement with the observed data. Excellent predictions of the Cmax and

23

AUC were obtained (Table 5) which suggested the excellent predictability of the final extended IVIVC model. According to the FDA guideline, the internal predictability of IVIVC is considered acceptable when prediction errors (%PE) for Cmax and AUC are below 15% for each formulation and the mean %PE values are below 10% for validation (FDA, 1997). So far, IVIVC studies have attempted to establish a mathematical relationship between in vitro property of the ER formulation and their in vivo response, which allows prediction of the in vivo pharmacokinetics from the in vitro dissolution characteristics, and vice versa. However, the present approach extended the scope of the IVIVC to the formulation composition and established the model correlating among the formulation composition, the in vitro dissolution, and the in vivo pharmacokinetics. Therefore, the present extended IVIVC approach broadened the IVIVC to the design of the formulation to achieve a desired outcome, i.e., in vivo pharmacokinetics, which has been also pursued by DoE in pharmaceutical development. DoE is a systemic approach to determine the effects of the controlled input factors of the process on the outcomes by intentionally varying the factors (S et al., 2017), (Yu et al., 2014). In pharmaceutical industry, the effects of the input factors including the formulation composition on the response can be evaluated by DoE (S et al., 2017), (Yu et al., 2014). Thus, DoE allows to determine the most influential factors, to identify the optimum factor settings, and to elucidate the interactions between the factors (S et al., 2017). Although this study determined the effects of only one factor, i.e., HPMC% on the response of the formulation, the present approach may be combined with DoE by including more input variables and process parameters in further studies. Combining with DoE with the extended IVIVC may allow to predict not only the in vitro dissolution but also in vivo pharmacokinetic profiles from the process parameters.

24

5. Conclusions A novel extended IVIVC approach was established for baclofen, which can correlate formulation composition, in vitro dissolution, and in vivo pharmacokinetics. The final extended IVIVC model was successfully applied for the prediction of the in vivo pharmacokinetics from the HPMC levels of the baclofen ER formulations. On the contrary, the developed model could also be used to predict the optimal HPMC composition of the ER formulations to achieve a desired in vivo plasma concentration-time profile. The present approach holds great promise to be applied to design new ER formulations, which would save the development time and improve the success rate.

Acknowledgements This work was supported by the National Research Foundation of Korea (NRF) grant numbers 2017R1D1A1A02018615 and 2018R1A2B6004928.

Author contributions B.S.S, S.S, T.H.K, and J.B.B participated in research design. B.S.S., S.S., T.H.K., and D-H.K. conducted the experiments. B.S.S., S.S., T.H.K, and J.B.B. analyzed the results. All authors reviewed the manuscript.

Competing interests The authors declare no competing interests.

References

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Figure captions

Figure 1. Structural model for the pharmacokinetics of baclofen following the oral administration of baclofen tablets in beagle dogs. Figure 2. In vitro dissolution profiles of baclofen ER tablets in the medium at (A) pH 1.2 and (B) pH 6.8 (n=4). Symbols represent the observations and the solid lines represent model predictions. Figure 3. Correlation between the HPMC level and the in vitro dissolution parameter, 1/Vmax at (A) pH 1.2 and (B) pH 6.8. Symbols represent the observed data and solid lines represent the model predictions. Figure 4. Comparisons between the observed and predicted in vitro dissolution profiles, the latter predicted from the HPMC level of the ER formulations at (A) pH 1.2 and (B) pH 6.8 (upper panel: internal validation, lower panel: external validation). Symbols represent the observed data and solid lines represent the model prediction values. Figure 5.

Comparisons between the observed and POP-PK model-predicted (A) plasma

concentration vs. time profiles after the oral administration of ER5%, ER10%, and ER30% baclofen tablets to beagle dogs, (B) in vitro and in vivo dissolution profiles at pH 1.2, and (C) dissolution profiles at pH 6.8. The symbols represent the observed data, the solid lines represent the POP-PK model predicted in vivo dissolution profiles from in vivo data, and the dotted line represent the converted dissolution profiles by the POP-PK-IVIVC model. Figure 6. Observed and predicted plasma concentration-time profiles from the composition of the formulation, level of HPMC, using the newly developed extended IVIVC model. Figure 7. Flowchart for the prediction of the complete plasma concentration-time profiles from the HPMC composition, using the final extended IVIVC model.

29

Supplementary material Supplementary Figure S1. Observed plasma concentrations of baclofen after the oral administrations of the reference tablet and the ER tablets to beagle dogs (n = 3-4). Supplementary Figure S2. Drug absorption fraction after dissolution (FAbs) along the gastrointestinal tract estimated by the population pharmacokinetic model. Supplementary Figure S3. Observed vs. fitted plasma concentrations of baclofen after oral administration of IR and SR tablets in Beagle dogs. Supplementary Figure S4. Normalized prediction distribution errors (NPDEs) of the population pharmacokinetic model. Supplementary Figure S5. Correlations between the in vivo dissolution rate, Vmax,in vivo, with the in vitro dissolution rates, (A) Vmax,in vitro at pH 1.2 and (B) Vmax,in vitro at pH 6.8 by linear regression.

30

Table 1. Composition of the baclofen ER formulations (w/w %).

Formulation

Composition (%) Baclofen

HPMC2208-100cps

Lactose

Mg stearate

ER2%

5.0 (30 mg)

2

92.0

1

ER5%

5.0 (30 mg)

5

89.0

1

ER10%

2.5 (15 mg)

10

86.5

1

ER15%

5.0 (30 mg)

15

79.0

1

ER25%

5.0 (30 mg)

25

69.0

1

ER30%

2.5 (15 mg)

30

66.5

1

ER40%

5.0 (30 mg)

40

54.0

1

ER60%

2.5 (15 mg)

60

36.5

1

31

Table 2. In vitro dissolution parameter estimates of the baclofen ER formulations. pH 1.2 dissolution medium

pH 6.8 dissolution medium

Parameter

Mean (SE%)

Parameter

Mean (SE%)

Vmax,ER2%,in vitro,pH1.2/dose (h-1)

6.06 (8.2%)

Vmax,ER2%,in vitro,pH6.8/dose (h-1)

3.43 (10.1%)

Vmax,ER5%,in vitro,pH1.2/dose (h-1)

4.15 (6.3%)

Vmax,ER5%,in vitro,pH6.8/dose (h-1)

2.27 (3.2%)

Vmax,ER10%,in vitro,pH1.2/dose (h-1) 2.37 (5.3%)

Vmax,ER10%,in vitro,pH6.8/dose (h-1) 1.08 (4.3%)

Vmax,ER15%,in vitro,pH1.2/dose (h-1) 1.56 (9.8%)

Vmax,ER15%,in vitro,pH6.8/dose (h-1) 0.61 (6.4%)

Vmax,ER25%,in vitro,pH1.2/dose (h-1) 1.08 (4.7%)

Vmax,ER25%,in vitro,pH6.8/dose (h-1) 0.43 (12.1%)

Vmax,ER30%,in vitro,pH1.2/dose (h-1) 0.79 (8%)

Vmax,ER30%,in vitro,pH6.8/dose (h-1) 0.40 (6.8%)

Vmax,ER40%,in vitro,pH1.2/dose (h-1) 0.67 (6.7%)

Vmax,ER40%,in vitro,pH6.8/dose (h-1) 0.26 (4.9%)

Vmax,ER60%,in vitro,pH1.2/dose (h-1) 0.59 (10.5%)

Vmax,ER60%,in vitro,pH6.8/dose (h-1) 0.25 (13%)

32

Table 3. Non-compartmental pharmacokinetic parameters of baclofen after the oral administrations of the reference tablet and the ER tablets to beagle dogs (n = 3-4). Parameter

Reference (n=4) ER5% (n=3)

ER10% (n=4)

ER15% (n=3)

ER30% (n=4)

Dose (mg)

5 × 2 (τ=8 h)

30

15

30

15

t1/2 (h)

3.2 ± 0.1a

3.0 ± 0.7

4.3 ± 2.6

4.3 ± 0.9

3.3 ± 0.9

Tmax (h)

0.3 ± 0.1a

1.0 ± 0.0

0.9 ± 0.3

1.3 ± 0.6

2.0 ± 1.7

Cmax (ng/mL)

881.0 ± 216.1a

3802.2 ± 1221.21533.2 ± 157.0 2585 ± 377.5

891.8 ± 91.7

Cmax/Dose

88.1 ± 21.6a

126.7 ± 40.7

102.2 ± 10.5

59.5 ± 6.1

AUCinfinity (ng·h/mL)

4288.7 ± 443.4

11427.4 ± 1940.8

5708.3 ± 720.3 10509.5 ± 944.95229.2 ± 656.2

AUC/Dose 428.9 ± 44.3

380.9 ± 64.7

380.6 ± 48.0

350.3 ± 31.5

348.6 ± 43.7

Vz/F (L)

10.7 ± 1.3

11.5 ± 3.9

15.6 ± 7.7

17.6 ± 2.9

13.4 ± 2.9

CL/F (mL/min)

39.2 ± 4.0

44.6 ± 7.3

44.3 ± 5.5

47.9 ± 4.1

48.4 ± 6.1

88.8 ± 15.1

88.7 ± 11.2

81.7 ± 7.3

81.3 ± 10.2

Relative BA (%) a The

86.2 ± 12.6

second dose of reference tablet was assumed to be administered at 0 h.

33

Table 4. Population pharmacokinetic parameter estimates. Mean (SE%)

BSVa (SE%)

Volume of distribution of the V1 (L) central compartment

4.604 (13.6%)

0.399 (39.0%)

Volume of distribution of the V2 (L) peripheral compartment

4.380 (15%)

0.477 (46.1%)

Systemic clearance

2.686 (4%)

0.274 (87.6%)

Distribution clearance to the CLD (L/h) peripheral compartment

2.904 (22%)

0.143 (41.8%)

Rate constant for absorption ka (h-1) from gut

9.891 (3.5%)

0.0106 (589%)

Time for half bioavailability

5.888 (20.9%)

0.108 (188%)

1.783 (8.3%)

0.0125 (123%)

Parameter

Symbol (unit)

CL (L/h)

maximal

TWindow50 (h)

Amount of baclofen in the solid compartment at 1/2 AM50 in vivo/dose Vmax in vivo Vmax in vivo for IR tablets

Vmax,IR in vivo/dose (h-1)

66.366 (23.1%)

0.0988 (184%)

Vmax in vivo for ER5%

Vmax,ER5% in vivo/dose (h-1)

8.254 (5.8%)

0.0525 (286%)

Vmax in vivo for ER10%

Vmax,ER10% in vivo/dose (h-1) 4.564 (14.2%)

0.0673 (95.3%)

Vmax in vivo for ER30%

Vmax,ER30% in vivo/dose (h-1) 1.391 (9.2%)

0.0509 (77.7%)

a

Between subject variability (BSV) estimates are apparent coefficients of variation on natural logarithmic scale.

34

Table 5. Observed and predicted Cmax and AUC0-24h of baclofen from the extended IVIVC modeling approaches and absolute percentages of the prediction errors between the observed and predicted values. Cmax (ng/mL)

AUC0-24h (ng·h/mL)

Observed Predicted PE (%)

Observed Predicted PE (%)

ER5%

3802.2

3902.7

2.64

11300.7

11187.4

1.00

ER10%

1533.2

1623.2

5.87

5383.4

5566.6

3.40

ER30%

891.8

938.7

5.26

5167.0

5462.5

5.72

ER15%

2585.0

2670.7

3.32

10328.8

11106.9

7.53

Validation Formulation

Internal

External Mean

4.27

35

4.41

36

37