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Physicochemical characterization of naproxen solid dispersionsprepared via spray drying technology

Khosro Adibkia a,b, Mohammad Barzegar-Jalali a,b, Hosein Maheri-Esfanjani b,d, Saeed Ghanbarzadeh b,d, Javad Shokri b,c, Araz Sabzevari e, Yousef Javadzadeh a,b,⁎

a Biotechnology Research Center, Tabriz University of Medical Sciences, Tabriz, Iranb Faculty of Pharmacy, Tabriz University of Medical Sciences, Tabriz, Iranc Dermatology & Dermopharmacy Research Team, Tabriz University of Medical Sciences, Tabriz, Irand Students Research Committee, Tabriz University of Medical Sciences, Tabriz, Irane Department of Pharmaceutics, Faculty of Pharmacy, Tehran University of Medical Sciences, Tehran, Iran

a b s t r a c ta r t i c l e i n f o

Article history:

Received 5 January 2013Received in revised form 27 May 2013Accepted 31 May 2013Available online 10 June 2013

Keywords:

NaproxenSolid dispersionSpray dryingRelease ratePhysicochemical characterization

The bioavailability of Naproxen (NPX), a non-steroidal anti-inammatory drug, is limited after oral administra-tion due to its low solubility in biological uids. The aims of this study were preparation and characterization of NPXsoliddispersions benetting hydrophilic polymers. Solid dispersions of NPXwere prepared at differentdrugto polymerratios(1:0.5, 1:1 and1:2) using crosspovidone andHPMC E4Mby means of spray dryingmethod. Thedissolution rate of NPX from the solid dispersions, drug/polymer physical mixtures and pure drug was deter-mined at two pH values of 3 and 7.4 simulating gastric and intestinal uids using USP dissolution apparatus II.The physicochemical properties of the prepared solid dispersions were also characterized by differential scan-ning calorimetry (DSC), scanning electron microscopy (SEM), X-ray diffractometry (XRD), and Fouriertransforminfrared spectroscopy(FT-IR). The dissolution rate of NPXwas noticeablyincreased in thesolid dispersionsso thatalmost 90% of drug was released at 60 min while the corresponding value for the physical mixtures and pure drugwas revealed to be around40%.The dissolution rates of the formulations were dependenton the natureand ratio of drug to carriers as well as pH of the medium. DSC and X-ray diffraction displayed reduced drug crystallinity in the

solid dispersions. Scanning electron microscopy revealed signicant decreased particle size of the drug in the soliddispersions. FT-IR spectroscopy demonstrated no obvious interactions between the drug and polymers.

© 2013 Elsevier B.V. All rights reserved.

1. Introduction

Naproxen (NPX), a propionic acid derivative, is extensively used ininammatory diseases such as rheumatoid arthritis and acute gout.The drugs with poor aqueous solubility like NPX, typically exhibitdissolution rate limited absorption and therefore, display poor bio-availability which result in multiplying of the drug dose as well asgreat uctuation in blood concentrations [1–5]. The oral administra-tion of the drug is the most common route of delivery due to conve-nience and patient compliance which make it more effective whencompared with other routes of administration. Many methods areavailable to improve solubility and dissolution rate of poorly solubledrugs including salt formation, micronization and addition of solventor surface active agents [4,6–9]. Solid dispersions represent a usefulpharmaceutical technique for increasing the dissolution, absorption,

bioavailability and consequently therapeutic ef cacyof poorly solubledrugs in dosage forms. Various mechanisms which involved in enhance-mentof drug solubility includereducing theparticle size to submicron ormolecular size and as a result the surface area enhancement; convertingthe crystalline forms of drug into amorphous form. Improvement in drugsolubility and wettability due to the surrounding hydrophilic carriers;increasing porosity; reduction or absence of aggregation and agglomer-ation may also contribute to increased dissolution rate. Furthermore,solid dispersions have been applied to obtain a homogeneous distribu-tion of a small quantity of drug in a solid state, stabilization of unstabledrugs, dispersion of a liquid or gaseous compounds into a solid dosageform, and formulation of sustained release dosage forms [10–17].

Various hydrophilic carriers such as polyethylene glycols,polyvinylpyrrolidone, hydroxyl propyl methylcellulose, gums, sucrose,mannitol and urea have been investigated for improvement of dissolu-tion characteristics and bioavailability of poorly aqueous soluble drugs[11,13,16–24].

Spray drying is used in many elds of pharmacy such as biotech-nology, pulmonary dosage forms, and encapsulation. This processoffers a variety of advantages compared to traditional technologiesused for preparation of the solid dispersions, including creation of

Powder Technology 246 (2013) 448–455

⁎ Corresponding author at: Faculty of Pharmacy, Tabriz University of Medical Sciences,Daneshgah Street, Tabriz, Iran. Tel.: +98 411 3341315; fax: +98 411 3344798.

E-mail addresses: [email protected], [email protected](Y. Javadzadeh).

0032-5910/$ – see front matter © 2013 Elsevier B.V. All rights reserved.

http://dx.doi.org/10.1016/j.powtec.2013.05.044

Contents lists available at SciVerse ScienceDirect

Powder Technology

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http://dx.doi.org/10.1016/j.powtec.2013.05.044http://dx.doi.org/10.1016/j.powtec.2013.05.044http://dx.doi.org/10.1016/j.powtec.2013.05.044mailto:[email protected]:[email protected]://dx.doi.org/10.1016/j.powtec.2013.05.044http://www.sciencedirect.com/science/journal/00325910http://www.sciencedirect.com/science/journal/00325910http://dx.doi.org/10.1016/j.powtec.2013.05.044mailto:[email protected]:[email protected]://dx.doi.org/10.1016/j.powtec.2013.05.044http://crossmark.crossref.org/dialog/?doi=10.1016/j.powtec.2013.05.044&domain=pdf


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amorphous structure andhigh surface area. The spray dried powderscould enhance the dissolution rate of drugs and subsequently im-prove their oral bioavailability [25,26].

The present investigation focused on the formulation of naproxensolid dispersions usingcrosspovidone (CP) and hydroxyl propyl methylcellulose (HPMC) at different drug: carrier ratios applying spray dryingtechnique. SEM, DSC, X-ray diffraction and FT-IR spectroscopy werealso performed in order to elucidate the mechanisms involved in disso-lution rate changes of the drug from the prepared solid dispersions.

2. Materials and methods

2.1. Materials

NPX was supplied from Shasum chemicals and drugs Company(Chennai, India). HPMC E4M was purchased from Colorcon Compa-

ny (Dartford, UK), Crospovidone (CP) was obtained from BASFCompany (Ludwigshafen, Germany), Ethanol and Hydrochloric acid

were purchased from Merck Company (Darmstadt Germany). All theother used chemicals and solvents were analytical grade.

2.2. Preparation of solid dispersions via spray drying

Solid dispersions of NPX were prepared using a mini spray dryer(Buchi B-290, Switzerland) operating an inert loop mode. Nitrogenwas used as the drying gas in a co-current mode with aspirator set-ting 100% so that the oxygen concentration was below 6%. Nitrogenatomization pressure was 6 bars, and the set cooling temperature was−10°. Inlet temperature was maintained at 80 ± 5 °C, and resultingoutlet temperature was 55 ± 5 °C. Aqueous solution (in the case of HPMC) or dispersion (in the case of CP) of the polymers were droppedinto ethanolic solution of NPX to obtain a clear ethanol/water solution(60:40) with total solid content of 1% w/w and drug to polymer ratiosof 1:0.5, 1:1 and 1:2. The feedstock was delivered with the rate of

4 ml/min to a two-uid nozzle (0.7 mm) via a peristaltic pump. Theobtained powder was further dried in an oven at 70 °C for 2 h. Physical

Table 1

Particle size, poly dispersity index (PDI), drug content as well as t50% and Q 60 (at pH 3) for pure NPX, physical mixtures (PMs) and solid dispersions (SDs) of NPX with HPMC and CPat different weight ratios.

Formulation code NPX CP HPMC Particle size (μ m) ± SD PDI ± SD Drug content(%) ± SD t50% (min) ± SD Q 60 (%) ± SD

Naproxen 1 0 0 13.73 ± 3.48 0.50 ± 0.21 – 97.02 ± 1.35 39.89 ± 2.65CP – – – 3.8 ± 1.22 0.30 ± 0.18 – – –HPMC – – – 24.56 ± 4.88 0.27 ± 0.12 – – –SD1 1 0.5 0 2.48 ± 0.91 0.18 ± 0.06 75.57 ± 1.4 30.25 ± 3.32 75.24 ± 2.43SD2 1 1 0 3.04 ± 0.87 0.21 ± 0.08 68.14 ± 2.3 25.11 ± 2.23 88.40 ± 2.76

SD3 1 2 0 2.94 ± 0.76 0.23 ± 0.08 61.04 ± 0.2 35.44 ± 1.88 70.33 ± 4.11SD4 1 0 0.5 1.48 ± 0.44 0.18 ± 0.08 90.45 ± 4.8 52.32 ± 4.55 58.14 ± 4.41SD5 1 0 1 2.24 ± 0.62 0.24 ± 0.07 90.69 ± 2.2 18.84 ± 3.85 81.45 ± 3.04SD6 1 0 2 2.84 ± 0.54 0.31 ± 0.08 94.17 ± 0.8 9.14 ± 1.21 88.21 ± 5.98PM1 1 0.5 0 – – – 54.14 ± 4.24 51.44 ± 4.76PM2 1 1 0 – – – 54.45 ± 4.11 51.38 ± 5.28PM3 1 2 0 – – – 78.72 ± 4.88 45.94 ± 4.09PM4 1 0 0.5 – – – 36.75 ± 4.78 63.15 ± 3.22PM5 1 0 1 – – – 44.18 ± 6.88 60.70 ± 5.22PM6 1 0 2 – – – 36.58 ± 7.43 68.45 ± 4.44

Fig. 1. Particle size distribution of of A (Pure Naproxen), B (CP), C (HPMC) and D (CP:NPX, 1:0.5, SD1).

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mixtures were also prepared by hand tumbling of NPX and polymersfor 20 min with the same weight ratios of the solid dispersions untilgetting uniform mixture. The samples were kept in the tightly closed

amber-colored glass bottles and stored at the room temperature.

2.3. Characterization of the solid dispersions

2.3.1. Particle size and morphology

The particle size and size distribution of the prepared solid disper-sions were determined using the laser diffraction particle size analyzer(Sald 2101, Shimadzu,Japan)equipped with theWing software (version1201). All measurements were performed after dispersing of theprepared powders in the distilled water adjusted with hydrochloricacid to a pH 1.2. The mean diameter andsize distribution of theresultedhomogeneous suspension were assessed, subsequently. Each valueresulted from triplicate determinations. The SEM photograph of NPXand solid dispersions prepared by spray drying method were also

obtained using scanning electron microscope (Tescan, Brno, CzechRepublic) operating at 15 kV. The specimens were mounted on a metalstub with double-sided adhesive tape and coated under vacuum withgold in an argon atmosphere using a sputter coater (SCD 005, Bal-Tec,Switzerland) prior to observation.

2.3.2. Differential scanning calorimetry (DSC)

Accurately weighed samples (pure NPX, polymers, physicalmixtures and solid dispersions), were placed into the sealed standardaluminum pans with lids. Subsequently, the physical status of thenaproxen inside the solid dispersions was established using the differ-ential scanning calorimetry thermogram analysis, DSC60 (Shimadzu, Japan). The heating rate was 20 °C/min and the heat ow wasrecordedfrom 25 °C to 250 °C. The aluminum oxide and indium powders were

used as reference and standard, respectively.

2.3.3. X-ray diffraction studies (XRD)

Thepowder X-ray diffraction patternswere determined forpure drug,polymers, physical mixtures and solid dispersions. X-ray diffractograms

were obtained using the X-ray diffractometer (Siemens D500, MunichGermany) and Cu-kα radiation (λ = 1.5406). Diffractograms were runat scanning speed of 2º/min and a chart speed of 0.6º/min.

2.3.4. Fourier transform infrared spectroscopy (FT-IR)

FT-IR spectra were obtained using FT-IR spectrometer (Shimadzu4300, Japan). Pure drug, polymers, physical mixtures and solid disper-sions were mixed with potassium bromide separately. The potassiumbromide discs were prepared by compressing the powders at pressureof 15 tons for 10 min in hydraulic press. Scans were obtained at a reso-lution of 2 cm−1, from 4000 to 400 cm−1.

2.4. Drug content

Equivalent to 60 mg of NPX were dissolved in 50 ml ethanol. Todissolve all of NPX, samples were stirred for 4 h and subsequentlycentrifuged at 6000 rpm for 10 min. The drug contentafter suitable dilu-tion was determined at 271.2 nm by UV spectrophotometer (Shimadzu, Japan). Drug content was calculated by the following equation:

Drug content % ð Þ ¼ Observed drug content=Theoretical drug contentð Þ 1001

2.5. Dissolution studies

In vitro release tests were performed for the prepared soliddispersions, intact NPX as well as drug/polymer physical mixtures

(all containing 20 mg NPX). To analyze the dissolution samples, the

Fig. 2. Scanning electron micrographs of A (Pure Naproxen), B (NPX:CP, 1:0.5, SD1), C (NPX:HPMC, 1:0.5, SD4) and D (NPX:HPMC, 1:2, SD6).

450 K. Adibkia et al. / Powder Technology 246 (2013) 448–455

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calibration curves of the drug were obtained at pH 3 and 7.4. Bothcurves were linear in the range of 2.5–80 μ g/ml (RSQ = 0.9999).The dissolution study was carried out applying USP apparatus typeII (Erweka, Germany), using 900 ml hydrochloric acid solution(pH 3) and phosphate buffer (pH 7.4) as dissolution mediums.Temperature was maintained at 37 ± 0.5 °C and agitation rate was50 rpm. Samples were withdrawn at predetermined time intervals(0, 5, 10, 15, 20, 30, 45, 60, 90 and 180 min) and ltered to remove

suspended and insoluble powder particles. The prewarmed fresh dis-solution medium was replaced immediately. Samples were suitablydiluted and analyzed by UV spectrophotometer at λ = 272.2 nm[27]. Cumulative percentage of drug released versus time were plot-ted for the solid dispersions, PMs and pure NPX. The mean calculatedvalues were obtained from 3 to 4 replicates.

2.6. Release kinetics

The release data obtained from in vitro dissolution studies were ttedto ten kinetic equations. The used kinetic models include zero-order,rst-order, Higuchi, Hixson–Crowell, cube root law, second root of mass, three secondsroot of mass, Weibull, linear Wagnerandlog Wagner(Table 2) [15].

3. Result and discussion

3.1. Characterization of the solid dispersions

3.1.1. Particle size and morphology

The results showed that mean particle size diameter for spray driedpowders were signicantly (p b 0.05) less than pure drug and carriers(Table 1 and Fig. 1).

SEM was alsoused to determine the surface morphology of pureNPX and solid dispersions. The microphotographs of pure NPX andits solid dispersion are shown in Fig. 2. All spray dried powdersexhibited irregularly shaped particles alongside a few sphericalmicrospheres with more or less smooth surface in contrast to theNPX particles which were composed of irregularly shaped lengthwise

crystals with rough texture. The spray dried particles had a reducedgeometric diameter and higher surface area than that of pure NPX.According to the Noyes–Whitney equation, the amount of solutedissolved per unit time, dM/dt, is proportional to the surface area of the solute (S) [8,20,26,28].

dMdt

¼ DSh

Cs−Cð Þ 2

where D is the diffusion coef cient of the solute in solution, h is thethickness of the diffusion layer, Cs and C are the solubility and theconcentration of the solute in the solution, respectively.

Then, one of the reasons of higher dissolution rate of the soliddispersions comparing to pure NPX could be explain by particle size

reduction during solid dispersion process.

3.1.2. Differential scanning calorimetry (DSC)

Differential scanning calorimetry displayed sharp endothermicfusion peak at 167.3 °C, which is corresponding to the melting pointof NPX (Fig. 3). The DSC spectra of PMs also exhibited endothermicmelting peak at 167.3 °C but with lower intensity which could beexplained by lower amount of NPX in PMs comparing to pure NPX.In formulations with high ratio of polymers, lower intensity is as aresult of dilution effect of the polymers. This reduction of the peakheight was seen in previous studies too [29–32]. The endothermicmelting peak was disappeared in DSC spectra of the solid dispersionswhich may be due to the lower crystallinity of NPX in thesolid disper-sions or dissolving of NPX in melted polymers [8,19,25]. These results

may suggest that the majority of crystalline NPX was converted to

Fig. 3. DSCproles of pure NPX, polymers, physical mixtures (PMs) and solid dispersions(SDs).

Fig. 4. Powder X-Ray Diffraction patterns of pure NPX, polymers, physical mixtures

(PMs) and solid dispersions (SDs).


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the amorphous state in the solid dispersions prepared by spray dryingmethod.

3.1.3. X-ray diffraction studies (XRD)

XRD results, as shown in Fig. 4, were in good agreement withthe DSC ndings. Pure NPX showed distinctive peaks in the regionof 5–40 (2θ) [6.5, 12.5, 13, 16.5, 18, 19, 20, 2.2, 23.5, 27 and 28.2(2θ)] that indicate the crystalline nature of NPX. The polymers andphysical mixtures showed different XRD pattern. Comparing heightof the peaks in the physical mixtures demonstrated the reduction inmagnitude of peaks due to the dilution effect of the carriers. Reductionin the height of the peaks and absence of some major peaks were seenin XRD patterns of the solid dispersions with high drug/polymerratios signifying a decrease of NPX crystallinity in these preparations(Fig. 4). These patterns were quite distinct in the solid dispersionscontaining high concentration of HPMC. Conversely, the crystallinityof NPX did not decreased in the solid dispersions prepared with bothCP and HPMC in the drug/polymer ratio of 1:0.5. The results conrmedthe decrease of NPX crystallinity in the spray dried formulations pre-pared with high amounts of polymers [8,11,13].

3.1.4. Fourier transform infrared spectroscopy (FT-IR)

To nd out the possible intermolecular interactions between theNPX and polymers FT-IR studies were done. The characteristic peaksof NPX, polymers, physical mixturesand solid dispersions are presented

in Fig. 5. Absorption peaks of 1724 cm

−1

and 1681 cm

−1

are relatedto the carboxylic acid bond and benzene ring and peaks of 1155 cm−1

and 1174 cm−1 are correlated to etheric bonds, respectively. Absenceof any other new peaks in the physical mixture and solid dispersionsand alsono differences in the positions of the absorption bands, indicatethe lack of signicant interactions between NPX and carriers duringspray drying process.

3.2. Drug content

Drug content of the formulations are presented in Table 1. NPXcontent in the solid dispersions containing CP and HPMC were inthe range of 61–75% and 90–94%, respectively. The highest drug con-tent was seen in SD6 formulation which contained maximum amount

of HPMC. It may be concluded that freely water solubility of HPMC

Fig. 5. FT-IR spectra of pure NPX, polymers, physical mixtures (PMs) and solid dispersions (SDs).

Fig. 6. Dissolution proles of pure NPX, physical mixtures and solid dispersionscontaining HPMC and CP in pH 3. SD and PM stand for solid dispersion and physical

mixture, respectively. (mean ± SD, n = 3).


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together with high viscosity of feedstock solution could increase drugloading in the related solid dispersions. Decreasing the drug contentin the CP contained samples could be owing to the fact that some of the ne droplets go out of the drying chamber during the spray dryingprocess. In view of that, a few tiny droplets of drug contained solventwere most likely withdrawn from the chamber whereas the insolubleCP larger particles could not be easily exited.

3.3. In vitro drug release

Dissolution proles of physical mixtures, solid dispersions andpure NPX powders prepared with various drug/carrier ratios at pH 3are presented in Fig. 6. The physical mixtures exhibited considerablyfaster initial dissolution rates than the pure NPX, which may be due tohigh hydrophilicity of the polymers. Hydrophilic polymers bring aboutaggregation reduction, wettability improvement and local solubiliza-tion by the carrier in the diffusion layer and thereby increasing inthe dissolution rate [16,33,34]. Although, a direct relationship betweenthe amount of carrier and NPX dissolution rate could not be establishedfrom the dissolution proles of the different physical mixtures, but dis-solution rate of all physical mixtures were much higher than the pureNPX. The spray dried particles with different drug to polymer ratiosshowed the higher drug release rate when compared to the relatedphysical mixtures and pure drug. The solid dispersions also provided agreater initial NPX dissolution rate compared to the pure drug powder.

Table 1 illustrates the time needed to release 50% of incorporateddrug (t50%) and the fraction of released drug in 60 min (Q 60) frompure NPX, physical mixtures and solid dispersions. Dissolution rateis faster, when the value of t50% is lower and Q 60 value is higher. Like-wise, these model independent parameters veried that the drugreleased faster from the solid dispersions. The improved drug releaserate could be attributed to the drug crystallinity reduction in the NPXloaded solid dispersions prepared by HPMC and CP (Figs. 3 and 4). Itis generally well known that a drug in a solid dispersions systemevery so often exists in an amorphous form [26]. The amorphous formof a drug has a higher thermodynamic activity than its crystallineform, leading to rapid dissolution of the drug [16,26,28,35,36]. Further-

more, the reduced particle size and accordingly elevated surface area(Figs.1and2) couldenhance thedissolutionrateof NPXin thesolid dis-persions [6,10,37,38]. In addition to latter evidences, increasing drugwettability and solubility as well as deaggregation of the drug particlesbrought about by the polymers could be the reasons for enhanced drugrelease rate from the solid dispersions.

Drug release rate was enhanced as a consequence of increasing CPconcentration, while HPMC contained solid dispersions showed themaximum release rate at the drug/carrier ratio of 1:2 ( Table 1 andFig. 6). The latter phenomenon could be explicated through two op-posite property of HPMC i.e. hydrophilicity and gel forming capacity[17,22,38,39]. The slower dissolution rate of SD4 compared withPM4 was possibly due to gel formation effect of HPMC since thedrug molecules are entrapped completely within the gel structure.

This effect was probably affected by hydrophilicity of HPMC in thehigher drug: carrier ratios.

Fig. 7 shows that the dissolution of NPX is considerably affected bypH of the dissolution media in the presence or absence of a carrier.The percentage of drug released at pH 7.4 is noticeably higher thanthe amount of drug dissolved at pH 3. This could be due to the bettersolubility of the weak acid NPXbecause of a greater ionizationat higherpH values.

3.4. Release kinetics

The in vitro release data were tted to 10 kinetic models (Tables 2and 3). The accuracy and prediction ability of the models werecompared by calculation of mean squared correlation coef cients

(MRSQ) and mean percent error (MPE). Considering the MRSQ and

MPEvalues,release data of theall formulationstted best to theWeibull'smodel with different slopes (β value which is also called shape factor).The mechanism of drug transport through the polymer matrix could bedenoted using the value of the exponent

β. The estimated values of

β ≤ 0.75 imply Fickian diffusion while β values in the range of 0.75–1state a combined mechanism of Fickian diffusionand swelling controlledrelease [40,41]. The value of shape factor for pure NPX and the drug/polymer physical mixtures ranged between 0.75–1; however, this valuewas estimated to be less than 0.75 for the spray dried samples(Table 3). Accordingly, diffusion phenomenon wasthe dominant mecha-nism of drug release from the solid dispersions, whereas the releasemechanism for pure NPX powder and drug/polymer physical mixturewas realized to fallow a combined pattern.

4. Conclusion

Bioavailability of poorly water-soluble drugs could be improved

as a result of release rate enhancement. Thus, the present study was

Fig. 7. Dissolution proles of pure NPX, physical mixtures and solid dispersionscontaining HPMC andCP inphosphate buffer(pH 7.4). SD andPM standfor solid dispersionand physical mixture, respectively.


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aimed to enhance the dissolution rate of NPX by means of spraydrying technique employing CP and HPMC as hydrophilic carriers. Inconclusion, spray drying method can be benecially applied to en-hance the dissolution rate of the poorly water-soluble drug, NPX.The results showed that drug/carrier ratio and type of polymer canperform a major role to control the dissolution rate from the spraydried samples. The solid state studies conrmed that spray drying of NPX with HPMC or CP can decrease crystallinity or increase amor-phousness of the drug. Overall, the increased dissolution rate of soliddispersions can be described by the several factors including the in-creased surface area, creation of amorphous polymorph of the drug, for-mation of drug loaded microspheres and dispersion of the drugmolecules into the hydrophilic excipients in the solid dispersions.

Acknowledgment

The authors would like to thank Biotechnology Research Center,Tabriz University of Medical Sciences, Tabriz, Iran. This article isbased on a thesis submitted for PharmD degree (No. 3504) in Facultyof Pharmacy, Tabriz University of Medical Sciences, Tabriz, Iran.

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Table 3

Shape factor (β) of the Weibull model, squared correlation coef cients (RSQ) and percent error (PE) of the kinetic models used for analysis of drug release data.

Model NPX SD1 SD2 SD3 SD4 SD5 SD6 PM1 PM2 PM3 PM4 PM5 PM6

Zero order RSQ 0.931 0.865 0.824 0.580 0.787 0.856 0.787 0.797 0.885 0.862 0.819 0.823 0.787PE 20.43 23.68 33.11 26.96 22.31 43.82 45.97 60.52 311.29 103.47 15.38 14.31 21.06

First order RSQ 0.976 0.945 0.991 0.958 0.926 0.966 0.921 0.902 0.985 0.981 0.892 0.882 0.860PE 12.81 17.20 10.15 18.15 15.33 13.60 33.19 53.79 142.13 66.70 13.13 12.10 18.80

Higuchi RSQ 0.985 0.958 0.934 0.749 0.924 0.948 0.917 0.921 0.967 0.959 0.945 0.946 0.926PE 9.41 8.91 19.53 20.40 11.54 17.12 22.67 32.92 74.20 46.97 7.74 6.95 11.58

Peppas RSQ 0.981 0.978 0.901 0.764 0.966 0.946 0.944 0.874 0.834 0.853 0.982 0.984 0.961PE 7.98 6.53 21.94 34.54 4.47 17.92 10.65 29.58 67.27 41.70 3.59 2.92 6.93

Hixson-Crowell RSQ 0.964 0.922 0.966 0.861 0.889 0.943 0.887 0.870 0.963 0.952 0.870 0.864 0.837PE 15.72 19.79 21.86 21.98 18.05 24.68 39.33 56.60 227.81 84.39 13.88 12.82 19.55

Square root of mass RSQ 0.957 0.908 0.940 0.793 0.866 0.926 0.865 0.853 0.947 0.933 0.858 0.854 0.825PE 17.02 20.86 25.56 23.33 19.20 31.26 41.40 57.74 256.88 90.68 14.25 13.17 19.92

Three seconds root of mass RSQ 0.949 0.895 0.907 0.720 0.8414 0.905 0.841 0.835 0.928 0.911 0.845 0.844 0.812PE 18.23 21.82 28.35 24.43 20.22 36.11 43.06 58.74 279.59 95.77 14.62 13.53 20.29

Weibull RSQ 0.980 0.981 0.987 0.924 0.988 0.989 0.980 0.924 0.894 0.919 0.991 0.987 0.979PE 7.87 6.80 6.30 10.65 3.89 5.01 7.28 19.23 40.64 24.40 2.98 3.55 5.44β 0.77 0.66 0.77 0.63 0.61 0.75 0.74 0.99 1.05 1.08 0.79 0.84 0.77

Linear probability RSQ 0.885 0.852 0.907 0.785 0.839 0.888 0.806 0.717 0.743 0.768 0.807 0.813 0.745PE 22.09 21.93 25.30 21.78 18.52 30.83 37.05 54.18 194.05 83.57 15.18 14.17 21.12

Log- probability RSQ 0.965 0.970 0.985 0.968 0.978 0.981 0.980 0.974 0.975 0.989 0.991 0.983 0.992PE 11.92 10.96 5.13 7.39 6.88 11.71 10.12 11.53 22.33 13.57 3.25 4.23 3.17

Table 2

Mean squared correlation coef cients (MRSQ) and mean percent error (MPE) of the kinetic models used for analysis of drug release data.

Model Name Model NPX SDs PMs

MRSQ MPE MRSQ MPE MRSQ MPE

Zero order F = k0t 0.93 20.43 0.78 32.64 0.83 87.55First order ln (1−F) = − kf t 0.98 12.81 0.95 17.92 0.92 51.11Higuchi F ¼ kH

ffiffi t

p 0.99 9.41 0.90 16.68 0.94 30.06

Peppas ln F = ln kp + plnt 0.98 7.97 0.91 16.00 0.91 25.31Hixson–Crowell

1− ffiffiffiffiffiffiffiffiffiffi 1−F 3p ¼ k13t

0.96 15.72 0.91 24.29 0.89 69.18

Second root of mass1−

ffiffiffiffiffiffiffiffiffiffi 1−F

p ¼ k1

2t

0.95 17.03 0.88 26.94 0.88 75.44

Three seconds root of mass1−

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1−F ð Þ23

q ¼ k2

3t

0.95 18.23 0.85 29.00 0.86 80.43

Weibull ln[-ln(1-F)] = βln td + βlnt 0.99 7.80 0.98 6.65 0.95 16.04Linear Wagner Z = Z0 + qt 0.89 22.09 0.85 25.99 0.76 63.71Log Wagner Z = Z0' + q'lnt 0.97 11.91 0.98 8.70 0.98 9.68

F denotes fraction of drug released up to time t. k0, kf , kH, p, kP, k1/3, k1/2, k2/3, td, β, Z0, Z0', q and q' areparameters of themodels. Z and Z' areprobits of fraction of drug releasedat anytime. Z0 and Z0' are the values of Z and Z' when t = 0 and t = 1, respectively. SD and PM stand for solid dispersion and physical mixture, respectively.


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