particle diffusional layer thickness in a usp dissolution

Particle Diffusional Layer Thickness in a USPDissolution Apparatus II: A Combined Functionof Particle Size and Paddle Speed

JENNIFER J. SHENG,1 PAUL J. SIROIS,2 JENNIFER B. DRESSMAN,3 GORDON L. AMIDON1

1College of Pharmacy, University of Michigan, 428 Church Street, Ann Arbor, Michigan 48109-1065

2Lilly Research Laboratories, Eli Lilly and Company, Indianapolis, Indiana 46285

3Institute for Pharmaceutical Technology, Biocenter-Johann Wolfgang Goethe-University, Frankfurt 60439,Germany

Received 2 August 2007; revised 25 December 2007; accepted 27 December 2007

Published online 3 March 2008 in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/jps.21345

Jennifer J. Smaceuticals, Wi

Corresponden2440; Fax: 734-

Journal of Pharm

� 2008 Wiley-Liss

ABSTRACT: This work was to investigate the effects of particle size and paddle speed onthe particle diffuisonal layer thickness happ in a USP dissolution apparatus II. After thedetermination of the powder dissolution rates of five size fractions of fenofibrate,including <20, 20–32, 32–45, 63–75, and 90–106 mm, the present work shows thatthe dependence of happ on particle size follows different functions in accordance with thepaddle speed. At 50 rpm, the function of happ is best described by a linear plot ofhapp ¼ 9:91

ffiffiffid

p� 23:31 (R2¼ 0.98) throughout the particle diameter, d, from 6.8 to

106 mm. In contrast, at 100 rpm a transitional particle radius, r, of 23.7 mm exists,under which linear relationship happ¼ 1.59r (R2¼ 0.98) occurs, but above which happ

becomes a constant of 43.5 mm. Thus, happ changes not only with particle size, but alsowith the hydrodynamics under standard USP configurations, which has been overlookedin the past. Further, the effects of particle size and paddle speed on happ were combinedusing dimensionless analysis. Within certain fluid velocity/particle regime, linearcorrelation of happ/d with the square-root of Reynolds number ðd$=yÞ1=2, that is,happ=d ¼ 1:5207 � 9:25 � 10�4ðd$=nÞ1=2 (R2¼ 0.9875), was observed. � 2008 Wiley-Liss,

Inc. and the American Pharmacists Association J Pharm Sci 97:4815–4829, 2008

Keywords: diffusion; diffusional laye
r thickness; dissolution; USP dissolutionapparatus; in vitro models; particle size; hydrodynamics; fluid velocity; dimensionlessnumber; gastrointestinal/mathematical models; bioequivalence; fenofibrate
INTRODUCTION

The Biopharmaceutics Classification System(BCS) categorizes drugs into four classes accord-ing to their solubility and permeability.1 The BCSII class of compounds exhibits high permeabilityand low solubility relative to the administered

heng’s present address is AstraZeneca Phar-lmington, DE 19850.ce to: Gordon L. Amidon (Telephone: 734-764-763-6423; E-mail: [email protected])

aceutical Sciences, Vol. 97, 4815–4829 (2008)

, Inc. and the American Pharmacists Association

JOURNAL OF PHARM

dose. For a BCS II drug formulated into animmediate release (IR) dosage form, the combina-tion of high drug permeability and adequate GItransit time will lead to a rate and extent of oralabsorption that is controlled by the in vivo processof drug dissolution.1,2

Mechanistically, one of the fundamental issuesin modeling and understanding dissolution is todetermine the relationship between the diffu-sional layer thickness (happ) and particle sizeunder a defined set of hydrodynamic conditions.In the past, the Noyes–Whitney equation dM/dt¼�(D/h)A(Cs�Ct) has been widely used to

ACEUTICAL SCIENCES, VOL. 97, NO. 11, NOVEMBER 2008 4815

4816 SHENG ET AL.

describe drug particle dissolution,3 where h is athin static liquid layer at the solid surface understeady state conditions. For the past half century,the Noyes–Whitney equation has served as thetheoretical basis for many classical dissolutionmodels that assumed various relationshipsbetween the drug particle size and happ. Forexample, happ was assumed to be a constant byHixson and Crowell,4 while Higuchi and Hie-stand5–7 proposed that it was approximately equalto the radius of the particle, and Niebergall et al.8

determined it to be equal to the square root of theparticle radius. All of these assumptions implythat the correlation between happ and particle sizeis applicable to all particle size ranges. In recentyears, this correlation has been advanced bysetting the existence of a transitional particle size,above and below which happ behaves differentlydepending on the magnitude of the drug particleradius. For example, based on modeling thedissolution of polydispersed powders, Hintz andJohnson9 proposed the concept of a transitionalparticle size. Specifically, 30 mm was the criticalparticle radius. This model stipulates that h is aconstant of 30 mm for particles with radii largerthan 30 mm, while for particles less than 30 mm hequals the particle radius. However, the transi-tional value of 30 mm is based on a rotating diskhydrodynamic system, uses a compressed tablet,and powder size plays no role. This hypothesisseemed to have correlated reasonably well withtheir powder dissolution profiles and those inseveral subsequent studies.10,11 Nevertheless,direct evidence of the relationship between hand various particle sizes r in a USP dissolutionapparatus II needs to be collected. Further, whensuch an assumption is extrapolated to a nonro-tating disk system, well-defined hydrodynamicconditions merit careful considerations. Recently,Nystrom and colleagues used a Coulter Counter todirectly measure particle size and concluded thata critical diameter of 15 mm existed for griseo-fulvin and oxazepam, below which the happ

decreased substantially with decreasing particlesize. The effect of particle size on happ became lesssignificant when particles diameters were above15 mm.12 More recently, employing the sameparticle size measuring technique, Figueiredoet al. concluded that the critical particle sizeshould be 22 mm for ibuprofen, where the value ofh was linearly proportional to particle diameter(kd) when the diameter was less than 22 mm butwas a constant (kdcri) when the particle diameterwas above 22 mm.13

JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 97, NO. 11, NOVEMBER 20

In previously reported studies, even though thedependence of happ on particle size has beenmathematically described, its dependence on thedissolution hydrodynamics has received very littleconsideration. Therefore, a complete examinationof happ as a function of both particle size andpharmaceutically relevant hydrodynamic factorsis theoretically and practically significant. In thisarticle, we employed Eq. (1) to do so

happ

d¼ a þ b

dn0

y

� �1=2

(1)

where d is the drug particle diameter, n0 is thelinear velocity of fluid in cm/s, y is the kinematicviscosity (cm2/s) of the fluid, a and b areparameters that can be estimated through experi-mental data. Mathematically, Eq. (1) is similar toEq. (2),

kd

D¼ 2:0 þ 0:6 � dn0

y

� �1=2y

D

� �1=3(2)

where k is the mass transfer rate (cm/s), and D isthe diffusion coefficient of the drug molecule (cm2/s). As early as 1952, Eq. (2) was theoreticallyderived and experimentally validated by Ranzand Marshall to describe the rate of evaporation ofpure liquid drops and water drops containingdissolved and suspended solids, such as in spray-drying operations.14,15 In a subsequent articlepublished in the same year, Ranz16 extrapolatedhis theory to mass transfer of single particles andpacked beads. In 1954, Garner and his colleaguesapplied this theory to dissolution from a fixed solidsphere in fluid flow.17 Specifically, they found thatthe dissolution of benzoic acid in a stream of waterwas correlated with another equation of similarfunctional form to the Ranz–Marshall equation(Eq. 2), kd/D¼ 44þ 0.48(dn0/y)1/2(y/D)1/3. In 1960,Bird18 elaborated the Ranz–Marshall equation todescribe simultaneous heat and mass transfer of aliquid or solid sphere under forced convection. In1962, Harriott19 applied Eq. (2) for depicting masstransfer of benzoic acid, boric acid, zinc and leadsulfate particles suspended in agitated and baffledtanks. More recently, Fogler et al. employed Eq.(2) to study the dissolution of poly-dispersedparticles.20 Drug powders dissolved in a USPdissolution apparatus II would encounter asimilar hydrodynamic environment to that inves-tigated in Harriott and Fogler’s studies: that is,mass transfer from solid spheres under forcedconvection.

08 DOI 10.1002/jps

PARTICLE DIFFUSIONAL LAYER THICKNESS IN USP DISSOLUTION APPARATUS II 4817

In this article, fenofibrate was selected to serveas a model BCS II drug. Selection of USP IIconditions is pharmaceutically relevant and ofparticular importance from a regulatory perspec-tive. Moreover, five size fractions were utilized inthe current study to further characterize andunderstand the impact of particle size on happ. Thefocus of this work is to: (1) determine the diffusionlayer thickness happ for a BCS II model drug,fenofibrate, in a USP dissolution apparatus II; and(2) illustrate the dependence of happ on particlesize and hydrodynamics using function formhapp/d¼aþ b(dn0/y)1/2.

THEORETICAL SECTION

Calculation of Diffusional Layer Thickness happ

The diffusion layer thickness happ of drug particlesin a USP dissolution apparatus II can becalculated based on their dissolution rates. Atdissolution time zero, the initial weight of a singledrug particle is M0 ¼ ð4p=3Þrr3

0;n. At any time tafterwards, the particle weight is Mt ¼ ð4p=3Þrr3

t;n,where r0,n and rt,n are the volume particle radius attime zero and t, respectively. M0 and Mt can bebrought together by the mass balance of the drugparticle, namely,

M0 � Mt ¼ðCtÞV

N(3)

where N is the total number of particles, Ct isthe drug concentration at time t, and V is thedissolution volume. In addition, the Noyes–Whitney equation was originally derived in theslab coordinate. When it is applied to a sphericalparticle using spherical coordinate, it can berewritten as21,22

� dM

dt¼ DAðCs � CtÞ

1

rþ 1

happ

� �(4)

Eq. (4) can be simplified to the following:

� drt

dt¼ DðCs � CtÞ

r

1

rtþ 1

happ

� �(5)

where r is the density of drug particles, Cs is thedrug solubility in the dissolution medium, andhapp is the apparent diffusion layer thickness.Thus, with known parameters including Cs, Ct, r,V, D, and N, the relationship between rt and t canbe established, the derivative of which is con-nected to happ through Eq. (5).

DOI 10.1002/jps JOURNA

For a system that is approximately spherical,Eq. (4) is still valid. However, in the case ofnonspherical shape, the particle mass M shouldbe related to the particle volume radius rn, and theparticle surface area A should be related to theparticle surface radius rs. The volume radius rncan be measured directly by Coulter Countermethod. The surface particle radius is calculatedusing equation A ¼ 4pr2

s , where the surface area Ais determined by BET methodology. Therefore,Eq. (4) can now be written as follows:

�r4pr2

t;n drt;n

dt

¼ D4pr2t;sðCs � CtÞ

1

rt;sþ 1

happ

� �(6)

Further, if the ratio of rs/rn is assumed to beconstant, then Eq. (6) can be simplified in thefollowing:

� drt;n

dt¼ rs

rn

� �1

happþ 1

rt;n

� �D

r

rs

rn

� �ðCs � CtÞ (7)

The ratio between the surface radius and volumeradius, that is, rs/rn, is defined as the shape factor.This ratio is a fundamental property related tothe particle dissolution rate in addition to drugsolubility and diffusivity that are the essentialfactors dictating the diffusion and convectionwithin the solid–liquid interface. The dissolutionof an individual particle presumably proceedsin an isometric manner at the initial stage of thedissolution test. Therefore, the shape factor couldbe assumed as a constant in calculating the happ

values. Assuming each size fraction is monodis-persed, we employed Eqs. (3) and (7) to calculatehapp. During early dissolution the change ofparticle radius and consequently that of happ

are minimal. Therefore, generally the initial fivedissolution data points were used for the deter-mination of average happ values.

Dependence of happ on Particle Size andFluid Velocity

The diffusion layer thickness happ for drugparticles in a particular geometry is a functionof drug properties including particle diameter dand diffusivity D, and fluid properties of fluidvelocity n0 and kinematic viscosity y23

happ ¼ f ðd;D; n0; yÞ (8)

Therefore we have n¼ 5 variables for happ of drugparticle dissolution in a USP vessel. These n¼ 5

L OF PHARMACEUTICAL SCIENCES, VOL. 97, NO. 11, NOVEMBER 2008

4818 SHENG ET AL.

variables are built up from k¼ 2 independentdimensions that are: length L (cm) and time T (s).According to the p-theorem, the variables n¼ 5can be reduced to three independent dimension-less numbers, which are defined as happ/d,Reynolds number Re¼dn0/y and Schmidt numberScQ2¼ y/D. Then, Eq. (8) can be expressed as

happ

d¼ f ðRe;ScÞ (9)

Most previous works, both theoretical andpractical,14–17,19,20,24 suggested the form of:

happ

d¼ a þ b � ðReÞ1=2ðScÞ1=3 (10)

In this study, the kinematic viscosity of dissolu-tion medium y and drug diffusivity of fenofibrateD are constant, thus Eq. (1) arrives

happ

d¼ a þ b � ðReÞ1=2 ¼ a þ b

dn0

y

� �1=2

(1)

where a and b are constants and can bedetermined using regression analysis of theexperimental data such as happ and d.

EXPERIMENTAL

Materials and Preparation

Fenofibrate (>99% purity), sodium lauryl sulfateand all other chemicals were of analytical gradeand were purchased from Sigma Chemical Com-pany (St. Louis, MO). Distilled, deionized andfiltered water was prepared in house and used forall experiments. Fenofibrate ‘‘as received’’ fromSigma had a broad size distribution, with whichfour size fractions, that is, 20–32, 32–45, 63–75,and 90–106 mm were obtained by sieving. In brief,the bulk material was initially dry sieved throughthe USA standard test sieves (Newark Wire ClothCompany, Clifton, NJ). Then, 300 mg of the drysieved fractions were well suspended into 60 mL of0.9% NaCl solution containing 0.05% SLS, andthe suspensions were wet sieved through thesame standard sieves. The wet sieved fractions onthe sieve were rinsed with 0.9% NaCl solutioncontaining 0.05% SLS and subsequently withwater, and then they were dried overnight in avacuum oven at 308C. The <20 mm size fractionwas achieved by jet-milling the bulk material asreceived from Sigma. About 100 g of fenofibratebulk material was jet-milled through a labscale size fluid energy grinder (Sturtevant Inc.,


Hanover, MA) that was operated using com-pressed nitrogen, with an approximate yield of95%. The milling air setting was 60–70 PSIG, andthe feed air pressure was operated between 90 and100 PSIG. The crystal form of the jet-milledfenofibrate was also characterized using powderX-ray diffraction (PXRD) and differential scan-ning calorimetry (DSC) to confirm the absence ofamorphous material and process induced changesin crystal form. All the five fractions of particleswere fully characterized with regards to theirspecific surface area, particle volume diameter,number diameter, and density. The USP pH 6.850 mM phosphate buffer without pancreatin wasprepared following standard procedures.25 Piece-wise regression analysis and parameter estima-tions were performed using Sigmaplot 10.0 (SPSSInc., Chicago, IL). Two segment linear piecewiseregression was applied to the particle radii r andthe corresponding happ, at each paddle speed.

Powder X-Ray Diffraction (PXRD)

Powder diffraction patterns of jet-milled and ‘‘asreceived’’ fenofibrate were recorded with a ScintagX-ray diffractometer (Franklin, MA) using Cu Ka

radiation (l¼ 1.54 A), tube voltage of 40 kV, andtube current of 20 mA. The intensities weremeasured at 2u values from 58 to 408 at acontinuous scan rate of 58/min.

Differential Scanning Calorimetry (DSC)

The thermal behavior of jet-milled and ‘‘asreceived’’ fenofibrate were studied using a TAInstruments 2920 modulated DSC (TA Instru-ments, New Castle, DE) with refrigerated coolingsystem (RCS) in standard mode. Approximately5–10 mg samples were weighed into aluminumDSC pans, crimped, equilibrated to �808C andthen heated up to 1008C at a rate of 5.08C/min,with nitrogen purge at 110 mL/min.

Particle Size Determination

The mean volume particle size diameters for allsize fractions were determined using the CoulterCounter (nonlaser light scattering) method. Thejet-milled material was first suspended in the0.9% NaCl solution containing 0.25% SLS, satu-rated with fenofibrate. Then the suspension wasquickly transferred into the 0.9% NaCl solution

08 DOI 10.1002/jps


containing 0.1% SLS and saturated with fenofi-brate, which served as the suspending mediumand testing electrolyte for all samples duringparticle size measurement. It should be empha-sized that the diameter given by the Coulter is avolume equivalent diameter, namely, dn¼ (6n/p)1/3,where n is the particle volume directly measuredby the Coulter.

Specific Surface Area Measurement

The specific surface area of fenofibrate powderswas determined at liquid nitrogen temperatureusing BET methodology employing nitrogen asthe adsorbate. The surface area was used tocalculate the particle surface radius by equationA ¼ 4pr2

s .26

Solubility Measurement

The aqueous solubility of fenofibrate was mea-sured at 378C in 0.25% SLS pH 6.8 phosphatebuffer, instead of water. Since SLS has a CMC of0.25% (w/v) in water, it serves as a reasonablesurrogate of the in vivo surfactant propertiesprovided by bile salts and provides the necessaryenhancement in solubility and dissolution rate forfenofibrate that is practically insoluble in waterwith a solubility of <0.3 mg/mL. Fenofibratesolubility was determined by suspending excessfenofibrate powder in 5 mL buffer in a screw-capped vial. The suspension was equilibrated byshaking in an orbital shaker water bath (LAB-LINE Instruments, Inc., Melrose Park, IL). Atsuitable time intervals, 1.0 mL of aliquots weredrawn and filtered through 0.45-mm membrane,and then diluted with an appropriate amount ofphosphate buffer prior to the spectrophotometricassay at l¼ 292 nm using a UV spectrophot-ometer (Beckman Coulter DU 650, Fullerton, CA).The equilibrium solubility of fenofibrate wasestablished when the difference between threeconsecutive measurements is within 1%, a processthat may take up to 7 days.

Dissolution Profiles in USP Dissolution Apparatus II

The dissolution profiles of various size fractions offenofibrate were measured in a USP dissolutionapparatus II at 378C using pH 6.8 phosphatebuffer containing 0.25% SLS. For the jet-milledfenobibrate, 50 mg powder was weighed into a1.0 mL of eppendorf tube, then 0.5 mL of thedissolution medium were added, and then the


suspension was sonicated at low power for 5 s. Thewell dispersed jet-milled suspension was thenimmediately transferred into the prepared dis-solution vessel, and rinsed with the dissolutionmedium three times of 5 mL each. The four biggersize fractions of fenofibrate powders (50 mg) weredirectly dropped into the 378C 500 mL dissolutionmedium that was previously degassed. Dissolu-tion experiments were conducted in triplicate atboth 50 and 100 rpm for each particle size. Aliquotswere drawn at 0.33–1 min intervals, filtered through0.45-mm membrane and diluted if necessary prior toUV spectroscopic analysis at l¼ 292 nm (Beckman-Coulter DU 650, Fullerton, CA).

RESULTS

Characterization of Fenofibrate Particles

As evident from the DSC traces of the jet-milledand ‘‘as received’’ fenofibrate (Fig. 1a and b), anegligible glass transition occurs around �458Cwith a very small enthalpy of �0.0051 W/g,followed by the melting point around 79.58C withan enthalpy of fusion of approximate 95 J/g. ThisDSC result indicates that no significant changesin crystal forms or amorphous content wereintroduced through the jet-milling process. Theseresults are further confirmed by PXRD (Fig. 2)where the slightly decreased peak intensities areconsistent with a reduction in particle size.

The volume particle size distribution of eachsize fraction is shown in Figure 3, and the surfacearea equivalent particle radius, shape factor anddensity for each size fraction are summarized inTable 1. Visual observation via SEM shows theirregular and multi-sided morphology of fenofi-brate particles (Fig. 4), suggesting that fenofibrateparticles would dissolve in a relatively isometricmanner.

The diffusivity of fenofibrate was calculated as7.4� 10�6 cm2/s using the ADMET PredictorTM

1.2.1 (Simulation Plus Co., Lancaster, CA), whichused the Hayduk-Laurie formula D ¼ 13:26�10�5=h1:4

waterV0:589.27 This value is consistent with

the literature reported experimental value of7.15� 10�6 cm2/s using the rotating diskmethod.28

Dissolution Profiles of Fenofibrate

The solubility of fenofibrate was determined to be150.4� 1.4 mg/mL in 0.25% SLS 50 mM pH 6.8


Figure 1. DSC thermogram of fenofibrate particles. a) Jet-milled fenofibrate particlesof <20 mm diameter; b) Fenofibrate sample ‘as received’ from Sigma Chemical Company.Thermal scans obtained using 5–10 mg samples in crimped aluminum pans over atemperature range of �808C to 1008C at a scan rate of 58C/min.

4820 SHENG ET AL.

phosphate buffer. The dissolution profiles offenofibrate particles at 50 and 100 rpm are shownin Figure 5. Several elements can be drawn fromthese dissolution profiles. First, as expected, thedissolution rates increase with decreasing particlesizes in the following order: jet-milled material(<20 mm)> 20–32> 32–45> 63–75> 90–106 mmsize fractions. This observation is consistent withthe larger surface area per unit weight of thesmaller particles. Secondly, the dissolution ratesof the jet-milled material are similar at the 50 and100 rpm. Finally, the four larger size fractions offenofibrate dissolve faster at a paddle speed of100 rpm than at 50 rpm, presumably due to thehigher fluid velocities at 100 rpm that lead to


thinning of happ and subsequently more efficientmass transfer.

Dependence of Diffusional Layer Thickness onHydrodynamics and Particle Sizes

The dependence of happ on particle size andhydrodynamics/fluid velocity were examinedand illustrated in the two following ways. Thefirst approach is bifunctional analysis demon-strating happ as a function of r under differentpaddle speeds, as shown in Figure 6. Thisapproach determined the transitional particlesize through which the value of happ exhibits a

08 DOI 10.1002/jps

Figure 2. Overlay of powder X-ray diffraction pat-terns of jet-milled fenofibrate particles of <20 mm dia-meter and fenofibrate sample ‘as received’ from SigmaChemical Company. Intensities were measured usingCu Ka radiation at 2u values from 58 to 408 at a scan rateof 58/min.


different correlation with particle radius. Deter-mination of transitional particle size has beenemployed previously in the literature.9,12,13 Thesecond approach is dimensionless analysis usingEq. (1), investigating the combined effects ofparticle sizes and paddle speeds on happ.

Bifunctional analysis: The transitional particlesize for fenofibrate in a USP dissolution apparatusII is fluid velocity dependant. Using piecewiseregression, the transitional particle sizes are deter-mined by the goodness of fitting using square rootof overall correlation coefficient (R2), and thevalues are 37.7� 5.4 mm (R2¼ 0.9972) and 23.7�

Figure 3. Semi-logarithmic plot of cumulativevolume fraction of jet-milled and sieved fenofibrateparticles as a function of particle diameter determinedusing a Coulter Counter.


0.6 mm (R2¼ 0.9998), under 50 and 100 rpm,respectively (Fig. 6). For drug particles smallerthan the transitional sizes, the happ displays alinear relationship with the drug particle radius.The linear slopes vary with paddle speeds, andthe values are 1.71 (R2¼ 0.9872) and 1.59(R2¼ 0.9828), at 50 and 100 rpm, respectively.In comparison, for drug particles larger than thetransitional sizes, at 100 rpm a constant happ wasobserved with an approximate value of 43.5mm forany particles with radius larger than 23.7mm; andat 50 rpm the happ value continues to increasewith particle size but at a slower rate. Thebifunctional analysis also leads to the plot of happ

versusffiffiffid

p, as shown in Figure 7. Evidently, at

50 rpm happ demonstrates a linear correlationwith

ffiffiffid

p, that is, happ ¼ 9:91

ffiffiffid

p� 23:31, R2¼

0.9769, throughout the tested particle size range6.8–106 mm in this work. Whether this linearrelationship applies to particles in near-micron orsubmicron range needs further research, partiallydue to the complex microfluid dynamics surround-ing these very small particles. In comparison, at100 rpm the linear relationship transforms intoplateau for larger particles. This dependence ofhapp on

ffiffiffid

pwas then further exploited in dimen-

sional analysis.Dimensionless analysis: According to Eq. (1)

happ/d¼aþ b(dn0/y)1/2, the Re number (dn0/y) wascalculated using drug particle diameter d (cm),linear fluid velocity n0 (cm/s), and kinematicviscosity y of dissolution medium (0.758�10�2 cm2/s) at 378C.29 The linear velocity offluid/dissolution medium in an agitated USPvessel depends on the rotational speeds of paddleand the location in the vessel. In addition, the useof the linear velocity of the fluid is not convenientin practice, and the rotational speed of the paddle$ is readily available and can be easily adjusted tothe linear velocity through paddle diameter, thatis, n0 ¼ $� paddle diameter. It therefore lends tothe calculation of the Reynolds number using $,that is, d$=y. The relationship between happ/dand d$=y is proposed in Eq. (11):

happ

d¼ a þ b

d$

y

� �1=2

(11)

where Re is calculated based on the following: d isthe particle diameter in mm, $ is the rotationalspeed of paddle in rpm, y is the kinematic viscosityof dissolution medium in cm2/s, and the diameterof the paddle is well defined according to USP.Figure 8 demonstrates that the happ of suspended


Table 1. Physical Characteristics of Various Size Fractions of Fenofibrate Powder

Particle Fractions(mm)

NumberRadiusa

(mean�SD)(mm)

SurfaceRadiusb

(mean�SD)(mm)

VolumeRadiusc

(mean�SD)(mm)

SpecificSurface Area(mean�SD)

(m2/g)

TappedDensity(g/mL)

Shapefactord

<20 mm (jet-milled) 1.2� 0.5 2.7� 0.5 3.4� 0.9 1.575� 0.058 0.36� 0.03 0.7920–32 mm 13.8� 6.2 16.2� 5.2 16.1� 0.6 0.296� 0.031 0.64� 0.02 1.0132–45 mm 19.7� 4.8 28.4� 3.0 26.3� 1.2 0.181� 0.002 0.76� 0.01 1.0963–75 mm 34.4� 4.4 44.6� 11.2 37.1� 1.0 0.154� 0.001 0.76� 0.02 1.2590–106 mm 51.1� 18.9 56.3� 14.5 53.0� 0.5 0.083� 0.006 0.77� 0.02 1.06

aNumber radius was measured using scanning electronic microscopy (SEM).bSurface radius was converted through the surface area that was measured by BET methodology.cVolume radius was directly measured using Coulter Counter method.dShape factor was defined as the ratio of the surface equivalent radius to the volume equivalent radius, that is, rs/rn.

4822 SHENG ET AL.

drug particles in the USP vessel can be success-fully described with the semitheoretical equation(Eq. 11). Here, happ/d exhibits a two-regionaldependence on particle Re, that is, ðd$=yÞ1=2. Oneregion is linear, where the particle Re is 592,and is described by happ=d ¼ 1:5207 � 9:25�10�4ðd$=yÞ1=2. Assuming the drug diffusivity is7.15� 10�6 cm2/s,28 this regression correspondsto an R2¼ 0.9875 (p< 0.0001), and estimates thevalues of a¼ 1.5207� 0.0417 and b¼�9.25�10�4� 4.66� 10�5. The other region describesthe relation for particles with smaller Re number(either smaller particle size and/or slower paddlespeeds), the relationship between happ/d and Remay be more complex.

DISCUSSION

Calculation of Diffusion Layer Thickness happ

Due to its mathematical simplicity, a sphericalshape is the best contour to select to experimen-

Figure 4. Typical Scanning Electron Micrograph offenofibrate particles (63–75 mm).


tally determine the value of happ, an approach thatwas elaborated by Wang and Flanagan.21,22

Numerous attempts to prepare spherical andcrystalline fenofibrate particles for this studywere unsuccessful because fenofibrate eitherformed amorphous spheres or crystalline needlesfollowing recrystallization processes as confirmedby polarized microscopy. Therefore, irregularshapes of fenofibrate particles were employedhere with consideration given to their shapefactor; that is, the ratio of particle surface radiusto volume radius. Here, it is assumed that drugparticles would dissolve in an approximatelyisotropic manner, implying that the shape factorwould remain unchanged. This assumption hasbeen used widely in the past when the shapefactors were considered constant, in the initialstages of the dissolution testing. Even in thecase of dissolving crystals with a high degree of

Figure 5. Dissolution profiles of jet-milled and sievedfenofibrate fractions in a USP Dissolution Apparatus IIat 50 rpm and 100 rpm. Dissolved fraction is shown as afunction of time. Data expressed as mean�SD, n¼ 3.

08 DOI 10.1002/jps

Figure 6. Bifunctional analysis of the dependence ofparticle boundary layer thickness, happ (mm), deter-mined in a USP Dissolution Apparatus II at 50 rpmand 100 rpm, on particle surface radius. Data expressedas mean�SD, n¼ 3.

Figure 8. Dimensionless analysis of the dependenceof diffusional layer thickness happ on particle sizes andhydrodynamics in a USP Dissolution Apparatus II.Data expressed as mean�SD, n¼ 3.


nonisometricity sharp edges such as needles andplates, the shape factor has been reported tochange insignificantly until considerable dissolu-tion occurs.30,31 In addition to the shape factor, thequantity of amorphous content, may also con-tribute to nonisometric dissolution. PXRD andDSC results confirmed the absence of detectableamorphous form for the jet-milled material.

The thickness of a hydrodynamic boundarylayer is often defined as the distance fromthe surface of the solid to the point where thetangential velocity attains a value of 90% of themain stream.23 In general, this layer thickness isnot easily evaluated from experimental workexcept under well-defined hydrodynamic condi-tions as in the case of the rotating-disk.23 In thiswork, the happ is calculated using Eq. (7) to

Figure 7. Plots of particle boundary layerthickness, happ (mm), determined in a USP DissolutionApparatus II at 50 rpm and 100 rpm, as a function ofsquare root of particle surface radius. Data expressed asmean�SD, n¼ 3.


describe the distance over which the diffusionprocess dominates the mass transfer. As such, itreveals the drug dissolution in terms of howresistance to mass transfer may occur in the solid–liquid interface in a simple model. In addition, thediffusional thickness can often be used to predictchanges in mass transfer caused by factors such aschemical reactions.32,33 It is important to notethat the happ determined in a USP dissolutionapparatus is an apparent averaged value from allparticles. This averaged value is contributed fromthe following two factors. One factor is the specifichydrodynamic conditions, where the local envir-onment of fluid dynamics surrounding eachindividual drug particle is not the same through-out the USP dissolution apparatus II vessel.34–38

The other factor is the monodispersion of the fivesize fractions is not perfect, even though they areall very narrowly distributed (Fig. 3).

Dependence of happ on Hydrodynamics andParticle Sizes

Bifunctional Analysis with Transitional Particle Sizes

Dissolution phenomena have been studied in aquantitative manner for more than a century,during which various relationships between happ

and particle size have been proposed.5,8,9,12,13

Bifunctional analysis of fenofibrate dissolutiondata suggests that Higuchi–Hiestand’s assump-tion5,6 and Hintz–Johnson’s hypothesis9 appear tobe valid, whereas careful considerations should begiven to the powder dissolution occurring underspecific hydrodynamic conditions.

Higuchi–Hiestand assumed that happ was equalto or greater than the particle radius, and conductedtheir experiments with 2.2 mg of micronizedmethylprednisolone (25 mm) in 100 mL of water


Table 2. Comparison of the Relationship between happ and r in: Higuchi–Hiestand’s Work, Hintz–Johnson’s Workand the Current Work in a USP Dissolution Apparatus II

Conditions

BelowCr: happ as aFunction of r

CriticalParticle Size: theValue of Cr (mm)

AboveCr: happ as aFunction of r

Higuchi–Hiestand1,2 happ is comparable to, or greater than the particle radius rHintz–Johnson3 happ¼ r (r< 30 mm) 30 Constant, 30 mmUSP dissolution apparatus II,

at 100 rpmhapp¼ 1.59r (r< 23.7 mm) 23.7 Constant, approximate 43.5 mm

USP dissolution apparatus II,at 50 rpm

happ¼ 1.71r (r< 37.7 mm) 37.7 happ increases with r slowly

4824 SHENG ET AL.

in bottles that were rotated at 6 rpm at 258C.5–7

In comparison with their work (Tab. 2), the currentstudy experimentally demonstrates that in a USPdissolution apparatus II happ may be equal to orgreater than particle radius r, only if the specifichydrodynamic conditions are provided. The firstobservation is based on the data that at paddlespeed of 100 rpm, the particle radius r of 44.6�0.4 mm is not significantly different from the corre-sponding happ value of 43.5� 11.2 mm. The secondpoint was observed at both paddle speeds. Forexample, at 50 rpm happ equals to 1.71r, and thevalue of happ decreases to 1.59r at a higher paddlespeed of 100 rpm, both suggesting that happ couldbe greater than particle radius.

The description of happ as a function of particlesize under both paddle speeds was compared withHintz’s work as well, as shown in Table 2. Bothsets of data consistently demonstrate the exis-tence of a transitional particle size Cr in the 30 mmsize range, and a linear relationship between happ

Table 3. Particle Sizes and Re: Comparison of Fenofibrateand Previous Studies Using the Function Form of Eq. (2)

System

USP dissolution apparatus IIa

Mass transfer from single particles and packed beds4–6

Mass transferb from a fixed solid sphere in fluid flow7

Mass transferc of solid particles suspended in agitated tankEstimated the k value of polydisperse solid particles9

Mass transfer of a single particle in creeping-flow10

aThe unit for rotational speed $ is rpm, for particle size d is cmbOverall mass transfer for the fixed sphere.cThe fluid velocity was estimated using slip velocity presented idk is the mass transfer coefficient and equals to D/happ.eThe experimental value is within 30% of the theoretical predict


and r when particle size is below Cr. When particlesize is above Cr, a constant happ value, however,was observed at 100 rpm. Further, despite thesimilar observations, it is evident that distinctdifferences exist between the Hintz–Johnson’sassumption and our work in the following specificaspects: (1) the value of Cr; (2) the linear slopevalue between the happ and r; and (3) the value ofconstant happ. These differences are attributed tothe differences in hydrodynamic conditions underwhich the dissolution studies are conducted. In arotating disk system, a planar constant surfacearea pertains rather than a powder dissolution ofspherical geometry where more complex hydro-dynamics pertains. For example, based onLevich’s equation h ¼ 1:61ðD=yÞ1=3ðy=$Þ1=2,23 adiffusivity of fenofibrate as 7.15� 10�6 cm2/s andkinematic viscosity of the dissolution mediumas 7.58� 10�3 cm2/s at 378C, for fenofibrate, arotational speed of 21 rpm would give a h equalsto 30 mm. Clearly, even though this assumption

Powder Dissolution in a USP Dissolution Apparatus II

ParticleDiameter

Range (mm) Reynolds Numbers of Fluids

2–106 0<Re< 5.8� 104

600–1100 1<Re< 7� 105

1270 20<Re< 103

s8 15–600 325<Re< 1.08� 105

Not defined Not defined in the articleNot defined The correlation is verye good as of:

1<Re< 103, reasonable as of:103<Re< 104

.

n Harriott’s article.

ed values.

08 DOI 10.1002/jps


seems to predict powder dissolution well in Hintz–Johnson study, the dissolution hydrodynamics inthese two systems are very different.

Dimensionless Analysis

The key dissolution variables employed in Eq. (1),particle size and Reynolds number as an indicatorof the fluid dynamics, were compared to theprevious utilization of the Ranz–Marshall equa-tion (Eq. 2). As shown in Table 3, the similaritiesand differences are discussed as follows. In Ranz’soriginal work on mass transfer of single particlesand packed beds,16 the theory was applied toparticle sizes in the range of 0.06–1.1 cm and Renumber ranging from 2 to as high as 105. Inlater studies, the particle size varied from 15 to1270 mm, and the Re number ranged from 1 to 105

(Tab. 3). Comparably, the Re number understandard USP dissolution conditions such as50 and 100 rpm is within the Re range testedin the original Ranz theory14–16 and otherwork.17,19,20,24,39 The Re number in a USPdissolution apparatus II encompass a consider-able range from a value of zero at the vessel wall tothe highest value at the paddle tip. Using equationRe ¼ $d2

$=y, the maximum Re numbers can bedetermined as 2.9� 104 and 5.8� 104 at 50 and100 rpm, respectively,35 where $ is the rotationalspeed of the paddle, d$ is the diameter of thepaddle, and n is the kinematic viscosity of thefluid. Although the mean particle size in thiswork, 32–106 mm, is generally smaller than thatutilized by Ranz’s and others, our results haveshown that the theoretical diffusion layer thick-ness happ/d¼aþ b(dn0/y)1/2 could be extrapolatedwith remarkable accuracy to the particle sizerange beyond the Ranz’s.

Industrial Significance of happ

Dependence of happ on Paddle Speeds and ParticleSize. Dimensionless analysis demonstrated abipartite behavior of the dependence of happ onpaddle speeds and particle size, which may becontributed by several factors. First, crystaldefects and roughness on the particle surfacerepresent a larger percentage of the crystal weightafter milling, since the surface area to volumeratio is increased. These effects were observed tohave a significant impact on dissolution rate forparticles with diameters in the micron range.Second, at small particle sizes, turbulence inthe form of microeddies begins to play a moreimportant role in the hydrodynamics near to the


dissolving surface, in other words a microenvir-onment different from the bulk hydrodynamics iscreated.40–42 It is also thought that the effectiveeddy diffusivity of drug molecule in the turbulentfluid may be very different from that in bulkfluid.43 Surface roughness, crystal defects andmicroeddies would lead to a faster dissolutionrate than expected using surface area and thebulk fluid velocity. Further, jet-milling processgenerally produces small particles with radiusof less than 10 mm, which is not perfectlymonodispersed even though it is considerednarrowly distributed compared with particleslarger than 20 mm. Subsequently, any nonperfectmonodisperse nature may contribute to thederivation of an accurate estimation of happ.Employing the assumption of monodispersity forthe jet-milled material may be an over-simplifica-tion, particularly if the dissolution investigation isprimarily focused on particles less than 10 mm.However, even with the consideration of poly-disperse nature (e.g., 1% particle with radius of0.7, 0.8, and 1.05mm, 7% of 1.3mm, 6% of 6mm, 4%of 7 mm and 1% of 9.5 mm), the happ value variesvery little. The most plausible reason is that smallparticles contribute to negligible amount of over-all weight fraction and the subsequent dissolutionrate. Nevertheless, this region of small Re numbermerits further research.

Eq. (11), happ=d ¼ a þ bðd$=yÞ1=2, was alsoapplied to in vitro dissolution behavior of otherdrugs including digoxin and oxazepam indepen-dently reported by Nystrom et al.12,44 In theirstudies, dissolution rates were measured with twodifferent particle sizes under three rotationalspeeds, that is, 350, 500, and 800 rpm. Dissolutionrate data for digoxin fit the following the relation-ship:

happ

d¼ 22:17 � 0:012

d$

y

� �1=2

;

Rsq ¼ 0:9403 ðp ¼ 0:0052Þ

For oxazepam, happ conforms to the followingequation:

happ

d¼ 3:05 � 0:016

d$

y

� �1=2

;

Rsq ¼ 0:9472 ðp ¼ 0:0063Þ

The successful fitting of digoxin and oxazepamdissolution data into the function form of Eq. (11)further supports the linear correlation betweenhapp/d and ðd$=yÞ1=2 and its use to estimate happ


4826 SHENG ET AL.

values for drug particles in the standard USPdissolution II apparatus, based on the measuredparticle size d and the rotational paddle speed $.

happ for Poorly Soluble Drugs

Recent estimates suggest that the percentage ofBCS II drugs in the top US 200 oral IR products isgreater than 25%.45 Probably as a result of thewidespread application of combinatorial chemis-try and high-throughout screening activitiesduring the drug discovery process,46,47 this per-centage will probably increase. To ensure satisfac-tory oral absorption, particle size reduction hasbeen widely used to increase the surface to volumeratio and thus improve the dissolution rate ofpoorly soluble drugs. The current work clearlyreveals that the happ values generally decreasewith decreasing particle size (Fig. 6). Therefore,an increase in the dissolution rate resulting from aparticle size reduction process is attributed notonly to an increase in the surface area to volumeratio, but also to a decrease in happ, an importantcontribution that is rarely addressed in theliterature.

In addition, since the layer thickness happ

depends on the drug diffusivity D, the correspond-ing happ for two drug substances with different Dvalues would be expected to be different. However,it is likely that the happ would only change slightlybecause: (1) according to the Levich theory,23 happ

is only dependent to the one-third power on D,that is, h ¼ 1:61ðD=yÞ1=3ðy=$Þ1=2 and (2) drugdiffusivity of most small drug molecules is low andin the range of 10�6–10�5 cm2/s.

Furthermore, the results in this article suggestthe following: (1) for drug particles with radius inthe range of 3.4–23.7 mm, happ is approximately 1.5-fold of particle radius (Fig. 6), (2) under the paddlespeed of 50 rpm, the diffusional happ exhibits a linearrelationship with the square root of particle diameter,across the studied particle size range (Fig. 7).

Finally, Figure 6 suggests that for small drugparticles, happ is not significantly different under50 and 100 rpm. The exact size range for the smallparticles, where happ is independent of paddlespeeds in a USP dissolution apparatus II, is yetto be determined. In this work, the jet-milledfenofibrate with a mean rn of 3.4 mm, demonstratesthat its happ is independent of fluid velocity. In the caseof cilostazol, the size limit could be in the low micronrange, that is, 13 mm. Cilostazol is a poorly solublecompound with a water solubility of 6.25 mg/mL at


37-C. Three size fractions with mean particle sizes of13, 2.4, and 0.22 mm were prepared using techniqueshammer-mill, jet-mill and spray-drying, respectively.In vitro powder dissolution profiles of 5 mg of thesecilostazol samples, in 900 mL of water, FaSSIF andFeSSIF at 37-C in USP apparatus II, were equivalentat the paddle speeds of 50 and 200 rpm.11 This resultindicates that the happ is independent of paddle speedswhen the cilostazol particles are smaller than 13 mm.Both results suggest that the hydrodynamic consid-erations are important for large particles, and verysmall particles in micron range are less influenced byhydrodynamics.

Relevance to In Vivo Conditions

The unique result, namely, happ is independent offluid velocity for the very small particles, suggeststhat the highly variable GI fluid velocity varyingwith GI motility phases may not impact on thehapp of low micron range particles in in vivo. Themicronized powder of felodipine, with a medianparticle size of 8 mm, may be an example of such adrug. Felodipine is a poorly soluble, neutral andlipophilic drug, and its oral absorption that isindicated by AUC does not appear to be affected bythe in vivo hydrodynamics in dog studies.48,49

The independence of happ on GI motility, for smallparticles such as jet-milled material, imply thatthe in vivo variability would be significantlyreduced within subjects and between subjects.Therefore, reducing particle size not only im-proves the dissolution rate and absorption frac-tion for poorly soluble drugs, but also potentiallyminimizes the in vivo variability.

However, it should be emphasized here thatestablishing in vitro dissolution methodologyreflecting in vivo scenario requires considerationsin many aspects. For example, pH and surfactantsare critical in selecting an appropriate dissolutionmedium. Additionally important factors includethe fluid velocity and device geometry, whichcombine to determine the dissolution hydrody-namics. One disparity between dissolution testingand the in vivo situation is that the paddle speedremains unchanged during a given dissolutiontest. By contrast, the GI tract regularly transi-tions through migrating motility cycles and fastedor fed states. Hence, the GI fluid velocity variesconsiderably along various regions of smallintestine,50–53 which can lead to large inter- andintrasubject variations in in vivo happ. To mimicthe wide range of in vivo happ, it may be more

08 DOI 10.1002/jps


appropriate to vary the in vitro hydrodynamicconditions during a test, for example, paddlespeed (Type II tester), dip rate (Type III) and flowrates (Type IV). It is unrealistic to assume that useof a single USP dissolution setting such as 50 rpmcan reflect the complete hydrodynamics of a fullGI motility cycle. However, a single paddle speedmight be used to represent one certain GI motility-fluid flow and particle size combination.

Revision of the test apparatus design to betterreflect the geometry of the intestinal tract and itsflow patterns should be considered. One particu-larly important aspect to consider is the repre-sentation of oscillating flow, corresponding to thesegmental mixing in the fed state, which is uniquein its effects on in vivo happ. Applying dimensionalprinciple, the in vivo happ is a function of:happ/d¼ f(Re, Sc, St), where Re and Sc are definedas previously, and St is the Strouhal numberdescribing oscillatory fluid. St number is calcu-lated as St¼fl/n0, where f is vortex shedding, l isthe characteristic length (hydraulic diameter),and n0 is the linear velocity of GI fluid.

Potentially, a dimensionless analysis of thein vitro hydrodynamics and the in vivo GI motilityusing the rule of happ/d¼ f(Re, Sc, St) would beuseful in improving accuracy of predicting in vivodissolution and absorption of drug products,enhancing correlation between in vitro dissolutionand in vivo response and developing in vitrobioequivalence methods.

CONCLUSIONS

The diffusional layer thickness happ was deter-mined through fenofibrate powder dissolutiontesting in a USP apparatus II with variousparticle sizes and paddle speeds. The dependenceof happ on drug particle size and dissolutionhydrodynamics, reveals that at 100 rpm the happ

is approximate 1.5-fold of the particle radius or aconstant, which occurs below and above a transi-tional size of 23.7 mm, respectively. Further, theresult at 50 rpm suggests that a diffusional happ

being linearly proportional to square root ofparticle diameter is an overall better functionalform. Further, dimensionless analysis supports alinear correlation of happ/d with particle Re withinspecific particle-hydrodynamic regime. However,the extrapolation of in vitro results to the in vivosituation requires further investigation due to the


in vivo hydrodynamics varying with various GImotility phases.

ACKNOWLEDGMENTS

J.J.S. gratefully acknowledges the support of theAmerican Foundation for Pharmaceutical Educa-tion and grant number GM07767 from NIGMS.

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particle diffusional layer thickness in a usp dissolution

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