Hydrodynamic, mass transfer, and dissolution effects induced by tablet location during dissolution testing

Hydrodynamic, Mass Transfer, and Dissolution Effects Induced by Tablet Location during Dissolution Testing GE BAI, PIERO M. ARMENANTE Otto H. York Department of Chemical, Biological and Pharmaceutical Engineering, New Jersey Institute of Technology, 323 M. L. King Boulevard, Newark, New Jersey 07102-1982

Received 1 April 2008; revised 11 June 2008; accepted 24 June 2008 Published online 9 September 2008 in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/jps.21512

ABSTRACT: Tablets undergoing dissolution in the USP Dissolution Testing Apparatus II are often found at locations on the vessel bottom that are off-center with respect to the dissolution vessel and impeller. A previously validated CFD approach and a novel experimental method were used here to examine the effect of tablet location on strain rates and dissolution rates. Dissolution tests were conducted with non-disintegrating tablets (salicylic acid) and disintegrating tablets (Prednisone) immobilized at different locations along the vessel bottom. CFD was used to predict the velocity profiles and strain rates when the tablets were placed at such locations. A CFD-based model was derived to predict the mass transfer coefficient and dissolution curves, which were then compared to the experimental results. Both non-disintegrating and disintegrating offcenter tablets experimentally produced higher dissolution rates than centered tablets. The CFD-predicted strain rate distribution along the bottom was highly not uniform and the predicted strain rates correlated well with the experimental mass transfer coefficients. The proposed CFD-based model predicts mass transfer rates that correlate well with the experimental ones. The exact tablet location has a significant impact on the dissolution profile. The proposed model can satisfactorily predict the mass transfer coefficients and dissolution profiles for non-disintegrating tablets. ß 2008 Wiley-Liss, Inc. and the American Pharmacists Association J Pharm Sci 98:1511–1531, 2009

Keywords: dissolution testing; USB dissolution testing apparatus II; computational fluid dynamics; mass transfer coefficient; CFD; modeling

INTRODUCTION Solid dosage forms such as tablets are among the most common and convenient methods to administer drugs. Tablet manufacturing, however, involves a number of operations that can affect the bioavailability of the active ingredient. Therefore, tablets are routinely tested for quality control before they can be released. Dissolution testing is one of the many tests that pharmaceu-

Correspondence to: Piero M. Armenante (Telephone: 973596-3548; Fax: 973-596-8436; E-mail: [email protected]) Journal of Pharmaceutical Sciences, Vol. 98, 1511–1531 (2009) ß 2008 Wiley-Liss, Inc. and the American Pharmacists Association

tical company must conduct on oral solid dosage forms, as required by the Food and Drug Administration (FDA) and specified in the United State Pharmacopoeia (USP). Dissolution testing serves as a surrogate for drug bioavailability through in vitro–in vivo correlation, and it additionally helps in guiding the development of new formulations and in assessing lot-to-lot consistency, thus ensuring product quality. Several dissolution apparatuses are listed in the US Pharmacopoeia (USP)1 and are currently in use. The USP Dissolution Testing Apparatus II (referred to here as USP Apparatus II) is designed to test solid dosage forms, and it is one of the most widely used dissolution apparatuses in the pharmaceutical industry. Although the USP

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Apparatus II was officially introduced more than 30 years ago2 and it is still commonly used today, a review of the literature shows that a number of test errors and failures associated with the use of this equipment have been reported.3–10 Such issues appear to arise even when the USP dissolution calibrator tablets are used,4,6,9,11,12 thus raising questions on the ability of the calibrating testing process and the use of calibrator tablets to capture the complexities of the dissolution process. Pharmaceutical companies are directly affected by such failures because of the high costs associated with them.13–15 Thus, a better understanding of the hydrodynamics of this device and the effect of tablet location on the dissolution rate can only be beneficial. Several investigators have already pointed out that the hydrodynamics in the USP Apparatus II can be responsible for some of the inconsistent results observed during dissolution testing. However, researchers have been able to study the hydrodynamics of the USP Apparatus II in some detail only in recent years.8,11,12,16–21 Computational and experimental studies have confirmed that the flow field in the USP Apparatus II is highly not uniform, especially at the bottom of the vessel where the tablet is usually located during a test. Because of such flow non-uniformities, the strain rate, a critical variable in mass transferdominated process such as dissolution, is also nonuniformly distributed along the bottom of the vessel.12,19–21 This, in turn, can have a dramatic effect on test results. A typical dissolution test using the USP Apparatus II begins by dropping the test tablet into the dissolution medium. At the start of the dissolution test, the tablet is supposed to sink to the lowest point in the vessel bottom (i.e., the center), where it undergoes dissolution. However, that is not always the case. Because of its physical and chemical properties, the tablet may not necessarily reach or remain at the center of the vessel bottom. For example, in many cases the tablet may adhere to the vessel bottom at offcenter locations, or move along the bottom during the dissolution process. The USP does not specify how to insure that the locations of the tested tablets are reproducibly the same. However, from previous reports on the hydrodynamics of the USP Apparatus II,18,21 there is enough evidence to suspect that, depending on its position along the bottom of the vessel, the tablet may experience different strain rate environments and therefore JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 98, NO. 4, APRIL 2009

produce different dissolution rates that can generate invalid or inconsistent test results. In this work, the impact of the location of the tablet on the dissolution rate and the overall dissolution process were studied quantitatively and in detail using a computational-based model as well as an experimental approach. Four different tablet locations were studied, including a central location at the vessel bottom and offcenter tablet locations 108, 208, and 408 off-center, respectively. Both disintegrating and non-disintegrating tablets were used. Through this approach, the mass transfer coefficient for nondisintegrating tablet could additionally be modeled. The resulting mass transfer models can be helpful to analyze dissolution process and guide further investigations.

EXPERIMENTAL EQUIPMENT AND METHOD All dissolution experiments were conducted using a Distek 5100 Bathless Dissolution Apparatus II (Distek Inc., North Brunswick, NJ). Although this equipment is provided with seven standard 1-L individual dissolution vessels, only two of the vessels were used at a time. A picture of the vessel and impeller used in the experiments is shown in Figure 1a, and their dimensions are given in Figure 1b and c. Additional details about the equipment are provided elsewhere.19–21 Dissolution studies were carried out with two types of tablets, that is, 10 mg Prednisone calibrator tablets (disintegrating tablets, NCDA #2), kindly provided by Dr. Zongming Gao (FDA, St. Louis, MO), and 300 mg salicylic acid calibrator tablets (non-disintegrating tablets; USP Lot Q0D200), purchased from USP (Rockville, MD). The dissolution medium for Prednisone consisted of de-aerated and de-ionized water, in accordance with the Dissolution Test Performance Standard #2.22 The dissolution medium for salicylic acid tablets consisted of a 0.05 M monobasic potassium phosphate buffer to which an NaOH solution (50% (w/w) concentration) was added to reach a final pH value of 7.4
0.05.23 The media were de-aerated according to the degassing method developed by Moore and Flanner24 (Fig. 2). The temperature of the dissolution medium was raised to 37
0.58C prior to its use in the experiments. In order to test the effect of tablet position on dissolution, a tablet was initially fixed in place at a predefined location at the bottom of the DOI 10.1002/jps

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Figure 1. USP Dissolution Testing Apparatus II and tablet locations used in this work: (a) dissolution vessel and impeller; (b) system used for the dissolution of prednisone tablets (liquid volume: 500 mL); (c) system used for the dissolution of salicylic acid tablets (liquid volume: 900 mL); (d) locations of tablet during dissolution experiments and in dissolution simulations.

dissolution vessel with a very small bead of a commercial available high-viscosity polymer (polybutene). Four tablet locations were tested, that is, at the center of the vessel bottom, 108 offcenter, 208 off-center and 408 off-center (Fig. 1d). All angles originated from the center of the hemispherical vessel bottom, and were measured DOI 10.1002/jps

starting from the vertical centerline to the point of interest (e.g., the angle would be zero for the central position below the impeller). After the vessel and the fixed tablet were placed in the dissolution equipment, the appropriate volume of dissolution medium (500 mL for Prednisone tablets, and 900 mL for salicylic acid JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 98, NO. 4, APRIL 2009

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curves generated using reference standards obtained with solutions of known concentrations. All experiments in which the tablets were placed at the central location were performed in triplicates to determine reproducibility.

DATA ANALYSIS Figure 2. Equipment used to de-aerate the dissolution medium (after Moore and Flanner24).

tablets) was slowly poured into the dissolution vessel in order to minimize initial dissolution. The first sample was taken right after the medium addition using the procedure described below. Immediately thereafter, the agitation was started at the prescribed rotational speed (50 rpm for Prednisone tablets, and 100 rpm for salicylic acid tablets). This time was defined as the zero-time point. All experiments lasted 45 min. The procedure outlined here, in which the liquid was added to a vessel that already contained the immobilized tablet, was, by necessity, slightly different from the procedure described in the USP,1 in which the tablet is dropped into the vessel after the medium has been added to the vessel, and the agitation is started only when the tablet has reached the bottom of the vessel. Samples were manually taken at 5-min intervals during a 45-min period, by removing 5-mL aliquots with a 5-mL syringe connected to a cannula, 2 mm in diameter, inserted only when a sample was taken. The sampling point was horizontally located midway between the impeller shaft and the vessel wall, and midway between the top edge of the impeller and the surface of the dissolution medium, that is, within the sampling zone prescribed by the USP.1 A total of 10 samples were taken in each experiment. The volume of medium removed by sampling was not replaced, in accordance to the USP.1,12 About 2 mL of each sample were discarded and the rest was filtered with a double layer PTFE/PES 0.8-mm filter (Drummond Scientific Co., Broomall, PA). The filtered samples were stored in small glass vials until analyzed. All samples were analyzed with a UV-visible spectrophotometer (Varian CARY 50 Bio) at the specified wavelengths, that is, 242 nm for Prednisone and 296 nm for salicylic acid.22,23 The results were compared to 9-point calibration JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 98, NO. 4, APRIL 2009

The dissolution profiles obtained with tablets at off-center locations were compared to those obtained with the centrally located tablets in order to determine whether the results were statistically different. Two approaches were used. The first approach consisted of using a modelindependent method based on the similarity factor ( f1) and difference factor ( f2) proposed by Moore and Flanner:12,24 9 8P n > > > R  T j j t t > = <  100 (1) f1 ¼ t¼1 n P > > > ; : Rt > t¼1

f2 ¼ 50 log10

8" < :

1þ

n 1X

n

t¼1

#0:5 ðRt  Tt Þ2

9 = 100 ; (2)

where Rt is the reference assay at time t, Tt is the test assay at the same time, and n is the number of points. The higher the similarity factor f1 (which can be in the range 0–100), the higher the average difference between reference and test curves is. The higher the difference factor f2 (which can be in the range 1 to 100) the lower the average difference between reference and test curves is.25 Public standards have been set by Food and Drug Administration (FDA) for f1 and f2. Accordingly, statistical similarity between the two curves being compared requires that both 0 < f1 < 15 and 50 < f2 < 100.12,26 The second approach to evaluate the similarity of dissolution profiles was based of the analysis of variance and the calculation of the p values using a standard Student’s t-test.

DETERMINATION OF THE TABLET-MEDIUM MASS TRANSFER COEFFICIENT FROM EXPERIMENTAL DISSOLUTION DATA In order to determine how the tablet-liquid mass transfer process, and the hence dissolution rate, is DOI 10.1002/jps

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affected by the location of the tablet, at least for the case in which the tablet is eroding and not disintegrating, the mass transfer coefficient must be extracted from the experimental data. This can be done by rearranging and integrating the basic mass transfer equation. The rate of dissolution of a chemical species, such as a drug, from a solid surface, such as a tablet, into the adjacent liquid, such as the dissolution medium, can be expressed as follows:27,28 dC kA ¼ ðCs  CÞ dt VL

(3)

where C is the drug concentration in the dissolution medium, Cs is the solubility concentration of the drug, k is the mass transfer coefficient, A is the tablet surface area exposed to the dissolution medium, and VL is the volume of dissolution medium, assumed to be well mixed. Of interest here is the determination of the mass transfer coefficient k from the experimental data: k¼

VL dC AðCs  CÞ dt

(4)

As time progresses and the tablet erodes, the surface area A is reduced. If the tablet is cylindrical and if it retains its original height-todiameter ratio, b, during the dissolution process (a reasonable assumption if the mass transfer coefficient is similar on all exposed surfaces), then A can be calculated knowing the ratio: b¼

hT dT

(5)

where hT and dT are, respectively, the height and the diameter of the tablet. In the case of the salicylic acid tablet, hT and dT were measured with a caliper and found to be 3.33 and 9.57 mm, respectively, yielding a b value equal to 0.348. If only the top and side surface of the tablet are exposed to the dissolution medium, the interfacial area available for mass transfer is:

2 1 þ 4b A ¼ pdT (6) 4 From a mass balance for the drug disappearing from the tablet and appearing in the dissolution medium it must be at any time that: C¼

rT ðVT0  VT Þ þ C0 VL

(7)

where rT, VT0, and VT are, respectively, the density, initial volume, and volume at time t of the tablet, and C0 is the initial concentration of the DOI 10.1002/jps

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drug in the dissolution medium (equal to zero in this work). Since the tablets are cylindrical, the tablet volume is given by: V T ¼ hT

pd3 pd2T ¼b T 4 4

(8)

By substituting this equation into Eq. (7), one can obtain the tablet diameter as the tablet dissolves and C increases:   4ðC  C0 ÞVL 1=3 dT ¼ d3T0  (9) pbrT Substituting this equation into Eq. (6), gives an expression for A as a function of C:

  4ðC  C0 ÞVL 2=3 1 þ 4b 3 AðCÞ ¼ p dT0  (10) 4 pbrT An estimate of the mass transfer coefficient k, assumed to be independent of time and varying tablet volume, can be obtained by substituting this expression for A in Eq. (4) and integrating it. The result is: VL k¼ t

Z

Ct

C0

4 ð1 þ 4bÞ ðCs  CÞ   dC 4ðC  C0 ÞVL 2=3 3 p dT0  pbrT

(11)

where Ct is the drug concentration in the dissolution medium at time t. Since experimental data of C versus t are available, this equation can be used to calculate k from by numerical integration, for the case of salicylic acid tablets since these tablets do not disintegrate.

PREDICTION OF THE TABLET-MEDIUM MASS TRANSFER COEFFICIENT In order to determine whether the experimentally derived tablet-medium mass transfer coefficients could be predicted theoretically or computationally for the non-disintegrating salicylic acid tablets, the following approach was used. The equations available in the literature for mass transfer coefficients in systems that approximately represent the tablet-medium interaction in the dissolution vessel were obtained. Since these equations are typically based on boundary layer theory, they require as input the approaching velocity of the incoming fluid. Such a velocity was estimated from CFD. For the case of a centrally located tablet, it was assumed that the tablet-dissolution medium mass JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 98, NO. 4, APRIL 2009

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transfer process at the top tablet surface is similar to the mass transfer between a rotating disk and the surrounding fluid, although here the tablet is stationary and the fluid is rotating. The rotating disk model predicts that the mass transfer coefficient is:29,30 2=3

ktop ¼ 0:62DAB n1=6 v1=2

(12)

where ktop is the mass transfer coefficient in cm/s, DAB is the diffusivity between the solute and the solvent in cm2/s, n is the kinematic viscosity of the liquid in cm2/s, and v is the angular velocity of the rotating disk in rad/s. In order to adapt this equation to the tablet-medium case, it was assumed that v is the rotational angular velocity of the dissolving medium above the tablet. Since the medium in this region of the USP Apparatus II was previously found to move approximately with solid body rotation,19 v was calculated by dividing the tangential velocity of the fluid at a location above the tablet by the radial distance of that location from the vessel centerline. Accordingly, it was found that v ¼ 12.94 rad/s. For comparison purposes, the angular velocity of the impeller for the salicylic acid case is 10.47 rad/s (corresponding to N ¼ 100 rpm). These results are in agreement with previous work, which showed, both experimentally and computationally, that the angular velocity of the fluid in the lower region of a USP Apparatus II is slightly larger than that of the impeller.19 The kinematic viscosity in Eq. (12) was taken as that of water at 378C (0.70  102 cm2/s). The diffusivity of salicylic acid in water was estimated from the Wilke–Chang correlation:30,31 DAB ¼ 1:173  1016 ðFMÞ1=2

T mVA0:6

(13)

where M is the molecular weight of the solvent in kg/kg-mol (18.02 for water), F is an association parameter of the solvent (2.6 for water), T is the temperature in K (310 in this case), VA is the solute molar volume at its normal boiling point in m3/kg-mol (0.09592 m3/kg-mol in this case, assuming the molar volume of salicylic acid at boiling point is the same as that at room temperature) The diffusivity value, DAB, for salicylic acid–water system was then calculated to be 1.47  105 cm2/s. In order to estimate the tablet-dissolution mass transfer coefficient on the side of the centrally located tablet it was assumed that this process is similar to the mass transfer between a rotating JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 98, NO. 4, APRIL 2009

cylinder and the surrounding fluid, although here the tablet is stationary and the fluid is rotating. The rotating cylinder model predicts that the mass transfer coefficient kside is as follows:32  1=3 kside dT ¼ 0:135 0:5 Re2V Sc DAB

(14)

where Sc is the Schmidt Number, Sc ¼ m/(DABrL) and ReV is defined as: ReV ¼

dT uV r L m

(15)

with uV being the velocity at the periphery of the rotating cylinder. In order to adapt this equation to the tablet-dissolving medium case, it was assumed that uV is the tangential velocity of the dissolving medium next to the tablet, which was estimated from CFD. A different approach was used to calculate the mass transfer coefficient when the tablet was offcenter. The mass transfer coefficients for the top and side surfaces of the off-center tablets were estimated using the mass transfer models for a flow parallel a flat plate (top surface) and past a single cylinder (side surface). The solid–liquid mass transfer coefficient for a liquid moving parallel to flat plate was calculated from:30,32 ktop ¼ 0:99uðReÞ0:5 ðScÞ2=3

(16)

where u is the approaching velocity of the liquid to the flat plate, Sc is the Schmidt number, and Re is the Reynolds number, defined as:30,32 Re ¼

LurL m

(17)

In the original equation for a flat plate, L is the distance from the beginning of the plate in the direction of the flow. Here it was assumed that L is equal to the diameter of the tablet, dT. The density of the fluid, rL, was taken to be that of water at 378C (995.73 kg/m3). The approaching velocity of the rotating liquid flowing over the tablet top surface, u, was obtained by calculating, through CFD, the tangential velocity of the liquid at eight equally spaced locations in the azimuthal direction on the plane where the tablet was located and at the same radial distance as the tablet radius. These values were averaged to determine the average velocity of the medium approaching the tablet in Eq. (16). The solid–liquid mass transfer coefficient on the cylindrical side of the tablet was obtained from the equation describing the mass transfer around DOI 10.1002/jps

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cylinders:30,32 kside ¼ 0:6uðReÞ0:487 ðScÞ2=3

(18)

where Re was calculated as before, and the approaching velocity u was predicted as just described above.

NUMERICAL CFD SIMULATION Predictions of the velocity distribution and strain rates inside the USP Apparatus II were obtained using a commercial pre-CFD mesh generator (Gambit 2.1.6) coupled with a CFD package (Fluent 6.2.16). The full 3608-vessel geometries were incorporated in the simulations.

Mesh Generation and Mesh Quality The basic geometry of the USP Apparatus II modeled in this work was same as that described in previous work by this group (Fig. 1c).19,21 The exact geometry of each element of the impeller was obtained by measuring the dimensions of an experimental apparatus provided by Merck researchers and reported elsewhere.19 The impeller modeled here had a slightly enlarged diameter shaft at the blade, resembling a collar, as opposed to the uniform shaft diameter, including the portion at the blade, typical of the USP design. The radius of this collar was only 1.6 mm larger than that of the rest of the shaft, and the geometric differences between this system and the typical USP system were so minimal that the results obtained here can be expected to be equally valid for the USP impeller with no collar.19,21 Ten sets of different meshes were generated for the CFD simulations in order to account for the presences of tablets at different locations along the USP Apparatus II vessel bottom and for the different operating conditions required by the dissolution test standards for different tablets (500 mL dissolution medium, 50 rpm impeller rotation speed for Prednisone tablets; 900 mL dissolution medium, 100 rpm impeller rotation speed for salicylic acid tablets). For the 900 mL case, the meshes contained about 80,000 cells, as described previously.19,21 For the 500 mL case, the meshes contained about 75,000 cells because of the lower volume of the dissolution medium. For both operating conditions, the meshes consist of hybrid cells. The upper portion of the vessel (from the lower edge of the impeller blade to DOI 10.1002/jps

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the liquid surface) was meshed with structured, Cooper-type hex cells. The lower portion of the vessel (from the lower edge of the impeller blade to the bottom of the vessel) was meshed with the unstructured, tetrahedral cells. Significant attention was paid to generate high-quality meshes, since this determined whether the simulation converged to a stable solution or not. The average EquiAngle Skew parameter (one of the most important parameters to determine the quality of the mesh) was typically in the range 0.3–0.4 (0: best; 1: worst) and was no larger than 0.82 for any individual cell in all cases.

Boundary Condition and Reference Frames In all simulations, the no-slip condition in the appropriate frame of reference was assumed at all solid surfaces. The air–liquid interface was always assumed to be flat (a very reasonable assumption given the low agitation speed, as experimentally verified), and it was modeled as a frictionless surface, that is, the normal gradients of all variables were zero at this interface. A single reference frame (SRF) approach was used in the CFD simulations with no tablet or with centrally located tablets. Accordingly, the vessel wall and the centrally located tablet were assumed to be rotating, and the impeller was stationary, although the appropriate body forces were included in the computation to account for the noninertial characteristics of the rotating reference frame. As for simulations in which the tablets were not in the center, a multiple reference frames approach (MRF) was used, since the flow fields were no longer symmetrical. The whole domain was divided into inner domain and outer domain. The inner domain contained the impeller and the outer domain contained the rest of the vessel, including the off-center tablets. The conservation equations in the inner domain frame were transformed into a rotating reference frame and the flow was computed in a steady state manner. The outer domain was modeled at steady state in a stationary reference frame. The results were transformed back to stationary reference frame at the end of the simulation. CFD Approach The conservation equations for mass and momentum were solved by FLUENT 6.2.16 (the CFD solver). Based on the results of previous work, all JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 98, NO. 4, APRIL 2009

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simulations were conducted using the k–v model with low Reynolds number correction as a turbulence model. This model was selected because its predictions matched more closely previously obtained experimental velocity data.19 All simulations were carried out on a Dell Precision 650 Workstation, equipped with two Intel XEON 2.8 Gigahertz processors and 4 gigabytes of random access memory (RAM). A typical simulation required some 40000 iterations and about 30 h of CPU time to achieve conversion.

RESULTS Results for Prednisone Tablets The centrally located Prednisone tablets became totally disintegrated into smaller granules within about 8 min from the beginning of the experiment (the latter time being defined when the very first sample was taken and the agitation was started). The granules formed a rotating ‘‘cone’’ at the center of the vessel bottom. The off-center tablets became totally disintegrated in about 5 min, that is, significantly more rapidly than the centrally located tablets. Although the off-center tablets were initially bonded to their location with polybutene, the granules that were formed after they disintegrated moved from the off-center location to the center of the vessel bottom, where they formed a rotating cone. Figure 3 shows the Prednisone dissolution profiles, that is, the % dissolved Prednisone in the dissolution medium (where 100% is achieved at the theoretical concentration of the label claim,

Figure 3. Experimental dissolution profiles for Prednisone tablets at different tablet locations. JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 98, NO. 4, APRIL 2009

when the tablet would become fully dissolved) as a function of time, for different initial locations of the Prednisone calibrator tablets at the bottom of USP Apparatus II vessel. The % dissolved fraction is identical to the concentration ratio C/C in the dissolution medium (with C being the theoretical concentration achieved when the tablet would become fully dissolved). The largest and smallest standard deviations for experiments with the centrally located tablets were, respectively, 3.72% at t ¼ 0 min and 1.27% at t ¼ 40 min. The variability at t ¼ 0 min was similar to that observed by previous researchers,12 and can be attributed to disintegrating characteristics of Prednisone tablets. In fact, when the dissolution medium was added to the vessel, an appreciable amount of Prednisone in the centrally located tablets (16.52
3.72%) became rapidly dissolved before the experiment even started. The criteria for dissolution profile comparison described in Eqs. (1) and (2) were first applied to each profile for the centrally placed tablets with respect to the average dissolution profile at the same central location. All 10 points in each curve were used for these calculations. In all cases, the f1 and f2 values were, respectively, much lower than 15 and at least above 77, indicating that the centrally placed tablets produced statistically similar dissolution profiles, according to the FDA public standards. Also, according to the DDA Dissolution Test Performance Standard #2,22 a dissolution profile should result in a dissolved fraction of Prednisone between 28% and 44% of the total amount of Prednisone contained in the tablet (10 mg) when sampling at 30 min. All the three profiles obtained for the centrally located tablets satisfied this criterion (dissolved fractions of Prednisone at 30 min equal to 39.4%, 41.1%, 39.9%, respectively), implying that the equipment was well calibrated and appropriate to conduct dissolution testing on Prednisone tablets. The experimental results reported in Figure 3 show that at times larger than 5 min the dissolution profiles for the off-center tablets were, in general, different from those for the centrally placed tablets and significant higher. However, the initial C/C values were found to be similar irrespective of where the tablet was initially located, and were equal to 17.03
2.45%. Since this value is significantly different from zero, this implies that appreciable dissolution resulted from the addition of medium to the vessel prior to the starting of the agitation and the beginning of the DOI 10.1002/jps

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experiment. For t 5 min, the dissolution profiles diverged, with the off-center tablets dissolving significantly faster than the centered tablets (Fig. 3). Although the profiles for all off-center tablets were similar to one another, the tablet located 108 off-center had the lowest dissolution profile among the three off-center tablets. For t 25 min, the 208 off-center tablet located had higher C/C values than the 408 off-center tablet, but the reverse was true for t > 25 min. The f1 and f2 factors (Eqs. 1 and 2) were calculated for the experimental dissolution profiles for each of the off-center tablets with respect to the average dissolution profile for the centrally located tablets. All 10 points in each curve were used for these calculations. The f1 values, f2 values, and p-values from the Student’s t-test are reported in Table 1. In all cases, f1 was larger than 15, and f2 was about 50, implying that the offcenter dissolution profiles were statistically different, according to the FDA criteria, from the baseline profile obtained with the centrally located tablets. At t ¼ 30 min the dissolved Prednisone fractions were found to be 49.38%, 51.30%, and 51.40% of the amount of Prednisone originally contained in the tablet (10 mg), for the 108, 208, and 408 off-center tablets, respectively. These values are all outside the 28–44% range specified by the DDA Dissolution Test Performance Standard #2,22 indicating that the test did not produced the expected results and was considered invalid as a calibration test. CFD simulations were conducted to determine the velocity flow field with and without Prednisone tablets, and with the tablets at different

Table 1. Statistical Evaluation of Similarity between Dissolution Profiles of Off-Center Tablets and Centrally Located Tablets for Prednisone and Salicylic Acid Tablets at Different Locations with Different Statistical Methods

Prednisone tablets 108 off center tablet 208 off center tablet 408 off center tablet Salicylic acid tablets 108 off-center tablet 208 off-center tablet 408 off-center tablet

p-Value

f1

f2

0.0544 0.0251 0.0370

21.26 26.63 25.47

54.55 49.67 50.60

0.1226 0.0531 0.1132

33.45 51.94 35.35

61.37 52.54 60.17

Gray boxes indicate a failing value according to FDA criteria. DOI 10.1002/jps

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locations. The results are presented in Figure 4 as velocity vectors originating on the plane of the impeller (y-plane). The key feature of the flow below the impeller is that the recirculation loop generated by the radial flow emanating from the paddle is not able to penetrate the inner core region located just at the center under the impeller. Consequently, the flow in this inner region, roughly as wide as the shaft, is very weak, as previously reported by this group.19,21 The axial velocities change rapidly with location along the vessel bottom especially when the vertical boundaries of the inner core region are crossed (Fig. 4). The presence of a tablet affects the overall and local flow, but the flow around the tablet is strongly determined by the exact location of the tablet. When the tablet is placed at the center of the vessel bottom, the tablet experiences a weak flow on its top surface. The overall flow in this case is still symmetrical and similar to that obtained with no tablet. When the tablet is off-center, the overall flow becomes, in general, asymmetric but only slightly, since the tablet is small. The flow in the central inner core region is still very weak, but the tablet may be more or less affected by it depending on its exact location on the vessel bottom. The flow field around the 108 off-center tablet is stronger than that around the centered tablet, but it is still affected by the proximity with the poorly mixed inner core region and the presence of the tablet itself, straddling the core region and the region surrounding it (Fig. 4). Even in this case, the flow field near the upper surface of the tablet can be seen to be significantly different from, and stronger than, that experienced by the centered tablet. Figure 4 also shows that the velocity fields surrounding more off-center tablets (208 and 408) are much stronger than the flow around the centered tablet. Interestingly, the 208 off-center tablet is in a region where the axial velocities are relatively strong, as a result of the closing of the recirculation loop generated by the impeller, as one can see from Figure 4. Figure 5 shows the distribution of strain rates near the vessel bottom in the absence and in the presence of Prednisone tablets at different locations. The darker red regions indicate strain rate values of 60 s1 and above. Of importance here is the strain rate at the tablet surfaces. For both the centrally located tablet and the 108 off-center tablet, high strain rate values occur mainly on the side surfaces of the tablets. However, for tablets JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 98, NO. 4, APRIL 2009

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Figure 4. CFD-predicted velocity vectors (m s1) on the impeller plane (y-plane) in the lower region of the USP Apparatus II vessel with and without Prednisone tablets and at different tablet locations.

Figure 5. CFD-predicted strain rate (s1) on the impeller plane (y-plane) in the lower region of the USP Apparatus II vessel with and without Prednisone tablets and at different tablet locations. Red regions indicate strain rate values of 60 s1 and above. JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 98, NO. 4, APRIL 2009

DOI 10.1002/jps

EFFECTS OF TABLET LOCATION ON DISSOLUTION TESTING

located 208 and 408 off-center, high strain rate values can be seen not only on the side surfaces but also on the top surfaces of the tablets, with possible implications for the tablet-medium mass transfer coefficient. In order to better quantify the strain rate experienced by an integral Prednisone tablet prior to disintegration, the average strain rate values on the exposed surfaces of the tablet (including the top face and the side surface, but not the bottom face in contact with the vessel bottom) were calculated from the strain rate maps obtained from the CFD simulations. The results, presented in Table 2, indicate that the off-center tablets experienced 22.5% (108 off-center tablet), 64.7% (208 off-center tablet), and 57.0% (408 off-center tablet) higher strain rates, respectively, than the centrally located tablet. Higher strain rate values can result in higher mass transfer rate at the tablets, but only prior to tablet disintegration, which typically occurred within 5 min from the beginning of the experiments. Once the tablet disintegrated, the resulting fragments migrated toward the center of the vessel to form a cone there, and experienced similar strain rate environment.

Results for Salicylic Acid Tablets In all dissolution tests with salicylic acid tablets, the tablets remained at their initial location for the entire duration of the experiment. Since these tablets did not disintegrate, the dissolution process was driven by erosion. Figure 6 shows the salicylic acid concentration ratio C/C versus time during the experiments, for different locations of the tablets. All the experiments with the centrally located salicylic acid tablets gave similar dissolution profiles, with a high standard devia-

Table 2. CFD-Predicted Average Strain Rate Values on the Top and Side Surfaces of Prednisone Tablets for Different Tablet Locations Prior to Tablet Disintegration

Tablet Location Centrally located tablet 108 off-center tablet 208 off-center tablet 408 off-center tablet DOI 10.1002/jps

CFD-Predicted Average Strain Rate on Tablet Surface (s1) 58.50 71.70 96.38 91.85

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Figure 6. Experimental dissolution profiles for salicylic acid tablets at different tablet locations.

tion value of 0.95% at 45 min and a low value of 0.21% at 5 min (Fig. 6). The f1 value and the f2 value (Eqs. 1 and 2) were calculated in order to compare each of the profiles for the centered tablets to the average profile at the same central location. In all cases f1 and f2 were, respectively, lower than 4.7 (i.e., much lower that 15, the FDA upper limit for similarity) and larger than 91 (i.e., much greater than 50), indicating that all the tests with centrally placed salicylic acid tablets produced statistically similar dissolution profiles. Based on the USP specifications for the salicylic acid calibrator tablets used in this work,23 each individual run should produce a dissolved amount of salicylic acid between 17% and 25% of the total amount contained in the tablet (300 mg) when sampling at 30 min. This was the case here, since the experimentally obtained fractions at 30 min were found to be 20.17%, 18.61%, and 19.87%, respectively, implying that the equipment was suited to conduct dissolution testing with salicylic acid tablets. The off-center tablets have different dissolution profiles than the centrally located tablets (Fig. 6), even though the initial C/C values were found to be similar to one another (3.38%
0.89%) irrespective of where the tablets were initially located. This low variability is consistent with the fact that salicylic acid tablets are nondisintegrating. Therefore, the effect on tablet dissolution of the initial addition of dissolution medium can be expected to be smaller than for the case of disintegrating Prednisone tablets. For t 25 min, the 108 off-center tablet showed slightly higher C/C values than the 408 off-center JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 98, NO. 4, APRIL 2009

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tablet, but the reverse was true for t > 25 min. The dissolution profiles for the tablets located 108 and 408 off-center were very similar to each other, but always above the profiles for the centered tablets. The profile for 208 off-center tablet was always higher than all the other profiles, except at t ¼ 0. Table 1 shows the f1 values, f2 values, and p-values from the Student’s t-test when the offcenter dissolution profiles were compared with the average dissolution profile for the centrally located tablets. In all cases, the f1 values were in the range 33–52, that is, much larger than the required 15, and the f2 values were around in the 50–60 range, implying that the off-center dissolution profiles were statistically different from the baseline profile obtained with the centrally located tablets or barely within the acceptance level, according to the FDA criteria. At t ¼ 30 min the dissolved salicylic acid fractions were found to be, respectively, 26.92%, 31.45%, and 27.38% of the amount of salicylic acid originally contained in the tablet (300 mg) for the 108, 208, and 408 off-center tablets. These values are all outside the 17–25% range specified by the USP,23 which would indicate that the apparatus is off calibration.

Figure 7 shows the CFD-predicted velocity vectors on the plane of the impeller (y-plane) for different locations of the salicylic acid tablets. Although the impeller speed is twice as large for salicylic acid as for the Prednisone dissolution cases, the two sets of velocity distributions are similar when appropriately scaled (Fig. 7 vs. Fig. 4), including the presence of a poorly mixed central inner core region just under the impeller. The flow around the tablet is strongly affected by the exact location of the tablet. When the tablet is centrally located, a weak flow sweeps its top surface; when the tablet is 108 off-center the flow is stronger but still affected by the nearby poorly mixed inner core region. However, when the tablet is 208 off-center, and, to a lesser extent, 408 off-center, the flow is appreciably stronger. The distribution of strain rates near the vessel bottom in the absence and in the presence of salicylic acid tablets at different locations is reported in Figure 8. The darker red regions indicate strain rate values equal to 120 s1 or above. The strain rate at the tablet surfaces vary with tablet location, as in the Prednisone case. The strain rate at the top face of the salicylic acid

Figure 7. CFD-predicted velocity vectors (m s1) on the impeller plane (y-plane) in the lower region of the USP Apparatus II vessel with and without salicylic acid tablets and at different tablet locations. JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 98, NO. 4, APRIL 2009

DOI 10.1002/jps

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Figure 8. CFD-predicted strain rate (s1) on the impeller plane (y-plane) in the lower region of the USP Apparatus II vessel with and without salicylic acid tablets and at different locations. Red regions indicate strain rate values of 120 s1 and above.

tablets is weaker when the tablet is centrally located, followed in order of increasing magnitude, by the tablets 108 off-center, 408 off-center, and finally 208 off-center, where the strain rate is the highest among the locations tested. The average CFD-predicted strain rate values on the surfaces of the tablet exposed to the medium (i.e., top and side surfaces) are summarized in Table 3. The off-center tablets experience strain rates that are, respectively, 73.7% (108 offcenter tablet), 123.8% (208 off-center tablet), and 87.2% (408 off-center tablet) higher than the

Table 3. CFD-Predicted Average Strain Rate Values on the Top and Side Surfaces of Salicylic Acid Tablets for Different Tablet Locations

Tablet Location Centrally located tablet 108 off-center tablet 208 off-center tablet 408 off-center tablet DOI 10.1002/jps

CFD-Predicted Average Strain Rate on Tablet Surface (s1) 77.91 135.32 174.33 145.81

strain rates experienced by the centrally located tablet, with possible implication for the tabletmedium mass transfer coefficient.

Tablet-Medium Mass Transfer Coefficients for Salicylic Acid Tablets The experimental dissolution data, from 0 to 30 min, presented in Figure 6 for the salicylic acid tablets, and the properties of the salicylic acid tablet and dissolution system reported in Table 4 were used as input in Eq. (11) to obtain the average tablet-medium mass transfer coefficients, k, at each tablet location. The k values were

Table 4. Properties of Salicylic Acid Tablet and Dissolution System Cs rT VL b dT0

3.14 kg/m3 1253.09 kg/m3 9.00  104 m3 0.348 9.57  103 m

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Table 5. Overall Mass Transfer Coefficients for Salicylic Acid Tablets at Different Tablet Locations, Calculated from Experimental Dissolution Data

Tablet Location Centrally located tablet 108 off-center tablet 208 off-center tablet 408 off-center tablet

Mass Transfer Coefficient from Experimental Dissolution Data, kexp (m s1) 5.04  105 8.59  105 10.31  105 8.43  105

obtained via numerical integration of Eq. (11). The results, reported in Table 5, show that the centrally located tablet had the smallest k value among all cases. The 108, 208, and 408 off-centered tablets had k values that were, respectively, 67.9%, 89.5%, and 62.3% larger than the base value for the centrally located tablet. The strain rate represents the rate at which the velocity varies with distance when moving away from the point of interest. According to the boundary layer theory30 the mass transfer from a solid surface to the surrounding fluid is proportional to the velocity gradient in the boundary layer surrounding the solid, that is, the strain rate at that surface (typically through Sc1/3, where Sc is the Schmidt Number, Sc ¼ m/ DABr). Therefore, one can expect that regions where the local strain rate is high will be associated with high mass transfer rates. In this work, the experimentally derived mass transfer coefficients k reported in Table 5 for different locations of the salicylic acid tablets were plotted against the CFD-predicted strain rate values on the surface of salicylic acid tablets listed in Table 3. The results are shown in Figure 9. The straight line through the points was obtained by regressing the data. The line was additionally forced to go through the origin since no strain should produce no mass transfer (Remark: this is not entirely correct since molecular diffusion also contributes to mass transfer, even in the absence of flow. However, it can be shown that this contribution would be negligible in this case). One can see that the there is a direct proportionality between the mass transfer coefficient and the strain rate at the tablet surface. The tablet located 208 off-center experiences the highest strain rate, has the highest overall mass transfer coefficient, and thus the highest dissolution rate. JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 98, NO. 4, APRIL 2009

Figure 9. Correlation between the experimentally derived overall mass transfer coefficient for salicylic acid tablets and the CFD-predicted average strain rate values on the surfaces of tablets.

In addition to determining the mass transfer coefficients from experimental data, an attempt was also made to predict them using the literature equations reported above (Eqs. 12, 14, 16, and 18), for which the velocity input were obtained through CFD. Figures 10 and 11 present, respectively, the CFD-predicted flows above the centered tablet and above the 408 off-center tablet. The flows on the top and side surfaces of 108 and 208 off-center tablets are similar to those of 408 offcenter tablet (results not shown). Figure 10 shows that the centrally located tablet experiences a rotating liquid flow on its top surface, thus substantially justifying the use of the rotating disk and rotating cylinder equations for ktop and

Figure 10. CFD-predicted velocity vectors (m s1) on the top surface of the centrally located salicylic acid tablet. DOI 10.1002/jps

EFFECTS OF TABLET LOCATION ON DISSOLUTION TESTING

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Figure 11. CFD-predicted velocity vectors (m s1) on the top surface and side surface of the 408 off-center salicylic acid tablet.

kside (Eqs. 12 and 14). Similarly, Figure 11 shows that the 408 off-center tablet is exposed to a crossover flow on its top surface (Fig. 11a) and around its side (Fig. 11b), thus substantially justifying the use of the mass transfer equations for flow parallel to a flat plate for the top surface (Eq. 16), and around a cylinder for its side surface (Eq. 18). The predictions for the mass transfer coefficients at the top and side surfaces are shown in the second and third column in Table 6. These mass transfer coefficients can be used to calculate the areaaveraged k value for the entire tablet as follows: k¼

ktop Atop þ kside Aside Atop þ Aside

(19)

The predicted mass transfer coefficients in Table 6 can be compared with the corresponding mass transfer coefficients derived from the experimental data (Tab. 5). From these tables one can see that kprd is on the same order of magnitude as kexp, and that a proportionality exists between the kexp values obtained for a given tablet location and the corresponding values of kprd. The results of Tables 5 and 6 are quantitatively compared in Figure 12. The experimental mass transfer coefficient kexp correlates well with the predicted mass transfer coefficient kprd and the resulting correlation equation is: kexp ¼ 2:247kprd

The last column in Table 6 presents these predicted area-averaged overall k values for different tablet locations. These data show that the predicted mass transfer coefficients for the 108, 208, and 408 off-center salicylic acid tablets are about 90%, 126%, and 84%, larger, respectively, than the base value for the centrally located tablet.

(20)

However, since the proportionality constant is not equal to 1, kprd underpredicts kexp by a factor of about 2. It should be remarked that equations such as Eqs. (16) and (18) have margins of error of
40% and
30%, respectively, and that these equations were originally developed for systems (such as long cylinders rotating in unagitated

Table 6. Mass Transfer Coefficients for Salicylic Acid Tablets at Different Locations Predicted from CFD Simulations

Tablet Location Centrally located tablet 108 off-center tablet 208 off-center tablet 408 off-center tablet DOI 10.1002/jps

Predicted Mass Transfer Coefficient at Top Surface of Tablet, ktop (m s1)

Predicted Mass Transfer Coefficient at Side Surface of Tablet, kside (m s1)

Predicted Area-Averaged Mass Transfer Coefficient for Tablet, kprd (m s1)

3.06  105 4.81  105 5.72  105 4.66  105

1.31  105 3.21  105 3.83  105 3.11  105

2.04  105 3.88  105 4.62  105 3.76  105

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Figure 12. Comparison between the mass transfer coefficient experimentally derived from dissolution tests, kexp, and that predicted in this work, kprd.

fluids) that are different from the system modeled here (such as the side surface of a short tablet in a complex flow field). In addition, it is well known that the intensity of the compression force used in tablet manufacturing can have a significant impact on the dissolution rate. Different relations between these two variables have been reported, where the compression force can promote, inhibit, or have no impact on the dissolution rate, depending on whether the increase in surface area caused by the crushing effect of high compression forces dominates over the simultaneous increase in particle bonding, thus producing an increase in density and solvent penetrability.27 Therefore, if all these factors are accounted for, the agreement between kexp and kprd can actually be considered quite satisfactory. Finally, the values of kesp and kprd obtained for each case and reported in Tables 5 and 6 were used to predict the dissolution profiles by inserting them in Eq. (3) as follows: dC kexp AðCÞ ¼ ðCs  CÞ dt VL

(21)

dC 2:247kprd AðCÞ ¼ ðCs  CÞ dt VL

(22)

Since the tablet-medium transfer area A(C) is a function of the drug concentration in the medium C, these equations were numerically integrated using the Runge–Kutta method. The results, shown in Figure 13, indicate that the predictions adequately match the experimental data. Since kexp was obtained by regressing the experimental data, the agreement between the data and Eq. (21) JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 98, NO. 4, APRIL 2009

can be expected to better, although just marginally, than that with Eq. (22). In conclusion, Eq. (20) can be used to calculate kexp using the CFD results as input, together with literature equations for k (Eqs. 12, 14, 16, and 18), and Eq. (19). More significantly, Eqs. (21) and (22) can be used to predict the dissolution profiles for any non-disintegrating dissolution system operating at the same agitation system, fill volume, and tablet shape even for drugs other than those used here, since the hydrodynamics of the dissolution system is not a function of tablet composition. In such cases however, the values of kexp and kprd must be scaled using the physical characteristics of the drug, such as the diffusivity DAB, which appear in the equations for the mass transfer coefficients.

DISCUSSION Both experimental and theoretical/computational results have been presented here to assess the importance of tablet location during dissolution testing. The experimental dissolution data for both disintegrating and non-disintegrating tablets clearly indicate that the location of the tablet produces statistically different dissolution testing results. This is in good agreement with the previous results of Baxter et al.12 The statistical difference between the results obtained here for different tablet locations can be quantified by examining the value of the difference factor, f1, which is always outside the range established by FDA for statistical similarity (Tab. 1). The difference factor f2 calculated for the off-center tablets versus the centered tablets produces more ambiguous results, since many of the values reported in Table 1 for this factor are within the FDA limits (50–100), although always borderline. This apparent conflict between the factors recommended by the FDA is caused by the fact that f2 is not a very sensitive statistical tool to assess differences among dissolution curves. The contradictory outcome of these two factors has also been reported by other researchers,12,25 who have pointed out that the conflict between the two methods shows that the similarity factor f2 may not be very robust for its intended task. The difference between the dissolution curves obtained at different tablet locations make intuitive sense for non-disintegrating, eroding tablets since the complex hydrodynamics of the USP Apparatus II can be expected to produce different DOI 10.1002/jps

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Figure 13. Comparison between the experimental dissolution data and the dissolution profiles predicted by numerically integrating Eqs. (21) and (22): (a) centrally located tablet; (b) 108 off-center tablet; (c) 208 off-center tablet; and (d) 408 off-center tablet.

flows around tablets at different locations. However, the different dissolution curves observed with disintegrating tablets may at first seem more difficult to explain, since the tablet fragments, once the tablet disintegrates, move toward the center of the vessel, thus possibly eliminating any further effect of the initial tablet location on the remaining portion of the dissolution process. The explanation for this apparent contradiction comes from a closer examination of Figure 3. This figure shows that at t ¼ 0 all curves start at the same point, and that the concentration ratio C/C at this time is appreciably high (17.54%). Within 5 min, the curves for the off-center tablets diverge from those for the centrally located ones. However, after this time the two sets of curves remain nearly parallel to each other. One can conclude that what happens during the first 5 min is critical to promote dissolution and disintegration, and that the remainder of the dissolution process simply adds to that initial baseline. In fact, it was visually observed that by t ¼ 5 min the off-center tablets were nearly completely disintegrated, DOI 10.1002/jps

whereas it took about 8 min for the centered tablet to do the same. Apparently, the improved hydrodynamics experienced by off-center tablets results in a more rapid dissolution and disintegration of the tablet, generating a higher dissolved concentration of the drug during the initial phase of the dissolution process. Once this initial process is complete and the tablet is fully disintegrated, the dissolution process proceeds at a similar rate irrespective of the initial location of the tablet in the vessel, as one can see from the similar slopes of all the curves in Figure 3. This also means that once a tablet becomes completely disintegrated the resulting fragments form the familiar ‘‘cone’’ under the impeller, as observed here, which is centrally located and no longer affected by the initial position of the tablet. In other terms, although the initial tablet position affects the initial rate of dissolution and disintegration, as shown in the initial slopes of the curves in Figure 3, once disintegration is complete the tablet fragments perform similarly, irrespectively of their origin, including producing similar JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 98, NO. 4, APRIL 2009

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‘‘coning’’ effects and generating similar dissolution rates (as shown in the slopes of the curves in Fig. 3 for t > 5–8 min). Even increasing the agitation speed to prevent coning is not likely to change the situation: the initial disintegration process would still be affected by the initial position of the tablet, while the resulting fragments, even if suspended, would still behave similarly and dissolve at a similar rate irrespective of their origin. In conclusion, it is likely that the initial tablet position affects the dissolution curves, and produce statistically different dissolution results, even under different suspension regimes. The process is different for non-disintegrating tablets. Here, since the tablets remain at their initial location during the whole process, the improved hydrodynamics experienced by offcenter tablets results in their faster dissolution rate throughout the entire dissolution test. This can be clearly seen in Figure 6, where the gap between the curves keeps growing as time increases (although this cannot go on forever, as correctly predicted by Eq. 3, since eventually all curves must reach the same C/C ratio of 1 if C < Cs). Unlike the disintegrating Prednisone tablets, the non-disintegrating salicylic acid tablets are subjected to higher dissolution rates during the entire test, and not only until disintegration occurs. Although a major difference in dissolution performance can be seen between off-center and centered tablets, not all off-center tablet positions are equal. A small tablet off-center displacement of only 108 is already capable of producing significantly and statistically different dissolution results. One can only speculate on how many dissolution tests routinely fail simply as a result of such small random variations in the tablet resting position after it has been dropped in the vessel. However, greater off-center deviations of the tablet location from the centerline can produce even larger variations in test results. Both Figures 3 and 6 show that the dissolution curves for tablets 208 off-center deviate the most from the curves for the centered tablets. This is especially significant for the salicylic acid tablets, resulting in deviations in dissolved concentration even higher than 40% when placed 208 off-center. Higher tablet locations in the vessel (e.g., 408 offcenter) do not result in greater deviations in the concentration profiles. The dissolution results nicely match the hydrodynamics in the vessel. Figures 4 and 6 show that centrally located tablets experience a very weak JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 98, NO. 4, APRIL 2009

flow around them, whereas slightly off-center tablets (e.g., 108) are immersed in much stronger flow. This can only improve the mass transfer rate and the dissolution rate. These figures additionally show that even if the tablet was displaced by an angle smaller than the smallest angle tested here (108), it would still be likely exposed to a flow significantly different from that of a perfectly centered tablet, and hence produce different dissolution profiles. When the tablet is displaced by 208 off-center, the flow that it experiences is stronger than in the other cases as a result of the upswinging recirculation flow in which the tablet is immersed, feeding the impeller from the bottom. This can be clearly seen in Figures 4 and 6. If the angle displacement is greater, the flow around the tablet is still strong but weaker than at 208. The contour plots for the strain rate, shown in Figures 5 and 8, also match the dissolution test results. These figures, as well as Tables 2 and 3, show that the strain rate around a centered tablet is much weaker than that for offcenter tablets, especially at 208. The difference in strain rates is especially large for salicylic acid tablets (Tab. 3). The hydrodynamics around the tablet and especially the strain rate experienced by the tablet appear to be the key variables in predicting mass transfer rates. This is evident from correlations, such as that shown in Figure 9, and visual representation of the CFD-predicted flow around tablets at different locations, such as those shown in Figures 10 and 11. Finally, the approach proposed here to correlate and predict dissolution profiles represents a first attempt to combine the results of actual dissolution data regression (to predict the mass transfer coefficient) with a basic mass transfer model. This approach, based as it is on the use of k values extracted from experimental data, appears to reproduce well the behavior of system under study, and can be simply extrapolated to be employed with other tablet shapes and active ingredients, provided that the geometric characteristics of the tablet and the physical properties of the drug are known. However, this approach requires that the tablet be always at the same location, which is not the case in the current dissolution testing USP Apparatus II, and appears to be a major drawback of this dissolution system. The predictive approach developed here, which is based on combining together several standard equations for mass transfer coefficient, the CFDpredicted velocity profiles, and the mass transferbased mass balance equations, appears to yield DOI 10.1002/jps

EFFECTS OF TABLET LOCATION ON DISSOLUTION TESTING

interesting results. The mass transfer coefficients obtained with this model correlate very well with the experimentally derived mass transfer coefficients, but are typically, and consistently, some 50% smaller than the experimental coefficients. Several factors could explain the discrepancy. The most important is probably the uncertainty in the area available for mass transfer, which was assumed to be the surface area exposed to the fluid for a smooth tablet. In other terms, the mass transfer area was taken her to be that of an object having the same overall geometry as the tablet. However, real tablets are agglomerates of granules that were subjected to compression forces to deform them and shape them into the desired tablet shape. Therefore, the real surface area available for mass transfer is actually the rough (and hence larger) area of the individually deformed and agglomerated granules located at the tablet surface. Therefore, the surface area available for mass transfer as derived from the dissolution experiments here is likely to be larger than that used in the calculation of kexp. Since kexp is inversely proportional to the surface area available for mass transfer (Eq. 4), the use of the smaller-than-real smooth surface area in this equation would result in an apparently larger value of kexp when compared to kprd. This implies that if one could measure the actual surface area available for mass transfer during the experiment, the resulting kexp values could probably be smaller than those reported in Table 5 and in closer agreement with the predicted kprd values shown in Table 6. Nevertheless, when appropriately scaled by a constant factor (2.247) the approach proposed here produces results in good agreement with the experimental dissolution data. More accurate mass transfer models can only be developed if the effects of solids processing, such as the compression pressure used during tableting, and better estimates of the mass transfer coefficients using CFD simulation are used to accurately predict the dissolution rates of drug tablets entirely from first principles.

2.

3.

4.

5.

CONCLUSIONS A number of conclusions can be drawn from this work: 1. The exact location of the tablet in the USP Dissolution Testing Apparatus II has a significant impact on the dissolution profile generated during the test. In all cases DOI 10.1002/jps

6.

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experimentally tested here with calibrator tablets, displacing and keeping the tablet offcenter by 108, 208, and 408 resulted in failing the dissolution test, as indicated by the systematic and statistically significant off-specification values of the similarity factor f1. In the same experiments, the difference factor f2 was less sensitive to detect differences in dissolution profiles, and its value was either off-specification or borderline. Test failures occurred with both disintegrating and non-disintegrating tablets, although the reasons for the failures are different. Non-disintegrating tablets fail because the flow fields surrounding them are appreciably different from the flow field surrounding a centrally placed tablet throughout the entire dissolution process. Disintegrating tablets fail because the initial disintegration and dissolution process during the first few minutes of the test is sufficiently different between off-center and centered tablets to generate different initial dissolution profiles. Once the initial disintegration process is complete, the fragments produced by the tablet migrate towards the vessel center irrespective of their origin, where they dissolve at similar rates, as indicated by the similar slopes of the dissolution curves. CFD can be used to predict the flow around tablets. CFD predictions indicate that the flow field and especially the shear rate at the tablet surface are significantly different depending on the location of the tablet. The flow field experienced by centrally located tablets consists of a rotating flow centered on the tablet, as opposed to that for off-center tablets, which is typically dominated by a crossover flow around the tablet. Tablets that are 208 off-center experience the highest shear rate and the most intense flow around them among all the tablet locations studied here. Tablet-medium mass transfer coefficients can be obtained from the experimental dissolution data for non-disintegrating tablets using a mass transfer model to fit the data. The CFD-predicted strain rate values at the tablets correlate well with the experimentally observed dissolution rates and the experimentally derived mass transfer coefficients, confirming that the hydrodynamics of the system, and especially the strain rate at the tablet, are critical to the dissolution process.

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7. A model was developed to predict the mass transfer coefficient from first principles, using as input literature equations mass transfer coefficients, CFD-predicted velocity profiles, and mass balance equations. The predicted coefficients correlate well with the experimentally derived mass transfer coefficients, but are typically about 50% smaller. 8. The results of this work clearly indicate that the velocity distribution and strain rates in the bottom region of the USP Apparatus II vessel are very nonuniform, and that even small changes in the tablet location, possibly even smaller than the smallest deviation in tablet location examined here (108 off-center), significantly alter the flow around the tablet and hence the dissolution profile. It is possible that some of the variability and test failures historically associated with this testing device can be attributed to the high sensitivity of the dissolution profiles to tablet location.

r Re Rt Sc t T T Tt u uaxial uradial utangential utip uV n VA

NOMENCLATURE A C C0 Cs C

dT D DAB f1 f2 hT k kside ktop kexp kprd

M

tablet surface area exposed to the dissolution medium (m2 or mm2) drug concentration in the dissolution medium (mg mL1) initial drug concentration in the dissolution medium (mg mL1) solubility concentration of the drug (mg mL1) theoretical concentration achieved in the dissolution medium when the tablet is fully dissolved (mg mL1) tablet diameter (mm) impeller diameter (m) diffusivity (m2 s1) similarity factor difference factor tablet height (m or mm) mass transfer coefficient (m s1) mass transfer coefficient on the side surface of tablet (m s1) mass transfer coefficient on the top surface of tablet (m s1) mass transfer coefficient derived from experimental data (m s1) mass transfer coefficient derived from CFD simulation and literature equations (m s1) molecular weight of the solvent (kg/ kg-mol)

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VL VT0 VT

radial coordinate measured from vessel centerline (m or mm) Reynolds number, LurL m1 reference assay at time t Schmidt number, m(DAB rL)1 time (min) vessel diameter (m) temperature (K) test assay at time t velocity (m s1) axial component of the velocity (m s1) radial component of the velocity (m s1) tangential component of the velocity (m s1) impeller tip velocity (m s1) velocity at the periphery of a rotating cylinder (m s1) kinematic viscosity of the liquid (cm2 s1) solute molar volume at its normal boiling point (m3 kg-mol1) volume of dissolution medium (mL) initial tablet volume (m3 or mm3) volume of tablet at time t (m3 or mm3)

Greek Symbols b g_ e m rL rT F v

tablet height-to-diameter ratio magnitude of strain rate (s1) turbulent energy dissipation rate (m2 s3) liquid viscosity (kg m1 s1) liquid density (kg m3) density of tablet (kg m3) association parameter of the solvent angular velocity (s1)

ACKNOWLEDGMENTS This work was partially supported through a grant from Merck & Co., West Point, PA, whose contribution is gratefully acknowledged. The authors wish to thank Dr. Russell Plank, Dr. Michael Gentzler, Dr. Kenneth Ford, Dr. Paul Harmon, and Dr. Scott Reynolds for their contribution and support. In addition, the authors would like to thank Mark Schreiber and James Hains and Berlex Laboratories, Wayne, NJ for their equipment donation. DOI 10.1002/jps

EFFECTS OF TABLET LOCATION ON DISSOLUTION TESTING

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JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 98, NO. 4, APRIL 2009