Cocrystal Intrinsic Dissolution Behavior Using a Rotating Disk

Cocrystal Intrinsic Dissolution Behavior Using a Rotating Disk H.-G. LEE,1 GEOFF G.Z. ZHANG,2 D. R. FLANAGAN1 1

College of Pharmacy, University of Iowa, Iowa City, Iowa 52242

2 Materials Science, Global Formulation Sciences − Solids, Global Pharmaceutical R & D, Abbott Laboratories, Abbott Park, Illinois 60064

Received 3 August 2010; revised 12 October 2010; accepted 13 October 2010 Published online 30 November 2010 in Wiley Online Library (wileyonlinelibrary.com). DOI 10.1002/jps.22400 ABSTRACT: The aim of this study was to investigate the dissolution characteristics of an acetaminophen/theophylline (AT) cocrystal compared with its pure components and physical mixtures. Intrinsic dissolution studies were conducted by a rotating-disk method. Solubility studies were conducted by collecting transient samples at 5, 30, and 60 min and equilibrium samples after 72 h, both at 37◦ C. The AT cocrystal had a faster dissolution rate than AT physical mixtures, and the dissolution profiles were congruent (1:1 mole ratio) under different pH conditions. Thus, the AT cocrystal dissolved congruently at short times and exhibited higher transient solubility compared with its two pure components. Equilibrium solubilities of theophylline from the cocrystal were lower than transient values due to theophylline hydrate precipitation but no precipitation of free acetaminophen occurred. The solubility behavior of acetaminophen and theophylline exhibited typical 1:1 complex formation in physical mixtures, cocrystal, and phasesolubility studies. The Levich equation was used to predict the dissolution behavior of the AT cocrystal as well as that of the single components. © 2010 Wiley-Liss, Inc. and the American Pharmacists Association J Pharm Sci 100:1736–1744, 2011 Keywords: dissolution; cocrystals; precipitation; mathematical model; solubility; complexation; acetaminophen; theophylline

INTRODUCTION Molecular interactions are important to the formation of binary complexes of pharmaceutical agents (PAs) with other compounds. Such complexes or associations can be utilized to manipulate pharmaceutically relevant properties1 and have led to the design of new materials called cocrystals.2 Complexation has been widely used in crystal engineering to create new solid materials with improved physicochemical properties.3–6 Adding a pharmaceutically acceptable cocrystal former to a PA to create a cocrystal can change its crystal lattice and produce physical or chemical properties, which are different from the parent solid. Thus, motivations for the study of pharmaceutical cocrystals include modifying the active pharmaceutical ingredient (API) properties such as melting point, solubility,7 dissolution rate,8 hygroscopicity, and physicochemical stability.9 Compared with the traditional strategies for optimizing API Correspondence to: D.R. FLANAGAN (Telephone: 319-3358827; Fax: 319-335-9349; E-mail: [email protected]) Journal of Pharmaceutical Sciences, Vol. 100, 1736–1744 (2011) © 2010 Wiley-Liss, Inc. and the American Pharmacists Association

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solubility (e.g., salts, polymorphs, cosolvent, micellar solubilization, and cyclodextrin complexation), pharmaceutical cocrystals are a novel alternative to modify API properties.10 Because in vivo dissolution is often the rate-limiting step in oral absorption for many insoluble drugs, dissolution improvement through cocrystal formation is an effective tool in enhancing bioavailability. For example, McNamara et al.11 used glutaric acid as a cocrystal former to improve the in vitro solubility/dissolution rate and the in vivo oral bioavailability for a poorly soluble compound. The rotating disk has been extensively used for intrinsic dissolution studies of pure drugs in water and reactive media.12–16 The dissolution rate from a rotating disk can be predicted by Levich’s hydrodynamic model under sink conditions because of the disk’s constant boundary layer thickness and constant surface area.17 This study examined the dissolution behavior of an acetaminophen/theophylline (AT) cocrystal, the pure APIs, and physical mixtures of the two components under different pH conditions. The observed dissolution rates were compared with values predicted by the extended Levich equation.18

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EXPERIMENTAL

Thermogravimetric Analysis

Materials

Thermogravimetric analysis (TGA) was performed using a Perkin-Elmer (Waltham, Massachusetts) TGA 7. Weight calibration was performed using a standard reference weight (100 mg). Small samples (4−6 mg) were used for all TGA runs from 25−180◦ C with a constant heating rate (10◦ C/min) under a nitrogen purge (40−50 mL/min).

Acetaminophen (Sigma–Aldrich, St. Louis, Missouri) and anhydrous theophylline (Sigma –Aldrich, St. Louis, Missouri) were used as received. A pH 4 medium was prepared by adjusting the pH of distilled water with 1.0 N HCl. A borate buffer at pH 10 was prepared by dissolving boric acid (3.0915 g, 0.05 M) in 900 mL distilled water and adjusting pH with 10 N NaOH with final dilution to 1 L. Preparation of Crystal Forms

Acetaminophen/Theophylline Cocrystal Suitable amounts of acetaminophen and anhydrous theophylline were added to acetonitrile (5 mL, HPLC grade, Sigma –Aldrich, St. Louis, Missouri) to prepare a slurry that was stirred to convert the physical mixture of two solids to a cocrystal by a solution-mediated phase transformation process.19 After being stirred for 24 h, the suspension was filtered and the isolated solid was analyzed by ultraviolet (UV) spectrophotometry to determine its molar composition. Powder X-ray diffraction and differential scanning calorimetry (DSC) were used to confirm the formation of a cocrystal20 and that the solid was free of the individual starting materials.

Theophylline Hydrate Excess anhydrous theophylline was added into 25% (v/v) aqueous methanol (20 mL) and stirred for 48 h. The suspension was filtered and the isolated solid was vacuum dried for 24 h at ambient temperature. Thermogravimetric analysis (TGA) was used to determine the water content in the isolated solid and confirm complete conversion to the hydrate. Powder X-Ray Diffraction Powder X-ray diffraction (PXRD) was performed using a powder X-ray diffractometer (Model #D5000, Siemens Energy and Automation, Inc., Madison, Wisconsin) over a 22 range of 5◦ −40◦ . The wavelength was CuKα (α1 = 1.5406 Å and α2 = 1.5444Å). The R diffraction software (Bruker Axs, Inc., Diffrac Plus
Madison, Wisconsin) was used for data processing and diffractogram presentation. Differential Scanning Calorimetry Differential scanning calorimetry (DSC) thermograms were obtained with a Perkin-Elmer (Waltham, Massachusetts) DSC 7. The DSC instrument was calibrated using an indium standard. Samples (2−5 mg), crimped in aluminum pans with an empty pan as a reference, were analyzed over a range from 40◦ C to 300 ◦ C with a constant heating rate (10◦ C/min) under a nitrogen purge (30−40 mL/min). DOI 10.1002/jps

Aqueous Solubility Studies Excess powdered solid was added to distilled water (10 mL) in a 20 mL screw-capped vial and rotated in a thermostated bath at 37◦ C for 72 h (n = 3). Shorter time solubility studies were conducted with samples taken at 5, 30, and 60 min. The solid suspension was R - GS, Millipore, Billerica, filtered (0.22 :m, MILLEX
Massachusetts) and the filtrate diluted with water. Diluted samples were analyzed by UV spectroscopy using an HP 8453 UV-visible (UV-Vis) photodiode array spectrophotometer (Agilent Technologies, Lexington, Massachusetts). Phase-Solubility Complexation Studies Excess powdered solid (acetaminophen or theophylline) was added to solution aliquots (10 mL) containing different concentrations (0.0125−0.40 M) of the other component (theophylline or acetaminophen) in 20 mL screw-capped vials and rotated in a thermostated bath at 37◦ C for 72 h (n = 3). The solid susR - GS, Milpension was filtered (0.22 :m, MILLEX
lipore, Billerica, Massachusetts) and the filtrate diluted with water. Diluted samples were analyzed by UV spectrophotometry using an HP 8453 UV-Vis photodiode array. Analysis of Pure Drug and Multicomponent Drug Mixtures Solubility or dissolution samples for pure drugs (i.e., single components) were assayed spectrophotometrically at a single UV wavelength for acetaminophen (243 nm) or theophylline (272 nm). These wavelengths were used for pH 4 aqueous media or distilled water, whereas at pH 10, acetaminophen and theophylline were assayed at 248 nm or 275 nm, respectively. In all cases, an HP 8453 UV-Vis photodiode array spectrophotometer and its analysis software were employed for data collection and analysis. Physical mixtures and the AT cocrystal were analyzed spectrophotometrically using a multicomponent method (maximum likelihood algorithm) in the HP 8453’s software over a wavelength range of 225–300 nm. Validation of the method was performed by preparing and analyzing known mixtures of the two components. JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 100, NO. 5, MAY 2011

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Colorimetric Assay of Acetaminophen In solutions containing high concentrations of theophylline (i.e., saturated or half-saturated), the multicomponent algorithm was not sensitive enough to detect acetaminophen in the presence of a large excess of theophylline in dissolution samples. Therefore, a specific colorimetric assay for acetaminophen was developed. A stock solution of acetaminophen (400 :g/ mL) was prepared in a half-saturated or saturated theophylline solution and further diluted with either a half-saturated or saturated theophylline solution to obtain 10–80 :g/mL concentrations. To the diluted stock solutions or dissolution samples (2 mL), 6 N HCl (0.2 mL) and 10% NaNO2 (0.5 mL) were added. The samples were mixed with a vortex mixer and allowed to react for 20 min at room temperature. Finally, 10% NaOH (1.5 mL) was added to the above solutions and mixed to stop the reaction. The absorbance of the resulting solutions was measured at 434 nm.21 Tablet Preparation Powdered materials (pure components, physical mixtures, or cocrystal) were sieved through a 60-mesh sieve (Fisher Scientific, Fair Lawn, New Jersey). A hydraulic press (Model C; Carver, Inc., Wabash, Indiana) was used to compress all powdered material R (250 mg) at a total force of 1000 lb (30 s) in a Varian
(Varian, Inc., Cary, North Carolina) rotating-disk intrinsic dissolution die (0.8 cm, diameter; 0.5 cm2 , area) (catalogue #124100). Dissolution Method R Using a USP dissolution apparatus (VK700, Vankel
, Cary. North Carolina), the flat-faced tablet (0.8 cm, diameter; 0.5 cm2 , area) was mounted in the dissolution holder and rotated at 100 rpm in 250 mL of vacuum filtered and degassed medium (pH 4, water, or pH 10) at 37◦ C (n = 3). For acetaminophen dissolution in a half-saturated or saturated theophylline solution, the dissolution medium contained excess solid theophylline (saturated) or 5.5 mg/mL of theophylline (half-saturated). Dissolution samples (5 mL) were taken at 5 min intervals for 40 min and analyzed by UV spectroscopy for acetaminophen, theophylline, or both in mixtures or cocrystal. For acetaminophen dissolution in theophylline solutions, the colorimetric assay for acetaminophen was used to assay dissolution samples. Sample volumes were replaced with an equal volume of fresh medium.

RESULTS AND DISCUSSION Acetaminophen/Theophylline Cocrystal Characterization Figure 1 shows the PXRD pattern for acetaminophen, theophylline, their physical mixture (mole ratio = JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 100, NO. 5, MAY 2011

1:1), and the cocrystal. It is obvious that the cocrystal has a unique powder pattern, which is different from the two pure drugs or their mixtures. Because the cocrystal contains an equal mole ratio of acetaminophen and theophylline, a peak appeared at a smaller 22 angle (11.4◦ ) compared with the equivalent Miller index 22 angles for the pure drugs (12.5◦ , theophylline; 12◦ , acetaminophen). The cocrystal thermogram exhibited a melting onset (Tm ) at 167.10◦ C and a heat of fusion (Hf ) of 110.9 J/g. These values were different from pure acetaminophen (Tm = 169.40 ◦ C, Hf = 186.9 J/g) and pure theophylline (Tm = 272.13 ◦ C, Hf = 168.4 J/g). Phase-Solubility Results Acetaminophen solubility increased linearly with theophylline concentration due to complex formation. Theophylline solubility, similarly, increased linearly with acetaminophen concentration. Using the slopes (ks ) of the solubility increase with added ligand, association constants (Kass ) of 16.5 M−1 (A vs. T) and 14.3 M−1 (T vs. A) at 37◦ C were calculated for a 1:1 complex. These values are in general agreement with a reported value of 16.1 M−1 obtained at 25◦ C.22 The equilibrium solubility of acetaminophen from the AT cocrystal (Table 1) increased 47% (30.98 vs. 21.02 mg/mL). However, theophylline solubility increased more than twofold (31.57 vs. 10.97 mg/mL) from the AT cocrystal compared with theophylline hydrate. The A/T molar ratio in a saturated solution from the AT cocrystal was 1.17. This apparent noncongruent solubility behavior was observed after cocrystal equilibration for 72 h at 37 ◦ C. Transient solubility studies (5, 30, and 60 min; Table 1) showed a cocrystal solubility stoichiometry of about 1:1, indicating likely precipitation of theophylline (hydrate) at longer times (i.e., 72 h). DSC and TGA analyses of the residual solid after 72 h indicated that theophylline hydrate precipitated. However, acetaminophen was not detected in the residual solid after AT cocrystal equilibration, thus its higher solubility from the AT cocrystal did not produce supersaturation of free acetaminophen. Thus, during AT cocrystal dissolution, a supersaturated free theophylline concentration is generated at short times, which is not maintained under equilibrium conditions. Similar solubility behavior has been reported for other solid complexes such as that of sulfanilamide/sulfathiazole in which free sulfathiazole precipitated from solution as the solid complex (i.e., cocrystal) dissolved.23 The acetaminophen and theophylline concentrations obtained after 72 h equilibration from phasesolubility data (A vs. T or T vs. A) are considered to be equilibrium values. Thus, at equilibrium, the saturated solution contained free and complexed acetaminophen and theophylline. In addition, the free DOI 10.1002/jps

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Figure 1. Powder X-ray diffraction (from bottom to top) for acetaminophen, theophylline, their physical mixture (1:1), and cocrystal. Table 1. Solubility of Acetaminophen, Theophylline, and Acetaminophen/Theophylline Cocrystal in Water at 37◦ C

Time 72 h AT cocrystal 5 min 30 min 60 min 72 h

Acetaminophen, A (mg/mL)

Theophylline, T (mg/mL)

A/T Molar Ratio

21.02 ± 0.13 –

– 10.97 ± 0.12

– –

29.79 30.56 29.88 30.98 ± 0.57

35.44 36.23 35.60 31.57 ± 0.53

1.00 1.01 1.00 1.17 ± 0.01

AT, acetaminophen/theophylline.

theophylline concentration was equivalent to its hydrate solubility. However, the short-term solubility results indicated a higher transient cocrystal solubility that represented what would occur at the AT solid surface during dissolution. Thus, the transient AT cocrystal concentration probably controls its intrinsic dissolution rate. Rotating-Disk Intrinsic Dissolution Results Under sink conditions, pure drug intrinsic dissolution behavior was linear for acetaminophen, as expected (Fig. 2). However, anhydrous theophylline’s dissolution profiles showed curvature due to conversion to its hydrate form. A second-order polynomial function was fit to all anhydrous theophylline dissolution profiles and the linear term coefficient was taken as the initial dissolution rate. The dissolution rate for theophylline at pH 4 was slightly lower than in water due to more effective suppression of theophylline ionization and lower apparent solubility (Fig. 3). The dissolution behavior of theophylline hydrate was quite DOI 10.1002/jps

linear (Fig. 3), as expected, because no solid transformation occurred during its dissolution. Physical mixtures of the two drugs exhibited dissolution profiles that were more complex because each component’s phase boundary moves at different rates.24 Both acetaminophen and theophylline appeared to dissolve more slowly from a 1:1 mole ratio mixture at pH 4 than in water. This is probably due to lower theophylline solubility at pH 4 that would also alter acetaminophen’s solubility indirectly through less complex formation (Table 2). All physical mixtures with anhydrous theophylline exhibited nonlinear dissolution profiles. From these results, it appeared that acetaminophen inhibited theophylline phase transformation to the hydrate during dissolution. As was done for pure anhydrous theophylline dissolution profiles, a second-order polynomial function was fit to both theophylline and acetaminophen dissolution profiles and the coefficient for the linear term was taken as the initial dissolution rate. Nonlinearity in some mixture dissolution profiles may also indicate non-steady-state dissolution behavior or other physical processes (i.e., theophylline hydrate precipitation) are occurring simultaneously with dissolution. Compared with anhydrous theophylline, theophylline hydrate exhibited linear dissolution profiles under sink conditions (Table 3). Linear dissolution profiles for physical mixtures were also observed for AT hydrate mixtures. Under more basic conditions, both anhydrous theophylline and its hydrate form had a higher solubility due to ionization. The curvature in dissolution profiles for the physical mixtures of anhydrous theophylline was due to a hydrate JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 100, NO. 5, MAY 2011

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x−

y R

y

x R

Figure 2. Intrinsic dissolution profiles of acetaminophen in water and at pH 10 at 37◦ C.

formation on the tablet surface that alters the dissolution behavior of each component and reduces any resulting complexation. With either theophylline form, acetaminophen complexes with theophylline in solution during dissolution and all dissolution rates of physical mixtures follow their initial molar ratio. Under sink conditions, AT cocrystal dissolution rates were not significantly different at pH 4 and in water. AT cocrystal dissolution rates at pH 10 were faster than in water or pH 4 because of theophylline’s ionization above its pKa (8.6) that increased AT cocrystal solubility (Fig. 4). Compared with an AT

y

physical mixture (1:1) in water, the AT cocrystal had a faster dissolution rate and its dissolution profile was more linear under any pH conditions. Like AT physical mixtures (1:1), the AT cocrystal dissolved congruently. Thus, the AT cocrystal probably dissolved into the dissolution media as the 1:1 complex and dissociated into equimolar free acetaminophen and free theophylline (Table 3). Such behavior could be anticipated as dissolution can be considered to be the reverse of cocrystal formation (i.e., precipitation of the complex). These dissolution phenomena are in general agreement with the dissolution behavior of a

x

x

y

x

y

x

x

Figure 3. Intrinsic dissolution profiles of anhydrous theophylline at pH 4, in water, and at pH 10, and theophylline hydrate in water at 37◦ C. JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 100, NO. 5, MAY 2011

DOI 10.1002/jps

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Table 2. Intrinsic Dissolution Rates for Pure Components and Physical Mixtures of Acetaminophen and Anhydrous Theophylline at 37◦ C

Material

Medium

Acetaminophen

H2 O pH 10 pH 4 H2 O pH 10 H2 O

Anhydrous theophylline

Physical mixture (1:1 mole ratio)

pH 4 Physical mixture (1:2 mole ratio)

H2 O

Physical mixture (2:1 mole ratio)

H2 O

Dissolution Rate (mg/cm2 -min)

Dissolution Rate (mmol/cm2 -min)

R2

2.14 2.40 1.84 1.88 3.37 A : 3.53 T : 4.16 A : 2.20 T : 2.56 A : 1.40 T : 3.19 A : 2.98 T : 1.79

0.014 0.016 0.010 0.010 0.019 A : 0.023 T : 0.023 A : 0.015 T : 0.014 A : 0.009 T : 0.018 A : 0.020 T : 0.010

0.9997 0.9995 0.9991 0.9999 0.9998 0.9997 0.9997 0.9998 0.9997 0.9995 0.9994 0.9999 0.9999

A, acetaminophen; T, anhydrous theophylline.

sulfanilamide/sulfathiazole “molecular compound” (i.e., cocrystal).23 Pure Acetaminophen and Cocrystal Dissolution Behavior in Theophylline Solutions Acetaminophen exhibited intrinsic dissolution behavior that was linear in water and in half-saturated or saturated theophylline solutions (Table 4). AT complexation increased the dissolution rate of acetaminophen ∼8% or 20% in these theophylline solutions. These observed increases in dissolution rate are expected for complexation, with theophylline which enhances the solubility of acetaminophen at the tablet surface. The AT cocrystal had a slower dissolution

Table 3.

rate in a saturated theophylline solution than that observed in water (2.25 vs. 2.53 mg/cm2 -min). This decrease was expected for two reasons. First, the saturated theophylline solution decreased the free acetaminophen at the tablet surface by about 30%. Second, this decrease in free acetaminophen means that a higher fraction of the diffusing acetaminophen was in the AT complex form, which has a diffusion coefficient about 20% less than free acetaminophen. In Table 4, the differences between experimental versus calculated dissolution rates in half-saturated or saturated theophylline solutions are larger than can be attributed to a choice of diffusion coefficients. This larger difference is probably due to the need to

Intrinsic Dissolution Rates for AT Cocrystal, Physical Mixtures and Pure Components at 37◦ C

Material

Medium

Acetaminophen

H2 O pH 10 H2 O pH 10 pH 4

Theophylline hydrate AT cocrystal

H2 O pH 10 Physical mixture (1:1 mole ratio)

H2 O pH 4 pH 10

Physical mixture (1:2 mole ratio)

H2 O

Physical mixture (2:1 mole ratio)

H2 O

Dissolution Rate (mg/cm2 -min)

Dissolution Rate (mmol/cm2 -min)

R2

2.14 2.40 1.06 2.26 A : 2.58 T : 3.13 A : 2.53 T : 3.07 A : 3.02 T : 3.56 A : 1.54 T : 1.83 A : 1.55 T : 1.88 A : 2.61 T : 3.08 A : 0.59 T : 1.34 A : 2.72 T : 1.59

0.014 0.016 0.006 0.013 A : 0.017 T : 0.017 A : 0.017 T : 0.017 A : 0.020 T : 0.020 A : 0.010 T : 0.010 A : 0.010 T : 0.010 A : 0.017 T : 0.017 A : 0.004 T : 0.007 A : 0.018 T : 0.009

0.9997 0.9995 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9997 0.9997 0.9998 0.9999 0.9999 0.9996

A, acetaminophen; AT, acetaminophen/theophylline; T, theophylline hydrate.

DOI 10.1002/jps

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x−

y

y

x

Figure 4. Dissolution profiles for acetaminophen/theophylline cocrystal in water and at pH 10 at 37◦ C.

incorporate a reactive dissolution model for predicting the dissolution rate of acetaminophen or the cocrystal in theophylline solutions. Our predictions did not assume a concentration gradient of theophylline from the bulk solution to the tablet surface. Such a refinement would bring the experimental and calculated dissolution rates into closer agreement and will be the basis for a future report. Dissolution Rates Compared with Theoretical Predictions The principal transport equation used to describe dissolution behavior includes diffusion, convective, and reactive terms,15,25 as shown below: ∂Ci /∂t = Di (∂2 Ci /∂x2 ) − Vx (∂Ci /∂x) + 

(1)

where ∂Ci /∂t is the rate of concentration change within the boundary layer, Di is the diffusion coefficient, ∂2 Ci / ∂x2 is the derivative of the concentration gradient in the axial direction, Vx is the fluid velocity in the axial direction, ∂Ci /∂x is the concentration gradient in the axial direction, and Φ is the summation of the reactive terms. At steady-state, ∂Ci /∂t and the reactive term (Φ) are zero that leads to: Di (∂2 Ci /∂x2 ) = Vx (∂Ci /∂x)

(2)

The above partial differential equation has been solved by Levich for the hydrodynamics surrounding a rotating disk.26 An analysis of our intrinsic dissoJOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 100, NO. 5, MAY 2011

lution results using the extended Levich equation for convective mass transfer from (or to) a rotating disk is shown below for theophylline: J (mg/cm2 −min) = 0.554(D2/3 <−1/6 T )Cs /[0.8934 1/2

+0.316(D/<)0.36 ]

(3)

where D is the diffusion coefficient (8.21 × 10−6 cm2 / s), ν is the kinematic viscosity (7.05 × 10−3 cm2 /s, 37◦ C), ω is the angular velocity (s−1 ), and Cs is the solubility (mg/mL). Acetaminophen (8.70 × 10−6 cm2 /s) and AT complex (6.70 × 10−6 cm2 /s) diffusion coefficients were estimated on the basis of the reported value for theophylline (8.21 × 10−6 cm2 /s)27 with correction for molecular weight differences. The theoretical dissolution rates showed that the extended Levich equation predicted the dissolution behaviors of the individual components and cocrystal within 5−15%, except for theophylline at pH 10 where the agreement between the experimental and calculated values is excellent (Table 5). The calculated diffusion coefficients are within the range expected for small molecules or complexes as are the values used (Table 5, column 5) in predicting the calculated dissolution rates. Also included in Table 5 are values of the diffusion coefficient (Table 5, column 6) required to obtain calculated dissolution rates (Jcalc ) that are equivalent to the experimental values (Jexpt ). Thus, the differences in experimental versus calculated dissolution rates are likely due to inaccuracies in estimated diffusion coefficients DOI 10.1002/jps

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Table 4.

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Acetaminophen Dissolution Rates in Theophylline Solutions at 37◦ C

Material

Medium

Acetaminophen

H2 O HST ST ST

AT cocrystal

Dissolution Rate (mg/cm2 -min)

R2

Calculated Dissolution Rate (mg/cm2 -min)

2.14 2.32 2.58 2.25

0.9997 0.9995 0.9997 0.9998

2.38 2.67 2.98 2.85

HST, half-saturated theophylline solution; ST, saturated theophylline solution; AT, acetaminophen/theophylline.

used in the theoretical calculations. For dissolution predictions, we assumed that the AT cocrystal dissolved as the AT complex and dissociation as it diffused into the bulk solution. For acetaminophen dissolution in half-saturated or saturated theophylline solutions, discussed earlier, the effective diffusion coefficient (Deff ) for acetaminophen is a function of free acetaminophen (A) and AT complex, which are related by the equilibrium process A + T
AT as shown below: Ctotal = CA + CAT

The calculated Deff was used to predict acetaminophen dissolution rates in half-saturated (8.43 × 10−6 cm2 /s) and saturated theophylline (8.22 × 10−6 cm2 /s) solutions. The calculated dissolution rates (Table 4) were compared with the experimental values and, as discussed earlier, the calculated values are higher by ∼15–27% than the experimental values. Again, better agreement will require inclusion of a reactive diffusion component to the overall model.

(4)

CONCLUSIONS Deff Ctotal /*eff = (DA CA /*A ) + (DAT CAT /*AT )

(5)

The diffusional boundary layer for each species (δi ) = 1.61 Di 1/3 ν1/6 ω−1/2 . Substituting for each δi gives the following expressions from which Deff can be obtained: 2/3

2/3

2/3

Deff Ctotal = DA CA + DAT CAT

(6)

Deff 2/3 (CA + CAT ) = DA 2/3 CA + DAT 2/3 CAT

(7)

CAT = ks CT (ks = slope from phase solubility)

(8)

2/3

2/3

2/3

Deff (CA + ks CT ) = DA CA + DAT CAT

(9)


2/3 2/3 2/3 Deff = DA CA + DAT ks CT )/(CA + ks CT

(10)

Below are two expressions for the dissolution rate (J ’) from the rotating disk using Deff and Ctotal or the individual diffusion coefficients (DA and DAT ) and individual component solubilities (CA and CAT ): 
2/3 J (mg/cm2 −min) = 0.554 Deff <−1/6 T1/2 Ctotal /[0.8934 + 0.316(Deff /<)0.36 ]

(11)


2/3  2/3 = 0.554 DA CA + DAT ks CT <−1/6 T1/2 /[0.8934 + 0.316(Deff /<)0.36 ] DOI 10.1002/jps

(12)

The dissolution behavior of an AT cocrystal exhibited congruent dissolution (i.e., 1:1 mole ratio). The cocrystal dissolution rate increased at pH 10 because both components were more soluble at this pH, which demonstrated that the cocrystal responded to pH conditions in the dissolution medium. Compared with a physical mixture (1:1 mole ratio), the cocrystal maintained constant dissolution behavior at neutral and acidic pH values. Acetaminophen dissolution behavior in theophylline solutions demonstrated that its dissolution rate increased due to complex formation with theophylline at the solid surface. Cocrystal solubility behavior under equilibrium versus under transient conditions showed that supersaturation existed for free theophylline, which led to precipitation of theophylline hydrate under equilibrium conditions. Using the extended Levich equation, the dissolution behavior of the AT cocrystal and pure components were reasonably well predicted under different pH conditions. The dissolution behavior of acetaminophen and AT cocrystal in theophylline solutions will require a reactive dissolution model to obtain better agreement between experiment and theory.

ACKNOWLEDGMENTS We acknowledge financial support from the Materials Science, Global Formulation Sciences − Solids, Global Pharmaceutical R & D, Abbott Laboratories. PXRD studies were conducted in the Department of Chemistry, X-ray Diffraction Facility, University of Iowa. JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 100, NO. 5, MAY 2011

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Table 5. Comparative Dissolution Results for Pure Components and Acetaminophen/Theophylline Cocrystal (Experimental Compared with Theoretical)

Material Acetaminophen (A) Theophylline (T) hydrate AT cocrystal

Medium H2 O pH 10 H2 O pH 10 H2 O pH 10

Experimental Dissolution Rate (mg/cm2 -min)

Calculated Dissolution Rate (mg/cm2 -min)

2.14 2.40 1.06 2.25 A : 2.53 T : 3.07 A : 3.02 T : 3.56

2.38 2.72 1.19 2.21 2.83 3.37 3.48 4.15

Da (cm2 /s) ×106

Db (cm2 /s) ×106

8.7 8.7 8.21 8.21 6.7

7.49 7.24 6.63 8.57 5.68

6.7

5.47

a

D using literature or Stokes–Einstein equation values. D required for J(calculated) = J(experimental). AT, acetaminophen/theophylline.

b

REFERENCES 1. Higuchi T, Zuck DA. 1953. Investigation of some complexes formed in solution by caffeine. II. Benzoic acid and benzoate ion. J Am Pharm Assoc Sci 42:132–138. 2. Desiraju GR. 1995. Supramolecular synthons in crystal engineering – A new organic synthesis. Angew Chem Int Ed Engl 34:2311–2327. 3. Desiraju GR. 1989. Crystal engineering: The design of organic solids. New York, New York: Elsevier Science Publishing Co. Inc., pp 261–283. 4. Ma ZB, Moulton B. 2007. Mixed-ligand coordination species: A promising approach for “second-generation” drug development. Cryst Growth Des 7:196–198. 5. Ma ZB, Moulton B. 2007. Supramolecular medicinal chemistry: Mixed-ligand coordination complexes. Mol Pharm 4:373–385. 6. Shakeel F, Faisal MS. 2010. Caffeine: A potential complexing agent for solubility and dissolution enhancement of celecoxib. Pharm Biol 48:113–115. 7. Fleischman SG, Kuduva SS, McMahon JA, Moulton B, Walsh RDB, Rodr´ıguez-Hornedo N, Zaworotko MJ. 2003. Crystal engineering of the composition of pharmaceutical phases: Multiple-component crystalline solids involving carbamazepine. Cryst Growth Des 3: 909–919. 8. Childs SL, Chyall LJ, Dunlap JT, Smolenskaya VN, Stahly BC, Stahly GP. 2004. Crystal engineering approach to forming cocrystals of amine hydrochlorides with organic acids. Molecular complexes of fluoxetine hydrochloride with benzoic, succinic, and fumaric acids. J Am Chem Soc 126:13335–13342. 9. Rodriguez-Spong B. 2005. Enhancing the pharmaceutical behavior of poorly soluble drugs through the formation of cocrystals and mesophases. Ph.D. Thesis. Ann Arbor, Michigan: University of Michigan. 10. Nehm SJ, Rodriguez-Spong B, Rodriguez-Hornedo N. 2006. Phase solubility diagrams of cocrystals are explained by solubility product and solution complexation. Cryst Growth Des 6:592–600. 11. McNamara DP, Childs SL, Giordano J, Iarriccio A, Cassidy J, Shet MS, Mannion R, O’Donnell E, Park A. 2006. Use of glutaric acid cocrystal to improve oral bioavailability of a low solubility API. Pharm Res 23:1888–1897. 12. Singh P, Desai SJ, Flanagan DR, Simonell AP, Higuchi WI. 1968. Mechanistic study of influence of micelle solubilization and hydrodynamic factors on dissolution rate of solid drugs. J Pharm Sci 57:959–965.

JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 100, NO. 5, MAY 2011

13. Mooney KG, Mintun MA, Himmelstein KJ, Stella VJ. 1981. Dissolution kinetics of carboxylic-acids 1. Effect of pH under unbuffered conditions. J Pharm Sci 70:13–22. 14. McNamara DP, Amidon GL. 1986. Dissolution of acidic and basic compounds from the rotating-disk – Influence of convective diffusion and reaction. J Pharm Sci 75:858– 868. 15. Southard MZ, Green DW, Stella VJ, Himmelstein KJ. 1992. Dissolution of ionizable drugs into unbuffered solution – A comprehensive model for mass-transport and reaction in the rotating-disk geometry. Pharm Res 9:58–69. 16. Avdeef A, Tsinman O. 2008. Miniaturized rotating disk intrinsic dissolution rate measurement: Effects of buffer capacity in comparisons to traditional Wood’s apparatus. Pharm Res 25:2613–2627. 17. Kuu WY, Prisco MR, Wood RW, Roseman TJ. 1989. Studies of dissolution behavior of highly soluble drugs using a rotatingdisk. Int J Pharm 55:77–89. 18. Gregory DP, Riddiford AC. 1956. Transport to the surface of a rotating disc. J Chem Soc 3756–64. 19. Zhang GZ, Henry RF, Borchardt TB, Lou XC. 2007. Efficient co-crystal screening using solution-mediated phase transformation. J Pharm Sci 96:990–995. 20. Childs SL, Stahly GP, Park A. 2007. The salt–cocrystal continuum: The influence of crystal structure on ionization state. Mol Pharm 4:323–338. 21. Chafetz L, Daly RE, Schriftman H, Lomner JJ. 1971. Selective colorimetric determination of acetaminophen. J Pharm Sci 60:463–466. 22. Chow YP, Repta AJ. 1972. Complexation of acetaminophen with methyl xanthines. J Pharm Sci 61:1454–1458. 23. Sekiguchi K, Ito K. 1965. Studies on the molecular compounds of organic medicinals. I. Dissolution behavior of the molecular compound of sulfanilamide and sulfathiazole. Chem Pharm Bull 13:405–413. 24. Higuchi WI, Mir NA, Desai SJ. 1965. Dissolution rates of polyphase mixtures. J Pharm Sci 54:1405–1410. 25. McNamara DP, Amidon GL. 1988. Reaction plane approach for estimating the effects of buffers on the dissolution rate of acidic drugs. J Pharm Sci 77:511–517. 26. Levich VG. 1962. Physiochemical hydrodynamics. Englewood Cliffs, New Jersey: Prentice-Hall, pp 39–72. 27. Grassi M, Colombo I, Lapasin R. 2001. Experimental determination of the theophylline diffusion coefficient in swollen sodium-alginate membranes. J Control Release 76:93– 105.

DOI 10.1002/jps