A Generalized Relation for Solid-State Drug Stability as a Function of Excipient Dilution: Temperature-Independent Behavior

A Generalized Relation for Solid-State Drug Stability as a Function of Excipient Dilution: Temperature-Independent Behavior

RESEARCH ARTICLE A Generalized Relation for Solid-State Drug Stability as a Function of Excipient Dilution: Temperature-Independent Behavior KENNETH C...

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RESEARCH ARTICLE A Generalized Relation for Solid-State Drug Stability as a Function of Excipient Dilution: Temperature-Independent Behavior KENNETH C. WATERMAN, PAUL GERST, ZHEN DAI Pfizer Global Research and Development, Groton, Connecticut 06340 Received 28 March 2012; revised 1 June 2012; accepted 28 June 2012 Published online in Wiley Online Library (wileyonlinelibrary.com). DOI 10.1002/jps.23268 ABSTRACT: A proposed generalized relationship for the impact of excipients on the solidstate chemical stability of drug products is presented and shown to be consistent across multiple degradation products with two example drugs. In this model, when the number of drug particles is comparable to the number of excipient particles, the impact of the excipient on the degradant formation rate is independent of drug concentration. In contrast, when the number of drug particles is in excess of the number of excipient particles, a power–law relation (linear correlation between the logarithm of the degradant formation rate and the logarithm of the reciprocal of the drug concentration) is proposed based on a “quasi-liquid” model where drug particles fill in interstices between excipients. As predicted by this model, the experimental power–law lines have slopes of about 2/3 independent of temperature (0.61 ± 0.13 for n = 30 counting multiple degradation products and a range of temperatures and relative humidities for two drug products). © 2012 Wiley Periodicals, Inc. and the American Pharmacists Association J Pharm Sci Keywords: excipients; stability; solid state; solid-state stability; thermodynamics; kinetics

INTRODUCTION The shelf life of a drug product is often limited by the rate of formation of degradation products or loss of the active pharmaceutical ingredient (API) potency. The kinetics of degradant formation in the solid state can be complicated by the heterogeneous nature of the system; that is, the API molecules can exist as a combination of nonequilibrating crystalline bulk, crystalline surface, and amorphous forms, each potentially with its own reactivity. For drug products, there is the additional complication that API molecules can be adjacent to or even homogeneously dissolved (solid solution) in a single or multiple excipients. Although in some cases an API will react directly with an excipient1 (e.g., the well-known Maillard reaction between primary and sometimes secondary amines and reducing sugars2,3 ) or an excipient impurity (e.g., reaction of an API with formaldehyde and formic acid,4 as well as other examples5 ), in many cases there is Correspondence to: Kenneth C. Waterman, FreeThink Technologies, Inc., PO Box 268, East Lyme, CT 06333; Telephone: +860-2874253; E-mail: [email protected] Journal of Pharmaceutical Sciences © 2012 Wiley Periodicals, Inc. and the American Pharmacists Association

no direct chemical reaction between the API and the excipient. In spite of this fact, the stability of the API can still be influenced significantly by the presence of excipients. To understand the effect of nonreactive excipients on the stability of APIs, we can define two types of fundamental interactions: catalytic and noncatalytic. In the former case, an excipient alters the rate of API degradation by either providing or eliminating catalysis, most commonly in the form of acid–base or oxidation initiation chemistry. For noncatalytic interactions, an excipient increases reactivity by (presumably) impacting the mobility of the API molecules at the excipient–drug interface. The present paper describes a mathematical framework for such noncatalytic drug–excipient interactions. Experimental data are used to support this model.

MATERIALS Methylprednisolone [as is and United States Pharmacopeia (USP) micronized] were purchased from Pfizer Inc. (Kalamazoo, Michigan). CP-481,715 was prepared as described in Ref. 6. Sucrose extra fine NF was purchased from Domino Food Products (West JOURNAL OF PHARMACEUTICAL SCIENCES

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R Palm Beach, Florida). Xanthan gum: Xantural 180 was purchased from CPKelco (Atlanta, Georgia). Hydroxypropyl cellulose: Klucel EXFTM was purchased from the Aqualon division of Ashland Inc. (Covington, Kentucky). Sodium benzoate and tartaric acid were purchased from Spectrum Chemical Mfg. Corporation (New Brunswick, New Jersey). Sucralose was purchased from Tate & Lyle (London, UK). Sodium chloride, acetonitrile, tetrahydrofuran, and phosphoric acid were purchased from JT Baker, a division of Capitol Scientific, Inc. (Austin, Texas). Sodium tartrate dihydrate was purchased from Fluka—Sigma–Aldrich (St. Louis, Missouri). Titanium dioxide was purchased from Brenntag Specialties, Inc. (South Plainfield, New Jersey). Microcrystalline cellulose (MCC) R PH102) was purchased from FMC Biopoly(Avicel mers (Philadelphia, Pennsylvania). Lactose monohyR R 316) was purchased from Sheffield drate (Fast Flo Bio-science (Norwich, New York). Sodium starch glyR ) was purchased from JRS Pharma colate (Explotab GmbH & Company (Rosenberg, Germany). Magnesium stearate was purchased from Mallinckrodt (now Covidien Corporation, Hazelwood, Missouri).

METHODS

adding 10.0 g of the 20% sample and 27.5 g of placebo mix in a 250-cm3 bottle and stirring for 15 min in a R mixer (Glen Mills, Inc.). The 5.3% samples Turbula were prepared by adding 10.0 g of 20% sample and 27.5 g of placebo mix in a 250-cm3 bottle and stirring R mixer (Glen Mills, Inc.). for 15 min in a Turbula The 1.4% samples were prepared by adding 20.0 g of 5.3% sample and 55.0 g of placebo mix in a 250-cm3 R bottle and stirring for 15 min in a Turbula mixer (Glen Mills, Inc.). The 0.38% samples were prepared by adding 10.0 g of 1.4% sample and 27.5 g of placebo mix in a 250-cm3 bottle and stirring for 15 min in a R mixer (Glen Mills, Inc.). The 0.38% samTurbula ples were prepared by adding 5.0 g of 1.4% sample and 13.8 g of placebo mix in a 250-cm3 bottle and R mixer (Glen Mills, stirring for 15 min in a Turbula Inc.). The samples were divided into 0.50 g portions and kept in 20 mL-capped scintillation vials for stability studies. Stability studies were conducted at 60◦ C, 70◦ C, and 80◦ C under uncontrolled humidity conditions. Samples in scintillation vials were kept in ovens of respective temperatures and pulled at various time points. They were then stored at 5◦ C in a refrigerator until being analyzed. Control samples were stored at 5◦ C for the entire time.

Dosage Form Preparation

CP-481,715 Tablets

Methylprednisolone Powder Blends

Blends were made by combining ingredients for each dilution as follows: 1% active: 0.1 g CP-481,715, 4.65 g MCC, 4.65 g lactose, 0.5 g sodium starch glycolate; 5% active: 0.5 g CP-481,715, 4.45 g MCC, 4.45 g lactose, 0.5 g sodium starch glycolate; 15% active: 14.0 g CP481,715, 39.5 g MCC, 39.5 g lactose, 0.5 g sodium starch glycolate; and 30% active: 3.0 g CP-481,715, 3.2 g MCC, 3.2 g lactose, 0.5 g sodium starch glycolate. R blender (Glen Each bottle was shaken in a Turbula Mills, Inc.) for 5 min, then 0.1 g of magnesium stearate was added to each followed by an additional 5 min of mixing. Tablets of each blend were prepared using 1/4 standard round concave tooling on a singlestation tablet press (compaction simulator) to a solid fraction of approximately 0.85. Stability studies were conducted with tablets in open amber glass bottles using temperature and relative humidity (RH)-controlled ovens, except for samples stored at 5% RH, which were stored closed with R ¨ canisters, from Sud-Chemie, one desiccant (Sor-bit Moosburg, Germany). Samples were removed at appropriate times and stored in a refrigerator before analysis.

Methylprednisolone with a number average diameter of 42 :m was prepared by passing vendor-supplied methylprednisolone through a 140-mesh hand sieve, and collecting material that did not go through a 325mesh sieve. USP micronized methylprednisolone with an average diameter of 7 :m was used as purchased. The average diameters were determined using a Sympatec (Clausthal-Zellerfeld, Germany) laser diffraction particle size analyzer. Extra fine sucrose was milled to give a number average diameter of 171 :m as determined using the Sympatec laser diffraction particle size analyzer. A placebo blend was prepared by adding 4.48 g of hydroxypropyl cellulose, 1.40 g of xanthan gum, 1.40 g of sodium benzoate, 2.37 g of sodium tartrate dehydrate, 2.65 g of tartaric acid, 280.25 g of sucrose, 8.87 g of sucralose, 0.93 g of titanium dioxide, and 1.87 g of sodium chloride to a 1250-cm3 glass bottle and stirR mixer (Glen Mills, Inc., ring for 15 min in a Turbula Clifton, New Jersey). Samples of methylprednisolone were prepared at 20%, 5.3%, 1.4%, 0.38%, and 0.10% (w/w) using serial dilution for both particle sizes of API. The 20% samples were prepared by adding 10.0 g of methylprednisolone and 40.0 g of placebo mix in a 250-cm3 R bottle and stirring for 15 min in a Turbula mixer (Glen Mills, Inc.). The 5.3% samples were prepared by JOURNAL OF PHARMACEUTICAL SCIENCES

Sample Analysis

Methylprednisolone The diluent constituted acetonitrile–water–phosphoric acid 50:50:0.1 (v/v/v). The 0.1% samples were DOI 10.1002/jps

SOLID-STATE DRUG STABILITY AS A FUNCTION OF EXCIPIENT DILUTION

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prepared by directly injecting 6 mL of diluent into the scintillation vials. The solution was shaken and sonicated for about 15 min until a homogeneous suspension was achieved. The 0.38% and 1.4% samples were prepared using a similar method but with 6.3 and 11.8 mL portions of diluent, respectively. The 5.3% samples were prepared by constituting 0.5 g of the sample with approximately 3 mL of deionized water, and shaking for 1–2 min to effect complete dissolution of the excipients and to distribute the methylprednisolone uniformly throughout the scintillation vials. The entire contents of the sample vials were transferred by pipette into individual 50 mL volumetric flasks. The sample vials were rinsed repeatedly with diluent, and the rinsate was transferred into the same volumetric flask. The flasks were filled approximately 2/3 full with diluent, swirled, and sonicated for 1–2 min. The flasks were filled to volume with diluent and mixed well. The 20% samples were prepared using a similar method into 200 mL volumetric flasks. All samples were filtered using Whatman (a division of GE Healthcare Corporation, Maidstone, Kent, UK) autovial polytetrafluoroethylene, PTFE, (0.45 :m) filters, discarding the first 2-mL of solution, directly into high-performance liquid chromatography (HPLC) vials. A 10-:L injection volume was used for 20%, 5.3%, and 1.4% samples. Injection volumes of 20 and 60 :L were used for 0.38% and 0.1% samples, respectively. Samples were analyzed using gradient separation with an Agilent Technologies, Inc. (Santa Clara, California) 1100 HPLC on a Supelco Discovery (Sigma–Aldrich, Inc., St. Louis, Missouri) HS C18, 150 × 4.6 mm2 , 3.5-:m column. The mobile phase A was prepared by adding 100 mL of acetonitrile, 900 mL water, 15 mL tetrahydrofuran, and 1 mL phosphoric acid. The mobile phase B consisted of 1000 mL acetonitrile, 15 mL tetrahydrofuran, and 1 mL phosphoric acid. The run time was 35 min at a flow rate of 1.5 mL/min with detection at 247 nm. The gradient was 14 min, 83:17; 16 min, 52:48; and 5 min, 83:17 A:B. The amounts of degradation were calculated on the basis of the area ratio of degradants to the area of methylprednisolone. Degradant formation rates were determined using the slopes of the degradant level as a function of time in periods with linear behavior.

run with a Phenomenex Luna C8 (2), 3 :m, 4.6 × 150 mm2 column at 30◦ C using isocratic 55:45 (v/v) water (with 0.2%, w/v, triethylamine adjusted to pH 3 with H3 PO4 )–acetonitrile with a flow rate of 1.0 mL/min and detection at 240 nm.

CP-481,715

Quasi-Liquid Model—Many API Particles/Few Excipient Particles

All tablets were crushed and placed into flasks where dissolving solvent [80:20 acetonitrile–methanol (v/v)] was added with a solution pump to make 5 mL for 1% active; 10 mL for 5%; 50 mL for 15%; and 100 mL for 30%. After shaking, the samples were filtered using 0.45-:m PTFE autovial filters before injection into an HPLC (14.0 :L for 1% active; 6.0 :L for 5% active; and 10.0 :L for 15% and 30% active). The HPLC was DOI 10.1002/jps

RESULTS AND DISCUSSION Although the specific interactions between an API and excipients in a solid drug product may be complex, it would seem logical that the effect of excipients, if any exist in a given system, would be proportional to the total contact area between the API and the excipients. In developing a model, we can first consider the case of a single API particle in a sea of excipient particles. All the surfaces of the API will be in contact with excipient to the maximum extent possible: whatever effect the excipient has on stability will be greatest at this infinite dilution limit. Obviously, we could increase the API’s interactions with the excipients by reducing the API particle size; that is, increase the surface of the API relative to the bulk. As more API particles are added to this highly dilute environment, each API particle will see the same interactions with excipient except for those particles that happen to abut other API particles. As the probability of such API particle–API particle becomes more common, the influence of the excipient interaction on the stability should decrease proportionately. The models discussed below are built from this conceptual framework. Dilute Model When the API is sufficiently dilute, each API particle will act independently rather than cohesively. The surface area of interaction would be anticipated to scale with the API volume percent, assuming a random (uniform) distribution of API and excipient particles. In other words, each drug particle would have the same amount of surface area in contact with excipient independent of the API concentration. This is shown mathematically in Eq. 1: k = k0 + a

(1)

where k0 is the reaction rate with pure API and a is the degradation rate increase for maximum dilution.

When the API particles are much smaller than the excipient particles, the number of API particles will significantly exceed the number of excipient particles except under very dilute conditions. For example, if the diameter of API particles and excipient particles are 5 and 150 :m, respectively, a 1% active blend would have 270 active particles per excipient particle JOURNAL OF PHARMACEUTICAL SCIENCES

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Figure 1. Schematic representation of two concentrations of small drug particles in the presence of larger excipient particles. In both a (more concentrated) and b (more dilute), the drug particles as a whole are represented by cubes with different side lengths. In this quasi-liquid model of the drug interaction with excipients, reactivity increases with drug–excipient surface contact, which in turn increases as a function of the square of the cube’s side length, whereas the volume (concentration) increases as the cube of that length (assuming the same density). In a power–law plot of the logarithm of the reciprocal of the drug concentration versus the logarithm of the reactivity, the slope would be expected to be 2/3.

(assuming cubic particles of equal density). Because of this, the API particles together can be viewed as a “quasi-liquid,” where the small particles fill in the interstitial spaces between larger excipient particles. This situation is shown schematically in Figure 1. In this case, the contact area of the API particles with the excipient particles will relate to a surface area of the total volume of API. If we further assume that the shape of this quasi-liquid remains essentially constant as its relative volume (RV) is altered, the overall surface area compared with the volume will follow as a square over a cube dimensional relationship. In the figure, this is shown by taking all the API particles as a whole in a unit area and considering them as condensed into a cube (of course, the shape the particles really form is quite convoluted). Figure 1a shows a greater number of drug particles relative to excipient particles (occupying a greater volume percentage) than with Figure 1b, representing a higher drug concentration with the former. The effective length of the wall of the cube corresponding to Figure 1a would be greater (L1 in the figure). In effect, the length of the side of the representative cubes will be proportional to the number of particles of API relative to the number of excipient particles, which in turn is proportional to the percentage API by volume (and therefore by weight). The relative surface areas (RSA) of the cubes JOURNAL OF PHARMACEUTICAL SCIENCES

(indicative of the total contact areas of the API particles with the excipient particles in each scenario) will equal the following: RSA =

6L21 6L22

=

L21 L22

(2)

The corresponding RVs (equal to the relative masses) of the cubes will be the following: RV =

L31

(3)

L32

As the weight percent of drug increases (proportional to the volume percent increase with the proportionality based on the relative densities of the API and excipients), the surface area, proportional to API reactivity in our model, will increase at a relatively slower rate: RSA = RV



L1 L2

2/3 (4)

A graph of the logarithm of RSA versus the logarithm of the RV gives a straight line with a slope of 2/3. In other words, one would anticipate that there DOI 10.1002/jps

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would be a scale-invariant, allometric, power–law relation between the volume of the API and the surface area of contact with the excipients. In this conceptual model, we would therefore anticipate that the rate constant for degradant formation (k) would be related to the API concentration (%API, i.e., weight percent active), which is proportional to the volume fraction, as shown in Eq. 5. 

100% log k = " log %API

 + log k0

(5)

where k0 is the rate constant for the pure API, and α is a fitting parameter. The slope in a plot of log k versus log(100%/%API) is α, which would be anticipated to vary from zero (i.e., excipient interactions do not influence the rate of formation of a specific degradation product) to 2/3, when every drug–excipient surface interaction increases reactivity relative to the quasi-liquid drug particles. In Eq. 5, the intercept will correspond to the logarithm of the degradant formation rate for pure API. This assumes that the pure API form is not altered in the preparation of the dosage form. In fact, we would suggest that deviation of the intercept with the actual pure API stability is symptomatic of a change in the physical form of the API, for example, amorphization, defect site formation, crystallization. Future studies, by us and others, will hopefully experimentally test this proposal. Equation 5 would be anticipated to hold whenever the number of API particles relative to the number of excipient particles is high.

Figure 2. Dilution study with methylprednisolone powder blends, analyzing degradation to degradant A. The drug particle size was 7 :m (number average).

Experimental Validation of Models In the present work, the degradation kinetics of two drugs (methylprednisolone and CP-481,715) was examined over a wide range of dilution with excipients. These APIs were known to be relatively unstable based on a range of reaction mechanisms. Methylprednisolone gives three degradants each having changes on the 14-hydroxy-(2-hydroxyacetyl) substituent: A, 14-carboxy; B, 14-(2-hydroxyacetyl); and C, 14-keto.7 CP-481,715 undergoes condensation to a lactone, CP-595,751. In addition, it undergoes degradation to two unknown degradation products, D and E.

Figure 3. Dilution study with methylprednisolone powder blends, analyzing degradation to degradant B. The drug particle size was 7 :m (number average).

Quasi-Liquid Model The quasi-liquid model suggests that when the number of drug particles compared with the number of excipient particles is high, the API particles will fill in the gaps between excipients, effectively acting as a liquid. Under this circumstance, a power–law relationship is anticipated (Eq. 5). This was examined with both of the model drug products studied for each corresponding degradant. As can be seen in Figures 2–5, both drugs (four total degradants shown) provide good DOI 10.1002/jps

Figure 4. Dilution study with CP-481,715 tablets, analyzing degradation to degradant D (at a fixed relative humidity of 5%). JOURNAL OF PHARMACEUTICAL SCIENCES

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Table 1. Power–Law Slopes (From Log Degradant Formation Rate Versus Log 100%/Weight Percent API) for a Range of Temperatures and Relative Humidities with Two Formulated Drugs API Methylprednisolone (7 :m particle size)

Excipients

Degradant

T (◦ C)

% RH

Slope

Hydroxypropyl cellulose, xanthan, sodium benzoate, sodium tartrate, tartaric acid, sucrose, sucralose, titanium dioxide, sodium chloride

A

60

5

0.54

70 80 60 70 80 70

5 5 5 5 5 5

0.62 0.56 0.67 0.73 0.54 0.84

80 60 70 80 50

5 5 5 5 75

0.64 0.57 0.52 0.57 0.47

60 60 70 70 80 80 50 60 60 70 70 80 80 50 60 60 70 80 80

5 40 5 75 5 40 75 5 40 5 75 5 40 75 5 40 5 5 40

0.62 0.68 0.62 0.70 0.60 0.55 0.70 0.69 0.80 0.77 0.84 0.74 0.63 0.46 0.36 0.55 0.32 0.37 0.55

B

Methylprednisolone (42 :m particle size)

Hydroxypropyl cellulose, xanthan, sodium benzoate, sodium tartrate, tartaric acid, sucrose, sucralose, titanium dioxide, sodium chloride

A

C

CP-481,715

Microcrystalline cellulose, lactose, sodium starch glycolate, magnesium stearate

D

CP-595,751

E

fits to Eq. 5 at each temperature and RH examined. The range of drug loading was in each case from about 30% down to less than 1% active. With methylprednisolone, the drug product was a simple blend, whereas with CP-481,715, tablets were used, yet the relationship held in both cases. Although we would anticipate that the log–log power law relationship of Eq. 5 would fail when the API becomes sufficiently dilute, we do not in fact observe this failure point even with our greatest dilution, 0.1% active for methylprednisolone (Figs. 2–3) using a small API particle size (number average of 7 :m). Even at 0.1% API concentration, the ratio of API to excipient particles is still greater than 10:1, assuming the same density of the particles. We anticipated based on the quasiliquid model, that the power–law slope would be less than or equal to 2/3, based on the surface to volume of the quasi-liquid state. In fact, for the 30 slopes determined (see Table 1) for nontemperature-dependent, power–law relationships, the slope was 0.61 ± 0.13. JOURNAL OF PHARMACEUTICAL SCIENCES

The consistency of this slope over the range of degradation rates and mechanisms and its approximate match with the anticipated 2/3 slope offer significant support to the proposed model; however, the data set of only two APIs, each with only one formulation cannot be considered proof. As others examine data according to the proposed relationship (Eq. 5), it should become clearer if indeed this relationship is general. Dilute Model: Impact of Particle Size As seen in Figures 2–5, the quasi-liquid model appears to apply over a wide range of drug loading. We also examined the methylprednisolone drug product using a larger particle size of the drug (42 vs. 7 :m, number average). As can be seen in Figure 6, for the nontemperature-dependent degradation process to form Degradant A, the power–law relationship appears to lose its linearity at a drug concentration below about 1%. The number of data points is very limited (as shown); therefore, experimental follow-up DOI 10.1002/jps

SOLID-STATE DRUG STABILITY AS A FUNCTION OF EXCIPIENT DILUTION

Figure 5. Dilution study with CP-481,715 tablets, analyzing degradation to degradant CP-595,751. The degradation was examined over a range of temperature and relative humidity conditions. As can be seen, the impact of dilution (i.e., similar slopes) is approximately the same over the entire range of conditions.

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Figure 7. Dilution study with methylprednisolone powder blends, analyzing degradation to degradant C. The drug particle size was 42 :m (number average).

of temperature. With the formation of degradant C, both the power–law slopes and the temperature dependence were altered.

CONCLUSIONS

Figure 6. Dilution study with methylprednisolone powder blends, analyzing degradation to degradant A. The drug particle size was 42 :m (number average).

will be needed to see if indeed a concentrationindependent behavior can be found at sufficient dilution. On the basis of the approximate particle sizes (42 :m for the API, 171 :m for the majority excipient sucrose), 1% active corresponds to a number concentration for the API that is close to that of the excipients (assuming equivalent densities). Interestingly enough, for the degradation to form degradant C, linearity is maintained in the power–law plot down to 0.1% active, even with the larger particle size (Fig. 7). The data for formation of degradant B were too noisy to draw conclusions. For formation of degradant A, the impact of going from a particle size of 7–42 :m (number average diameter) results in approximately 0.5 log unit (threefold) decrease in reaction rate, independent DOI 10.1002/jps

A proposed generalized relationship for the impact of excipients on the solid-state chemical stability of drug products is presented and shown to be consistent across multiple degradation products with two example drugs. In this model, when the number of drug particles is comparable to the number of excipient particles, the impact of the excipient on the degradant formation rate is independent of the drug concentration. In contrast, when the number of drug particles is in excess of the number of excipient particles, a power–law relation (linear relationship between the logarithm of the degradant formation rate and the logarithm of the reciprocal of the drug concentration) is proposed based on a “quasi-liquid” model where drug particles fill in interstices between excipients. The power–law lines have slopes that are independent of temperature with a value of 2/3 (that is, they follow the surface to volume ratio of the overall amount of drug present) when the excipients do not show catalysis or anticatalysis. It is also suggested that the intercept (corresponding to pure API) should match with the actual pure API stability only when formation of the dosage form does not alter the physical form of the drug. The models proposed here with only limited experimental validation should be viewed as preliminary hypotheses. It is hoped that this will inspire further investigations into the nature of drug–excipient interactions in solids. JOURNAL OF PHARMACEUTICAL SCIENCES

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ACKNOWLEDGMENTS The authors would like to thank the following Pfizer scientists: Matt Mullarney, Jon Hiller, and Dr. Parag Shah (now with Ikaria, Inc.) for preparing samples, Monica Dumont and Jeff Savoie for analyzing samples, Dr. Degui Tang for assistance in preparing and analyzing samples, and Dr. Garry Scrivens for helpful discussions. We would like to acknowledge Dr. Michael Hawley (now at Boehringer-Ingelheim) for asking whether we could predict the effect of dilution, which inspired the work. Finally, we would like to acknowledge FreeThink Technologies, Inc. for its support of completing this work.

REFERENCES 1. Bharate SS, Bharate SB, Bajaj AN. 2010. Interactions and incompatibilities of pharmaceutical excipients with active pharmaceutical ingredients: A comprehensive review. J Excipients Food Chem 1:3–26.

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2. Byrn SR, Xu W, Newman AW. 2001. Chemical reactivity in solid-state pharmaceuticals: Formulation implications. Adv Drug Del Rev 48:115–136. 3. Kumar V, Banker GS. 1994. Maillard reaction and drug stability. Special Publication R Soc Chem 151 (Maillard reactions in chemistry, food, and health):20–27. 4. Waterman KC, Arikpo WB, Fergione MB, Graul TW, Johnson BA, MacDonald BC, Roy MC, Timpano RJ. 2008. Nmethylation and N-formylation of a secondary amine drug (varenicline) in an osmotic tablet. J Pharm Sci 97:1499– 1507. 5. Waterman KC, Adami RC, Hong J. 2003. Impurities in drug products. In Handbook of isolation and characterization of impurities in pharmaceuticals; Ajira S, Alsante KM, Eds. pp 75–85. 6. Li B, Andresen B, Brown MF, Buzon RA, Chiu CK-F, Couturier M, Dias E, Urban FJ, Jasys VJ, Kath JC, Kissel W, Le T, Li ZJ, Negri J, Poss CS, Tucker J, Whritenour D, Zandi K. 2005. Process development of CP-481715, a novel CCR1 antagonist. Org Proc Res Dev 9:466–471. 7. Solomun L, Ibric S, Vajs V, Vuckovic I, Vujic Z. 2010. Methylprednisolone and its related substances in freeze-dried powders for injections. J Serb Chem Soc 75:1441–1452.

DOI 10.1002/jps