The Effect of Annealing on the Stability of Amorphous Solids: Chemical Stability of Freeze-Dried Moxalactam

The Effect of Annealing on the Stability of Amorphous Solids: Chemical Stability of Freeze-Dried Moxalactam AHMAD M. ABDUL-FATTAH,1 KAREN M. DELLERMAN,2 ROBIN H. BOGNER,1 MICHAEL J. PIKAL1,2 1

Department of Pharmaceutical Sciences, University of Connecticut, Storrs, Connecticut 06269

2

Eli Lilly and Co., Lilly Research Laboratories, Indianapolis, Indiana 46285

Received 24 July 2006; revised 8 November 2006; accepted 15 December 2006 Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/jps.20947

ABSTRACT: The objective of this study was to investigate the effect of annealing on the chemical stability and calorimetric structural relaxation times of freeze-dried moxalactam. Moxalactam disodium was freeze dried with 12% mannitol and split into several batches after freeze drying. One batch was held as a control while others were subjected to a further heating (annealing) treatment at 608C, 708C, and 808C for different periods of time. Isothermal microcalorimetry studies using thermal activity monitor (TAM) were performed on the freeze-dried samples to measure relaxation times (t) and stretched exponential values (b). Modulated DSC experiments were carried out to determine Tg and DCP for moxalactam-12% w/w mannitol systems at various moisture contents to allow extrapolation of these quantities to zero residual moisture. Storage stability studies were performed at 258C, 408C and 508C. Decarboxylated moxalactam and parent contents after various storage times were measured by reverse phase HPLC. Annealing moxalactam-12% mannitol amorphous systems improved chemical stability of moxalactam and reduced molecular mobility, as measured by TAM. Moxalactam-12% w/w mannitol systems annealed at higher temperatures and for longer times had higher tb values than the ‘‘control’’ sample, with tb values increasing as annealing temperature increased. Additionally, tb value increased as annealing time at the same temperature increased. These observations indicated that higher temperature annealing decreased molecular mobility in the glass, as expected. Further, chemical stability improved as annealing temperatures and annealing times increased. For example, the rate of decarboxylation of the sample annealed at 708C for 8 h was roughly 1.7 times lower than the ‘‘control.’’ Note that in spite of degradation during the annealing process, the level of degradation at the end of storage is actually less in the annealed sample than in the control sample; thus, annealing can result in samples having less degradation at the end of a storage period. Chemical stability and relaxation times are correlated, thus indicating that molecular mobility and structural relaxation time are coupled. ß 2007 Wiley-Liss, Inc. and the American Pharmacists Association J Pharm Sci 96:1237–1250, 2007

Keywords: amorphous; annealing; decarboxylation; glass transition temperature (Tg); moxalactam; stability; structural relaxation time (t); thermal activity monitor

INTRODUCTION The amorphous state represents the most energetic solid state of a material.1–3 It is common to Correspondence to: Michael J. Pikal at the University of Connecticut (Telephone: (860)-486-3202; Fax: (860)-486-4998; E-mail: [email protected]) Journal of Pharmaceutical Sciences, Vol. 96, 1237–1250 (2007) ß 2007 Wiley-Liss, Inc. and the American Pharmacists Association

prepare amorphous pharmaceuticals to improve the dissolution and bioavailability of poorly soluble compounds, to stabilize proteins or to improve certain physical properties of excipients.1–4 Changes in the properties of amorphous systems during prolonged storage are a fundamental concern to the pharmaceutical and food scientist. Changes may involve physical aging, chemical reactions, crystallization, protein

JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 96, NO. 5, MAY 2007

1237

1238

ABDUL-FATTAH ET AL.

unfolding (i.e., destabilization) and others leading to a loss of potency and/or quality. This has prompted much interest in the study of molecular motions that occur below the glass transition temperature (Tg) of amorphous systems that may be predictive of instability.3,5–8 It is useful to understand and be able to predict changes in the physical properties of amorphous pharmaceutical materials, as well as predict the chemical changes that can accompany such aging, largely due to the impact of such changes on formulation and processing designs.

The Amorphous State and Structural Relaxation When a melt of a glass-forming material is cooled, molecular mobility in the matrix is greatly reduced, free volume is reduced and interaction between molecules (e.g., hydrogen bonding) is maximized.9,10 Below the glass transition temperature (Tg), vitrification of the melt occurs thus forming the ‘‘glassy’’ state,9,11 accompanied by an increase in viscosity to very high values (typically >1012 Pa.s).11–13 The material is now regarded as a super-cooled liquid—a metastable state—that retains much of the disorder in the previous melt.9,11 The very high viscosity, or low free volume and low molecular mobility in a glass, greatly slow a-relaxations (global segmental motions involving translational and rotational motions of entire molecules).3,6,8 A higher degree of cooperativity is needed among neighboring molecules to initiate motion in the solid state, and the time taken for a given molecule to ‘‘move’’ to another position increases.14 This time is referred to as the ‘‘relaxation time,’’ and is denoted by t.11,13–15 Mobility may be regarded as the reciprocal of relaxation time.6 A freshly prepared ‘‘glass’’ is usually not in thermodynamic equilibrium and will have excess volume, enthalpy, and entropy.10,16 Therefore, even below Tg, there is a tendency for many amorphous solids to either crystallize or at least slowly ‘‘relax,’’ in order to restore the system to equilibrium. For amorphous materials that ‘‘relax,’’ many of their properties continue to change over time without the influence of any external factors or forces. For example, the free volume decreases (volume relaxation), structural order increases (i.e., configurational entropy decreases) and energy is decreased thereby giving off heat (enthalpy relaxation).10,16,17 This slow change below Tg is called physical aging, JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 96, NO. 5, MAY 2007

structural relaxation, or stabilization.18 Physical aging results in changes of other material properties such as water permeation, hardness, brittleness, density, creep- and stress relaxation rates, and dielectric constant.11,18–20 The kinetics of relaxation at and below Tg is both nonexponential and nonlinear.21–26 Nonlinearity is discussed in detail elsewhere and is not the subject of this research.21–26 Nonexponentiality means that relaxation toward equilibrium is described by a nonexponential decay function, F(t).21–25 It is commonly accepted that nonexponentiality arises from microheterogeneity of states in a glass. A glass is assumed to be a collection of ‘‘substates’’ or a heterogeneous set of microscopic regions (micro-domains) of various sizes and configurational entropies (SC). In the initial phase of glass formation, configurations of the ‘‘substates’’ are considered to be ‘‘frozen-in’’ during processing.27–29 After glass formation, various regions relax at different rates. That is, there is a distribution of relaxation times.26 The overall structural relaxation time (t) measured in the usual process is the most probable time for motion of a particular type to occur, given the distribution of individual relaxation times in the various substates.29,30 The Kohlrausch– Williams–Watts (KWW) equation (Eq. 1) is commonly used to describe the time dependence of structural relaxation or ‘‘a-relaxation’’ data, as obtained by calorimetric means:29–32 "
 # t  FðtÞ ¼ exp
ð1Þ
where F(t) is the relaxation or decay function (fraction of initial state) and t is time. b (0 < b  1) is the ‘‘stretching parameter’’—which is a measure of distribution of relaxation times.32,33 As b approaches unity, the distribution of states is narrow and as the distribution of states broadens, b decreases to small values. Typical values of b for organic amorphous materials range from 0.3 to 0.8,34 but the values of the parameters, b and t, depend on the property that is measured.31 Therefore, characterizing b and t aid in describing relaxation behavior of a glass upon physical aging.

Molecular Mobility and Chemical Reactivity in Pharmaceutical Glasses below Tg Although the high viscosity of a glass (>1012 Pa  s) greatly slows molecular mobility,11,13 many DOI 10.1002/jps

EFFECT OF ANNEALING ON STABILITY OF AMORPHOUS SOLIDS

1239

reactions do proceed at a measurable rate below Tg,7,8,31,29,11,33,35–40 regardless of whether the reaction is unimolecular or bimolecular.40 These reactions occur since there is sufficient molecular mobility and free volume in the amorphous state to facilitate the acquisition of molecular configurations favorable for a chemical or physical reaction (or both) to occur.27–31,33,35–39 Since both chemical degradation and structural relaxation in the solid state require molecular mobility of some type, it is expected that chemical stability and structural relaxation are correlated.6,27,33,37 Moreover if the molecular mobility required for a certain degradation reaction to occur requires the same type of mobility as structural relaxation, then relaxation time and stability should be proportional. Therefore, one may evaluate the effect of molecular mobility on chemical degradation rates in amorphous pharmaceuticals by comparing degradation rates with structural relaxation times.29 A perfect coupling means direct proportionality. One, however, should not generally expect a direct proportionality between stability and structural relaxation time, since the free volume requirement for chemical decomposition may not be exactly the same as that for structural relaxation.3 Good correlations have been reported between chemical reaction rates and structural relaxation time for low molecular weight drugs,3,8,41 as well as for peptides and proteins.7 Pikal et al.3 reported that an amorphous freeze dried cefamandole sodium system had a lower chemical degradation rate and a higher relaxation time as compared to amorphous freeze dried cephalothin sodium system prepared under the same freeze drying conditions. Guo et al.8 reported the similarity of temperature dependence for the rate of chemical decomposition (cyclization) of quinapril and t (calculated using Adam–Gibbs–Vogel equation) below Tg, suggesting that cyclization of quinapril is related to molecular mobility. A similarity of temperature dependence between t90 for an acetyl transfer reaction (between aspirin and sulfadiazine) and t below Tg in amorphous matrices with dextran and polyvinyl pyrrolidone was reported by Yoshioka et al.,41 suggesting that t90 for acetyl transfer rate was related to molecular mobility. Roy et al.7 found a good correlation between chemical degradation rates of lyophilized formulations of a Vinca alkaloid-antibody conjugate with T – Tg for systems at various moisture contents at two different temperatures. Keeping in mind that the motions that prevail as T approaches Tg are

the a-motions,12,35 results of this study indicate that a-motions do correlate, or are coupled, with the motions involved in typical degradation processes. Where a few examples presented above suggested good coupling between rates of chemical reactions in the amorphous state and molecular mobility, there are also examples in literature that suggest a poor correlation. Hydrolysis of cephalothin, a bimolecular reaction with water, in lyophilized formulations with dextran was not significantly affected by changes in molecular mobility. It was suggested that the diffusion barrier of water molecules was smaller than the ‘‘chemical’’ activation barrier for hydrolysis.42 The contribution of molecular mobility was found to be small in insulin degradation and dimerization in formulations freeze dried with trehalose under high (but not low) humidity conditions,43 as well as with PVP.43,44 Therefore, while there do exist numerous examples of a correlation between structural relaxation and reactivity, the correlations are not necessarily perfect.

DOI 10.1002/jps

JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 96, NO. 5, MAY 2007

Can ‘‘Annealing’’ Improve Chemical Stability in a Glass? The present study was motivated by an observation made a number of years ago that exposing a sample to high temperature appeared to stabilize.45 That is, the stability of a freeze-dried b-lactam antibacterial, moxalactam (Fig. 1) disodium, seemed to be superior if secondary drying were carried out at 608C rather than just 408C— even though the moisture contents were essentially identical. We now believe that the origin of this effect is the reduction of molecular mobility in the solid brought about by ‘‘extra’’ physical aging at 608C. Physical aging has been shown to arrest a-motions in glasses, thereby increasing structural relaxation time.8,35 Physical aging can be accomplished by several means, for example, by subjecting a glass to high pressure isothermally26 or by annealing—otherwise also referred to as

Figure 1. Chemical structure of moxalactam (free acid).

1240

ABDUL-FATTAH ET AL.

‘‘densification.’’27,34,37,46,47 The term ‘‘annealing’’ simply means heating an amorphous sample below its Tg for a period of time. A real glass will approach the ‘‘equilibrium glassy state’’ asymptotically during an annealing process, thereby slowing a-relaxations and to the extent that a-relaxation and reactivity are coupled, should minimize the reaction rate in the amorphous state.35 That is, heating a glass should improve the stability of the active pharmaceutical ingredient!—a result that is counterintuitive. While there is little information in the literature of direct relevance to this ‘‘counterintuitive postulate,’’ there are several reports of interest. The earliest report on the possible beneficial effect of annealing on the glassy state was by Mardaleishvili et al.48 In their study, polymethyl methacrylate (PMMA) films (with an initiator for formation of free radicals via a photochemical reaction) were annealed at two different temperatures below Tg for different periods of time. This treatment was followed by sample irradiation to initiate free radical formation. The rate of free radical formation in the films decreased as annealing temperature increased, and as annealing time increased. In another report, Madsen et al.47 followed the stability of annealed and untreated borophosphosilicate glass films. Degradation via loss of boron (B) was followed by observing the ratio of B-O to SiO peak intensities using FTIR. A 2-year storage period revealed more significant changes in untreated films than in annealed films. Recently, Hill et al.11 investigated the Maillard reaction between lysine and glucose in both annealed and untreated glasses. Analysis of the initial linear portion of the data showed that aging moderately lowered the rate of glucose consumption (20%) for the annealed sample. In our studies, a system of moxalactam disodium formulated with 12% w/w mannitol was used to systematically investigate the relationship between physical aging and chemical stability, to test the reproducibility of this stabilization effect, and to explore the impact of variations in annealing conditions on relaxation time, t, and chemical stability.

(Lilly) was from Eli Lilly & Co. (Indianapolis, IN) and Lot B was a gift from Shionogi Pharmaceuticals (Osaka, Japan). Pure decarboxylated moxalactam (as reference standard), was also a gift from Shionogi Pharmaceuticals (Japan). Methanol (HPLC grade) and dibasic sodium phosphate (HPLC grade) were purchased from Fisher Scientific (Fairlawn, NJ). Meta-phosphoric acid (ACS grade) was purchased from Spectrum Quality Products (New Brunswick, NJ). All chemicals were used as received. Freeze Drying Lot A (Lilly) Lot A was prepared, annealed, stored, and analyzed at Eli Lilly. This is the lot referred to earlier.45 Each vial contained roughly 500 mg of freeze-dried product. Amorphous samples of moxalactam disodium with 12% w/w mannitol were prepared by lyophilization from aqueous solutions using a Virtis 25 SRC-X lyophilizer (Gardiner, NY). The lyophilization cycle was similar to that previously reported,49 except that half of the samples was first frozen at a shelf temperature of
258C and the second half was frozen at a shelf temperature of
408C followed by primary drying below the collapse temperature. Secondary drying was performed for 8 h at 408C. Half of the vials initially frozen at a shelf temperature of
258C and half of the vials initially frozen at
408C were subjected to an additional secondary drying (annealing) treatment at 608C for 3 h after the secondary drying step conducted at 408C. All vials were sealed under dry nitrogen. Lot B Lot B was split into 2 lots, Lot B1 and Lot B2. Lot B1 was prepared to refine the calorimetric methodology and to investigate the precision and reproducibility of the calorimetric measurements. Lot B2 was prepared for both calorimetric and storage stability studies. Lot B1

Two lots of moxalactam disodium (for simplicity labeled Lot A (Lilly) and Lot B) were used, Lot A

Amorphous samples of moxalactam disodium with 12% w/w mannitol were prepared by lyophilization from aqueous solutions using an FTS Systems Dura Stop/Dura Dry MP freeze dryer (Kinetics Thermal Systems, Stone Ridge, NY). Two batches of aqueous solutions of the formulation at a solids content of 5% w/v were lyophilized

JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 96, NO. 5, MAY 2007

DOI 10.1002/jps

MATERIALS AND METHODS Materials

EFFECT OF ANNEALING ON STABILITY OF AMORPHOUS SOLIDS

in 20 mL serum vials with a fill volume of 3 mL. Samples were placed on precooled shelves at 58C; the shelves were cooled to
408C at a rate of 2.58C/min. Samples were held at
408C for 4 h followed by primary drying well below the collapse temperature. The shelf temperature was held at
158C for 24 h during primary drying while maintaining a vacuum of 70 mTorr (to maintain an average product temperature of
318C). Secondary drying of one batch (Lot B1 40) was accomplished at 408C for 5 h, and of the second batch (Lot B1 60) at 608C for 5 h.

1241

Both glass transition temperature of dry amorphous moxalactam-12% mannitol (Tg, dry)

and the associated change in heat capacity (DCp) values are required for evaluation of t. It was not possible to measure Tg and DCp of the dry moxalactam system by differential scanning calorimetry (DSC), since this system behaves as a strong glass. However, samples containing a small amount of residual moisture do show a DSC glass transition. To estimate Tg, dry and the associated DCp, an amorphous system of moxalactam-12% mannitol was stored overnight under different relative humidities (provided by saturated solutions of different salts) at 258C. After equilibration with the salt solutions overnight under vacuum, samples were transferred to a glove bag flushed with dry nitrogen. A humidity detector was used to insure the environment remained dry (<1% relative humidity) to prevent further moisture sorption by the samples during preparation. Each sample (10–15 mg) was hermetically sealed in aluminum DSC pans. The samples were analyzed under a dry nitrogen purge in a TA Instrument 2920 DSC (New Castle, DE), using a modulated mode. Scan rate was 28C per minute at a modulation of þ/
0.58C every 60 s. Measurements were done in triplicate. Moisture content of the samples was measured by Karl–Fischer titration. Tg, dry and DCp were estimated by extrapolation to zero moisture. Isothermal microcalorimetry studies were performed to directly measure the rate of enthalpy relaxation, Power ¼ P ¼ d((Hr)/dt, of lots B1 and B2 during aging experiments using a Thermal Activity Monitor (TAM) (Thermometric, Ja¨rfa¨lla, Sweden). TAM experiments were performed at 408C and 608C for formulations of Lot B1, and at 408C and 508C for formulations of Lot B2 (the temperatures used for storage stability studies of Lot B2) for at least 60 h. Samples were loaded into stainless steel cylinders in a dry bag purged with dry nitrogen to minimize moisture uptake during loading. Glycine of roughly the same mass as the sample was used as a reference for the solid samples. The sample and reference containers were lowered to a thermal equilibrium position in the calorimeter and allowed to equilibrate with the calorimeter for about 30 min. The sample and reference were then slowly lowered into the measuring zone of the calorimeter and power was recorded (mWatt/g) as a function of time (h). Tg, dry and DCp at Tg, dry values obtained from MDSC studies were used in our studies to evaluate the maximum enthalpy recovery at any given

DOI 10.1002/jps

JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 96, NO. 5, MAY 2007

Lot B2 The secondary drying protocol was somewhat different from that described above. Secondary drying of all batches was accomplished initially at 408C for 5 h to bring the moisture level below 1% w/w. Then, all vials were sealed under vacuum. A batch was removed after this process and labeled ‘‘Control.’’ The remaining batches were annealed at different temperatures for different periods of time (see Tabs 3 and 6 for annealing treatments). Karl Fischer Moisture Determination Residual moisture content of all formulations was measured by direct injection using coulometric Karl Fischer titration (Denver Instrument Company, Denver, CO). Powders were weighed and filled into vials in a glove bag where a low relative humidity was maintained by flushing with dry nitrogen. Powders were dissolved in 2 mL low moisture formamide and 0.5 mL of the solution was injected. Blank corrections were applied. Standard deviation from replicate measurements was not more than 0.1% w/w. Detection of Crystallinity Crystallinity was assessed in Lot A (Lilly) using polarized light microscopy. Crystallinity was assessed in Lot B2 batches by X-ray powder diffraction (XRPD) studies using an XRD-6000 (Schimadzu Corporation, Kyoto, Japan). Samples were scanned from 3 to 408 2y, at 28/min, and a step size equal to 0.048, using a Cu radiation source with a wavelength of 1.54 A, voltage 40 kV and current 40 mA. Calorimetry

1242

ABDUL-FATTAH ET AL.

temperature - DHr(1)—used in TAM experiments (i.e., 40, 50, and 608C) using Eq. 2:27,37 DHr ð1Þ ¼ ðTg; dry
TÞ  DCP

ð2Þ

where T is the experimental temperature. Enthalpy relaxation (expressed in J/g  s) is nonexponential and is well described by the KWW equation (Eq. 1). Upon differentiating the KWW equation, we obtain an expression for P, the heat power per gram of sample used (mWatt/g) with time in hours (Eq. 3). Therefore, b and t were evaluated using calculated DHr(1) values by nonlinear regression by fitting the derivative version of the KWW equation (Eq. 3) to the power-time data. P ¼ 277:8  DHr ð1Þ  ð=
Þ  ðt=
Þ
1  exp½
ðt=
Þ  ð3Þ where 277.8 is a units conversion factor from J/ g  h to mW/g. We report the results for relaxation time of samples of both Lot B1 and Lot B2 as tb— the stretched time—and ln tb values. These values are a more robust means for reporting relaxation time than t and b separately.27,37 The MSE function, developed for characterizing NMR relaxation,50 was also used for characterizing TAM relaxation data for Lot B1 to compare with relaxation times obtained from the KWW expression. It is reported that the MSE derivative function is superior to the KWW derivative function at short time periods where KWW equation fails to yield physically reasonable results, since P approaches infinity as time approaches zero.27,37,50 The MSE function is expressed for heat power (P) (mW/g) with time in hours as follows:27,37

chemical decomposition of moxalactam in the reaction vessel are included in the model and we are able to evaluate structural relaxation times with better accuracy. P ¼ 277:8  DHr ð1Þ  ð=
Þ  ðt=
Þ
1  exp½
ðt=
Þ  þ Pr

ð5Þ

Characterization of Degradation Rates Moxalactam disodium decomposes by 2 parallel reaction pathways, one involving decarboxylation of a carboxyl group on the p-hydroxyphenylmalonyl side chain (endothermic) and the other involving rupture of the b-lactam ring (exothermic) with the expulsion of the methyltetrazolethio side chain (the activation energies for both reactions are essentially equal 88 KJ/mole).49 Several methods are available in literature for the RP HPLC assay of moxalactam disodium and its decarboxylated product.49,51 HPLC Assay Methodology Lot A (Lilly). Decarboxylated moxalactam was measured by a reverse phase isocratic HPLC method49,51 by the Lilly analytical division. The column used was a Dupont Zorbax1 C8 column (5 m, 4.6 mm internal diameter). The mobile phase consisted of 20:80 (v/v) Methanol-0.1 M ammonium acetate aqueous buffer (pH 6.5). The flow rate was 1 mL/min. The wavelength for detection was 270 nm and the column temperature was ambient.

Previous experience with moxalactam disodium suggested the use of a modified expression of the differentiated KWW equation (Eq. 5) in TAM experiments carried out at 508C and 608C to separate the power due to relaxation processes from the power due to decomposition.27 This expression includes a chemical reaction factor (Pr), a parameter that accounts for the heat released by decomposition of moxalactam disodium during TAM experiments at 508C and 608C. Therefore, thermal changes attributed to the

Lot B2. Both moxalactam and decarboxylated moxalactam were measured in Lot B2 by a reverse phase HPLC method only slightly different than that used for Lot A (Lilly). The column used was a Zorbax1 SB-CN (Cyano) column (5 m, 150  4.6 mm internal diameter). The mobile phase consisted of 8.5:91.5 (v/v) Methanol-0.05 M sodium phosphate dibasic aqueous buffer (pH 6.5 adjusted with m-phosphoric acid). The flow rate was 1 mL/ min. The wavelength for detection was 270 nm, the column temperature was ambient and the injection volume was 20 mL. Products of b-lactam ring rupture do not absorb at the wavelength of detection and hence cannot be quantified by this HPLC method of analysis. Intra-day variability for decarboxylated moxalactam was not more than 2.5% (percent relative standard deviation— %RSD). Intra-day variability for moxalactam was not more than 2.4% (%RSD).

JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 96, NO. 5, MAY 2007

DOI 10.1002/jps

P ¼ 277:8 ½DHr ð1Þ=
0 ½1 þ ðt=
1 Þ  ½1 þ ðt=
1 Þ
2  exp½
ðt=
0 Þ  ½1 þ ðt=
1 Þ


1

ð4Þ



EFFECT OF ANNEALING ON STABILITY OF AMORPHOUS SOLIDS

Stability Protocol Lot A (Lilly). Formulations of Lot A were stored at 258C and 408C. The samples were assayed for decarboxylated moxalactam content initially and after 1, 3, 6, and 12 months. Lot B2. Formulations of Lot B2 were stored at 408C and 508C. The samples were assayed by the reverse phase HPLC method for both moxalactam disodium (parent) and decarboxylated moxalactam contents initially and after 1, 3, and 6 months. Higher variability was obtained with moxalactam disodium. This may have resulted from the proximity of moxalactam disodium peaks to the solvent front, or simply the need to dilute further the solutions, which in this case would compromise assay sensitivity for decarboxylated moxalactam. At each time point, moxalactam disodium and decarboxylated moxalactam were evaluated using standard calibration curves of peak area versus concentration of known moxalactam and decarboxylated moxalactam standard solutions.

1243

Table 1. Tg and DCP Values for Moxalactam Samples with Varying Moisture Content from MDSC Studies %Moisture*

Tg (8C)  SD**

2.6 3.7 5.7 8.6

99.2  0.2 93.5  0.9 72.0  0.3 51.6  0.2


Cp ðgJ CÞ  SD** 0.21  0.03 0.29  0.01 0.25  0.01 0.35  0.04

*Standard deviation for moisture content was not more than 0.1. **SD, standard deviation.

polarized light microscopy, after exposure to various RH (pictures not shown). Tg decreased and DCp increased with an increase in moisture content of the sample. Extrapolation to 0% moisture yielded a Tg, dry of 121.8  3.58C and an associated DCP value of 0.172  0.050 J/g  8C. Substituting these values into Eq. 2, DHr(1) at 408C ¼ 14.05 J/g, DHr(1) at 508C ¼ 12.33 J/g and DHr(1) at 608C ¼ 10.61 J/g with a standard error of 1.5 J/g for all DHr(1). These DHr(1) values were used for evaluating t and b values for samples analyzed by isothermal calorimetry at 40, 50, and 608C (Eqs. 3,4 and 5).

RESULTS AND DISCUSSION General Characterization Studies

TAM with Lot B1

No glass transition event was observed by MDSC for the dry moxalactam-12% mannitol system (MDSC scan not shown), perhaps because it behaves as a strong glass or because the glass transition temperature (Tg0 ) of the dry system simply coincides with decomposition. Tg and heat capacity change at Tg (DCP) for this system stored under different relative humidities (% RH) at room temperature (RT) are summarized in Table 1, along with the moisture content. None of the samples were birefringent, as observed by

Results from TAM studies showed excellent reproducibility. Results for reproducibility with samples of Lot B1 are summarized in Table 2. We report tb values determined from fitting both the MSE and KWW functions to the power-time data for the 408C TAM experiments, and tb values determined from fitting the modified KWW expression to the power-time data for the 608C TAM experiments. Fitting KWW and MSE expressions to data from 508C and 608C gave poor fits, resulting in significant errors in the parameters. The problem was the need to include the power term (Pr) in the modified KWW equation (see Eq. 5) to account for higher heat flow arising from the degradation reaction itself. The powertime curves of annealed and control (un-annealed) samples were dramatically different in TAM runs (Fig. 2), this difference being reflected in the vastly different values of tb that we extract from the data (Tab. 2). Annealing at 608C resulted in significantly higher tb values as compared to no annealing for TAM runs performed at both 40 and 608C. As expected, tb values at the higher analysis temperature were lower, but the effect of annealing was qualitatively the same.

DOI 10.1002/jps

JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 96, NO. 5, MAY 2007

All cakes produced by freeze drying moxalactam with 12% mannitol were elegant with excellent retention of cake structure. Initial moisture levels in freeze dried samples, as measured by Karl Fisher titration, were 1% w/w. Freeze dried samples were amorphous by either birefringency or XRPD. Both birefringence and XRPD studies, therefore, suggest amorphous freeze dried systems (data not shown). Thermal Analysis Studies MDSC

1244

ABDUL-FATTAH ET AL.

Table 2. Experimental Relaxation Times in Hours Measured at 408C and 608C (Reported as tb) for Lot B1 which Underwent Secondary Drying at 408C and 608C Analysis Temperature Secondary drying temperature Post TAM Moisture content (%w/w)  SD* KWW b
 MSE b


408C 408C 0.77  0.33 0.54 35.5 0.45 31.2

608C 608C 0.71  0.04

0.56 33.4 0.48 28.1

0.56 164.4 0.60 180.1

408C 0.63  0.04

0.57 163.7 0.68 191.7

0.24 1.28 ** **

608C 0.64  0.21

0.24 1.36 ** **

0.58 20.53 ** **

0.54 19.11 ** **

There was no significant increase in moisture contents of samples after TAM experiments indicating no leakage of moisture into the test system. *SD, standard deviation. **Pr term is needed and Pr term could not be used with the MSE expression since the number of adjustable parameters became too great to allow each parameter to be uniquely determined by the regression analysis.

Chemical Stability Studies

TAM with Lot B2 b

Reproducibility of t from TAM measurements for ‘‘Lot B2 control’’ was good at both 408C and 508C. Fitting the KWW and the MSE functions to experimental data of ‘‘Lot B2 control’’ at 408C (measured multiple times) yielded tb of 28.9  2.3 from KWW and 30.1  1.3 from MSE. Fitting the modified KWW function to the experimental data at 508C (measured multiple times) yielded tb of 7.30.7. tb increased as annealing temperature increased, and increased as annealing time increased at fixed temperature (Tab. 3). Formulations annealed at higher temperatures for the longest time period showed the highest tb values (708C for 8 h and 808C for 2 h) when analyzed at both 408C and 508C.

Since the ensemble of configurational states are not in equilibrium in a glassy solid, one would expect degradation to proceed in independent exponential fashion from each of the multitude of states in the distribution having different degradation rates, thereby producing multi-exponential decay kinetics or ‘‘stretched exponential’’ kinetics.27,33,36,52 Such kinetics are similar to the time dependence shown by relaxation kinetics, and in both degradation kinetics and relaxation kinetics, the nonexponential kinetics are a natural consequence of the lack of equilibrium between different structural states in the solid. That is, the ‘‘more reactive’’ states degrade fastest and as such are depopulated quickly, leaving less reactive states, which then degrade more slowly. The net result is

Table 3. Experimental Relaxation Time Constants for Different Batches of Lot B2 from Replicate Measurements Analysis Temperature Annealing Sample Lot Lot Lot Lot Lot Lot Lot

B2 B2 B2 B2 B2 B2 B2

control 60(6) 60(24) 70(4) 70(8) 80(1) 80(2)

Temperature

408C tb

Time

Control 60 60 70 70 80 80

6 24 4 8 1 2

508C

28.9  2.3 145.8  2.6 224.0  4.8 * 452.8  2.8 184.1  4.7 368.1  1.7

7.3  0.7 27.2  7.3 * 139.2  23.0 237.4  22.6 * 220.8  40.5

*Not determined. JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 96, NO. 5, MAY 2007

DOI 10.1002/jps

EFFECT OF ANNEALING ON STABILITY OF AMORPHOUS SOLIDS

Figure 2. Progress of TAM runs at 608C for Lot B1.

a degradation process that depends on some power of time, b, which is less than unity, with a broad distribution of states giving lower values of b. Often the time dependence is very close to square root of time.36 In the moxalaxtam case, percent of degradation product (decarboxylated moxalactam), %P, did increase linearly with square root of time:33,36,52–54 pffiffi %P ¼ P0 þ k t ð6Þ where P0 is the initial level of degradation product and k is the apparent rate constant (see Figs. 3–4). Multiple linear regression was performed using a general linear model (GLM) to fit

1245

Figure 3. Decarboxylation of Moxalactam disodium as a function of time: Lot A (Lilly) subjected to freezing at
258C with storage at 408C (squares) and 258C (circles). Annealing means additional secondary drying at 608C for 3 h. [Note: Lot A subjected to freezing at
408C showed essentially the same behavior as shown here by Figure 3]. Symbols Key: Open squares: not annealed, 408 Storage, k ¼ 1.12; Filled squares: annealed, 408 Storage, k ¼ 0.97; Open circles: not annealed, 258 Storage, k ¼ 0.33; Filled circles: annealed, 258 Storage, k ¼ 0.23. Assay results given are means of duplicate samples. Uncertainty in the assay results is less than the size of the plotting symbol.

the most appropriate model (%P ¼ P0 þ ktn) to the assay data-time points for each batch, and k at each storage temperature was determined from the slope of the straight line for each batch. F-values for each GLM model with different

Figure 4. Decarboxylation of Moxalactam disodium as a function of time: Lot B2 with various annealing treatments and storage at 508C. DOI 10.1002/jps

JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 96, NO. 5, MAY 2007

1246

ABDUL-FATTAH ET AL.

Table 4. F-values* for Fitting %P ¼ P0 þ ktn to Storage Stability Data of Moxalactam Samples Using Different Exponents for Time (n) Analysis Temperature n

408C

508C

1 0.6 0.5 0.4 0.3 0.1

30 92 130 143 102 28

47 320 805 546 159 27

Mean sum of square of an effect/Mean Square of Errors. *F-value statistic is calculated when all data are collectively fitted to a general linear model. It indicates the goodness of fit for all data to the general model used. The higher the F-value, the more appropriate the model is. F-stat is computed using the following equation: Mean sum of square of an effect : Mean Square of Errors

exponents, n, showed that the model using square-root of time kinetics fit the data most appropriately (Tab. 4). F-value was highest with square root of time at 508C. F-value at 408C data was high at both t0.4 and t0.5. However, to be consistent in treatment of data, we analyzed the data in terms of t0.5.

Lot A (Lilly) Batches of Lot A annealed at 608C had slightly higher initial degradation than the control samples (Tab. 5). The apparent decarboxylation rate

constants of annealed samples were 13–14% lower than that of the control (un-annealed) samples. Although the differences were small, rates were significantly different at a confidence level of 90% for both storage temperatures.

Lot B2 Apparent rate constants for loss of parent and formation of decarboxylated product in batches of Lot B2 at a storage temperature of 408C and 508C for 6 months are summarized in Table 6. The results were consistent with the data for Lot A batches; that is, annealing improved the chemical stability of moxalactam. Higher assay variance, however, was associated with quantifying the parent molecule. To answer the general question ‘‘does annealing impact decarboxylation of moxalactam significantly?’’ a 2-way analysis-ofvariance (ANOVA) was done on the raw assaytime data to determine the effect of both annealing treatment (i.e., annealing temperature and time) and storage time (i.e., 0, 1, 3, and 6 months). Results of the 2-way ANOVA for decarboxylation at both storage temperatures (408C and 508C) showed a significant contribution of both storage time ( p < 0.0001) and annealing treatment ( p  0.002) to the differences observed in decarboxylation rate between different samples. Annealing temperature impacted significantly kdecarb.. p values for an unpaired t-test (results not shown) showed that kdecarb. of ‘‘Lot B2 Control’’ and ‘‘Lot B2 60(6)’’ were significantly higher (at storage temperatures of 408C and 508C) than kdecarb. of all other annealed samples (at a confidence level of

Table 5. Initial Decarboxylated Moxalactam Content and Chemical Stability Data for Lot A (Lilly) Stored for 12 Months at 258C and 408C kdecarb (%/month0.5) Sample Lot Lot Lot Lot

A A A A

(
25) (
25)S* (
40) (
40)S**

Moisture Content (% w/w)

Initial Decarboxylated Moxalactam Content (%)

258C

408C

0.4 0.3 1.1 0.9

2.26 2.57 2.21 2.51

0.327 0.228 0.333 0.251

1.124 0.967 1.146 0.998

The standard error associated with all rate constants (kdecarb) estimated with a general linear model was 0.025 at 258C and 0.053 at 408C. kdecarb was determined by regression analysis. *Both lots underwent secondary drying at 408C for 8 h. Lots ending in S were annealed at 608C for an additional 3 h. **Different freezing protocols resulted in differences in moisture content between both control samples (i.e., Lot A (
25) vs. Lot A (
40)), as well as both samples annealed at 608C (i.e., Lot A (
25)S vs. Lot A (
40)S). JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 96, NO. 5, MAY 2007

DOI 10.1002/jps

EFFECT OF ANNEALING ON STABILITY OF AMORPHOUS SOLIDS

1247

Table 6. Initial Decarboxylated Moxalactam Content and Chemical Stability Data for Batches of Lot B2 Stored for 6 Months at 408C and 508C kparent** (%/month0.5)

Annealing Temperature (8C)

Time (h)

Moisture content (% w/w)

Initial % Dec. Moxa  SD*

408C

508C

408C

508C

6 12 24 4 8 1 2

0.3 0.5 0.6 0.9 0.7 0.9 0.5 0.4

1.46  0.02 2.07  0.02 2.41  0.01 2.97  0.04 2.95  0.00 3.66  0.03 3.00  0.08 3.32  0.01

6.40 6.29 5.75 5.23 4.79 4.63 4.91 5.22

9.40 8.85 9.20 8.02 8.33 7.38 7.04 7.08

2.16 1.62 1.42 1.37 1.30 1.10 1.64 1.25

2.68 2.38 2.10 1.96 1.91 1.59 1.93 1.78

Control 60 60 60 70 70 80 80

kdecarb*** (%/month0.5)

The standard error associated with all decarboxylation rate constants (kdecarb) estimated using a general linear model was 0.134 at 408C and 0.07 at 508C. The standard error associated with all rate constants for loss of parent molecule (kparent) was 0.7 at 408C and 0.5 at 508C. kdecarb and kparent were determined by regression analysis. *SD, standard deviation. **kparent ¼ Total rate for chemical decomposition (loss of moxalactam (parent)). ***kdecarb ¼ decarboxylation rate constant.

90%). Moreover, there was a statistical difference in kdecarb. as a function of annealing time. kdecarb. at 508C for the sample annealed at 608C for 6 h (Lot B2 60(6)) was significantly higher than the rate constant for the samples annealed at 608C for 12 and 24 h (Lot B2 60(12) and Lot B2 60(24)). Similarly, the sample annealed at 708C for 4 h (Lot B2 70(4)) had a significantly higher kdecarb. than that annealed at 708C for 8 h (Lot B2 70(8)). Due to high assay variation, the same conclusions could not be reached at for loss of parent compound (at a confidence level of 90%), even though apparent rate constants for loss of parent compound showed similar trends as did decarboxylation. Not only did annealing improve chemical stability, but also annealing also improved purity during or near the end of the storage period. That is, the purity curves cross at a time point (see Figs. 3 and 4) such that after this time, the purity for the annealed samples was slightly better in spite of the lower purity at the beginning of the stability study. The major decomposition routes for moxalactam in the solid state (decarboxylation and b-lactam ring rupture) are well known.49,51 A study by Byrn et al.55 indicated that decarboxylation is dominant above 908C. An early study by Dellerman et al.49 determined that the activation energy was roughly 88 kJ/mol for both decarboylation and b-lactam rupture. This would mean a

degradation rate at 508C about a factor of 2.8 higher than the degradation rate at 408C. However, for unknown reasons, the values of k (decarb) at 508C for all batches of Lot B2 were only 1.2 to 1.5 times higher than the corresponding values at 408C. Similarly, k (parent) at 508C for all batches of Lot B2 were 1.4 to 1.6 times higher than k (parent) at 408C. Thus, the calculated energies of activation were much smaller than one would expect.

DOI 10.1002/jps

JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 96, NO. 5, MAY 2007

Correlation of Chemical Stability to Structural Relaxation We have demonstrated that annealing reduces molecular mobility below Tg. Since decarboxylation of moxalactam in the solid state takes place in several steps that involve mainly the rotation of the carboxylic acid group into coplanarity with the carbonyl group,55 reduced mobility should create conditions less favorable for this rotation, thereby leading to a decrease in the rate of decarboxylation. Since the decarboxylation rate constants were based on stretched time (i.e., t0.5), then
 , the ‘‘stretched time constant’’ associated with structural relaxation (see Eq. 7), is the kinetic parameter of interest when comparing degradation rate with structural relaxation: dðln FÞ=dðt Þ ¼
ð1=
 Þ

ð7Þ

1248

ABDUL-FATTAH ET AL.

To the extent that the motion facilitating instability is correlated with the motion critical for the structural relaxation, we might expect a relationship between stability and tb as follows: k ¼ Að
 Þc

ð8Þ

where A is a constant and c is the ‘‘coupling coefficient,’’ expected to be less than unity since the scale of motion involved with a chemical decomposition reaction is likely less than that required for the global relaxation events measured by structural relaxation time.6 Plots of ln (k) values (for decarboxylation and loss of parent) versus ln tb (Fig. 5) show a better linear correlation with decarboxylation rate constants (R2 values of 0.9189 and 0.948 at 408C and 508C, respectively) than with loss of parent (R2 values of 0.643 and 0.84 at 408C and 508C, respectively), likely because of greater accuracy in the decarboxylation rate constants as compared to the rate constants describing the loss of parent. Note that the coupling coefficients are small (0.1–0.2), suggesting the motion critical to degradation is only weakly coupled to the motion involved in structural relaxation. Higher coupling coefficients are expected with aggregation in proteins, and diffusion-controlled reactions since these processes would be expected to involve mobility much more like the mobility involved in structural relaxation.33 Finally, it may be argued that one of the possible causes of a slower degradation rate in annealed samples is the accumulation of degradation products, which increase the ‘‘back-reaction’’ of a reversible chemical reaction. There is a correlation between initial degradation product and degradation rate, but correlation is not cause–effect, and there are several facts that suggest such an explanation is not viable. First, accumulation of degradation products during annealing would not lead to higher purity (i.e., less degradation) in the annealed sample after storage for a time. Second, and perhaps more important, the degradation processes under consideration here, decarboxylation and rupture of the b-lactam, are not reversible reactions. Thus, it seems very unlikely that the effect we observe has anything to do with the impact of degradation product on the reaction rate. Rather, there is a correlation between degradation rate and initial level of degradation product because during annealing, the same combination of factors that cause effective annealing and reduction of mobility also cause chemical degradation. JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 96, NO. 5, MAY 2007

Figure 5. Relationship between apparent rate constants [for decarboxylation (kdecarb) and loss of parent molecule (kparent)] and relaxation times. Symbols key: Squares ¼ loss of parent; Diamonds ¼ decarboxylation. (A) 408C: coupling coefficient, c ¼ 0.23 (decarboxylation) and c ¼ 0.14 (loss of parent). (B) 508C: coupling coefficient, c ¼ 0.11 (decarboxylation) and c ¼ 0.07 (loss of parent).

CONCLUSIONS For a moxalactam-12% w/w mannitol system, annealing or ‘‘heat treating’’ below Tg improved chemical stability in the glass and increased structural relaxation time. Annealing did cause greater initial decarboxylation as compared to no annealing, however, initial degradation differences were small relative to the change in decarboxylation rate constant such that sample purity was better with annealing at the end of the stability study. Stabilization by annealing, although small, was reproducible and increased as annealing time and annealing temperature increased. Thus, if the molecular motion required for degradation and structural relaxation are DOI 10.1002/jps

EFFECT OF ANNEALING ON STABILITY OF AMORPHOUS SOLIDS

coupled in other amorphous systems, then annealing these systems will, in general, improve their stability.

1249

1. Hancock BC, Parks M. 2000. What is the true solubility advantage for amorphous pharmaceuticals? Pharma Res 17:397–404. 2. Hilden LR, Morris KR. 2004. Physics of amorphous solids. J Pharma Sci 93:3–12. 3. Pikal MJ. 2002. Chemistry in solid amorphous matrices: Implication for biostabilization, in Amorphous Food and Pharmaceutical Systems. Cambridge, UK: The Royal Society of Chemistry. 257– 272. 4. Zhou D, Zhang GGZ, Schmitt EA. 2002. Physical stability of amorphous pharmaceuticals: Importance of configurational thermodynamic quantities and molecular mobility. J Pharma Sci 91:1863– 1872. 5. Tanaka K, Kitamura S, Kitagawa T. 2005. Effect of structural relaxation on the physical and aerosol properties of amorphous form of FK888 (NK1 antagonist). Chem Pharma Bullet 53:498– 502. 6. Pikal MJ. 2004. Mechanisms of protein stabilization during freeze-drying and storage: The relative importance of thermodynamic stabilization and glassy state relaxation dynamics. Drugs Pharma Sci (Freeze-Drying/Lyophilization of Pharmaceutical and Biological Products) 137:63–107. 7. Roy ML, Pikal MJ, Maloney AM. 1992. The effects of formulation and moisture on the stability of a freeze-dried monoclonal antibody-vinca conjugate: A test of the WLF glass transition theory. Dev Biol Standardiz (Biol Prod Freeze-Dry Formul) 74:323– 340. 8. Guo Y, Byrn SR, Zografi G. 2000. Physical characteristics and chemical degradation of amorphous quinapril hydrochloride. J Pharma Sci 89:128–143. 9. Gedde UW. 1999. The glassy amorphous state, in Polymer Physics. Dordrecht, The Netherlands: Kluwer Academic Publishers:77–98. 10. Andreozzi L, Faetti M, Zulli F. 2005. Molecularweight dependence of enthalpy relaxation of PMMA. Macromolecules 38:6056–6067. 11. Hill SA, MacNaughtan W, Whitcombe MJ. 2005. The effect of thermal history on the maillard reaction in a glassy matrix. J Agri Food Chem 53:10213–10218. 12. Searles JA, Carpenter JF, Randolph TW. 2001. Annealing to optimize the primary drying rate, reduce freezing-induced drying rate heterogeneity, and determine Tg’ in pharmaceutical lyophilization. J Pharma Sci 90:872–887.

13. Tong P, Zografi G. 1999. Solid-state characteristics of amorphous sodium indomethacin relative to its free acid. Pharma Res 16:1186–1192. 14. Angell CA. 1995. Formation of glasses from liquids and biopolymers. Science (Washington, DC) 267: 1924–1935. 15. Boehmer R, Senapati H, Angell CA. 1991. Mechanical stress relaxation in inorganic glasses studied by a step-strain technique. J Non-Crystall Solids 131:182–186. 16. Struik LCE. 1978. Physical aging in amorphous polymers and other materials. 242 pp. 17. Lammert AM, Lammert RM, Schmidt SJ. 1999. Physical aging of maltose glasses as measured by standard and modulated differential scanning calorimetry. J Thermal Anal Calor 55:949–975. 18. Hodge IM. 1995. Physical aging in polymer glasses. Science (Washington, DC) 267:1945–1947. 19. Guo JH. 1994. A theoretical and experimental study of additive effects of physical aging and antiplasticization on the water permeability of polymer film coatings. J Pharma Sci 83:447–449. 20. Guo JH. 1993. Effects of plasticizers on water permeation and mechanical properties of cellulose acetate: Antiplasticization in slightly plasticized polymer film. Drug Dev Industrial Pharm 19:1541– 1545. 21. Hodge IM, Berens AR. 1981. Calculation of the effects of annealing on Tg endotherms. Macromolecules 14:1598–1599. 22. Hodge IM. 1986. Adam-Gibbs formulation of nonlinearity in glassy-state relaxations. Macromolecules 19:936–938. 23. Hodge IM, Berens AR. 1982. Effects of annealing and prior history on enthalpy relaxation in glassy polymers. 2. Mathematical modeling. Macromolecules 15:762–770. 24. Hodge IM. 1997. Adam-Gibbs formulation of enthalpy relaxation near the glass transition. J Res Natl Inst Stand Technol 102:195–205. 25. Hodge IM. 1984. The effects of physical aging on enthalpy relaxation in polymers. A phenomenological approach, in Relaxations in complex systems. 65–79. 26. Moynihan CT. 1995. Structural relaxation and the glass transition. Rev Mineral 32:1–19. 27. Liu J, Rigsbee DR, Pikal MJ. 2002. Dynamics of pharmaceutical amorphous solids: The study of enthalpy relaxation by isothermal microcalorimetry. J Pharma Sci 91:1853–1862. 28. Yoshida H, Kanbara H, Kobayashi Y. 1983. Effect of hydrogen bond formation on physical aging of ethylene-vinyl alcohol copolymers with annealing below Tg. Sen’i Gakkaishi 39:T512–T518. 29. Shamblin SL, Hancock BC, Pikal MJ. 2000. Interpretation of relaxation time constants for amorphous pharmaceutical systems. J Pharma Sci 89: 417–427.

DOI 10.1002/jps

JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 96, NO. 5, MAY 2007

REFERENCES

1250

ABDUL-FATTAH ET AL.

30. Baysal C, Atilgan AR. 2005. Relaxation kinetics and the glassiness of native proteins: Coupling of timescales. Biophys J 88:1570–1576. 31. Hancock BC, Shamblin SL, Zografi G. 1995. Molecular mobility of amorphous pharmaceutical solids below their glass transition temperatures. Pharma Res 12:799–806. 32. Pauly S, Kammer HW. 1994. Physical aging in copolymer based blends. Polymer Networks Blends 4:93–99. 33. Yoshioka S, Aso Y, Kojima S. 2001. Usefulness of the Kohlrausch-Williams-Watts stretched exponential function to describe protein aggregation in lyophilized formulations and the temperature dependence near the glass transition temperature. Pharma Res 18:256–260. 34. Shalaev E, Zografi G. 2002. The concept of ‘structure’ in amorphous solids from the perspective of the pharmaceutical sciences. Special Publication—Royal Soc Chem (Amorp Food Pharma Syst) 281:11–30. 35. Cicerone MT, Tellington A, Sokolov A. 2003. Substantially improved stability of biological agents in dried form: The role of glassy dynamics in preservation of biopharmaceuticals. BioProcess Int 40:46–47. 36. Pikal MJ, Rigsbee DR. 1997. The stability of insulin in crystalline and amorphous solids: Observation of greater stability for the amorphous form. Pharma Res 14:1379–1387. 37. Kawakami K, Pikal MJ. 2005. Calorimetric investigation of the structural relaxation of amorphous materials: Evaluating validity of the methodologies. J Pharma Sci 94:948–965. 38. Streefland L, Auffret AD, Franks F. 1998. Bond cleavage reactions in solid aqueous carbohydrate solutions. Pharma Res 15:843–849. 39. Duddu SP, Dal Monte PR. 1997. Effect of glass transition temperature on the stability of lyophilized formulations containing a chimeric therapeutic monoclonal antibody. Pharma Res 14:591–595. 40. Parker R, Gunning YM, Ring SG. 2002. Glassy state dynamics, its significance for biostabilisation and the role of carbohydrates. Special Publication—Royal Soc Chem (Amorp Food Pharma Syst) 281:73–87. 41. Yoshioka S, Aso Y, Kojima S. 2004. Temperatureand glass transition temperature-dependence of bimolecular reaction rates in lyophilized formulations described by the Adam-Gibbs-Vogel equation. J Pharma Sci 93:1062–1069. 42. Yoshioka S, Aso Y, Kojima S. 2000. Temperature dependence of bimolecular reactions associated with molecular mobility in lyophilized formulations. Pharma Res 17:925–929.

43. Yoshioka S, Aso Y. 2005. A quantitative assessment of the significance of molecular mobility as a determinant for the stability of lyophilized insulin formulations. Pharma Res 22:1358–1364. 44. Yoshioka S, Aso Y, Miyazaki T. 2006. Negligible contribution of molecular mobility to the degradation rate of insulin lyophilized with poly(vinylpyrrolidone). J Pharma Sci 95:939–943. 45. Pikal MJ. 1996. The study of relaxation enthalpy in glassy pharmaceuticals with the thermal activity monitor (TAM). In Thermometric Seminars on Calorimetry in Materials Sciences. Stockholm, Sweden. 46. Deschenes LA, Vanden Bout DA. 2001. Singlemolecule studies of heterogeneous dynamics in polymer melts near the glass transition. Science 292:255–258. 47. Madsen LD, De Wilton AC, Mercier JS. 1991. Examination of the stability of borophosphosilicate glass films. Chemtronics 5:35–42. 48. Mardaleishvili IR, Anisimov VM. 1987. b-Transition and relaxation of impurities in molecules in their reactions in glass polymers. Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya 1431– 1432. 49. Pikal MJ, Dellerman KM. 1989. Stability testing of pharmaceuticals by high-sensitivity isothermal calorimetry at 25 Deg C: Cephalosporins in the solid and aqueous solution states. Int J Pharma 50:233–252. 50. Peyron M, Pierens G, Stewart R. 1996. The modified stretched-exponential model for characterization of NMR relaxation in porous media. J Mag Reson Ser A 118:214–220. 51. Lorenz LJ, Thomas PN. 1984. Moxalactam disodium. Analyt Prof Drug Subst 13:305–332. 52. Yoshioka S, Tajima S, Aso Y, Kojima S. 2003. Inactivation and aggregation of b-galactosidase in lyophilized formulation described by KohlrauschWilliams-Watts stretched exponential function. Pharma Res 20:1655–1660. 53. Chang L, Shepherd D, Pikal MJ. 2005. Mechanism of protein stabilization by sugars during freeze-drying and storage: Native structure preservation, specific interaction, and/or immobilization in a glassy matrix? J of Pharma Sci 94:1427– 1444. 54. Chang L, Shepherd D, Pikal MJ. 2005. Effect of sorbitol and residual moisture on the stability of lyophilized antibodies: Implications for the mechanism of protein stabilization in the solid state. J Pharma Sci 94:1445–1455. 55. Byrn SR, Perrier P, Pfeiffer RR. 1987. The solidstate decarboxylation of the diammonium salt of moxalactam. Pharma Res 4:137–141.

JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 96, NO. 5, MAY 2007

DOI 10.1002/jps