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

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1 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. PIKAL 1,2 1 Department of Pharmaceutical Sciences, University of Connecticut, Storrs, Connecticut Eli Lilly and Co., Lilly Research Laboratories, Indianapolis, Indiana Received 24 July 2006; revised 8 November 2006; accepted 15 December 2006 Published online in Wiley InterScience ( DOI /jps 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 T g and DC P 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 t b values than the control sample, with t b values increasing as annealing temperature increased. Additionally, t b 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: , 2007 Keywords: amorphous; annealing; decarboxylation; glass transition temperature (T g ); 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) ; Fax: (860) ; michael.pikal@uconn.edu) Journal of Pharmaceutical Sciences, Vol. 96, (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

2 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 (T g ) 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 (T g ), vitrification of the melt occurs thus forming the glassy state, 9,11 accompanied by an increase in viscosity to very high values (typically >10 12 Pa.s) 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 T g, 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 T g is called physical aging, 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 T g is both nonexponential and nonlinear Nonlinearity is discussed in detail elsewhere and is not the subject of this research Nonexponentiality means that relaxation toward equilibrium is described by a nonexponential decay function, F(t) 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 (S C ). In the initial phase of glass formation, configurations of the substates are considered to be frozen-in during processing 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: " FðtÞ ¼exp t # 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 T g Although the high viscosity of a glass (>10 12 Pa s) greatly slows molecular mobility, 11,13 many JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 96, NO. 5, MAY 2007 DOI /jps

3 EFFECT OF ANNEALING ON STABILITY OF AMORPHOUS SOLIDS 1239 reactions do proceed at a measurable rate below T g, 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 ,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 T g, suggesting that cyclization of quinapril is related to molecular mobility. A similarity of temperature dependence between t 90 for an acetyl transfer reaction (between aspirin and sulfadiazine) and t below T g in amorphous matrices with dextran and polyvinyl pyrrolidone was reported by Yoshioka et al., 41 suggesting that t 90 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 T g for systems at various moisture contents at two different temperatures. Keeping in mind that the motions that prevail as T approaches T g 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. 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 isothermally 26 or by annealing otherwise also referred to as Figure 1. acid). Chemical structure of moxalactam (free DOI /jps JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 96, NO. 5, MAY 2007

4 1240 ABDUL-FATTAH ET AL. densification. 27,34,37,46,47 The term annealing simply means heating an amorphous sample below its T g 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 T g 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 Si- O 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. MATERIALS AND METHODS Materials Two lots of moxalactam disodium (for simplicity labeled Lot A (Lilly) and Lot B) were used, Lot A (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 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 /jps

5 EFFECT OF ANNEALING ON STABILITY OF AMORPHOUS SOLIDS 1241 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. 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, at28/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 Both glass transition temperature of dry amorphous moxalactam-12% mannitol (T g, dry ) and the associated change in heat capacity (DC p ) values are required for evaluation of t. It was not possible to measure T g and DC p 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 T g, dry and the associated DC p, 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. T g, dry and DC p 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((h r )/dt, of lots B1 and B2 during aging experiments using a Thermal Activity Monitor (TAM) (Thermometric, Järfälla, 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). T g, dry and DC p at T g, dry values obtained from MDSC studies were used in our studies to evaluate the maximum enthalpy recovery at any given DOI /jps JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 96, NO. 5, MAY 2007

6 1242 ABDUL-FATTAH ET AL. temperature - DH r (1) used in TAM experiments (i.e., 40, 50, and 608C) using Eq. 2: 27,37 DH r ð1þ ¼ ðt g; dry TÞDC P 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 DH r (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 DH r ð1þ ð=þðt=þ 1 exp½ ðt=þ Š ð3þ where is a units conversion factor from J/ g htomw/g. We report the results for relaxation time of samples of both Lot B1 and Lot B2 as t b the stretched time and ln t b 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 P ¼ 277:8 ½DH r ð1þ= 0 Š½1 þðt= 1 ÞŠ ½1þðt= 1 ÞŠ 2 exp½ ðt= 0 Þ ½1þðt= 1 Þ 1 ŠŠ ð4þ 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 (P r ), 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 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 DH r ð1þ ð=þðt=þ 1 exp½ ðt=þ ŠþP r 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 method 49,51 by the Lilly analytical division. The column used was a Dupont Zorbax 1 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. 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 Zorbax 1 SB-CN (Cyano) column (5 m, 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 /jps

7 EFFECT OF ANNEALING ON STABILITY OF AMORPHOUS SOLIDS 1243 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. RESULTS AND DISCUSSION General Characterization Studies 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 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 (T 0 g ) of the dry system simply coincides with decomposition. T g and heat capacity change at T g (DC P ) 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 Table 1. T g and DC P Values for Moxalactam Samples with Varying Moisture Content from MDSC Studies %Moisture* T g (8C) SD** C p ð J g C ÞSD** *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). T g decreased and DC p increased with an increase in moisture content of the sample. Extrapolation to 0% moisture yielded a T g, dry of C and an associated DC P value of J/g 8C. Substituting these values into Eq. 2, DH r (1) at 408C ¼ J/g, DH r (1) at508c ¼ J/g and DH r (1) at608c ¼ J/g with a standard error of 1.5 J/g for all DH r (1). These DH r (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). TAM with Lot B1 Results from TAM studies showed excellent reproducibility. Results for reproducibility with samples of Lot B1 are summarized in Table 2. We report t b values determined from fitting both the MSE and KWW functions to the power-time data for the 408C TAM experiments, and t b 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 (P r ) 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 t b that we extract from the data (Tab. 2). Annealing at 608C resulted in significantly higher t b values as compared to no annealing for TAM runs performed at both 40 and 608C. As expected, t b values at the higher analysis temperature were lower, but the effect of annealing was qualitatively the same. DOI /jps JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 96, NO. 5, MAY 2007

8 1244 ABDUL-FATTAH ET AL. Table 2. Experimental Relaxation Times in Hours Measured at 408C and 608C (Reported as t b ) for Lot B1 which Underwent Secondary Drying at 408C and 608C Analysis Temperature 408C 608C Secondary drying temperature 408C 608C 408C 608C Post TAM Moisture content (%w/w) SD* KWW b MSE b ** ** ** ** ** ** ** ** 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. **P r term is needed and P r 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. TAM with Lot B2 Reproducibility of t b 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 t b of from KWW and from MSE. Fitting the modified KWW function to the experimental data at 508C (measured multiple times) yielded t b of t b 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 t b values (708C for 8 h and 808C for 2 h) when analyzed at both 408C and 508C. Chemical Stability Studies 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 408C 508C Sample Temperature Time t b Lot B2 control Control Lot B2 60(6) Lot B2 60(24) * Lot B2 70(4) 70 4 * Lot B2 70(8) Lot B2 80(1) * Lot B2 80(2) *Not determined. JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 96, NO. 5, MAY 2007 DOI /jps

9 EFFECT OF ANNEALING ON STABILITY OF AMORPHOUS SOLIDS 1245 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 p %P ¼ P 0 þ k ffiffi t ð6þ where P 0 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 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 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 P 0 þ kt n ) 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 /jps JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 96, NO. 5, MAY 2007

10 1246 ABDUL-FATTAH ET AL. Table 4. F-values* for Fitting %P ¼ P 0 þ kt n to Storage Stability Data of Moxalactam Samples Using Different Exponents for Time (n) n 408C Analysis Temperature 508C 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 t 0.4 and t 0.5. However, to be consistent in treatment of data, we analyzed the data in terms of t 0.5. 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 < ) and annealing treatment ( p 0.002) to the differences observed in decarboxylation rate between different samples. Annealing temperature impacted significantly k decarb.. p values for an unpaired t-test (results not shown) showed that k decarb. of Lot B2 Control and Lot B2 60(6) were significantly higher (at storage temperatures of 408C and 508C) than k decarb. 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 Sample Moisture Content (% w/w) Initial Decarboxylated Moxalactam Content (%) k decarb (%/month 0.5 ) 258C 408C Lot A ( 25) Lot A ( 25)S* Lot A ( 40) Lot A ( 40)S** The standard error associated with all rate constants (k decarb ) estimated with a general linear model was at 258C and at 408C. k decarb 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 /jps

11 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 Annealing k parent ** (%/month 0.5 ) k decarb *** (%/month 0.5 ) Temperature Moisture Initial % Dec. (8C) Time (h) content (% w/w) Moxa SD* 408C 508C 408C 508C Control The standard error associated with all decarboxylation rate constants (k decarb ) estimated using a general linear model was at 408C and 0.07 at 508C. The standard error associated with all rate constants for loss of parent molecule (k parent ) was 0.7 at 408C and 0.5 at 508C. k decarb and k parent were determined by regression analysis. *SD, standard deviation. **k parent ¼ Total rate for chemical decomposition (loss of moxalactam (parent)). ***k decarb ¼ decarboxylation rate constant. 90%). Moreover, there was a statistical difference in k decarb. as a function of annealing time. k decarb. 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 k decarb. 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. Correlation of Chemical Stability to Structural Relaxation We have demonstrated that annealing reduces molecular mobility below T g. 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., t 0.5 ), 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 Þ¼ ð1= Þ ð7þ DOI /jps JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 96, NO. 5, MAY 2007

12 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 t b as follows: k ¼ Að Þ c 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 t b (Fig. 5) show a better linear correlation with decarboxylation rate constants (R 2 values of and at 408C and 508C, respectively) than with loss of parent (R 2 values of 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 ( ), 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. Figure 5. Relationship between apparent rate constants [for decarboxylation (k decarb ) and loss of parent molecule (k parent )] 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 T g 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 JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 96, NO. 5, MAY 2007 DOI /jps

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