Modeling Physical Stability of Amorphous Solids Based on Temperature and Moisture Stresses

Journal of Pharmaceutical Sciences xxx (2016) 1e8

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Pharmaceutics, Drug Delivery and Pharmaceutical Technology

Modeling Physical Stability of Amorphous Solids Based on Temperature and Moisture Stresses Donghua (Alan) Zhu 1, George Zografi 2, Ping Gao 1, Yuchuan Gong 1, Geoff G.Z. Zhang 1, * 1 2

Drug Product Development, Research and Development, AbbVie Inc., 1 North Waukegan Road, North Chicago, Illinois 60064 School of Pharmacy, University of Wisconsin-Madison, 777 Highland Avenue, Madison, Wisconsin 53705

a r t i c l e i n f o

a b s t r a c t

Article history: Received 13 December 2015 Revised 5 March 2016 Accepted 22 March 2016

Isothermal microcalorimetry was utilized to monitor the crystallization process of amorphous ritonavir (RTV) and its hydroxypropylmethylcellulose acetate succinateebased amorphous solid dispersion under Ea  b,wc, where t is the various stressed conditions. An empirical model was developed: lnðtÞ ¼ lnðAÞ þ RT crystallization induction period, A is a pre-exponential factor, Ea is the apparent activation energy, b is the moisture sensitivity parameter, and wc is water content. To minimize the propagation of errors associated with the estimates, a nonlinear approach was used to calculate mean estimates and confidence intervals. The physical stability of neat amorphous RTV and RTV in hydroxypropylmethylcellulose acetate succinate solid dispersions was found to be mainly governed by the nucleation kinetic process. The impact of polymers and moisture on the crystallization process can be quantitatively described by Ea and b in this Arrhenius-type model. The good agreement between the measured values under some less stressful test conditions and those predicted, reflected by the slope and R2 of the correlation plot of these 2 sets of data on a natural logarithm scale, indicates its predictability of long-term physical stability of amorphous RTV in solid dispersions. To further improve the model, more understanding of the impact of temperature and moisture on the amorphous physical stability and fundamentals regarding nucleation and crystallization is needed. © 2016 American Pharmacists Association®. Published by Elsevier Inc. All rights reserved.

Keywords: amorphous solid dispersion physical stability isothermal microcalorimetry mathematical model crystallization nucleation crystal growth

Introduction The high-energy state of amorphous materials results in higher apparent aqueous solubility and improved dissolution rates for poorly water-soluble drugs, which in turn can lead to improved oral absorption and bioavailability. However, an amorphous drug in solid dispersions is, intrinsically, physically unstable and tends to re-crystallize to its crystalline counterpart. The rate of crystallization, both nucleation and crystal growth, depends on factors such as the nature of the compound, the composition of

Present address for Zhu: Drug Product Development, Janssen China R&D, Johnson & Johnson, Shanghai, China. This study was funded by AbbVie. AbbVie participated in the study design, research, data collection, analysis, and interpretation of data, as well as writing, reviewing, and approving the publication. D.A.Z. is a former employee of AbbVie, currently employed by Johnson & Johnson, and has no conflicts of interest to report. G.Z. is a retired professor from the University of Wisconsin-Madison, and has no conflicts of interest to report. P.G., Y.G., and G.G.Z.Z. are AbbVie employees and may own AbbVie stock/options. * Correspondence to: Geoff G.Z. Zhang (Telephone: þ1-847-937-4702; Fax þ1847-937-7756). E-mail address: [email protected] (G.G.Z. Zhang).

amorphous solid, temperature, and relative humidity (RH), and sometimes process. Crystallization of amorphous drug in solid dispersions may occur even at temperatures below their glass transition temperatures, Tg. Thus the risk of crystallization of amorphous solids is always present during manufacture, handling, and storage. Solid dispersions, in which amorphous drugs are molecularly dispersed in polymer matrices, offer an attractive means of not only increasing the dissolution rate, but also further improving the physical stability of amorphous drugs by inhibiting crystallization through a variety of mechanisms including solvation of the drugs in polymer matrices, an increase in the glass transition temperature (Tg) of the dispersion, and specific interactions between polymer and drug.1,2 Hydrophilic polymers (e.g., polyvinylpyrrolidone and hydroxypropylmethylcellulose [HPMC]) are often used to prepare solid dispersions. However, because such hydrophilic polymers are usually more water soluble than the drug, and hence more polar, the presence of the polymer could result in increased moisture uptake of solid dispersions compared with the pure amorphous drug. Absorption of water into amorphous dispersions, in most cases, facilitates crystallization. Thus, in addition to the type of polymer and the nature of the drug, the

http://dx.doi.org/10.1016/j.xphs.2016.03.029 0022-3549/© 2016 American Pharmacists Association®. Published by Elsevier Inc. All rights reserved.

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D. Zhu et al. / Journal of Pharmaceutical Sciences xxx (2016) 1e8

physical stability of the solid dispersion is often influenced by the balance between drug loading and moisture absorption under storage conditions.3,4 The conventional means of monitoring the crystallization process of amorphous materials is to store samples under various temperature and RH conditions, and then measure the Tg and Xray diffraction patterns of the samples at various periods of time.5 This method is not only tedious and labor intensive, but also less sensitive largely due to the detection limit of powder Xray diffraction which often varies from 2% to 5% of crystalline component in amorphous samples depending on drug loading and crystallinity. As a result, the onset time of crystallization, one of the critical measures of physical stability, is often missed or overestimated. In addition, because of the complexity of crystal growth kinetics, such as the discontinuity of crystal growth rate as a function of temperature across Tg, the conventional methods which often focus only on crystal growth may merely provide a qualitative rank order among various solid dispersions, rather than a quantitative prediction. It is technically challenging, if not impossible, to quantitatively estimate the long-term physical stability of amorphous drugs and solid dispersions within a reasonable time frame. Although many studies on the physical stability of amorphous materials have been reported,1,6,7 to the best of our knowledge, a reliable methodology to estimate the long-term physical stability of amorphous solids has yet to be developed. Most of the published literature has been focused on measuring the crystal growth kinetics from the amorphous state, rather than the nucleation process. Attention has been directed toward enthalpy relaxation and fragility parameters which reflect mobility, one of the determining factors of nucleation and crystal growth. Although the correlation between those parameters and physical stability of amorphous solids is reasonably well established,8 it is still relatively difficult to translate these parameters directly into an estimate of the shelf life of amorphous drugs under regular storage conditionsdone of the most critical factors in determining the probability of success for developing an amorphous solid dispersion. In searching for a better and more predictive method, isothermal microcalorimetry was identified as a potential alternative for overcoming the shortcomings associated with the existing methods, owing to its high sensitivity, continuity of response over time, and labor-saving sample preparation characteristics. A thermal activity monitor (TAM), the most frequently used isothermal microcalorimeter, has been widely used for studying the kinetics of chemical reactions (e.g., degradation, drug-excipient compatibility) and/or physical processes (e.g., relaxation, crystallization) of sample substances at a constant temperature.9,10 Herein we describe a methodology mainly using isothermal microcalorimetry and a modified Arrhenius model to estimate the long-term physical stability of amorphous ritonavir (RTV) and its solid dispersions from studies carried out under accelerated test conditions. In addition to the experimental approaches, we will discuss in detail both data interpretation and the scientific rationale for such predictions as a function of temperature and RH. The effects of excipients on the physical stability of amorphous RTV solid dispersions will also be characterized and discussed.

Theory Crystallization from the amorphous state evolves from a combination of thermodynamic factors, coupled to dynamic factors controlled in large part by molecular mobility. For quantitative understanding of crystallization from the amorphous state, both of these factors must be considered. From the classical theory, the

rates of nucleation (I) and growth (U) can be expressed by the following equations11:


I ¼ Ae

 DGD þDGK RT



(1)


 v i h  DG RT U ¼ k=h 1  e

(2)

where DGD is the Gibbs free energy change for the formation of a nucleus, a thermodynamic term related to supersaturation or supercooling; DGK is the Gibbs free energy associated with the transport of molecules across an interface, a dynamic term related to mobility. In Equation 2, R is a temperature-independent constant, h is viscosity, 1/h is a dynamic factor describing the effect of molecular mobility; 1exp(DGv/RT) is the thermodynamic driving force of crystal growth where k is a constant and DGv is the free energy difference between the amorphous and crystalline phases. In accelerated studies, temperature and RH are commonly the major variables, and the effects of such parameters on thermodynamic and kinetic factors must be taken into consideration. There are many ways to show the dual effects of temperature and RH. Consider an amorphous solid that is undergoing some type of spontaneous transformation at a rate constant k'. We can write an expression that combines the thermodynamic driving force for the transformation and the kinetic barrier primarily controlled by the dynamics in the amorphous solids, that is, molecular mobility. To generalize this latter factor we can express it in terms of free volumedthe greater the free volume, the greater the molecular mobilitydexpressed12 as Equation 3:

" 0

0

kT ¼ A e

!# ERTa 

V* Vf

(3)

where V* is the critical volume for molecular mobility and Vf is the free volume.11 Here we assume that the thermodynamic part is governed by the Arrhenius equation with the activation energy (Ea) as the major barrier. The second term (V * =Vf ) represents the ratio of the critical volume needed for molecular motion to the free volume of the solid. When Vf is large relative to V*, as in solution, the term (V * =Vf ) approaches zero, and Equation 3 collapses to the simple Arrhenius equation. Equation 3 can be used to account for factors related to the transformation itself and those determined by the physical state of the solid that influences the rate. Thus Equation 3 may also be considered as a different mathematical expression for Equations 1 and 2 with similar physical meaning. Genton and Kesserling developed an empirical expression, Equation 4, for the effects of temperature and RH on solid state reactions,13 which is based on Equation 3:

ðArrhenius model with humidityÞ

  Ea þ bh ln kT;h ¼ lnðAÞ  RT (4)

In Equation 4, b is considered to be a moisture sensitivity term independent of temperature, h is relative humidity, Ea is the apparent activation energy, A is the Arrhenius pre-exponential factor, and kT,h is the rate constant under a given condition. Studies on chemical reactivity, particularly demonstrated by Waterman et al.,14 show that some “predictions” of long-term chemical stability as a function of absolute temperature T and relative humidity h were quite good. Equation 4 assumes, with

D. Zhu et al. / Journal of Pharmaceutical Sciences xxx (2016) 1e8

reasonable validity, that the temperature dependence of b is negligible in the narrow range of temperatures studied and that the natural logarithm of the rate constant has a linear dependence on h. In this study, we use similar equations involving induction time (t) and crystallization time (tx%t) as reflections of nucleation and crystal growth rates, expressed as Equations 5 and 6 respectively:

!

3

for at 25 C and at a particular RH, say 60% for example, under which the water content (wc) of the amorphous sample is 2.5%.

! EN a bN 2:5 R298

t298; 2:5% ¼ Ae

(7)

The pre-exponential factor A, in turn, can be expressed as Equation 8:

!

EN a bN wc RT

t ¼ Ae

EN

a bN 2:5R298

(5) A ¼ t298;2:5% e

! EG a bG wc RT

tx%  t ¼ Ae

(6)

In Equation 5, wc is the water content of the sample under particular conditions obtained from the moisture isotherm. Given the nonlinear relationship between moisture absorption and RH, particularly at the transition region from moderate to high RH, water content was used in the equations. t is the induction period, reflecting the overall nucleation rate (f I1) at which primary nucleation can occur. In Equation 6, tx% is the time required for a given percentage, x, of amorphous material to crystallize. In this study, we have taken 5% as a criterion for estimating crystal growth rate. The induction period, t, and tx% can be determined from the power versus time curve obtained using TAM, as shown in Figure 1. In Equations 5 and 6, EaN and EaG represent the apparent activation energies for nucleation and crystal growth, respectively. EaN and EaG are mainly governed by the combination of DGD with DGK or DGv. Those 2 activation terms, EaN and EaG , are also affected by molecular mobility and may be related to the fragility of the material as well. An additional “free volume-dependent” term, bN or bG, is linked to the effects of moisture absorption, wc, on free volume. In accelerated studies, t and t5% under various test conditions were measured. Two approaches can be taken to calculate t or t5% under regular storage conditions from such accelerated data. One approach is to solve for Ea, b, and the pre-exponential factor A by fitting the experimental data using model Equations 5 and 6. The value for t(298,2.5% wc)dinduction period for a given amorphous solid which has 2.5% weight gain of moisture at 25 C, for instance, can then be calculated. However, solving for the pre-exponential A term and the propagation of errors associated with all the estimated values proved to be problematic. Thus in this study we took another approach, the approach of King et al.15 to obtain the estimated values. In brief, in this approach we can rewrite Equation 5 as Equation 7, where t(298,2.5% wc) is the estimated value we aim

(8)

Substituting the A term in Equation 5 by Equation 8 leads to Equation 9:

"
EN a R

tT1 ;wc1 ¼ t298;2:5% e

#

 1 1 T1 298

b ðwc1 2:5Þ N

(9)

Equation 9 can be further rewritten, by taking the natural logarithm of both sides, as follows:

    EN ln tT1 ;wc1 ¼ ln t298;2:5% þ a R




 1 1  bN ðwc1  2:5Þ  T1 298 (10)

where tT1 ;wc1 is the induction period under the stressed condition T1 and wc1. By fitting the data (time) obtained from accelerated studies to Equation 10, EaN , bN , and t under the selected storage condition (e.g., 25 C, 60% RH) can be estimated along with their respective standard deviations, using conventional nonlinear regression methods. The estimation of crystal growth time described as t5%t can be conducted in a similar fashion and expressed as follows:

lnðt5%  tÞT1 ;wc1 ¼ lnðt5%  tÞ298;2:5% þ  bG ðwc1  2:5Þ


EaG 1 1  R T1 298 (11)

where t5%;T1 ;wc1 is the time required for 5% crystal growth obtained under the stressed condition T1 and RH1, where the amorphous sample gains wc1% of water. There are 2 key assumptions in this approach: both A and Ea terms are constant in the temperature range of interest. The preexponential factor A for amorphous solids is generally considered to be independent of temperature; although this assumption is reasonable over small temperature ranges (e.g., 20-60 C), it is not valid over wide temperature ranges. Although the activation energy term Ea for primary nucleation may be a constant in the temperature range which is below the Tmax of its nucleation rate, it may or may not be the case for crystal growth. Zhu et al.16 and Zhou et al.17 recently reported a discontinuity of crystal growth rate and its temperature dependence across Tg in some dry amorphous drugs, such as nifedipine and griseofulvin. Experimental Methods Material

Figure 1. Representative TAM thermal trace.

RTV, an inhibitor of HIV protease, discovered and developed in Abbott Laboratories (Abbott Park, IL) was used in this study. HPMC acetate succinate (HPMCAS) was purchased from Shinetsu and was used as received. The salts used to control RH including potassium acetate, potassium carbonate, sodium bromide and sodium

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D. Zhu et al. / Journal of Pharmaceutical Sciences xxx (2016) 1e8

chloride were purchased from Sigma (St. Louis, MO). Methanol (HPLC grade) was purchased from Spectrum (Gardena, CA).

Results Characterization of Amorphous RTV and RTV-HPMCAS ASD

Characterization of Solid Dispersions The amorphous RTV and RTV-HPMCAS (90/10) spray-dried solid dispersion (RTVSDD) were prepared at lab-scale using a Pro-C-epT microcapacity spray dryer (Procept, Zelzate, Belgium). The feed solutions containing 7.5% total solids loading were prepared in a 500 mL media jar containing 200 mL methanol. A stir bar was added and the feed solution was stirred until the excipients were dissolved. The solutions were placed into a 20 mL syringe that was then inserted into a syringe pump. The solvent was rapidly removed from the above solution by spraying into the spray dryer. They were equilibrated under 4 RH environments (e.g., 22%, 44%, 57%, and 75% RH) at ambient temperature for at least 2 days before measuring the Tg (mid-point). Sealed T-zero pans without pinhole were used. Samples were first equilibrated at 20 C, then heated up to 120 C at 20 C/min using a differential scanning calorimetry (Q-2000; TA Instruments, New Castle, DE). Moisture isotherms of amorphous samples at different temperatures were evaluated on a dynamic moisture sorption balance (IGAsorp; Hiden Isochema, Warrington, UK) equipped with a data analyzer (IGAsorp version 6.0.0.23; Hiden Isochema). The balance was calibrated using standardized weights of 20, 50, and 100 mg. The RH probe was calibrated using standardized saturated salt solutions of lithium chloride, potassium carbonate, and sodium chloride. During the experiment, the flow rate of nitrogen gas at different RH was maintained at 250 mL/min.

Crystallization Measurements Using TAM

Crystallization of Amorphous RTV and RTV-HPMCAS ASD Monitored by TAM The crystallization process, including nucleation and crystal growth, of amorphous samples was monitored by TAM under various stressed conditions. The data mapping and calculation of estimated induction periods, t, and time for 5% crystal growth, t5%, under less stressed conditions were conducted as described in Theory. Two 3-dimensional maps of t versus wc and T and t5%t versus wc and T are shown in Figures 4 and 5. All the pure amorphous RTV samples crystallized as RTV Form I, the kinetically favored metastable polymorph, as confirmed by powder X-ray diffraction. The crystallization process of RTV-HPMCAS ASD samples was monitored in the same manner as the amorphous RTV samples. In contrast to amorphous RTV, all the solid dispersion samples crystallized as a mixture of RTV Form I and Form II, with the majority as Form II, the most stable form. Two 3-dimensional maps of t versus h and T and t5%t versus h and T are shown in Figures 6 and 7. The apparent activation energy Ea, moisture sensitivity parameter b, for both primary nucleation t and crystal growth t5%t of amorphous RTV and RTV-HPMCAS ASD, calculated using the water content % (wc) determined in the sample as an input, are listed in Table 1. Long-Term Stability Measurement The real time-long term stability results of amorphous RTV and RTV-HPMCAS ASD under conditions including 30 C/75% RH and

70 60 50

Tg (C)

Crystallization of RTV either in its amorphous form or in solid dispersions was detected at various combinations of temperatures (e.g., 40 C, 52 C, 56 C, and 60 C) and RH using isothermal microcalorimetry (TAM model 2277; Thermometric AB, Sweden). Amorphous solids (approximately 200 or 300 mg) were loaded into a stainless steel calorimeter cell with an insert containing saturated salt solution, such that the powder was physically separated from the liquid, but was exposed to the vapor produced by the saturated salt solution. The stainless steel cell was sealed with an air-tight stopper and lowered into the measuring position of the calorimeter after approximately 30 min of temperature equilibration. Pure crystalline solids or crystalline solids with physically mixed polymers were loaded into the reference cell as controls. Because the enthalpy change for water vaporization is approximately equal and opposite to that for condensation of the vapor onto the solid, or can be minimized by control, the measured net enthalpy in this system should result from heat of crystallization and form conversion. The measured values, including onset (t) and t5%t, were fitted to the models as described in Theory using SigmaPlot 9.0 (Systat Software Inc., San Jose, CA).

As shown in Figure 2, the Tg of amorphous RTV and RTVHPMCAS ASD equilibrated under various RH at ambient temperatures shows a good linear relationship with RH. These values were further used to guide the selection of the temperatures for the isothermal crystallization studies using TAM. The dynamic moisture sorption isotherms of amorphous RTV and RTV-HPMCAS ASD were evaluated at different temperatures used in the isothermal crystallization studies and long-term stability studies. The sample remained amorphous during the entire experiment. For one example of data shown in Figure 3, we can see that RTV-HPMCAS ASD gains more water than amorphous RTV across all RHs at 40 C, and that moisture absorption versus RH% does not follow a linear relationship. This trend holds true at all the temperatures studied.

40 30

Long-Term Stability Measurement 20

RTV and its amorphous solid dispersion were stored under less stressful conditions such as 30 C/57% RH, 30 C/75% RH and 40 C/ 44% RH. The samples were examined periodically for crystallization using an X-ray diffractometer (UltimaTM II D/Max-2000-PC with model SA-HF3 3 kW X-ray generator; Rigaku, Woodlands, TX). In this study, we assumed that the first sign of crystallization detected by X-ray corresponded to 5% crystallization.

10 0 0

10

20

30

40 RH (%)

50

60

70

80

Figure 2. Glass transition temperatures of amorphous RTV and RTV-HPMCAS ASD as a function of relative humidity. , RTV-HPMCAS ASD; , amorphous RTV.

D. Zhu et al. / Journal of Pharmaceutical Sciences xxx (2016) 1e8

5

4.5 4

Weight Change (%)

3.5 3 2.5 2 1.5 1 0.5 0 0

10

20

30

40

50

60

70

80

RH (%)

Figure 3. Moisture sorption isotherm of amorphous RTV and RTV-HPMCAS ASD at 40 C. , RTV-HPMCAS ASD; , amorphous RTV.

40 C/44% RH are summarized in Table 2, along with the predicted values. The sum of estimated t (primary nucleation) and t5%t (5% of crystallization) agrees well with the measured values under some less stressed conditions where all the temperatures are below the wet Tg of the amorphous samples at any given RH. These results indicate that the empirical model developed in this study was able to predict the long-term physical stability of amorphous RTV samples within a certain degree of accuracy and confidence using the data generated at temperature above Tg. Due to the low crystallization tendency of RTV, for samples stored at 30 C/57% RH a longer time is needed to observe the occurrence of crystallization. Real time stability of those samples was collected and no sign of the crystallization was detected for at least 18 months. In addition to its mean value, lower one-standard deviation confidence intervals (68% CI) are also listed in Table 2. These were calculated using King’s approach as described in Theory. Such wide calculated CIs under normal conditions may result from many factors including the nature of Arrhenius-type extrapolation, the relatively small sample size, applicability of the model, and the nature of nucleation. With

Figure 4. Three-dimensional data mapping of t vs. water content and temperature for amorphous RTV. Red circles ( ) represent measured data and black net lines represent fitted planes (R2 ¼ 0.94).

Figure 5. Three-dimensional data mapping of t5%t vs. water content and temperature for amorphous RTV. Red circles ( ) represent measured data and black net lines represent fitted planes (R2 ¼ 0.95).

respect to the last factor, many published accounts have reported the randomness of nucleation for a given compound.18 Discussion The Goodness of the Model and Its Limitations Given the practical purpose of estimating long-term stability of amorphous solids under relevant storage conditions, an expanded Arrhenius model (Eqs. 5 or 6) was developed. This model stems from Equation 3, which can account for factors related to the transformation itself and those determined by the physical state of

Figure 6. Three-dimensional data mapping of t vs. water content and temperature for RTV-HPMCAS ASD (90/10). Red circles ( ) represent measured data and black net lines represent fitted planes (R2 ¼ 0.94).

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D. Zhu et al. / Journal of Pharmaceutical Sciences xxx (2016) 1e8

which will be discussed in detail in the following section. The correlation between natural logarithm of the predicted t (mean) and those measured under less stressed conditions is shown in Figure 8. Due to the technical difficulty of determining the onset of crystallization using X-ray for experiments lasting months or longer, the lower ends listed in Table 2 were used in the plot as measured values. Given some inherent experimental errors, a slope of 0.95 and R2 of 0.97 demonstrates the feasibility of using the model to estimate the physical stability of RTV amorphous systems even in a conservative scenario where crystallization may not occur yet. Thus, from a practical perspective how well the model can predict the induction period t rather than 5% crystal growth, t5%, becomes critical. Some key factors, theories, or assumptions for describing nucleation are evolving. Lee et al.20 recently proposed a 2-step nucleation theory based on the results of the nucleation induction time of lysozyme. This evolution will certainly benefit our work on estimating induction time by adding more terms and/or by expressing the existing terms more correctly in the future. The Effect of Temperature and Humidity on Crystallization Figure 7. Three-dimensional data mapping of t5%t vs. water content and temperature for RTV-HPMCAS ASD (90/10). Red circles ( ) represent measured data and black net lines represent fitted planes (R2 ¼ 0.96).

the solid that influences the rate, such as temperature and RH. Although similar models have been shown to be feasible for estimating the long-term chemical stability of solid pharmaceuticals as a function of T and % RH,14 this is the first study, to our knowledge, to apply such an approach to determine the physical stability of amorphous drug in ASD. Because of the complexities of nucleation and crystal growth mechanisms, Equations 5 or 6 must be considered to be oversimplified as exemplified by the large CIs discussed in previous section. For instance, one complexity, probably the most important one for crystal growth, involves the potential discontinuity in temperature dependence of crystal growth rate across Tg due to the imperfect or different correlation between mobility and growth rate.13 Similar to the crystal growth, discontinuity of temperature dependence of the nucleation rate may also occur in some systems, primarily due to polymorphism. One good example is the nucleation of amorphous indomethacin. It nucleates the g polymorph at low temperatures, but the a polymorph at high temperatures; each with its own nucleation rate-temperature dependence.19 Although we did not observe a similar discontinuity in the amorphous RTV, it certainly could create some uncertainties when extrapolating induction periods from highly stressed conditions to regular storage conditions for compounds behaving like indomethacin. Another complexity or uncertainty arises from the lack of a clear understanding of the nucleation mechanism for small molecules, from either solution or amorphous, largely due to analytical difficulties. As demonstrated in Table 2, the induction periods are always much longer than the time required to reach 5% crystal growth. This suggests a nucleation rate determined mechanism,

Table 1 Estimated Model Parameters for Amorphous RTV and RTV-HPMCAS ASD (90/10) Variable

Ea (KJ/mol)

RTV (nucleation) RTV (5% crystallization) RTV-HPMCAS ASD (nucleation) RTV-HPMCAS ASD (5% crystallization)

255 128 245 157

± ± ± ±

20.7 9.6 21.9 11.2

b 0.75 0.42 1.20 0.94

± ± ± ±

0.14 0.06 0.12 0.07

With regard to the effects of temperature and humidity on crystallization, the effects of humidity come primarily from effects on molecular mobility, and particularly on the primary a relaxations associated with whole molecule translational and rotational diffusion. Temperature affects both molecular mobility (as reflected in fragility) and thermodynamic driving forces. A model proposed originally by Genton and Kesselring (Eq. 4),13 and applied more recently by Waterman et al.,14 adds an additional term for the effects of humidity on the classical Arrhenius equation. Its exponential form is given as follows:


Ea kT;%RH ¼ A exp bh  RT

(12)

In the above equations, h is the water activity or relative humidity expressed as % RH (ranging from 0% to 100%). Typical values of b ranged from 0.01 to 0.09 in the literature surveyed by Waterman et al.14 for chemical reactions. The lower the b value, the less sensitive the solid is to moisture. To estimate the effect of moisture on the physical stability (nucleation and crystal growth) of amorphous solids, we applied a similar concept as expressed by Equations 5 and 6. In these 2 equations, b reflects the effects of humidity, in terms of water content, on free volume and molecular mobility for amorphous solids. A large b value in Equation 5 or 6 usually indicates high sensitivity to moisture for a given system. Compared with pure amorphous RTV, the RTV-HPMCAS ASD has higher b values for both primary nucleation and crystal growth, indicating that moisture has a bigger impact on the physical stability of the solid dispersion than on amorphous RTV. Such a difference is, most likely, due to the hydrophilic nature of the polymer, HPMCAS. The difference in moisture sorption isotherms between amorphous RTV and the RTV-HPMCAS ASD is also consistent with the rank order with respect to their b terms. Because the effect of humidity on t can be quantitatively described as bwc or bh, in addition to estimating the shelf life, it leads to several other practical applications of using the b term, such as selecting the optimal RH for storage or packaging of amorphous drug products and having a good risk assessment for accidental moisture exposure. The b term may also guide us to select the optimal solid dispersion formulations which have a physical stability that is less sensitive to moisture. This application is exemplified by Figure 9 where the estimated induction periods (t) for amorphous RTV and the RTVHPMCAS ASD were plotted as a function of RH at 25 C. Given the

D. Zhu et al. / Journal of Pharmaceutical Sciences xxx (2016) 1e8

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Table 2 Estimated t and t5%t Values and Real-Time Stability for Amorphous RTV and RTV-HPMCAS ASD Amorphous System

Condition

Amorphous RTV

25 C/75% 30 C/75% 30 C/57% 40 C/44% 40 C/75% 25 C/75% 30 C/75% 30 C/57% 40 C/44% 40 C/75%

RTV-HPMCAS ASD

RH RH RH RH RHa RH RH RH RH RHa

Tg/T

Predicted Mean t (months; One-Standard Deviation CI Low Boundary)

Predicted Mean t5%t (months; One-Standard Deviation CI Low Boundary)

Measured Real-Time Value (months)

1.32 1.11 1.35 1.22 0.84 2.03 1.69 1.85 1.43 1.27

23.0 (13.0) 4.0 (2.5) 15.3 (9.1) 1.0 (0.7) 0.2 (0.1) 26.0 (13.0) 7.5 (4.2) 59.8 (30.8) 3.1 (2.1) 0.3 (0.2)

1.8 0.7 1.3 0.4 0.1 3.6 1.7 8.7 1.3 0.1

14 < t < 15 2
(1.3) (0.6) (1.0) (0.3) (0.1) (2.5) (1.3) (6.1) (1.1) (0.1)

NSC, no sign of crystallization by powder X-ray diffraction. a For samples, 40 C/75% RH was measured by TAM; the time was reported as induction period measured by TAM. For samples under other conditions, which were measured by X-ray, the data were reported as intervals in which no sign of crystallization was reported at lower end while peaks were detected at higher end.

similar apparent Ea values for nucleation as listed in Table 1, a crossover point between 20% and 40% RH for those 2 amorphous solids exist that could be mainly attributed to differences in their b terms. A similar trend was recently reported for felodipine solid dispersion systems by Rumondor et al.4 At high RH, felodipine in polyvinylpyrrolidoneebased ASD crystallized much faster than that in the HPMCAS-based ASD, in spite of the similar crystallization inhibition ability for those 2 polymers at lower RH. In their studies, the authors concluded that the physical stability of solid dispersions as a function of RH is highly dependent on the polymer. It would be interesting to see if such dependency could have been quantitatively described by b terms, in the model discussed in this article. The Importance of Nucleation Versus Crystal Growth As described in Theory, the apparent activation energy Ea, which is governed by a combination of DGD and DGK (or DGv), indicates big differences between the temperature dependences of nucleation and crystal growth for amorphous RTV and its HPMCAS-based solid dispersion. As listed in Table 2, the estimated induction period is much longer than the t5%t values for amorphous RTV, under the same conditions, indicating that the physical stability of amorphous RTV is mainly dictated by its primary nucleation kinetics. The larger Ea of primary nucleation (255 ± 20.7 kJ/mol) over that of crystal growth (128 ± 9.6 kJ/mol) reflects the higher energy barrier needed to be overcome for nucleation than for crystal growth.

In general, factors primarily related to nucleation govern rates of the first appearance of crystals during crystallization from the amorphous state, as well as the polymorphic form that is created. Thus, the primary nucleation should be dominant in most cases. The situation with solid dispersions could be more complex. For example, it is possible that the presence of the polymer in a molecular mixture simply acts as a diffusion barrier, and does not affect the thermodynamic factors. The interaction between active pharmaceutical ingredient (API) and polymer may also influence parameters governing nucleation rates disproportionately. It is very difficult to assess whether secondary factors could affect nucleation. For the case of RTV-HPMCAS ASD, based on estimated time listed in Table 2 and Ea values of primary nucleation (245 ± 21.9 kJ/mol) and crystal growth (157 ± 11.2 kJ/mol), the physical stability of the amorphous RTV solid dispersion is also governed by its primary nucleation. Of course, it is important to recognize that in some cases the method of preparing the amorphous materials might produce “seeds” that would favor secondary nucleation and more importantly crystal growth. However, regardless of which factors influence nucleation, if nucleation cannot occur, then crystallization will not occur. It is even possible that although nucleation occurs to a critical size, growth cannot occur. For instance, the local mobility of the drug may allow nucleation to occur, but be insufficiently high to cause growth. Thus, it may be a reasonable assumption that the nucleation in amorphous solid dispersions is the most critical mechanism related to physical stability. Given the practical goal to achieve more than 2-year shelf life for an amorphous drug-based product, a higher priority should be placed on preventing or

50 3

y = 0.9535x - 0.1717 2

LN (Measured Value, months)

2.5

R = 0.9742

2 1.5 1 0.5 0 -1.5 -0.5

-1

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

Estimated Induction Time (year)

3.5

45 40 35 30 25 20 15 10 5

-1

0

-1.5

0

-2

10

20

30

40

50

60

70

RH (%) LN (Predicted Value, months)

Figure 8. Correlation between predicted t and measured values.

Figure 9. Estimated induction period at 25 C as a function of relative humidity. RTV-HPMCAS ASD; , amorphous RTV.

,

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D. Zhu et al. / Journal of Pharmaceutical Sciences xxx (2016) 1e8

delaying nucleation. In this study, we used isothermal microcalorimetry to determine the induction period, which reflects the overall rate (f I1) at which primary nucleation can occur. This method has proven to be one of the most sensitive and quantitative means to characterize nucleation kinetics. Focusing on nucleation not only can significantly reduce the experimental time, since it is not necessary to monitor the entire crystallization process, but more importantly, it allows us to circumvent the potential complexity of crystal growth, such as the discontinuity of temperature dependence of crystal growth rates across Tg. In contrast, direct experimental studies of nucleation mechanisms or kinetics are not easily done in a routine and rapid manner. It is interesting to discover that all pure amorphous RTV samples crystallized as RTV Form I under the stressed conditions tested. In comparison, RTV in the RTV-HPMCAS ASD crystallized as a mixture of Form I and Form II. This raises the general question about polymorphic selection upon crystallization from the amorphous state and the influence of additives and environment. For a pure amorphous API, upon approaching crystallization, the most unstable crystal form, which is closest in energy to the “liquid,” will tend to crystallize first. Indeed, pure amorphous RTV has been shown to follow that rule, the so-called Ostwald21 step-rule. However, the situation with solid dispersions made with polymers is, of course, more complex. Is the polymer simply a diffusion barrier for nucleation and growth, or is the manner in which the polymer hydrogen bonds with the API affecting the interfacial energy to the extent that certain polymorphs are favored? These are the fundamental questions that need to be addressed more fully in the future. Conclusions In conclusion, we have utilized isothermal microcalorimetry to monitor the crystallization process of amorphous RTV and its HPMCAS-based solid dispersion under various conditions. An expanded Arrhenius model appears feasible for estimating the long-term physical stability under less stressed conditions based on the short-term data generated under accelerated conditions. A nonlinear approach initially developed by King et al.15 is applied in the data analyses to minimize the propagation of errors associated with the estimates. For amorphous RTV and the RTV-HPMCAS ASD, its physical stability appears to be mainly governed by primary nucleation. The impact of polymer and moisture on the crystallization process can be quantitatively described as a function of the apparent activation energy Ea and moisture sensitivity parameter b in this empirical model. The large calculated CIs of estimated values under normal conditions indicate the need for continued improvements in the proposed model. A better understanding of the fundamentals, of both nucleation and crystal growth, will definitely enhance our ability to make more precise long-term predictions.

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