Predicted amorphous solubility and dissolution rate advantages following moisture sorption: Case studies of indomethacin and felodipine

Accepted Manuscript Predicted Amorphous Solubility and Dissolution Rate Advantages Following Moisture Sorption: Case Studies of Indomethacin and Felodipine Peter J. Skrdla, Philip D. Floyd, Philip C. Dell'Orco PII: DOI: Reference:

S0378-5173(18)30857-3 https://doi.org/10.1016/j.ijpharm.2018.11.042 IJP 17935

To appear in:

International Journal of Pharmaceutics

Received Date: Revised Date: Accepted Date:

19 September 2018 1 November 2018 15 November 2018

Please cite this article as: P.J. Skrdla, P.D. Floyd, P.C. Dell'Orco, Predicted Amorphous Solubility and Dissolution Rate Advantages Following Moisture Sorption: Case Studies of Indomethacin and Felodipine, International Journal of Pharmaceutics (2018), doi: https://doi.org/10.1016/j.ijpharm.2018.11.042

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Predicted Amorphous Solubility and Dissolution Rate Advantages Following Moisture Sorption: Case Studies of Indomethacin and Felodipine Peter J. Skrdla*, Philip D. Floyd and Philip C. Dell’Orco

GlaxoSmithKline, 1250 S. Collegeville Road, Collegeville, Pennsylvania, USA 19426

For submission to: International Journal of Pharmaceutics

*corresponding author e-mail: [email protected] tel: 908-361-1548 (mobile)

Predicted Solubility Advantage

2

8

Amorphous Indomethacin

7 6

Amorphous Felodipine

5 4

3 2

1 0 0.0

0.2

0.4

0.6

0.8

1.0

Mole Fraction of Drug

Graphical Abstract Water is often readily absorbed by amorphous compounds, lowering their glass transition temperature (Tg) and facilitating their recrystallization (via nucleation-and-growth). At the same time, the increase in moisture content translates to a decrease in both the thermodynamic solubility and intrinsic dissolution rate, as compared to the corresponding dry (pure) amorphous phase, e.g. see [Murdande SB, Pikal MJ, Shanker RM, Bogner RH. 2010. Solubility advantage of amorphous pharmaceuticals: I. A thermodynamic analysis. J Pharm Sci 99:1254-1264.]. In the case of pure indomethacin and felodipine, the solubility advantage of each amorphous phase over its crystalline counterpart were previously determined to be 7.6 and 4.7, respectively, using a new methodology together with basic calorimetric data taken from the literature. Herein, we demonstrate that, theoretically, following the uptake of just ~ 0.5% w/w water, the solubility ratios decrease to 6.9 and 4.5, in the same order. Moreover, as the predicted intrinsic dissolution rate (based on the Noyes-Whitney equation) is directly proportional to the solubility advantage of a given amorphous-crystalline pair, it decreases proportionately upon moisture uptake. Applying the methodology presented herein, one can directly predict the extent of Tg-lowering observed at any moisture content, for a given amorphous phase. Knowing that value, it is possible to estimate the relative decrease in the solubility and/or intrinsic dissolution rate of the plasticized phase compared to the pure glass, and vice-versa. Key Words: amorphous, Gordon-Taylor equation, plasticizer, solubility advantage, Noyes-Whitney, Nernst-Brunner, intrinsic dissolution rate

3 1. Introduction 1.1 Background and Goals It has been estimated that between 75% and 90% of new drug candidates in development and at least 40% of marketed oral solid dosage (OSD) products require specialized, “bio-enhanced” formulations, e.g., leveraging amorphous solid dispersion (ASD) or hot melt extrusion (HME) technology to help overcome their solubility limitations1-3. From ref. [4], polymorphic (crystalline) phase selection can provide at most a 2-fold increase in solubility, while the use of a non-crystalline phase can often achieve closer to a 10-fold enhancement. And while the use of salts can likewise generate a significant solubility advantage5, many compounds (e.g., APIs; active pharmaceutical ingredients) are not readily ionizable. And if they are, the disproportionation6 risks associated with salts requires thoughtful consideration during development. The successful progression of poorly bioavailable drug candidates in development can be better enabled through greater fundamental understanding of non-crystalline phases. The aim of this work is to put forth a methodology for the accurate prediction of the thermodynamic solubility and intrinsic dissolution rate enhancement (advantage) offered by non-crystalline compounds containing different amounts of absorbed water. The interest in water, in the present work, stems from the propensity of amorphous phases to absorb moisture from the atmosphere7. Water has a known plasticizing effect on amorphous drugs that is a widespread and challenging problem in the context of amorphous phase stabilizatione.g.8. Different routes of preparation, as well as thermal history, can impart differences to the relative thermodynamic energy of a given glass, as can the duration and conditions (temperature, humidity) of its storage9,14. The addition of excipients, common to most ASD and HME formulations10,11, that help stabilize the amorphous phase (e.g. by increasing the system Tg and/or inhibiting nucleation of the active pharmaceutical ingredient) can contribute further complexity to the mathematical treatment for the accurate prediction of physical properties (solubility, dissolution rate, Tg-lowering). The aim of this work is to take a first step in understanding of amorphous mixture behavior, through the examination of binary systems of the API and water. Longer term, the extension of this scientific approach to more common ternary systems, containing an excipient, would further enable the understanding and design of relevant pharmaceutical products. Returning to the problem at hand, it is widely accepted that water can accelerate the recrystallization of amorphous APIs8,10,11,14-17. However, its impact on the solubility of the amorphous phase relative to the crystalline phase (which can be calculated algebraically using a methodology put forth recently by the authors9) has remained less clear. Curiously, “solubility advantage” calculations for pure compounds have been historically plaguede.g.18 by over-predictinge.g.9,12 the maximum solubility enhancement that is observed experimentally (often severely); moreover, some popular treatments lack definitive conclusions9. Important factors in the accurate determination of the solubility advantage were discussed previously, in the context of pure phases9. However, from a practical perspective, including water in the predictions

4 can be an important consideration as it is a well-known plasticizer that lowers the glass transition temperature (Tg) of the material19 and, resultantly, accelerates its recrystallization20. While correlations have been attempted/established21-23 that link the recrystallization kinetics to some other physicochemical property of the material, such as the primary dielectric relaxation rate of the glassy composite, the authors are unaware of a first-principles thermodynamic treatment of the Tg-lowering effect being put forth in the literature, to-date, that, in turn, allows for the direct prediction of the thermodynamic solubility and intrinsic dissolution rate. This work seeks to answer the two fundamental questions: Is there a physical basis for linking the observed Tg-lowering to the thermodynamic description of a given system that can be used to predict the solubility enhancement of the amorphous phase relative to the crystalline phase after it is plasticized? What kind of intrinsic dissolution rate enhancement might one expect, before and after an amorphous phase has absorbed a given amount of water from the atmosphere? These questions will be addressed in the present work using two different model compounds, indomethacin and felodipine (selected because of the significant amount of physicochemical data available on them in the literature), with water serving as the plasticizer, in common. Despite this limited “sample set”, the relationships put forth are thought to be sufficiently general to be applicable to most glassy compounds (including some polymeric systemse.g.24) whose composite mixtures give rise to a single Tg.

1.2. Theory 1.2.1. Amorphous Solubility Advantage of a Pure Compound The increased oral bioavailability of amorphous compounds9-11, relative to their crystalline counterparts, comes about because of their higher solubility and faster (intrinsic) dissolution rate that, fundamentally, are linked to their metastable nature. This thermodynamic instability originates predominantly from the lack of a lattice energy to stabilize the solid structure, thus imparting a greater diversity of molecular environments within the glass. Solubility enhancements often have finite duration i.e., they are transient in nature8,12 (hence the term “kinetic solubility”, which can be considered against the backdrop of the spring-and-parachute model25 often used in biopharmaceutics) due to the potential for recrystallization. Recrystallization comes about because the amorphous solubility generates supersaturation relative to the solubility of the crystalline phase, triggering nucleation of the latter13. Note that the kinetic solubility will not be considered further herein. Regarding the thermodynamic solubility, one can define the solubility ratio, , of a given compound (API) as follows: (1) where the numerator, aa, represents the activity of a saturated solution of the amorphous phase and the denominator, ax, is the corresponding activity of the dissolved crystalline phase, both at standard temperature and pressure (STP) and fixed pH, ionic strength. Note that drug ionization is a solution

5 phase phenomenon that is determined by the pKa(s) of the molecule; as the pKa is not a solid-state property, it does not factor into Eq. 1. Consequently, the solubility enhancement offered by a given amorphous phase over its crystalline counterpart is generally not a function of the pKa (e.g. disregarding disproportionation). That is because dissolution must precede ionization and, once in solution, the pKa is the same regardless of whether a given drug molecule originated from an amorphous phase or crystalline one. The higher concentration of ionized molecules in solution that can be measured in equilibrium with an amorphous solid is simply a reflection of the higher overall concentration of dissolved drug (solubility enhancement), per Eq. 1, particularly at dilute levels (for poorly soluble APIs, like the ones presented in this work, that are candidates for “amorphization”). The solubility ratio is related to a Gibbs free energy difference between the two solid phases, ∆Ga-x, at a given temperature, T, per: (2) where R is the Universal Gas constant. In the absence of comparative solubility measurements (which can suffer from complications noted elsewhere9), ∆Ga-x can be estimated from thermo-analytical data. In accordance with Fig. 1, it was shown previously that9: (3) where T is the temperature of interest (selected to be 298 K in this work) for determining the solubility advantage, T2 is a common temperature that falls between Tg and the fusion/melting temperature, Tf, T1 is a second, common temperature falling below Tg, and is the Gibbs free energy change associated with the formation of the crystal lattice. Using Eq. 3,  values (“solubility advantages”) were previously calculated for the two APIs of interest in this work—felodipine and indomethacin—estimated to be 7.6 and 4.7, respectively9, at room temperature.

1.2.2. Linear Dependence of Tg on the Moisture Content: The GT and DGT Equations

The traditional Gordon-Taylor (GT) equation26 phenomenologically relates the commonly observed linear variation in Tg, as a function of the weight fraction of a given component, in a (binary) glassy composite that exhibits a single glass transition falling between the Tg values of each of the pure components. It is frequently written as follows: (4)

6 where wA is the weight fraction of the lower Tg phase (plasticizer), wB is the weight fraction of the higher Tg material (drug), and are the respective glass transition temperatures of each of the pure substances in °C and k is a proportionality constant that can be (crudely) estimated using different approximations27,28 or extracted via the (often time-consuming) construction of empirical plots9 following Eq. 4. While intermolecular (attractive or repulsive) forces can cause deviations (positive or negative) from linearity29, the GT equation is easily extended to multiple-component glasses, so long as the linearity is retained30. In a recent work31, the authors modified the GT equation to allow the direct prediction of k based on standard thermo-analytical quantities that are available in the literature (or readily measured), thereby facilitating accurate Tg predictions in binary systems without the need for construction of empirical plots. In linear form32,33, this modified equation, hereby called the Detailed Gordon-Taylor (DGT) equation (in part, because it is derived from first principles using basic thermodynamics), is written as: (5) The Tg-lowering effect on the drug (see Fig. 1) predicted by Eq. 5 is related by the term, (in degrees Kelvin), while the corresponding increase in the Tg value of the composite relative to that of component A (pure water, in our case) is given by , with the respective mole fractions of each component being related by the x terms. The new (unit-less) constant, k’’, whose detailed physical interpretation is provided elsewhere31, is defined through the relationships: ;

(6)

to remove its dependence on the mole ratio. Its value is determined using standard thermo-analytical quantities (of both of the pure phases in the binary composite glass) using the following:

(7)

where

is the (constant pressure) heat capacity change associated with the glass transition

temperature of pure compound A (water), having units of JK-1mol-1, is that of pure B (drug), R is -1 -1 the Universal Gas constant (8.3144 JK mol ) and the other parameters are as described above. Eq. 7 allows one to predict k’’ directly and, hence, to calculate the value of k for any system composition (mole ratio). Then, by inputting the resulting k values into Eq. 5, one can reconstruct the linearized Gordon-Taylor plot for any system of interest—without collecting any additional data, experimentally.

2. Results and Discussion

7

2.1. Estimated Tg-Lowering as a Function of Water Content: Predicted GT Plots for Indomethacin-Water and Felodipine-Water Systems, With and Without Intermolecular Interactions Using the values provided in Table 1, one can leverage the DGT equation to determine the extent of Tg lowering due to moisture sorption, at various water contents, for each system of interest. Those values are summarized in Table 2. Applying the k values determined at each system composition, the predicted (reconstructed) GT plots for both systems of interest are plotted in Fig. 2. While both plots exhibit satisfactory linearity, there is a slight bias in the k values as a function of mole fraction (they are not randomly distributed around the mean value); in both cases, giving rise to a slight curvature in the plots that contributes to the observed non-zero intercepts. Note that error bars are not included in any of the plots in this work because they are all theoretical, calculated using only a handful of experimental parameters taken from the literature (that are held constant throughout). Solving the DGT equation for

and combining the result with Eqs. 6 and 7 yields:

=

(8)

Eq. 8 directly links the amount of moisture in the system to the predicted degree of Tg-lowering. Resultantly, using Eq. 8, one can estimate the water content giving rise to a specific extent of Tg depression or, conversely, knowing the moisture content in the glass, one can predict the Tg-lowering relative to the pure (anhydrous) amorphous phase. To this point, only ideal behavior (i.e., non-interacting systems) has been considered. To treat non-ideal behavior, which can cause deviations from linearity in Gordon-Taylor plots, the DGT equation requires further modification to account for the effects of intermolecular interactions. To this end, one can leverage the values of the Flory-Huggins (F-H) interaction parameter34-36, Θ, that were determined elsewhere37 for both the indomethacin-water and felodipine-water systems; they are 2.50 and 3.18 (obtained at 25°C and 95% RH), respectively. Then, by applying the Margules activity model, in its simplest modality38, one can replace the mole quantity of interest in Eq. 8, , as follows: (9) to obtain the new result:

8

=

(10)

Fig. 3 shows a comparison of the predictions of both Eq. 8 and Eq. 10 for the indomethacin-water system. While both plots exhibit the expected negative correlation, the pronounced nonlinearity exemplified by Eq. 10 at intermediate values was deemed worthy of further consideration with regard to its potential impact on the predicted Gordon-Taylor plot. For that reason, Fig. 4 was constructed; it shows that the linearity is improved by the incorporation of the interaction term (into this “modified DGT” equation), for both systems of interest. The linear regression fit quality is improved, supporting the notion that the use of Eq. 10 is more reflective of reality in treating these two systems.

2.2. Solubility-Lowering of Plasticized Amorphous Phases as a Function of Water Content: Ideal and Non-Ideal Mixing

To determine the solubility advantage following moisture uptake by a pure amorphous compound, one can leverage the thermodynamics of mixing as a first approximation. Recent works similarly investigating this effect are found in refs. [39, 40], providing a parallel thermodynamic treatment to the one described below. In an ideal solution, whereby the two components are non-interacting (so that the enthalpy of mixing is zero; , the Gibbs free energy41 is lowered (i.e., the glassy composite is stabilized) solely as the result of an increase in the entropy of mixing (which is maximized at = = 0.5), per the equalities: (11) The mixing is irrespective of the nature of components, A and B, in the ideal case. The solubility impact of this mixing is captured by modifying Eq. 3 as follows: (12) whereby the “adjusted amorphous solubility enhancement”, the mixing contribution from Eq. 11.

, following moisture sorption, includes

On the other hand, in non-ideal mixtures, an energetic contribution stemming from the intermolecular interactions between components A and B must be incorporated into Eq. 11, per Flory-Huggins theorye.g.42-44, as noted earlier. Doing so yields:

9 (13) where Θ is the F-H interaction parameter (that can be measured using various techniques45,46, including melting point depression47). Regardless of whether the ideal relationship in Eq. 11 or its non-ideal counterpart, Eq. 13, is applied, one can summarize: (14) whereby was determined previously9, at T = 298 K, for both indomethacin and felodipine (using T2 = 355K and 373K, respectively). Summarized in Table 2 and plotted in Fig. 5 are the predicted solubility advantages for each drug, as a function of water content, whereby Eq. 14 is applied to reflect both the ideal and “real-world” scenarios. Note that in the latter case, since the Θ values are both > 2, one might expect that thermodynamicallydriven phase separation (akin to liquid-liquid phase separation41,47) could occur at intermediate levels of the moisture content (i.e., as the point, xA = xB = 0.5, is approached) due to the presence of the two minima38 in Fig. 5B. Fig. 5A shows that in the ideal mixing case the maximal reduction in amorphous solubility advantage, independent of the drug and/or plasticizer, is always observed at exactly . Arbitrarily selecting 10 mol% moisture sorption (representing ~ 0.56% w/w and ~ 0.52% w/w water, for indomethacin and felodipine, respectively), one could expect solubility enhancements of 5.5-fold and 3.4-fold for amorphous indomethacin and amorphous felodipine, in the same order, over their respective crystalline counterparts. These values represent a 38% decrease in the absolute solubility advantage provided by the neat amorphous drug. On the other hand, per the theoretical plots in Fig. 5B and tabulated values in Table 3, the “real-world” solubility enhancements are estimated to be closer to 6.9-fold and 4.6-fold, accordingly – mirroring losses in solubility advantage of only ~10% and ~4%, in the same order (these differences are sufficiently small that they might not be noticeable if experimental data were to be generated). Interestingly, from that figure it is also possible to observe that while the optimal solubility advantage at higher moisture contents likewise occurs at , in the case of felodipine-water, it (5.2) is predicted to exceed the solubility enhancement provided by the pure amorphous phase (4.7). As discussed earlier, this behavior represents deviation from ideality (e.g. Raoult’s law, for a dilute solution) and it can also reflect a tendency of the system to phase-separate/demix at moisture contents approaching 50 mol%. The negative deviation from the ideal/linear case, shown in Fig. 3, suggests endothermic mixing with unfavorable drug-water interactions. Applying Eq. 10 (see also Table 3 and Fig. 4), one finds that when the Tg is lowered by ~6 degrees for indomethacin, i.e., , then xA = 0.059 (0.32% w/w water) and the solubility advantage drops to ~ 7.0. Likewise, for felodipine-water, for almost the same extent of Tg-lowering, the solubility advantage over its pure crystalline form is ~ 4.5, which is, in turn, linked to a water content of 0.30% w/w.

10 Regarding the use of Flory-Huggins theory, in general, the authors acknowledge the limitation in predicting the solubility enhancements of hydrophilic APIs in aqueous media that can be important in biorelevant assessments (in addition to the other simplifying assumptions inherent in that theory). Fortunately, bio-enhanced (amorphous) formulations are most often applied to poorly soluble, hydrophobic compounds that are not readily ionizable.

2.3. Intrinsic Dissolution Rate Reduction of a Plasticized Amorphous Drug as a Function of Water Content

The dissolution rate, dC/dt, predicted by the Noyes-Whitney/Nernst-Brunner equation48,49 is written in differential form as: (15) where D is the diffusion coefficient, S is the surface area of the dissolving interface (approximately equivalent to the area of the diffusion layer), V is the mean particle volume, h is the diffusion layer thickness and CS is the saturation solubility of the drug. Under sink conditions (CS >> C), assuming also that S and h are the same for both the crystalline and amorphous phases, by holding both D (a molecular, not solid-state, property) and V fixed, one can see that the dissolution rate is directly proportional to CS. Therefore, per Table 2, one would expect, to a first approximation, the intrinsic dissolution rate of pure amorphous indomethacin to be 7.6 times faster than that of the crystalline phase, whereas with xA = 0.1 (equivalent to 0.52% w/w) water the amorphous mixture would realize only a 6.9-fold dissolution rate enhancement over the crystalline drug (before it precipitates oute.g.9). Likewise, at the same molar concentration of water (corresponding to 0.56% w/w), plasticized amorphous felodipine can be expected to have a 4.5-fold dissolution rate advantage over its pure, crystalline drug counterpart. The “dissolution rate ratio”, β, can be determined for a given system using the relationships:

(16)

where the subscript, B, is hereby selected to denote the pure crystalline drug while A-B denotes the amorphous drug containing some amount of absorbed moisture (molar basis). Applying an intrinsic dissolution rate of 3.35 x 10-2 µmol.cm-2.min-1 (equivalent50 to 0.2 µg/cm2/s), the predicted dissolution curves for amorphous indomethacin containing 0.1 mole equivalents of water (assuming no precipitation and neglecting any hydration of the amorphous phase that might be required prior to dissolution) as well as pure, crystalline indomethacin, are plotted in Fig. 6. Those plots were obtained using an integrated, concentration-normalized form of Eq. 15:

11

(17) where Cmax represents the final concentration of the dissolved solid that depends on the solubility of the drug, the system volume, and the amount of solid put into the vessel at t = 0. Similar plots (not shown) can be constructed for amorphous (containing various amounts of water) and crystalline felodipine, showing similar behavior.

2.4. Towards Predicting/Modeling Ternary Behavior

With a line-of-sight to predicting the solubility and intrinsic dissolution rate enhancements of amorphous solid dispersions (ASDs), this section presents two additional equations that could be useful in that goal. Following from Eq. 5 and treating each pairwise interaction independently, in a ternary system comprised of A, B and C, the overall extent of Tg-lowering of phase B (e.g. the drug) can be described mathematically via the following equation: (18) whereby, in a typical scenario, A might be the plasticizer (e.g. water) and C the polymer. Each of the two constants in Eq. 18 can be determined separately, as described above, using Eq. 7. Thus, the expected degree of Tg-lowering of the drug depends on the relative amounts of both the water and polymer as well as the relevant thermal parameters of each phase. The Gibbs free energy of mixing in the ternary system can be written as follows, in accordance with F-H theory: (19) where the terms represent volume fractions (due to the dramatic size difference between the polymer and drug/water), while the other parameters are as described in Eq. 13. Using Eq. 19 in Eq. 14, one can estimate the solubility (and maximum dissolution rate) enhancement of the ternary system.

3. Conclusions

For many OSD formulations, solubility and dissolution rate play a key role in achieving clinically relevant exposures in the body. While a pure amorphous phase can be expected to have a higher solubility, and exhibit faster dissolution kinetics, relative to its crystalline counterpart, the absorption of moisture from the atmosphere can prove detrimental – not just in enhancing the rate of recrystallization of the drug,

12 but, as shown in this work, by reducing its solubility and (intrinsic) dissolution rate advantages and, ultimately, limiting the in vivo performance. Building on a recent work31, a new methodology is put forth herein that allows the direct prediction (via the DGT/modified DGT equation) of the moisture content in each amorphous drug that correlates with a specific extent of Tg-lowering (of the compound), and vice-versa. Those predictions can be input into equations to further predict the solubility advantage and dissolution rate enhancement provided by the plasticized amorphous phase, across varying moisture contents. While the present treatment focuses on binary systems, it can be readily extended to multiple-component glassy mixtures (alternatively, to consider plasticizers other than water, such as glycerol24). A logical next step for this work is to extend it to ternary and quaternary systems40 that tend to be more realistic. Moreover, including a recrystallization rate component into the dissolution rate (enhancement) equation could make it more reflective of real-world behavior. On the other hand, the equations put forth herein also suggest that if one experimentally measures the solubility (or intrinsic dissolution rate) enhancement of a system, together with the amount of plasticizer/water contained therein (or the extent of Tg-lowering), then one can use the relationships provided herein to determine the F-H parameter, Θ, in an orthogonal manner to approaches described in the previous literaturee.g.34-37, 45-47 . For instance, by experimentally measuring knowing xA (and, therefore, xB) of the binary system, one can use Eq. 14 (or Eq. 12 together with the thermal quantities in Table 1, as described in ref. [31]) to estimate . The value of , in turn, allows one to solve Eq. 13 to determine Θ.

13

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14 15. Trasi NS, Purohit HS, Taylor LS. 2017. Evaluation of the crystallization tendency of commercially available amorphous tacrolimus formulations exposed to different stress conditions. Pharm Res 34:2142-2155. 16. Mehta M, Suryanarayanan R. 2016. Accelerated physical stability testing of amorphous dispersions. Mol Pharm 13:2661-2666. 17. Rumondor ACF, Stanford LA, Taylor LS. 2009. Effects of polymer type and storage relative humidity on the kinetics of felodipine crystallization from amorphous solid dispersions. Pharm Res 26:2599-2606. 18. Hancock BC, Parks M. 2000. What is the true solubility advantage for amorphous pharmaceuticals? Pharm Res 17:397-404. 19. Hancock BC, Zografi G. 1994. The relationship between the glass transition temperature and the water content of amorphous pharmaceutical solids. Pharm Res 11:471-477. 20. Konno H, Taylor LS. 2008. Ability of different polymers to inhibit the crystallization of amorphous felodipine in the presence of moisture. Pharm Res 25:969-978. 21. Alhalaweh A, Alzghoul A, Mahlin D, Bergström CAS. 2015. Physical stability of drugs after storage above and below the glass transition temperature: Relationship to glass-forming ability. Int J Pharm 495:312-317. 22. Graeser KA, Patterson JE, Zeitler JA, Gordon KC, Rades T. 2009. Correlating thermodynamic and kinetic parameters with amorphous stability. Eur J Pharm Sci 37:492-498. 23. Fung MH, Suryanarayanan R. 2017. Use of a plasticizer for physical stability prediction of amorphous solid dispersions. Cryst Growth Des 17:4315-4325. 24. Yuan X, Sperger D, Munson EJ. 2013. Investigating miscibility and molecular mobility of nifedipine-PVP amorphous solid dispersions using solid-state NMR spectroscopy. Mol Pharm 11:329-337. 25. Brouwers J, Brewster ME, Augustijns P. 2009. Supersaturating drug delivery systems: the answer to solubility-limited oral bioavailability? J Pharm Sci 98:2549-2572. 26. Gordon M, Taylor JS. 1952. Ideal copolymers and the second-order transition of synthetic rubbers, I. non-crystalline copolymers. J Appl Chem 2:493-500. 27. Simha R, Boyer RF. 1962. On a general relation involving the glass transition temperature and coefficient of expansion of polymers. J Chem Phys 37:1003-1007. 28. Fox TG. 1956. Influence of diluents and of copolymer composition on the glass temperature of a polymer system. Bull Am Phys Soc 1:123-125. 29. Kalogeras IM. 2010. Description and molecular interpretations of anomalous compositional dependences of the glass transition temperatures in binary organic mixtures. Thermochim Acta 509:135-146. 30. Lu Q, Zografi G. 1998. Phase behavior of binary and ternary amorphous mixtures containing indomethacin, citric acid and PVP. Pharm Res 15:1202-1206. 31. Skrdla PJ, Floyd PD, Dell’Orco PC. 2017. The amorphous state: first-principles derivation of the Gordon-Taylor equation for direct prediction of the glass transition temperature of mixtures; estimation of the crossover temperature of fragile glass formers; physical basis of the “rule of 2/3”. Phys Chem Chem Phys 19:20523-20532.

15 32. Penzel E, Rieger J, Schneider HA. 1997. The glass transition temperature of random copolymers: 1. Experimental data and the Gordon-Taylor equation. Polymer 38:325-337. 33. Schneider HA, Rieger J, Penzel E. 1997. The glass transition temperature of random copolymers: 2. Extension of the Gordon-Taylor equation for asymmetric Tg vs composition curves. Polymer 38:1323-1337. 34. Nedoma AJ, Robertson ML, Wanakule NS, Balsara NP. 2008. Measurements of the Flory-Huggins interaction parameters using a series of critical binary blends. Ind Eng Chem Res 47:3551-3553. 35. Liu Y, Shi B. 2008. Determination of Flory interaction parameters between polyimide and organic solvents by HSP theory and IGC. Polymer Bull 61:501-509. 36. Pajula K, Taskinen M, Lehto V-P, Ketolainen J, Korhonen O. 2010. Predicting the formation and stability of amorphous small molecule binary mixtures from computationally determined FloryHuggins interaction parameter and phase diagram. Mol Pharm 7:795-804. 37. Rumondor ACF, Marsac PJ, Stanford LA, Taylor LS. 2009. Phase behavior of poly(vinylpyrrolidone) containing amorphous solid dispersions in the presence of moisture. Mol Pharm 6:1492-1505. 38. Atkins P, de Paula J. Physical Chemistry, 7th ed., Freeman & Co., New York, 2001, p. 148. 39. Li N, Taylor LS. 2018. Tailoring supersaturation from amorphous solid dispersions. J Control Release 279:114-125. 40. Huang S, Mao C, Williams III RO, Yang C-Y. 2016. Solubility advantage (and disadvantage) of pharmaceutical amorphous solid dispersions. J Pharm Sci 105:3549-3561. 41. Donnelly C, Tian W, Potter C, Jones DS, Andrews GP. 2015. Probing the effects of experimental conditions on the character of drug-polymer phase diagrams constructed using Flory-Huggins theory. Pharm Res 32:167-179. 42. Calahan JL, Azali SC, Munson EJ, Nagapudi K. 2015. Investigation of phase mixing in amorphous solid dispersions of AMG 517 in HPMC-AS using DSC, solid-state NMR, and solution calorimetry. Mol Pharm 12:4115-4123. 43. Marsac PJ, Li T, Taylor LS. 2009. Estimation of drug-polymer miscibility and solubility in amorphous solid dispersions using experimentally determined interaction parameters. Pharm Res 26:139-151. 44. Meng F, Dave V, Chauhan H. 2015. Qualitative and quantitative methods to determine the miscibility in amorphous drug-polymer systems. Eur J Pharm Sci 77:106-111. 45. Knopp MM, Tajber L, Tian Y, Olesen NE, Jones DS, Kozyra A, Löbmann K, Paluch K, Brennan CM, Holm R, Healy AM, Andrews GP, Rades T. 2015. Comparative study of different methods for the prediction of drug-polymer solubility. Mol Pharm 12:3408-3419. 46. Marsac PJ, Shamblin SL, Taylor LS. 2006. Theoretical and practical approaches for prediction of drug-polymer miscibility and solubility. Pharm Res 23:2417-2426. 47. Ilevbare GA, Taylor LS. 2013. Liquid-liquid phase separation in highly supersaturated aqueous solutions of poorly water-soluble drugs: Implications for solubility enhancing formulations. Cryst Growth Des 13:1497-1509. 48. Wurster DE, Taylor PW. 1965. Dissolution rates. J Pharm Sci 54:169-175. 49. Dokoumetzidis A, Macheras P. 2006. A century of dissolution research: From Noyes and Whitney to the Biopharmaceutics Classification System. Int J Pharm 321:1-11.

16

Specific Volume, Enthalpy

50. Shekunov B, Montgomery ER. 2016. Theoretical analysis of drug dissolution: I. Solubility and intrinsic dissolution rate. J Pharm Sci 105:2685-2697.

T’g Tg

T’f Tf

Temperature

Figure 1. Schematic depiction of the origins of the glass transition temperature, Tg, and melting/fusion temperature, Tf, of the amorphous and crystalline phases, respectively, of a pure compound. While the __

former is a first-order phase transformation ( ), the latter is second-order, per the Ehrenfest classification. The Tf-lowering (so-called “freezing point depression”, T’f) occurs to a lesser extent than the corresponding Tg-lowering upon the introduction of a fixed amount of a plasticizer, such as water, to

17 the pure compound. Recrystallization is often kinetically faster for a plasticized amorphous drug in the solid-state (---); it is energetically closer to the crystalline phase.

400 350 300 250 200 150 100 50 0 0

20

40

60

80

100

120

140

160

180

▪

Figure 2. Predicted (Eq. 5) GT plots for indomethacin-water (•) and felodipine-water ( ), using the methodology described in ref. [31] and the literature parameters summarized in Table 1. The units of each axis are in degrees Kelvin. The mole fraction of water in each system is given by xA whilst that of the drug is xB. The broken lines represent linear regression fits to the predicted data points (summarized in Table 2). The slope, intercept and fit quality (R2) of each line is as follows (including the point (0,0) ….

….

that is not shown in the above plots): 2.139, -6.2 and 0.9989 ( ); 2.213, -7.2 and 0.9986 ( ). A small bias is apparent in that the lines do not pass through the origin.

18

1.0 0.9

Predicted xB

0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0.0

0.2

0.4

xA

0.6

0.8

1.0

▪

Figure 3. Predicted plots of xB as a function of xA using Eq. 8 (•) and Eq. 10 ( ) in the text, for the indomethacin-water system (Θ = 2.50). The data points are plotted in increments of ΔxA = 0.05. Ideally, xB = 1 - xA is linear, such that the expected plot mirrors the blue line, which is actually a linear regression fit to the data points predicted by Eq. 8 (undefined at xA = 0), having R2 = 1. The non-ideality captured via Θ in Eq. 10 causes notable deviation from linearity and whose impact on the corresponding GT plot is depicted in Fig. 4.

19

450 400

350 300 250 200 150 100 50 0 0

Figure 4.

50

100

150

200

▪

Predicted “modified DGT” plots for indomethacin-water (•) and felodipine-water ( ),

including the relevant F-H interaction term for each system (see also Table 3). The units of each axis are in degrees Kelvin. The mole fraction of water in each system is given by xA whilst that of the drug is xB. The broken lines represent linear regression fits to the predicted data points. The slope, intercept and fit quality (R2) of each line are as follows (including the point (0, 0) that is not shown in the above plots): ….

….

2.174, -4.9 and 0.9994 ( ); 2.270, -8.5 and 0.9992 ( ). The two plots show improved linearity over the corresponding plots in Fig. 2.

20

A

B Predicted Solubility Advantage

Predicted Solubility Advantage

8

8

7 6 5 4 3

2 1

0 0.00

0.20

0.40

0.60

xA

0.80

1.00

7 6

5 4 3 2 1 0 0.00

0.20

0.40

0.60

0.80

1.00

xA

Figure 5. Comparison of solubility behavior of ideal and non-ideal (“real-world”) systems of amorphous APIs plasticized by water (see Table 2). A: Predicted solubility advantage (over the corresponding, thermodynamically stable crystalline phase) of amorphous indomethacin (•) and amorphous felodipine

▪

( ) at different mole ratios of absorbed moisture (xA), assuming ideal mixing in Eq. 14. B: Predicted

▪

solubility advantage of amorphous indomethacin (•) and amorphous felodipine ( ) at different mole ratios of water (xA), applying the drug-water interaction (F-H) parameters, 2.50 and 3.18, respectively, taken from ref. [37]. Both sets of axes are unit-less.

21

1.0 0.9

Fraction Dissolved

0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0

10

20

30

40

50

60

t (min) Figure 6.

Predicted concentration-normalized dissolution transients for amorphous indomethacin

▪

containing xA = 0.1 (~ 0.56% w/w) water ( ) and for pure, crystalline indomethacin (•) over the initial 60 min of dissolution time (T = 298 K). The latter curve is plotted using the intrinsic, kinetic dissolution rate from ref. [50], while the red curve reflects a 6.9-fold dissolution rate enhancement for the plasticized amorphous phase, per Eq. 17 in the text. For each curve, the data points are plotted are at 1-minute intervals; sink conditions are assumed in both cases.

22

Table 1. Physical parameters of interest for pure indomethacin, felodipine and water, extracted from ref. [9] and ref. [31]. Compound

M.W. (g/mol)

Tf, K

Tg, K

ΔCp,Tg, JK-1mol-1

Indomethacin

357.8

435

315

161

Felodipine

384.3

415

320

250

Water

18.015

373

138

32.77

23

Table 2. Summary of values used in the determination of k’’ (see Eq. 7) and k in the DGT equation (per the plots in Fig. 2), as well as the predicted, idealized solubility enhancements for the indomethacinwater and felodipine-water systems (α’; plotted in Fig. 5A). The mean value (%RSD) of k is 1.98 (4.9%) for indomethacin-water and 2.03 (5.4%) for the felodipine-water system.

xB

xA

%w/w water/ indo

%w/w water/felo

k", indowater

k", felowater

k, indowater

Tg, indowater k, felowater

1.00

0.00

0.00

0.00

N/A

N/A

N/A

N/A

0.95

0.05

0.32

0.25

29.03

35.44

1.83

1.87

0.90

0.10

0.56

0.52

16.64

16.93

1.85

1.88

0.85

0.15

0.88

0.82

10.56

10.76

1.86

1.90

0.80

0.20

1.24

1.16

7.51

7.66

1.88

1.92

0.75

0.25

1.65

1.54

5.68

5.80

1.89

1.93

0.70

0.30

2.11

1.97

4.45

4.55

1.91

1.95

0.65

0.35

2.64

2.46

3.57

3.65

1.92

1.97

0.60

0.40

3.25

3.03

2.91

2.98

1.94

1.99

0.55

0.45

3.96

3.69

2.39

2.45

1.96

2.00

0.50

0.50

4.79

4.48

1.97

2.02

1.97

2.02

0.45

0.55

5.80

5.42

1.63

1.67

1.99

2.04

0.40

0.60

7.02

6.57

1.34

1.38

2.01

2.06

0.35

0.65

8.55

8.01

1.09

1.12

2.03

2.08

0.30

0.70

10.5

9.86

0.87

0.90

2.04

2.11

0.25

0.75

13.1

12.3

0.69

0.71

2.06

2.13

0.20

0.80

16.8

15.8

0.52

0.54

2.08

2.15

0.15

0.85

22.2

21.0

0.37

0.38

2.10

2.17

0.10

0.90

31.2

29.7

0.24

0.24

2.12

2.19

0.05

0.95

48.9

47.1

0.11

0.12

2.14

2.22

0.00

1.00

100.0

100.0

0

0

N/A

N/A

Tg-TgA, indowater

TgB - Tg, indowater

0

0

310.1

9.1

4.9

305.0

18.6

299.7

Tg-TgA, felowater

TgB - Tg, felowater

α' ideal, indo

α' ideal, felo

0

0

7.6

4.7

315.0

9.3

5.0

6.2

3.9

10.0

309.9

19.1

10.1

5.5

3.4

28.5

15.3

304.5

29.4

15.5

5.0

3.1

294.2

39.1

20.8

299.0

40.2

21.0

4.6

2.8

288.5

50.2

26.5

293.2

51.7

26.8

4.3

2.7

282.5

61.9

32.5

287.2

63.9

32.8

4.1

2.6

276.3

74.5

38.7

280.9

76.9

39.1

4.0

2.5

269.7

87.8

45.3

274.3

90.8

45.7

3.9

2.4

262.8

102.1

52.2

267.2

105.7

52.8

3.8

2.4

255.5

117.5

59.5

259.8

121.8

60.2

3.8

2.4

247.7

134.0

67.3

251.9

139.2

68.1

3.8

2.4

239.3

152.0

75.7

243.4

158.1

76.6

3.9

2.4

230.3

171.5

84.7

234.2

178.7

85.8

4.0

2.5

220.7

192.9

94.3

224.3

201.4

95.7

4.1

2.6

210.1

216.4

104.9

213.5

226.5

106.5

4.3

2.7

198.6

242.4

116.4

201.6

254.4

118.4

4.6

2.8

185.9

271.4

129.1

188.4

285.6

131.6

5.0

3.1

171.8

304.0

143.2

173.7

321.0

146.3

5.5

3.4

155.9

340.9

159.1

157.0

361.4

163.0

6.2

3.9

N/A

177.0

N/A

182.0

N/A

N/A

(predicted) 315.0

320.0

138.0

xA = mole fraction of water (plasticizer) xB = mole fraction of drug indo = indomethacin

Tg, felowater (predicted)

138.0

24 felo = felodipine α’ ideal = solubility enhancement determined using Eq. 14, assuming no drug-water interaction N/A = not applicable

Table 3. Summary of values used in the determination of k’’ (see Eq. 7) and k in the “modified DGT” equation, for the indomethacin-water and felodipine-water systems (plotted in Fig. 4). The mean value (%RSD) of k is 2.08 (5.2%) for indomethacin-water and 2.13 (6.0%) for the felodipine-water system. Shown in the far-right columns are the corresponding solubility enhancement (α’) values, plotted in Fig. 5B. Tg, indowater k", felowater

k, indowater

k, felowater

Tg-TgA, indowater

TgB - Tg, indowater

0

0

Tg, felowater (predicted)

Tg-TgA, felowater

TgB - Tg, felowater

xB, indo

xA, water

xB, felo

xA, water

k", indowater

1.000 0.941

0.000 0.059

1.00 0.940

0.000 0.060

N/A 29.06

N/A 29.30

N/A 1.84

N/A 1.87

0

0

309.1

10.8

5.9

314.0

11.2

0.848

0.152

0.854

0.146

10.39

11.11

1.86

1.90

299.5

29.0

15.5

305.0

0.708

0.292

0.740

0.260

4.62

5.51

1.91

1.94

283.5

60.0

31.5

0.534

0.466

0.606

0.394

2.25

3.05

1.96

1.98

260.6

106.8

0.367

0.633

0.468

0.532

1.17

1.79

2.02

2.04

233.5

0.238

0.762

0.342

0.658

0.65

1.09

2.07

2.09

0.155

0.845

0.240

0.760

0.39

0.67

2.10

0.105

0.895

0.164

0.836

0.25

0.42

0.075

0.925

0.110

0.890

0.17

0.058

0.942

0.074

0.926

0.046

0.954

0.051

0.038

0.962

0.031

(predicted)

α', indo 7.6

α', felo 4.7

6.0

7.0

4.5

28.5

15.0

6.8

4.7

292.0

54.1

28.0

7.0

5.1

54.4

275.1

89.1

44.9

7.1

5.3

164.7

81.5

254.8

132.8

65.2

7.0

4.9

207.6

222.1

107.4

232.8

182.0

87.2

6.9

4.4

2.13

187.2

268.5

127.8

211.2

231.8

108.8

6.9

4.1

2.12

2.16

173.2

300.7

141.8

192.1

276.8

127.9

6.9

4.1

0.27

2.13

2.19

164.2

321.6

150.8

176.8

313.5

143.2

6.9

4.1

0.13

0.18

2.14

2.21

158.5

335.0

156.5

165.4

341.1

154.6

7.0

4.3

0.949

0.10

0.12

2.15

2.22

154.6

344.1

160.4

157.3

360.7

162.7

7.0

4.4

0.036

0.964

0.08

0.08

2.15

2.22

151.8

350.8

163.2

151.8

374.2

168.2

7.1

4.5

0.969

0.025

0.975

0.07

0.06

2.15

2.23

149.5

356.0

165.5

148.0

383.5

172.0

7.1

4.6

0.026

0.974

0.018

0.982

0.06

0.04

2.15

2.23

147.6

360.5

167.4

145.3

390.0

174.7

7.2

4.6

0.021

0.979

0.013

0.987

0.05

0.03

2.16

2.24

145.9

364.5

169.1

143.4

394.7

176.6

7.2

4.7

0.017

0.983

0.010

0.990

0.04

0.02

2.16

2.24

144.3

368.3

170.7

141.9

398.3

178.1

7.3

4.7

0.012

0.988

0.007

0.993

0.03

0.02

2.16

2.20

142.7

372.1

172.3

140.8

401.2

179.2

7.3

4.7

0.008

0.992

0.004

0.996

0.02

0.01

2.20

2.20

141.1

375.8

173.9

139.8

403.6

180.2

7.4

4.7

0.004

0.996

0.002

0.998

0.009

0.005

2.20

2.20

139.6

379.5

175.4

138.9

405.9

181.1

7.5

4.7

0.000

1.000

0.000

1.00

0

0

N/A

N/A

N/A

177.0

N/A

182.0

N/A

N/A

315.0

320.0

138.0

xA = mole fraction of water (plasticizer) xB = mole fraction of drug

138.0

25 indo = indomethacin felo = felodipine α’ = solubility enhancement determined using Eq. 14, including the F-H interaction parameter of each system N/A = not applicable

Predicted Solubility Advantage

26

8

Amorphous Indomethacin

7 6

Amorphous Felodipine

5 4

3 2

1 0 0.0

0.2

0.4

0.6

0.8

1.0

Mole Fraction of Drug

Graphical Abstract Water is often readily absorbed by amorphous compounds, lowering their glass transition temperature (Tg) and facilitating their recrystallization (via nucleation-and-growth). At the same time, the increase in moisture content translates to a decrease in both the thermodynamic solubility and intrinsic dissolution rate, as compared to the corresponding dry (pure) amorphous phase, e.g. see [Murdande SB, Pikal MJ, Shanker RM, Bogner RH. 2010. Solubility advantage of amorphous pharmaceuticals: I. A thermodynamic analysis. J Pharm Sci 99:1254-1264.]. In the case of pure indomethacin and felodipine, the solubility advantage of each amorphous phase over its crystalline counterpart were previously determined to be 7.6 and 4.7, respectively, using a new methodology together with basic calorimetric data taken from the literature. Herein, we demonstrate that, theoretically, following the uptake of just ~ 0.5% w/w water, the solubility ratios decrease to 6.9 and 4.5, in the same order. Moreover, as the predicted intrinsic dissolution rate (based on the Noyes-Whitney equation) is directly proportional to the solubility advantage of a given amorphous-crystalline pair, it decreases proportionately upon moisture uptake. Applying the methodology presented herein, one can directly predict the extent of Tg-lowering observed at any moisture content, for a given amorphous phase. Knowing that value, it is possible to estimate the relative decrease in the solubility and/or intrinsic dissolution rate of the plasticized phase compared to the pure glass, and vice-versa. Key Words: amorphous, Gordon-Taylor equation, plasticizer, solubility advantage, Noyes-Whitney, Nernst-Brunner, intrinsic dissolution rate