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Evaluation of accuracy of amorphous solubility advantage calculation by comparison with experimental solubility measurement in buffer and bio-relevant media Wei Zhang, Abbe Haser, Hao Helen Hou, and Karthik Nagapudi Mol. Pharmaceutics, Just Accepted Manuscript • DOI: 10.1021/acs.molpharmaceut.8b00125 • Publication Date (Web): 09 Mar 2018 Downloaded from http://pubs.acs.org on March 12, 2018
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Molecular Pharmaceutics
Evaluation of accuracy of amorphous solubility advantage calculation by comparison with experimental solubility measurement in buffer and bio-relevant media Wei Zhang, a,† Abbe Haser,b,† Hao Helen Hou,a and Karthik Nagapudia,* a
Small Molecule Pharmaceutical Sciences, Genentech Inc., South San Francisco, CA 94080. b College of Pharmacy, University of Texas-Austin, Austin, TX 78712. †Equal contribution. *Corresponding author
ABSTRACT The accuracy of amorphous solubility advantage calculation was evaluated by experimental solubility measurement. Ten structurally diverse compounds were studied to test the generality of the theoretical calculation. Three reported methods of calculating Gibbs free energy difference between amorphous and crystalline solids were evaluated. Experimental solubility advantage was measured by direct dissolution of amorphous solid in buffer. When necessary, hydroxypropyl methylcellulose acetate succinate (HPMCAS) was pre-dissolved in buffer to inhibit desupersaturation. By direct dissolution, the effect of different preparation methods on amorphous solubility was also studied. Finally, solubility measurement was performed in Fasted State Simulated Intestinal Fluid (FaSSIF) to assess the effect of bile salt on the concentration-based amorphous solubility advantage. The results showed that the assumption of constant heat capacity differences between crystal and supercooled liquid or amorphous solid is sufficient for accurate theoretical calculation, which is attributed to the fact that the heat capacity of crystal is nearly parallel to that of supercooled liquid or amorphous solid. Different preparation methods do not have significant impact on amorphous solubility advantage. Experimental measurement agrees with the theoretical calculation within a factor of 0.7 to 1.8. The concentration-based amorphous solubility advantage in FaSSIF agrees well with theoretical calculation. This work demonstrates that theoretical calculation of
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amorphous solubility advantage is robust and can be applied in early drug development for assessing the utility of amorphous phase. Keywords: solubility advantage, amorphous, crystal, thermodynamics, supersaturation.
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Molecular Pharmaceutics
INTRODUCTION In drug development for oral administration, sufficient aqueous solubility is required for absorption. However, a significant number of drug molecules are poorly water soluble.1,2 Among various solubility enhancement methods, the use of amorphous solids is an attractive one as the increased solubility by an amorphous form does not come at the expense of reduced molecular permeability.3 Strictly speaking, the term “solubility” does not apply to an amorphous solid since it is a non-equilibrium system. Practically, a sustained plateau concentration after dissolution of an amorphous solid can be defined as its apparent solubility. Prior to formulation development, it is critical to know the amorphous solubility advantage to decide if it is worth investing in amorphous formulation development. However, it has been shown that accurate measurement of amorphous solubility is difficult due to crystallization.4,5,6 Therefore theoretical calculation of amorphous solubility advantage can provide valuable insight at early stage of drug development.4,5 The most commonly used model to predict amorphous solubility advantage in buffer was developed by Murdande et al, 5 and is shown in equation 1:
= exp (
∆ →
) ∙ exp [−( )]
(1)
In equation 1, Sa and Sc are the solubility of amorphous and crystal solids, respectively. ∆Gc→a is the Gibbs free energy difference between amorphous and crystal solids. Exp[-I (a2)] represents amorphous solubility reduction caused by the impact of water sorption on the chemical potential of a molecule in the amorphous state. In literature, three methods have been reported to calculate ∆Gc→a.5,7,8 ∆→ = ∆→ = [∆ − ∆
∆→ = (∆ + *
∆ ( )∙
(2)
!,→#$ ⁄
!, +&
∙ (& − &)] − & ∙ (
− *
!,#$ ⁄ +&)
∆
−&∙(
−∆
∆
!,→#$ ⁄ ,-,
+ *
∙ '(
)
(3)
,-,./⁄
+& − *
+&)
(4)
In these equations, ∆Hm and Tm are the melting enthalpy and temperature, Cp,c and Cp,sl/a the heat capacity of crystal, supercooled liquid or amorphous solid, ∆Cp,c→sl/a the heat capacity difference between crystal and 3 ACS Paragon Plus Environment
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supercooled liquid or amorphous solid. In equations (3) and (4), when the temperature of interest T is below glass transition temperature, Tg, Cp, sl and ∆Cp,c→sl are used between Tm and Tg and Cp, a and ∆Cp,c→a are used between Tg and T. In equation 3, ∆Cp,c→sl and ∆Cp,c→a are assumed constant, whereas in equation 4, Cp,c, Cp,sl and Cp,a have been treated as linear functions of temperature.8 From a practical standpoint, the Hoffman equation (equation 2) is the simplest while equation 4 is the most complicated but provides a better model since it involves the least number of assumptions. Two methods of solubility measurement have been used to test theoretical calculation. The first method is by direct dissolution of amorphous solid in the chosen aqueous media.4,5,6 In this case, there are no agents added to the media to inhibit desupersaturation. Thus, most of the compounds tested by this method do not reach a sustained plateau concentration thereby leading to measurement of lower amorphous solubility advantage. In subsequent studies, Murdande et al. modified the direct dissolution method by using 1% HPMCAS in the media to inhibit crystallization.9 Sustained plateau concentration was obtained and agreement between experimental measurement and calculation was within a factor of 2. However, only three systems were tested using this method, thereby limiting the generality of the conclusion. The second method for solubility measurement employs the concept of liquid-liquid phase separation (LLPS).8 In this method, a concentrated drug solution in an organic solvent miscible with water is introduced into an aqueous medium. Spontaneous phase separation occurs at the drug-water spinodal point, which is close to the amorphous solubility.10 The phase separation can be detected by light scattering or the change of fluorescence spectra of probes. While this method is useful for theoretical understanding and has been successfully applied,10 it is neither applicable for understanding the dissolution performance of amorphous solid dosage form nor for assessing the impact of different preparation methods on amorphous solubility advantage. In this work, ten model compounds that show a propensity to maintain supersaturation were studied to test the calculation of the amorphous solubility advantage. The three methods for calculating ∆Gc→a as per equations 2 to 4 were evaluated. Experimental solubility was measured by direct dissolution of 4 ACS Paragon Plus Environment
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Molecular Pharmaceutics
amorphous solid into buffer. When necessary, hydroxypropyl methylcellulose acetate succinate (HPMCAS) was predissolved in buffer to inhibit desupersaturation. By direct dissolution, the impact of different methods of preparing amorphous solids and the effect of bio-relevant media on amorphous solubility advantage were studied.
MATERIALS AND METHODS Materials. Ritonavir, ketoconazole, clotrimazole, carvedilol and loratadine were purchased from Sigma-Aldrich (St. Louis, MO) and used as received. Terfenadine was purchased from Toronto Research Chemicals (Toronto, Canada). Four compounds, labeled as GNE A, B, C, and D, were synthesized by the process chemistry organization in Genentech Inc. and were used as received. FaSSIF version 1 powder was purchased from Biorelevant (London, UK) and FaSSIF medium was prepared according to the supplier’s recipe. The prepared FaSSIF contains 3 mM sodium taurocholate and 0.75 mM lecithin. Blank FaSSIF was used as a pH 6.5 buffer in order to facilitate comparison with solubility measurement in FaSSIF. The blank FaSSIF was prepared according to the recipe of FaSSIF version 1 without addition of the bile salts powder. Potassium phosphate salts, sodium hydroxide and deionized water were used to prepare pH 6.8 and 7.7 buffers. HPMCAS-MF was acquired from Shin-Etsu (Totowa, NJ) and used as received. Thermal parameters and water sorption measurements. A differential scanning calorimeter (DSC) Q2000 (TA instruments, New Castle, DE) was used to measure ∆Hm, Tm and Tg in 10 ⁰C/min heating and cooling cycles. 5 – 10 mg sample was prepared in a hermetic T0 pan. The onset of Tm during first heating cycle and inflection point of Tg during second heating cycle are reported in this work. Indium was used to calibrate the melting enthalpy and temperature. To obtain high quality Cp data, modulated DSC runs were performed using a discovery DSC (TA instruments, New Castle, DE). The linear heating rate was 2 ⁰C/min, and modulation amplitude was 1 ⁰C for every 100 s. 10 – 20 mg crystal sample was prepared in a
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hermetic T0 pan. The powder was gently compressed if necessary to reach at least 10 mg mass in the pan. Cp,c was measured in the first heating cycle, then the crystal was melted in DSC pan and cooled down at 2 ⁰C/min to form an amorphous solid. The amorphous solid was subsequently heated using the same modulated DSC method to obtain Cp,a and Cp,sl. Sapphire was used to calibrate the Cp measurement. At least three samples were measured for each thermal parameter. To calculate exp [-I (a2)] term, water sorption measurement was conducted by a DVS Q5000 SA (TA instruments, New Castle, DE). Amorphous solid was prepared by spray-drying or melt-quenching. The melt-quenched sample was ground to powder prior to DVS measurement. 10 – 20 mg amorphous powder was placed into an aluminum pan. The sample was dried at 0% RH until weight loss was less than 0.005% in 15 min with a maximum step length of 120 min. Subsequently the relative humidity (RH) was increased to 95% by a step of 5%. The equilibrium criterion was weight change less than 0.005% in 15 min with a maximum step length of 300 min. After DVS experiment, each sample was confirmed as amorphous by powder X-ray diffraction (Miniflex 600, Rigaku, Tokyo, Japan). The X-ray diffractometer was operated using Cu Kα radiation (40 kV, 15 mA) with a scanning range of 2 to 40 in 2θ degree and a scanning rate of 1 degree/min. Preparation of amorphous solids. Melt-quenching and spray-drying were the primary methods to prepare amorphous solids in this work. For melt-quenching, each sample was melted at Tm + 5 ⁰C on a hot plate and immediately air cooled to room temperature. For spray-drying, dichloromethane/methanol (1:1, v/v) or tetrahydrofuran (THF) were used as solvents. 5% (w/v) solution of the compound was prepared and then spray-dried using a Buchi mini spray-dryer B-290 (Buchi, New Castle, DE). The inlet temperature was 85 ⁰C for dichloromethane/methanol and 122 ⁰C for THF. The condenser temperature was 6 ⁰C for both solvent systems. Liquid feed rate was 10 mL/min. Nozzle gas flow was set at 60 mm and aspirator was set at 96%. Precipitation and lyophilization were used to prepare amorphous solids for ritonavir and GNE-B to study the impact of preparation method on amorphous solubility advantage. For precipitation, concentrated
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Molecular Pharmaceutics
methanolic solutions of ritonavir and GNE-B were prepared and then mixed with deionized water of 10 folds volume. The precipitated solids were then obtained by centrifuging the suspension at 15000 rpm for 5 min. For lyophilization, acetonitrile solutions of ritonavir and GNE-B were prepared at 4 mg/mL and 10 mg/mL concentration, respectively. The solutions were frozen at – 70 ⁰C. Primary drying was conducted at – 50 ⁰C, 100 mTorr for 10 hrs, followed by secondary drying at – 15 ⁰C, 100 mTorr and 5 ⁰C, 10 mTorr. Spray-dried, lyophilized and precipitated amorphous solids were further dried at 30 ⁰C in a vacuum oven at 160 mBar pressure for 24 hrs. All prepared solids were confirmed as amorphous by powder X-ray diffraction using the same method mentioned above. Experimental measurement of amorphous solubility advantage. Solubility of amorphous form or crystal was measured at 25 ⁰C by µDiss. ProfilerTM (Pion Inc., Billerica, MA). A UV probe was used in this instrument for concentration determination. The default path length used is 10 mm. For measurement of low solubility, 20 mm path-length UV probes were used. The scanning wavelength of the UV probe ranges from 200 to 710 nm. A calibration curve was built with standard solutions before each solubility measurement. To do so, stock solutions were prepared in methanol or THF at appropriate concentrations to ensure in total less than 200 µL stock solution was added into aqueous medium for building the entire calibration curve. The stock solution was pipetted into 20 mL buffer or FaSSIF by 10 or 20 µL volume increments. At each step, concentration was calculated by the stock concentration and the sum volume. Before recording a data point, the aqueous solution was stirred until a constant UV absorption was reached. For amorphous solubility measurement, the highest concentration in the calibration curve was close or slightly higher than the liquid-liquid phase separation concentration to cover the solubility measurement of dissolving an amorphous solid. Therefore to minimize the interference from non-absorbance light scattering, the area under the second derivative curve, was used to build the calibration curve and to measure solubility. All calibration curves had a R2 > 0.99 in the desired concentration range. To measure solubility, excess amount of amorphous solid or crystal were added into 20 mL of aqueous media. Concentration was recorded by the UV probe in real time at an interval of 2 min in order to monitor any possible desupersaturation. The 7 ACS Paragon Plus Environment
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solubility of GNE-C in FaSSIF was too high for measurement by µDiss. Profiler in real time. Thus the measurement was performed by reverse phase high performance liquid chromatography (Agilent HPLC 1260, Santa Clara, CA) using a C18 column (length 150 mm, internal diameter 4.6 mm, particle size 3 µm) and water and acetonitrile as mobile phase. For concentration measurement, a 2 mL suspension was centrifuged at 15000 rpm for 3 min. The supernatant was diluted by methanol before HPLC measurement. The calibration curve was built using standard solutions prepared in methanol. The concentration of the solution was measured at 22 hrs and then at 27 hrs to confirm a plateau concentration was reached from both crystal and amorphous samples. After measurement, the remaining GNE-C solid in solution was confirmed to be amorphous by powder X-ray diffraction using the same method mentioned above. The crystal solubility of loratadine in FaSSIF with 100 µg/mL HPMCAS, and the crystal solubility of clotrimazole in FaSSIF, FaSSIF + 50 µg/mL HPMCAS and FaSSIF + 100 µg/mL HPMCAS were also measured by the same HPLC method.
RESULTS AND DISCUSSION Evaluation of different methods for calculating
∆G
to
predict
amorphous
solubility advantage. As mentioned in the introduction, one goal of this work was to evaluate the different methods to calculate ∆Gc→a. For the Hoffman method (c.f. equation 2), only the values of ∆Hm and Tm are required. However, for using equations 3 or 4, glass transition temperature (Tg) and specific heat capacity (Cp) are required as well. An example of
Figure 1. Cp measurement of ritonavir by modulated DSC. ∆Cp between amorphous solid or supercooled liquid and crystal was evaluated at region away from glass transition zone for calculation in equation 3. Linear fitting of Cp vs. T (dotted lines and equations) was performed for calculation in equation 4.
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Molecular Pharmaceutics
Cp calculation in the case of ritonavir is provided. A similar procedure was used for other compounds in the study. Figure 1 shows the Cp as a function of temperature for ritonavir. For equation 3, ∆Cp of ritonavir was evaluated at temperatures 25 ⁰C above or below Tg to avoid interference from the glass transition zone. The Cps of crystal, supercooled liquid and amorphous solid were fitted as linear functions of T, as shown in Figure 1 and were then used in equation 4 to obtain ∆Gc→a as per the procedure described in ref. (8). Figure S1 in Supporting Information shows the Cp-T plots for all the rest systems. It should be noted that even though Cp calibration was performed by sapphire, the variation of Cp measurements between samples is still relatively significant. Therefore, to minimize its effect on solubility advantage calculation, the Cp of crystal, supercooled liquid and amorphous solid was measured from the same sample in this work. To calculate exp [-I (a2)] term, water sorption measurement was performed from 0% to 95% RH. Figure S2 in supporting information presents the water sorption data and the calculated exp [-I (a2)] for ritonavir. The integration of Gibbs-Duhem equation was performed up to 95% RH and exp [-I (a2)] at water activity of 1 (100% RH) was obtained by a linear extrapolation. The exp [-I (a2)] term was determined as 0.29 for ritonavir. Table 1 shows molecular weights, pKa values,11,12,13,14 measured thermal properties and the term exp Table 1. Molecular weight, pKa (A: acid, B: base) and measured properties for amorphous solubility advantage calculation. Thermal properties were average data from three samples. Standard deviation is shown for ∆Cp. For Tm and Tg, standard deviation is within 0.5 ⁰C. For ∆Hm, standard deviation is within 2 J/g. Molecule Mw (g/mol) pKa Tm (⁰C) ∆Hm (J/g) Tg (⁰C) exp[-I (a2)] ∆Cp, c->a (J/g/⁰C) ∆Cp, c->sl (J/g/⁰C) Ritonavir Loratadine Clotrimazole Ketoconazole
720.9 382.9 344.8 531.4
118.2 134.8 144.8 147.5
72.8 74.2 94.9 95.9
49.0 33.1 30.3 43.9
0.290 0.571 0.745 0.136
0.049 ± 0.005 0.015 ± 0.002 0.058 ± 0.014 0.053 ± 0.003
0.526 ± 0.003 0.29 ± 0.06 0.347 ± 0.011 0.444 ± 0.009
471.7 406.5 462.6 608.5 446.9
3.48 (B) 5.25 (B) 5.89 (B) 3.16 (B) 6.13 (B) 8.6 (B) 7.75 (B) 4.4 (A) 2.7 (B) 4.3 (A)
Terfenadine Carvedilol GNE-A GNE-B GNE-C form 1 GNE-C form 2 GNE-D
149.4 114.7 154.6 147.1 174.1
110.4 119.5 82.0 40.5 60.9
60.0 40.2 57.8 86.3 127.0
0.793 0.470 0.898 0.755 0.575
0.041 ± 0.013 0.050 ± 0.013 0.075 ± 0.011 0.030 ± 0.007 0.084 ± 0.029
0.581 ± 0.011 0.80 ± 0.03 0.384 ± 0.014 0.45 ± 0.04 0.42 ± 0.03
446.9
4.3 (A)
226.5
80.4
127.0
0.575
0.095 ± 0.004
0.496 ± 0.004
543.5
3.9 (A) 8.6 (B)
174.2
102.3
77.1
0.593
0.042 ± 0.014
0.734 ± 0.016
[-I (a2)] for all the studied compounds in this work. Ritonavir, loratadine and terfenadine used in this work are different polymorphs from that used in previous amorphous solubility studies.6,15 The PXRD of model 9 ACS Paragon Plus Environment
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compounds is shown in the supporting information (Figure S3). Ritonavir was used as the metastable polymorph II16 while loratadine was used as the stable polymorph A.17 Terfenadine as-received was a mixture of two polymorphs. Slurry in n-propanol was performed to convert the sample to the stable polymorph I.18,19 Among the ten compounds, seven are free bases; GNE-A and GNE-C are free acids; GNED is a zwitterion. Table 2. Calculation of amorphous solubility advantage (Sa/Sc) using Hoffman equation, assuming ∆Cps are constants between amorphous solid or supercooled liquid and crystal and fitting Cps as linear functions of temperature. For the latter two methods, Sa/Sc was calculated from Cp measurement of each individual sample and reported as an average of three samples. Calculated Sa/Sc Molecule Hoffman equation, eq. 2 ∆Cp constant, eq. 3 Cp linear fitting, eq. 4 Ritonavir 13.5 8.0 8.4 Loratadine 5.4 6.1 6.4 Clotrimazole 11.1 13.1 15.1 Ketoconazole 9.5 8.6 11.1 Terfenadine 62.3 49 46.5 Carvedilol 15.3 10.5 11.8 GNE-A 22.7 21.2 24.7 GNE-B 5.9 2.8 3.2 GNE-C, form 1 6.6 6.2 6.7 GNE-C, form 2 18.8 7.9 8.9 GNE-D 86.7 20.8 21.8
Table 2 shows the calculated amorphous solubility advantage by equation 1 and 2 – 4 using the data from Table 1. In theory, ∆G calculation by fitting Cp as a linear function of temperature is more accurate than using Hoffman equation or assuming ∆Cp is a constant. Therefore in subsequent sections we have compared the other two calculation methods against the “Cp linear fitting” method. The Hoffman equation was derived for calculating ∆G between crystal and supercooled liquid only.7 A major assumption made in deriving the Hoffman equation is that, the supercooling extent (Tm – T) is small. However, for the compounds investigated in this work, the supercooling extent ranges between 89 and 200 ⁰C. Secondly, Hoffman equation only applies to the ∆G calculation between crystal and supercooled liquid. If Tg is significantly higher than the temperature of solubility measurement (which is the case for majority of the compounds in this study), the calculation may not be accurate. While convenient, based on the limitations discussed, the Hoffman equation is not expected to quantitatively agree with the “Cp linear fitting” method. An additional assumption in Hoffman equation is that ∆Cp between crystal and supercooled liquid can be 10 ACS Paragon Plus Environment
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Molecular Pharmaceutics
treated as a constant. We test this assumption separately by comparing calculations from equation 3 with that from equation 4. Comparing the results calculated by Hoffman equation and “Cp linear fitting” method in Table 2, it is clear that a large discrepancy does exist, especially for systems of high Tm or Tg including GNE-B, GNE-C form 2, GNE-D and terfenadine. The discrepancy can be as significant as 4 folds in the case of GNE-D. Therefore, the use of Hoffman equation for ∆G calculation to evaluate amorphous solubility advantage is not recommended. Equation 3 assumes ∆Cp values between amorphous solid or supercooled liquid and crystal are constants. Figure 2 shows the calculated results by “∆Cp constant” against “Cp linear fitting” method. A near quantitative agreement is observed between the two methods. The residual error is due to the different temperature dependence of Cps of crystal, supercooled liquid and amorphous solid (as shown by the fitted slopes in Figure 1 for ritonavir).
Nevertheless,
the
agreement
demonstrates that, practically, such difference does not significantly impact amorphous solubility advantage calculation. Therefore, while caution may still be needed if Cp temperature dependence is largely different, the “∆Cp constant” method is recommended to simplify
the
calculation
solubility advantage.
of
amorphous
Figure 2. Comparison of amorphous solubility advantage calculation by assuming ∆Cps are constants with the method of treating Cps as linear functions of temperature. Green diagonal line is guide to the eye.
Experimental solubility measurement and evaluation of accuracy of theoretical calculation. To evaluate the amorphous solubility advantage calculation, the effect of preparation methods was studied first since different processes can be applied to produce amorphous forms in drug development. This study was necessary to understand the variation in solubility measurement, if any, due to the method of preparation. 11 ACS Paragon Plus Environment
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During early stage of drug development, lyophilization and bench-scale spray-drying are typically used to generate the amorphous phase.20 For clinical formulation development or commercial production, spraydrying and hot melt extrusion (HME) are often used.21 For compounds that have both high melting temperatures and low solubilities in volatile solvents, co-precipitation can also be used at small or large scale.22,23 Since amorphous solid is a non-equilibrium system, different processes can generate amorphous solids with different physical properties.24,25,26 For the amorphous solubility calculation, the thermal properties were obtained from melt-quenched samples. Therefore, it is of interest to test whether the calculation can predict the solubility advantage of amorphous solids prepared by other pharmaceutically relevant methods. Ritonavir and GNE-B were used as model compounds since they can easily form
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Molecular Pharmaceutics
amorphous solids by lyophilization, precipitation, spray-drying and melt-quenching (used as a surrogate for HME process). Figure 3 shows a representative dissolution profile for ritonavir. In the measurement, different dissolution rates were observed, which is attributed to different particle sizes. When dissolution curves reached plateau concentration, amorphous solids prepared by different methods did not exhibit different solubility. Table 3 shows the measured solubility of amorphous solid and crystal for ritonavir and GNE-B. Similar to ritonavir, different preparation methods did not have a significant effect on amorphous solubility of GNE-B either. The measured solubility advantages for them agree
Figure 3. Solubility measurement for amorphous ritonavir prepared by lyophilization, spray-drying, precipitation and melt-quenching, compared with crystalline solubility. The measurement was conducted at 25 ⁰C in blank FaSSIF (pH = 6.5) containing 50 µg/mL HPMCAS to inhibit desupersaturation. Measurements were performed in triplicate. In each measurement, concentration was recorded at time interval of 2 min. For clarification, only one sample with representative data points is shown.
Table 3. Experimentally measured amorphous and crystalline solubility of ritonavir and GNE-B. Amorphous solids were prepared by spray-drying, melt-quenching, lyophilization or precipitation (Mean ± SD, N = 3). Sa (µg/mL) Molecule Sc (µg/mL) Spray-dried Melt-quenched Lyophilized Precipitated Ritonavir
38.9 ± 0.1
37.5 ± 0.4
39.1 ± 0.5
39.6 ± 0.4
4.8 ± 0.3
GNE-B
7.8 ± 0.9
8.2 ± 0.3
7.9 ± 0.4
7.2 ± 0.1
4.3 ± 0.2
with theoretical calculations by the “Cp linear fitting” and “∆Cp constant” methods (c.f. Table 2) within a factor of 1.8. It has been shown that different preparation methods do not significantly affect Tg or heat capacity change at glass transition,24,27 thus they do not affect ∆Cp,c→a and therefore the ∆G calculation
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according to “∆Cp constant” method. For the water sorption term, DVS measurement was performed on both spray-dried and melt-quenched GNE-B. The calculated exp[-I (a2)] from the two samples did not show significant difference (0.755 for spray-dried and 0.748 for melt-quenched sample). Therefore, according to equation 1, the amorphous solubility advantage will not be affected by different preparation methods. It Table 4. Preparation method, medium, crystal solubility, amorphous solubility, experimentally measured amorphous solubility advantage by direct dissolution of the ten compounds in this work at T = 25 ⁰C (Mean ± SD, N ≥ 3). Molecule Preparation method a Medium Sc (µg/mL) Sa (µg/mL) Measured Sa/Sc Ritonavir SD, Lyo., Pre., MQ 4.8 ± 0.3 38.9 ± 0.1 8.1 ± 0.5 Loratadine MQ pH 6.5 buffer 1.6 ± 0.2 11.9 ± 0.6 7.4 ± 1.0 Clotrimazole MQ 50 µg/mL HPMCAS 0.52 ± 0.03 8.4 ± 0.5 16.1 ± 1.3 GNE-A SD 0.50 ± 0.13 11 ± 3 22 ± 8 Terfenadine MQ pH 7.7 buffer 0.84 ± 0.11 21.8 ± 0.3 26 ± 3 Carvedilol MQ 50 µg/mL HPMCAS 4.7 ± 0.9 36.9 ± 2.4 7.9 ± 1.6 Ketoconazoleb MQ pH 6.5 buffer 5.4 ± 0.2 55 ± 4 10.2 ± 0.9 100 µg/mL HPMCAS GNE-B SD, Lyo., Pre., MQ 4.3 ± 0.2 7.8 ± 0.9 1.8 ± 0.2 GNE-C, form 1 SD pH 6.5 buffer 1.01± 0.12 4.90 ± 0.10 4.9 ± 0.6 GNE-C, form 2 SD 0.50 ± 0.13 4.90 ± 0.10 9.8 ± 2.6 GNE-Db SD pH 6.8 buffer 3.5 ± 0.3 100 ± 3 28.6 ± 2.6 50 µg/mL HPMCAS a SD: spray-dried, Lyo.: Lyophilization, Pre.: Precipitation, MQ: Melt-quenched. b Desupersaturation of amorphous solid solution occurred after reaching a plateau concentration.
should be noted that samples prepared by different methods may have different enthalpy relaxation upon heating,24 indicating different extent of enthalpy loss during process. It was observed in this work that spraydried GNE-B showed larger enthalpy relaxation than the melt-quenched sample (Figure S4 in supporting information). Interestingly, such difference in enthalpy relaxation did not affect the amorphous solubility measurement. This may be attributed to the additional relaxation of amorphous solids after saturation with water during dissolution process. Especially, the plasticizing effect of water can reduce Tg28 and thus lead to faster relaxation. It is probable that by the time of recording amorphous solubility, different amorphous solids had relaxed to the same energy state. Further study is needed to test this hypothesis. Due to insignificant solubility difference observed, it was concluded that the amorphous solubility advantage calculation using thermodynamic data from the melt-quenched sample is applicable to predicting the solubility advantage of amorphous samples prepared by other common pharmaceutical processes. To test the amorphous solubility advantage calculation against the experimental measurement, the amorphous and crystal solubilities of the ten compounds in Table 1 were measured in buffered media. For 14 ACS Paragon Plus Environment
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Molecular Pharmaceutics
ketoconazole and GNE-D, desupersaturation occurred even though HPMCAS was added to the media. Figure S5 (supporting information) shows the dissolution of amorphous ketoconazole as an example. But for these two systems, a plateau concentration was sustained for at least 1 hr and this concentration was taken as the amorphous solubility. Table 4 shows the preparation method, medium, amorphous solubility, crystal solubility and the solubility advantage for the ten compounds. Figure S6 shows the typical data of dissolution and solubility measurements of the systems in addition to ritonavir and ketoconazole. To apply equation 1 for the amorphous solubility advantage prediction, the requirement is that the solubility measurement must be performed in buffer where the ionization extent is independent of solute concentration.5 In previous studies, such measurements were performed at a buffer pH where the tested compounds did not ionize and intrinsic solubility was measured.8,15 To guide formulation development, majority of amorphous solubility advantage measurements were intentionally conducted at physiologically relevant pH 6.5 in this work. At this pH, according to the pKa values in Table 1, clotrimazole, ketoconazole, GNE-A and GNE-C are substantially ionized, and GNE-D exists as a zwitterion. According to Indulkar et al,29 in a wide pH range, the amorphous solubility advantage calculation agrees with the concentration where liquid-liquid phase separation occurs for clotrimazole and atazanavir. Therefore, in our study, as long as no insoluble salts are formed, the theoretical calculation is still expected to quantitatively predict the amorphous solubility advantage from the totality of ionized and unionized species. Carvedilol and terfenadine are known to form chloride and phosphate salts of low solubilities,30,31 therefore the solubility measurement for these two compounds were conducted at a buffer pH 7.7 to reduce their ionization extent and the impact from saturated ionized species on amorphous solubility measurement.
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Figure 4a shows the experimentally measured amorphous solubility advantage (Sa/Sc) versus that calculated theoretically by the “Cp linear fitting” method. Figure 4b shows the ratio of calculated Sa/Sc to experimentally measured Sa/Sc. Overall, reasonable experimental
quantitative
agreement
measurement
and
between theoretical
calculation is observed. For all ten compounds in this work, the experimentally measured Sa/Sc agrees with the theoretical calculation within a factor of 0.7 to 1.8 as shown in Figure 4b. Similar
quantitative
agreement
was
also
observed between experimental measurement and calculation by “∆Cp constant” method (Figure S7). Note that the amorphous solids of GNE-A, C and D for solubility measurement were prepared by spray-drying, therefore the agreement further demonstrates that calculation made from the data of melt-quenched samples can successfully predict the solubility advantage of the amorphous form prepared by other methods. The compounds selected in this work are all slow crystallizers. In addition, HPMCAS
Figure 4. (a) Comparison of experimentally measured amorphous solubility advantage vs. theoretical calculation by Cp linear fitting method. Green diagonal line is guide to the eye. (b) The ratio of calculated amorphous solubility advantage over experimentally measured amorphous solubility advantage for the ten compounds.
was added to inhibit desupersaturation. Thus the apparent solubility, not the peak concentration, of amorphous solid was successfully measured by direct dissolution method. The agreement observed in our study is comparable with the reported in ref. (8) and (9). It should be noted that the calculation by equation 1 16 ACS Paragon Plus Environment
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Molecular Pharmaceutics
predicts the solubility advantage of a freshly melt-quenched amorphous solid equilibrated with water in an infinitesimal amount of time, during which no structural
relaxation
occurs.
In
reality,
amorphous solid absorbs water and relaxes towards a lower energy state during the solubility measurement,32 which might explain the
overall
solubility
greater
advantage
predicted than
amorphous
experimentally
measured. Overall, the data presented on the model compounds, quantitatively validates the calculation method for assessing amorphous solubility advantage. Given the fact that the material
needed
for
DSC
and
DVS
Figure 5. Solubility measurement for amorphous and crystal ritonavir in FaSSIF at 25 ⁰C. Measurements were performed in triplicate. In each measurement, concentration was recorded at time interval of 2 min. For clarification, only representative data are shown.
measurements is only ca. 100 mg, applying this calculation model is even more attractive during early stage drug development. The solubility advantage calculation may be further applied to predict the dissolution advantage of amorphous drugs through the use of Noyes-Whitney Equation.33 Evaluation of amorphous solubility advantage in FaSSIF. In this section, the influence of biorelevant media on amorphous solubility advantage is explored. FaSSIF was chosen as the representative biorelevant medium as it is a commonly used medium to evaluate solid dosage form dissolution to correlate with in vivo performance.34 There are bile salts in FaSSIF that can form micelles which in turn can affect the solubility of the drug. Therefore besides ionization at pH 6.5, micellar solubilization is an additional secondary equilibrium process that must be taken into account for the solubility measurement in FaSSIF. Ritonavir, loratadine, clotrimazole, GNE-B and the two forms of GNE-C were selected for this study. Figure 5 shows the representative solubility measurement for amorphous and crystal ritonavir in FaSSIF at 25 ⁰C. Desupersaturation was not observed for amorphous ritonavir solution in the entire measurement up to 17 ACS Paragon Plus Environment
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10 hours, and thus amorphous solubility was robustly determined. Compared to Figure 3, one can find that both crystal and amorphous solubility of ritonavir increased in FaSSIF, but their ratio, the amorphous solubility advantage remained unchanged. Figure 6a shows the dissolution measurement for loratadine in FaSSIF
at
amorphous
25
⁰C.
Unlike
loratadine
ritonavir,
desupersaturated
before reaching a plateau concentration, preventing
determination
of
amorphous
solubility in FaSSIF medium. Therefore, HPMCAS was added to FaSSIF to inhibit desupersaturation (Figure 6b). Interestingly, in FaSSIF, 50 µg/mL HPMCAS was not effective in inhibiting desupersaturation even though it was effective in blank FaSSIF which does not contain bile salts (Figure S6A). The HPMCAS concentration was then increased to 100 µg/mL. No additional inhibitory effect was observed (Figure S8A). This indicates the presence of bile salts impacted the effectiveness of HPMCAS in inhibiting
desupersaturation.
Similar
phenomenon has been observed for sodium lauryl sulfate (SLS) with posaconazoleHPMCAS amorphous solid dispersion, in which SLS competitively interacts with HPMCAS, reducing the effectiveness of
Figure 6. Dissolution measurements for amorphous and crystal loratadine in FaSSIF at 25 ⁰C. a. Measurement was performed in FaSSIF. b. Measurement was performed in FaSSIF containing 50 µg/mL HPMCAS. Three samples (S1, S2, S3) were measured and the highest peak concentration achieved was used for evaluating amorphous solubility advantage calculation. 18
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Molecular Pharmaceutics
HPMCAS in inhibiting crystallization of amorphous posaconazole.35 Even though desupersaturation occurred, compared to FaSSIF, the presence of HPMCAS increased the peak concentration that amorphous loratadine could achieve, and the peak concentration was used to semi-quantitatively compare with the measurement in buffer and calculation from equation 1. Clotrimazole behaved similarly to loratadine in FaSSIF, thus only a peak concentration could be obtained (Figure S8 B – D). The other two systems, GNEB (Figure S8E) and GNE-C (Tablet S1 ) behaved similarly to ritonavir, enabling amorphous solubility to be measured in FaSSIF. Table 5 shows the solubility measurement results in FaSSIF for the five systems along with their amorphous solubility advantage measured in buffer and predicted from calculation. In our measurement, the solubility in FaSSIF refers to the total concentration of the solubilized drugs including free drug, ionized drug, drug in micelles, drug bound to polymer, etc. Compared with the solubility measured in buffer in Table 4, the crystal solubility of the six systems all increased. The increase was anywhere between 2 to 200 folds, which is probably caused by the difference of hydrophobicity. Importantly, the amorphous solubility (or highest achievable peak concentration) increased as well by a similar multiple. For ritonavir, GNE-B and the two forms of GNE-C, the amorphous solubility advantage measured in FaSSIF shows excellent agreement with that measured in buffer and by theoretical calculation. For loratadine and clotrimazole, amorphous solubility advantage calculated by the highest achievable peak concentration is also in Table 5. Measurement of crystal and amorphous solubility in FaSSIF. The experimentally measured solubility ratio in FaSSIF is compared with that measured in pH 6.5 phosphate buffer (blank FaSSIF) and that calculated by “Cp linear fitting” method. For loratadine and clotrimazole, the reported Sc and Speak were from FaSSIF + 50 µg/mL HPMCAS. The solubility ratios measured in both FaSSIF + 50 or 100 µg/mL HPMCAS are reported (Mean ± SD, N = 3 when solubility was successfully measured). Sa/Sc Sc in FaSSIF Sa or Speak Calculation Experimental measurement Molecule (µg/mL) in FaSSIF by Cp linear Measured in FaSSIF FaSSIF + 50 FaSSIF + (µg/mL) fitting buffer µg/mL 100 µg/mL HPMCAS HPMCAS Ritonavir 8.6 ± 0.3 66.7 ± 3.3 8.4 8.1 ± 0.5 7.8 ± 0.5 GNE-B 21.0 ± 0.8 35.3 ± 0.5 3.2 1.7 ± 0.1 1.8±0.2 GNE-C form 1 173 ± 14 930 ± 17 6.7 4.9 ± 0.6 5.4 ± 0.5 GNE-C form 2 113.2 ± 0.8 930 ± 17 8.9 9.8 ± 2.6 8.2 ± 0.2 Loratadine 20 ± 2 133.2 6.4 7.4 ± 1.0 2.1 6.7 4.5 Clotrimazole 8.8 ± 0.2 95.8 15.1 10.7 10.9 12.3 16.1±1.3
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reasonable agreement with data measured from buffer and predicted by calculation. The effect of surfactant and bile salts on concentration-based amorphous solubility advantage has been investigated. Results reported in literature suggest that surfactant may or may not impact the amorphous solubility advantage expressed by the ratio of total solubilized drug concentration. In earlier studies, Raina et al.36 reported that in FaSSIF and Vit. E TPGS solution above its critical micelle concentration (CMC), liquid-liquid phase separation of felodipine occurred at two times lower concentration than the predicted amorphous solubility. On the other hand, Ilevbare and Taylor reported that the presence of Tween 80 micelles did not alter the amorphous solubility advantage of ritonavir in phosphate buffer.15 In more recent studies, Indulkar et al. reported that SLS micelles reduced the amorphous solubility advantage of atazanavir by two times because of the change of solubilization mechanism as solute concentration increases, however, the molecular activity ratio was consistent with the theoretical calculation.37 On the other hand, Lu et al observed that for sodium taurocholate (one component in FaSSIF in this work), at concentration of 1.86 mM, which is below its CMC, the amorphous solubility advantage of telaprevir was consistent with that in buffer.38 Even at 12 mM, a concentration above CMC, the sodium taurocholate micelle only reduced observed solubility advantage by a factor of ca. 1.2 (estimated from the slopes in Figure 10 of ref. 38). In our study, the FaSSIF version 1 contains 3 mM sodium taurocholate and 0.75 mM lecithin.39 The sodium taurocholate concentration is below its CMC,40 and lecithin concentration is above its CMC.41 Therefore observation reported by Lu et al38 that sodium taurocholate did not significantly impact concentration-based amorphous solubility advantage partially explains the observation in this work. It will be of interest to study whether lecithin behaves similarly to SLS in ref. (37) or sodium taurocholate in ref. (38) to further understand how current FaSSIF components affect amorphous solubility advantage expressed by concentration ratio. Overall, the observation in this work and reported results suggest that the effect of surfactant on the amorphous solubility advantage might be both drug and surfactant dependent. Further test on more systems will be beneficial to provide a fuller understanding on whether amorphous solubility
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Molecular Pharmaceutics
advantage in complex media (FaSSIF) can represent its activity advantage, which is critical for the modeling of drug permeation and crystallization. Figure 7 shows all the equilibrium processes that may occur during dissolution in FaSSIF. The calculation by equation 1 accounts for process A. The undissolved amorphous solid is saturated with absorbed water, and the difference of molar chemical potential between this system and a crystal is represented by ∆Gc→a – RT·I (a2). This chemical potential difference is solely dependent on the properties of amorphous solid and its crystal counterpart. In the first equilibrium process A, such chemical potential difference dictates the free drug solubility ratio between an amorphous solid and a crystal. Multiple secondary
processes
occur
with
the
dissolved free drug including ionization (a free base was taken as an example in Figure 7), micellar solubilization, drug-polymer (HPMCAS in this work) binding, etc. which is not taken account by equation 1. As shown in Table 5, the amorphous solubility advantage
measured
by
total
drug
concentration in FaSSIF is consistent with that measured in buffer. This suggests that the equilibrium constants for all the secondary processes are independent of drug concentration in the range from crystal
Figure 7. First and secondary equilibrium processes after reaching solubility by dissolving an amorphous solid in FaSSIF containing polymers. A free base was taken as an example to illustrate the ionization process.
solubility to amorphous solubility for the five compounds in this study, which is the basis for the success of predicting amorphous solubility advantage in FaSSIF by calculation. For a system if amorphous solubility advantage is high enough to result in the change of solubilization mechanism in micelle or precipitation of
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poorly soluble salts with buffer components, the observed consistency between measurement and calculation may break down.
CONCLUSIONS In this work, the accuracy of amorphous solubility advantage calculation was explored. From thermodynamic measurements, it was found that using constant ∆Cp between amorphous solid or supercooled liquid and crystal (c.f. equation 3) can simplify the calculations with results that are in excellent agreement with calculations where Cp is treated as a linear function of temperature. Slow crystallizers and desupersaturation inhibition by HPMCAS were utilized in this work to enable amorphous solubility measurement by direct dissolution to assess the theoretical calculation. For the ten compounds studied in this work, the experimentally measured amorphous solubility advantage by direct dissolution shows an agreement with theoretical calculation within a factor of 0.7 to 1.8. In addition, the solubility ratio measured in FaSSIF agrees well with that measured in buffer and predicted by calculation for five compounds studied in this work. The study demonstrates that theoretical models can be used to predict amorphous solubility advantage in early stage of drug development. These calculations can then be used to guide amorphous formulation development in terms of selecting the appropriate polymer type and loading. To further understand the amorphous solubility advantage in complex media (e.g. FaSSIF), it would be of interest to study more systems to test the drug and surfactant dependence of the concentration-based amorphous solubility advantage. For drug development, it should be systematically assessed whether the predicted amorphous solubility advantage can successfully translate to proportionally enhanced exposure in vivo.
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Molecular Pharmaceutics
SUPPORTING INFORMATION. Cp-T curves for the systems other than ritonavir; Water sorption measurement and analysis for ritonavir; PXRD for all model compounds; DSC traces of spray-dried and melt-quenched GNE-B; Dissolution and solubility measurement curves in buffer for the rest systems; Comparison of experimentally measured solubility advantage vs. calculation with ∆Cp constant assumption; Dissolution and solubility measurement curves in FaSSIF for the rest systems. ACKNOWLEDGMENTS This work was in part supported by summer internship program of Genentech Inc. The authors would also like to thank Genentech Small Molecule Pharmaceutics department for supporting this work. The authors also feel grateful for discussion with Prof. Gyan Johari and support from Alamelu Banda and Grace May Alba. Abbe Haser would like to thank Prof. Feng Zhang for granting her the opportunity to pursue a summer internship during her Ph.D. study. *Corresponding author: Karthik Nagapudi, E-mail:
[email protected]. Office phone: +1 (650) 225 2917. REFERENCES 1. Fahr, A.; Liu, X. Drug Delivery Strategies for Poorly Water-soluble Drugs. Expert Opin. Drug Delivery 2007, 4, 403 – 416. 2. Leuner, C.; Dressman, J. Improving Drug Solubility for Oral Delivery Using Solid Dispersions. Eur. J. Pharm. Biopharm. 2000, 50, 47 – 60. 3. Miller, J. M.; Beig, A.; Carr, R. A.; Spence, J. K.; Dahan, A. A Win-win Solution in Oral Delivery of Lipophilic Drugs: Supersaturation via Amorphous Solid Dispersions Increases Apparent Solubility without Sacrifice of Intestinal Membrane Permeability. Mol. Pharm. 2012, 9, 2009 – 2016. 4. Hancock, B. C.; Parks, M. What is the True Solubility Advantage for Amorphous Pharmaceuticals? Pharm. Res. 2000, 17, 397 – 404. 5. Murdande, S. B.; Pikal, M. J.; Shanker, R. M.; Bogner, R. H. Solubility Advantage of Amorphous Pharmaceuticals: I. A Thermodynamic Analysis. J. Pharm. Sci. 2010, 99, 1254 – 1264. 6. Murdande, S. B.; Pikal, M. J.; Shanker, R. M.; Bogner, R. H. Solubility Advantage of Amorphous Pharmaceuticals: II. Application of Quantitative Thermodynamic Relationships for Prediction of Solubility Enhancement in Structurally Diverse Insoluble Pharmaceuticals. Pharm. Res. 2010, 27, 2704 – 2714. 7. Hoffman, J. D. Thermodynamic Driving Force in Nucleation and Growth Processes. J. Chem. Phys. 1958, 29, 1192 – 1193. 8. Sousa, L. A. E.; Reutzel-Edens, S. M.; Stephenson, G. A.; Taylor, L. S. Assessment of the Amorphous “Solubility” of a Group of Diverse Drugs Using New Experimental and Theoretical Approaches. Mol. Pharm. 2015, 12, 484 – 495.
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30. Loftsson, T.; Vogensen, S. B.; Desbos, C.; Jansook, P. Carvedilol: Solubilization and Cyclodextrin Complexation: a Technical Note. AAPS PharmSciTech 2008, 9, 425 – 430. 31. Streng, W. H.; His, S. K.; Helms, P. E.; Tan, H. G. H. General Treatment of pH-solubility Profiles of Weak Acids and Bases and the Effects of Different acids on the Solubility of a Weak Base. J. Pharm. Sci. 1984, 73, 1679 – 1684. 32. Johari, G. P.; Shanker, R. M. On the Solubility Advantage of a Pharmaceutical’s Glassy State over the Crystals State, and of its Crystal Polymorphs. Thermochimi. Acta. 2014, 598, 16 – 27. 33 Johari, G. P. Increasing the Ambient Pressure Solubility by Forming a Glass at High Pressure and its Thermodynamics, a Much Sought-After Pharmaceutical Advantage. J. Phys. Chem. B 2018, 122, 2031 – 2039. 34 Sinha, S.; Ali, M.; Baboota S.; Ahuja, A.; Kumar, A.; Ali, J. Solid Dispersion as an Approach for Bioavailability Enhancement of Poorly Water-Soluble Drug Ritonavir. AAPS PharmSciTech 2010, 11, 518 – 527. 35. Chen, Y.; Wang, S.; Wang, S.; Liu, C.; Su, C.; Hageman, M.; Hussain, M.; Haskell, R.; Stefanski, K.; Qian, F. Sodium Lauryl Sulfate Competitively Interacts with HPMCAS and Consequently Reduces Oral Bioavailability of Posaconazole/HPMC-AS Amorphous Solid Dispersion. Mol. Pharm. 2016, 13, 2787 – 2795. 36. Raina, S. A.; Zhang, G. G.Z.; Alonzo, D. E.; Wu, J.; Zhu, D.; Catron, N. D.; Gao, Y.; Taylor, L. S. Impact of Solubilizing Additives on Supersaturation and Membrane Transport of Drugs. Pharm. Res. 2015, 32, 3350 – 3364. 37. Indulkar, A. S.; Mo, H.; Gao, Y.; Raina, S. A.; Zhang, G. G.Z.; Taylor, L. S. Impact of Micellar Surfactant on Supersaturation and Insight into Solubilization Mechanism in Supersaturated Solutions of Atazanavir. Pharm. Res. 2017, 34, 1276 – 1295. 38. Lu, J.; Ormes, J. D.; Lowinger, M.; Xu, W.; Mitra, A.; Mann, A. K. P.; Litster, J. D.; Taylor, L. S. Impact of Endogenous Bile Salts on the Thermodynamics of Supersaturated Active Pharmaceutical Ingredient Solutions. Cryst. Growth Des. 2017, 17, 1264 – 1275. 39. Galia, E.; Nicolaides, E.; Hörter, D.; Löenberg, R.; Reppas, C.; Dressman, J. B. Evaluation of Various Dissolution Media for Predicting in Vivo Performance of Class I and II Drugs. Pharm. Res. 1998, 15, 698 – 705. 40. Natalini, B.; Sardella, R.; Gioiello, A.; Ianni, F.; Michele, A. D.; Marinozzi, M. Determination of Bile Salt Critical Micellization Concentration on the Road to Drug Discovery. J. Pharm. Biomed. Anal. 2014, 87, 62 – 81. 41. Martínez-Landeira, P.; Ruso, J. M.; Prieto, G.; Saarmiento, F. Surface Tensions, Critical Micelle Concentrations and Standard Free Energies of Micellization of C8-lecithin at Different pHs and Electrolyte Concentrations. J. Chem. Eng. Data 2002, 47, 1017 – 1021.
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1.9 Cp,sl = 0.0023T + 1.606
1.8 1.7
Reversing Cp (J/g/⁰C)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
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1.6
∆Cp, c->sl
1.5 1.4 Cp,a = 0.0048T + 1.0006
1.3 1.2 Cp,c = 0.0038T + 0.9708
1.1
∆Cp, c->a
1 0.9
0
20
40
60
80
100
T (⁰C) Figure 1. Cp measurement of ritonavir by modulated DSC. ∆Cp between amorphous solid or supercooled liquid and crystal was evaluated at region away from glass transition zone for calculation in equation 3. Linear fitting of Cp vs. T (dotted lines and equations) was performed for calculation in equation 4.
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50
∆Cp constant assumption
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Molecular Pharmaceutics
40 30 20 10 0 0
10
20
30
40
50
Cp linear fitting method Figure 2. Comparison of amorphous solubility advantage calculation by assuming ∆Cps are constants with the method of treating Cps as linear functions of temperature. Green diagonal line is guide to the eye.
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45
Ritonavir 40 35
Concentration (μg/mL)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
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Lyophilized Spray-dried Precipitated Melt-quenched
30 25 20 15
Crystal
10
5 0
0
200
400
600
800
1000 1200 1400
t (min) Figure 3. Solubility measurement for amorphous ritonavir prepared by lyophilization, spray-drying, precipitation and melt-quenching, compared with crystalline solubility. The measurement was conducted at 25 ⁰C in blank FaSSIF (pH = 6.5) containing 50 µg/mL HPMCAS to inhibit desupersaturation. Measurements were performed in triplicate. In each measurement, concentration was recorded at time interval of 2 min. For clarification, only one sample with representative data points is shown.
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a
Measured Sa/Sc
50 40 30 20 10 0
0
10
20
30
40
50
Calculated Sa/Sc by “Cp linear fitting”
3 Calculated ratio/Measured ratio
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2.5
b
2 1.5
1 0.5 0
Figure 4. (a) Comparison of experimentally measured amorphous solubility advantage vs. theoretical calculation by Cp linear fitting method. Green diagonal line is guide to the eye. (b) The ratio of calculated amorphous solubility advantage over experimentally measured amorphous solubility advantage for the ten compounds.
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Ritonavir 60
Concentration (μg/mL)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
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Amorphous 50 40 30 20
Crystal
10 0
0
100
200
300
400
500
600
t (min) Figure 5. Solubility measurement for amorphous and crystal ritonavir in FaSSIF at 25 ⁰C. Measurements were performed in triplicate. In each measurement, concentration was recorded at time interval of 2 min. For clarification, only representative data are shown.
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Concentration (μg/mL)
50 45 40
Amorphous
35 30
2.1 times
25 20 15
Crystal
10 5
a
0 0
50
100
150
200
250
300
t (min) 140
Concentration (μg/mL)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
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Amorphous
120 100
S3
80
S2
60
S1
6.7 times
40
Crystal
20
b
0 0
20
40
60
80 100 120 140 160
t (min) Figure 6. Dissolution measurements for amorphous and crystal loratadine in FaSSIF at 25 ⁰C. a. Measurement was performed in FaSSIF. b. Measurement was performed in FaSSIF containing 50 µg/mL HPMCAS. Three samples (S1, S2, S3) were measured and the highest peak concentration achieved was used for evaluating amorphous solubility advantage calculation.
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Molecular Pharmaceutics 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
First equilibrium
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Amorphous drug saturated with water
A Solubilized free drug in medium Secondary equilibrium + +
C
D
+ +
+
B
+
Ionized drug in medium
Micellar drug in medium
Drug bound to polymer
Figure 7. First and secondary equilibrium processes after reaching solubility by dissolving an amorphous solid in FaSSIF containing polymers. A free base was taken as an example to illustrate the ionization process.
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Measured Sa/Sc
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56
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40
30 20 10
0 0
10
20
30
40
50
Calculated Sa/Sc
TOC: Title: Evaluation of accuracy of amorphous solubility advantage calculation by comparison with experimental solubility measurement in buffer and bio-relevant media
Authors: Wei Zhang, Abbe Haser, Hao Helen Hou, and Karthik Nagapudi
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