Predicting the Solubility Advantage of Amorphous ... - ACS Publications

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Predicting the solubility advantage of amorphous pharmaceuticals – a novel thermodynamic approach Raphael Paus, Yuanhui Ji, Lisa Vahle, and Gabriele Sadowski Mol. Pharmaceutics, Just Accepted Manuscript • DOI: 10.1021/mp500824d • Publication Date (Web): 24 Jun 2015 Downloaded from http://pubs.acs.org on July 4, 2015

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Molecular Pharmaceutics

Predicting the solubility advantage of amorphous pharmaceuticals – a novel thermodynamic approach Raphael Paus, Yuanhui Ji, Lisa Vahle and Gabriele Sadowski* TU Dortmund, Department of Biochemical and Chemical Engineering, Laboratory of Thermodynamics, Emil-Figge Str. 70, D-44227 Dortmund, Germany

Keywords: amorphous, thermodynamic model, phase behavior, solubility, poorlysoluble drug, PC-SAFT

ACS Paragon Plus Environment


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ABSTRACT To improve the solubility and bioavailability of poorly-soluble active pharmaceutical ingredients (APIs), the transformation of crystalline APIs into the amorphous state has often been shown to be advantageous. As it is often difficult to measure the solubility of amorphous APIs, the application of thermodynamic models is the method of choice for determining the solubility advantage. In this work, the temperature-dependent solubility advantage of an amorphous API versus its crystalline form was predicted for five poorly-soluble APIs in water (glibenclamide, griseofulvin, hydrochlorothiazide, indomethacin and itraconazole) based on modeling the API/solvent phase diagrams using the Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT). To evaluate the performance of this approach, the predicted solubility advantage was compared to experimental data and to the solubility advantage calculated by the commonly-applied Gibbs-energy-difference method. For all systems considered, PC-SAFT predictions of the solubility advantage are significantly more accurate than the results obtained from the Gibbs-energy-difference method.


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INTRODUCTION Improving the solubility of poorly-soluble active pharmaceutical ingredients (APIs) is of high importance in pharmaceutical research and development.1 The transformation of crystalline APIs into their amorphous form often leads to a high increase in both, API solubility and API release rate.2-7 For this reason, an accurate estimation of the solubility advantage of an amorphous API compared to its crystalline form is beneficial for developing formulation strategies of these types of APIs. As the pure amorphous API often tends to recrystallize as soon as it gets in contact with the solvent,4, 5, 8, 9 the experimental estimation of the solubility advantage of amorphous API is often difficult, requires many experiments and is poorly reproducible. Currently, there is no gold standard for measuring the solubility of an amorphous API; thus, predicting this property using a thermodynamic model is an appropriate alternative. Parks and co-workers10,

11

proposed the Gibbs-energy-difference (henceforth referred to as

GED) method, which determines the difference in Gibbs energy between the crystalline and the amorphous API to obtain the solubility advantage of amorphous API versus its crystalline form. Hancock et al.8 applied this method to calculate the solubility advantage of a series of poorly-soluble APIs reporting estimated values that were up to 100 times higher than the measured values.8 Later, this approach was modified by Murdande et al.5, 6 They noted that the thermodynamic activity of amorphous APIs is changed by the absorption of water. To account for this change, the authors introduced a correction term and accounted for the amount of absorbed water when calculating the thermodynamic activity of the amorphous API.6 The amount of absorbed water was determined based on measured water-sorption from a humid atmosphere. However, the estimation of the activity of an amorphous API based on the water-sorption isotherms is



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difficult, as most amorphous APIs recrystallize immediately upon contact with water.1 Moreover, the calculation of the solubility advantage as function of temperature turns out to be complex and time-consuming, as the water sorption data have to be measured for each temperature. Murdande et al.5 investigated five APIs at 298.15 K using the modified GED and calculated solubility advantages which were 4 to 53 times higher than the experimental ones. To the best of our knowledge, the influence of the solvent on the solubility advantage of the amorphous API versus its crystalline form has been neglected in all approaches reported so far. 6, 8, 12, 13 Thus, the objective of this work is to apply a thermodynamic model to predict the solubility advantage of an amorphous API versus its crystalline form. In this approach, the solubility advantage is predicted based on the thermodynamic phase behavior of an API in a solvent (often, but not necessarily water), in which the following three aspects are taken into account: first, the change in activity of the amorphous API due to the absorption of solvent; second, the influence of the solvent on the solubility of amorphous and crystalline API; and third, the temperature-dependence of the solubility advantage. As the Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT)14 has already been successfully applied to calculate and predict API solubilities in different solvents, solvent mixtures,15, 16 and (co)polymers,17, 18 as a function of pH19, and to predict the ‘‘oiling-out’’ phenomenon (liquid-liquid equilibrium; LLE) of APIs and other organic molecules in solvents,20-22 the same model was used in this work to predict the solubility advantage of amorphous versus crystalline APIs in water. The results are compared with those from the commonly-used GED method and with experimental data from literature.8, 10-13 Five

poorly-soluble

APIs

(see

Figure

1),

namely

glibenclamide,

griseofulvin,

hydrochlorothiazide, indomethacin and itraconazole were selected as model compounds, as all


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have been reported to show a solubility advantage upon transformation from the crystalline to the amorphous form.5, 6, 8, 12, 13

(a)

(b)

(c)

(d)

(e) Figure 1: Chemical structures of glibenclamide (a), griseofulvin (b), hydrochlorothiazide (c), indomethacin (d) and itraconazole (e)

THEORY Calculation of the Solubility Advantage The solubility advantage ( ) of an amorphous API (A) versus its crystalline form (C) is defined as shown in Eq. (1).


(1)


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Here, is the solubility of the amorphous API and is the solubility of the crystalline

API, both in mole fractions. The solubility advantage can be predicted based on the knowledge of the thermodynamic phase diagram of the API in solution (as schematically shown in Figure 2).21-23 The solubility line represents the concentration of the API in the solvent-rich phase which is in equilibrium with the pure crystalline API. This concentration is the solubility of the crystalline API

which is obtained by calculating the solid-liquid equilibrium (SLE)24 of the API. Above the

solubility line, the API is fully dissolved in the solvent. Below the solubility line, the solution is supersaturated. In this region, the API tends to crystallize. In addition, some API/solvent systems demix into two liquid (amorphous) phases (a solventrich phase (L1) and an API-rich phase (L2)). This liquid-liquid demixing is often (as in Figure 2) -but not necessarily- metastable with respect to crystallizatio n. In those cases, the API also tends to crystallize in the liquid-liquid-demixing region. This is the main reason why the solubility of amorphous APIs in solvents is difficult to determine experimentally. Nevertheless, the liquid-liquid demixing is sometimes observed during crystallization processes of complex organic molecules known as “oiling-out”.21-23, 25-27 In systems where a polymer acts as the solvent and crystallization is hindered due to high viscosity, the liquidliquid demixing is even more often observed and usually called “amorphous demixing”. Tian et al.28 investigated the thermodynamic phase behavior of felodipine in Soluplus and in hydroxypropyl methylcellulose acetate succinate and postulated an amorphous demixing in these sytems. Duarte et al.29 proclaimed amorphous phase separation of itraconazole in different copolymers and Qian et al.30 found a partial immiscibility of an amorphous API and a polymer.


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From thermodynamic point of view both, “oiling out” as well as “amorphous demixing” are liquid-liquid equilibria (LLE). Here, the solvent-rich phase is in equilibrium with the liquid (amorphous) API-rich phase. In analogy to the solubility line, the API concentration of the solvent-rich phase is assumed to represent the solubility of the amorphous API in the solvent . As shown in the schematic API/solvent-phase diagram (see Figure 2), the

amorphous API-rich phase L2 not only comprises the pure amorphous API as assumed by Parks et al. and Hancock et al.

8, 10, 11

, but also contains a certain amount of solvent. This

agrees with Murdande et al.,5, 6 who noticed that it is not suitable to treat an amorphous API as a pure amorphous-API phase when in contact with a solvent (in their case water). Knowing the LLE-region and the solubility of the crystalline API, the solubility advantage (SAPI) of the amorphous API relative to its crystalline form (see Eq. (1)) can be determined at any temperature as the ratio of the two solubilities and (as shown in Figure 2).

Figure 2: Schematic phase diagram of an API in a solvent. The black solid line represents the solubility line of the crystalline API, the shaded region represents the amorphous demixing (liquid-liquid equilibrium, LLE) of the amorphous API and the solvent. L1 (dotted gray line) represents the concentrations in the amorphous solvent-rich phase and L2 (dashed gray line) represents the concentrations in the the amorphous API-rich phase. is the solubility of

the crystalline API, and is the solubility of the amorphous API at the same temperature.



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Solid-Liquid Equilibrium Calculation The solubility of crystalline API (in mole fraction) in a solvent can be calculated

according to the solid-liquid equilibrium (SLE) between the crystalline API solid and the liquid API/solvent phase,24 as described by Eq. (2).

∆ !, ∆ℎ − 1 − − #$% − + 1'(

1

(2)

where R is the ideal gas constant in J/(molK) and T the temperature of the system in Kelvin.

The melting temperature , the melting enthalpy ∆ℎ (J/mol) and the difference in heat

capacities between the crystalline solid and liquid API ∆

!,

(J/(molK)) are pure-component

properties and can be determined e.g., by differential scanning calorimetry. The influence of the solvent on the API solubility is considered via the API activity coefficient in a

solution saturated with crystalline API. This quantity is a measure of the differences in molecular shapes as well as the inter- and intramolecular interactions between the API and the solvent.15 The activity coefficient was calculated by PC-SAFT, as discussed in further detail later. Liquid-Liquid Equilibrium Calculation The liquid-liquid equilibrium24 of amorphous API/solvent systems is determined by Eqs. (3) and (4).

) )

* *

) ) * * +,-./0 +,-./0 +,-./0 +,-./0

(3) (4)

Here, 1) and 1* are the mole fractions of the API and the solvent in the solvent-rich phase L1 and in the amorphous API-rich phase L2, respectively (see Figure 2). The corresponding


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activity coefficients of the API and the solvent, 1) and 1* , are calculated by PC-SAFT. The same PC-SAFT parameter set is used for both, LLE calculations and SLE calculations. According to Figure 2 the solubility of the amorphous API is equal to .

)

PC-SAFT Within PC-SAFT, the residual Helmholtz energy ares of an API/solvent system is calculated as the sum of different contributions 14, 31. Dependent on the physicochemical properties of the molecules, different contributions to Helmholtz-energy can be attributed to hard-chain repulsion ahc, van der Waals attractions (adisp, where ‘disp’ indicates dispersion interactions),14

polar contributions (2!+,34 ),32 and the association contribution (aassoc).31 Therefore, the residual Helmholtz energy can be written as:

24.5 267 + 2815! + +2!+,34 + 2355+7

(5)

The detailed expressions of the different terms have been described in previous works 14, 15, 17, 31-36

and are not rewritten here. PC-SAFT considers an organic compound as a chain of 9 5.:

spherical segments with a diameter ;. To characterize a component, three pure-component

parameters (segment number 9 5.: , segment diameter ;, and dispersion energy parameter

? ) are required. For an associating compound that may form hydrogen bonds, two

additional parameters, namely the association-energy parameter @6AB B />? and the association?

volume parameter C B ?B , are required within PC-SAFT. Additionally, the number of association sites D1355+7 that can form hydrogen bonds has to be specified for each molecule

(see Figure 3). In summary, five pure-component parameters have to be determined to describe an associating component (e.g., an API) within PC-SAFT. This is depicted in Figure 3 for itraconazole as an example.



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Figure 3: Modeling scheme of itraconazole within PC-SAFT. It is described as a chain consisting of spherical segments (gray circles) and Niassoc association sites (dark gray circles). Here, Niassoc is equal to four: two electron donors and two electron acceptors.

To describe a binary mixture consisting of API i and solvent j, the Berthelot-Lorentz combining rules37 are applied for the segment diameter ;1E and the dispersion energy 1E,5,+!. ∙ KLM + >1E,1/0.47.!0

(8)

In API/solvent systems, cross- association between API and solvent molecules often occurs, and these interactions between the API and the solvent can be described by applying the

following combination rules for the mixture’s association energy @ B ?N and association volume C B?N , as proposed by Wolbach and Sandler38 (see Eqs. (9) and (10)).

1 @ B?N @ B ?B + @ N ?N

2


(9)

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C B ?N IC B?B C N ?N O

I;1 ;E

R 1 P2Q G;1 + ;E H

S

(10)

Calculation of Activity Coefficients from PC-SAFT The activity coefficient 1 of an API or solvent is defined as the ratio of the fugacity

coefficient T1 of the API or solvent in the API/solvent system and the corresponding fugacity coefficient T1 of the pure liquid compound i (see Eq. (11)).

1

T1 T1

(11)

The two coefficients (T1 T1 1 → 1 ) are calculated based on the residual chemical

potential μ4.5 (see Eq. (12): 1

ln T1

μ4.5 Z 1 − ln Y \ > >? D[

(12)

Here >? is the Boltzmann’s constant, the temperature of the system in Kelvin, the

pressure in N/m2, Z the molar volume in m3/mole and D[ Avogadro’s number. The residual chemical potential of the API or solvent is the partial derivation of the residual Helmholtz

energy of the system 24.5 (see Eq. (13)) with respect to its concentration at constant volume and temperature.

μ4.5 24.5 ]24.5 />?

1 +Y \ >? >? ]1 ^,-,_ +

Z − 1 >? D[

`aB

]24.5 />?

− b cE ]E ^,-,_ E

`aB

d

(13)

The activity coefficient of the API in the API/solvent mixture calculated by PC-SAFT is used for the calculation of the solubility of crystalline API (Eq. (2)). The activity coefficients of



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both, the API and the solvent +,-./0 calculated by PC-SAFT are applied for the

prediction of the API/solvent LLE (Eqs. (3) and (4).

Gibbs-Energy- Difference Method According to the method of Parks et al.10, 11, the solubility advantage is calculated based on

the Gibbs-energy difference (GED) between the pure amorphous and crystalline API, ∆e , according to Eq. (14).

∆e ln

2 2

(14)

In Eq. (14), R is the ideal gas constant in J/(molK), T is the temperature in Kelvin, and 2

and 2 are the activities of the API in saturated solution in equilibrium with pure amorphous

and pure crystalline API, respectively. In literature it is assumed that in diluted solutions, the activity ratio can be approximated by the solubility ratio and the advantage of the amorphous API relative to its crystalline form can be obtained according to Eq. (15).12

∆e

ln f

g

(15)

The Gibbs-energy difference ∆e is further estimated from the difference in enthalpy

∆ℎ and entropy ∆h between the amorphous and crystalline API according to Eqs. (16)(18).

∆ℎ ∆h

i

i

op ^klmn !

^

∆e ∆ℎ − ∆h

op ^klmn

^

! j

(16)

+ ∆ℎ +i

j + ∆h + i

^

op ^klmn

!

^

op ^klmn

! j

j qrsℎ ∆h


(17) ∆ℎ

(18)

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In the literature8,

13

, Eqs. (17) and (18) are often simplified by assuming a temperature-

independent heat capacity difference between the amorphous and crystalline API, which is assumed to be equal to the difference in the heat capacity of the amorphous API below and above its glass-transition temperature Tg (∆

!,^t .

Using these assumptions, the solubility

advantage can be calculated (based on Eqs. (15)- (18)) according to Eq (19).

f

g

∆ℎ ∙ 1 − − ∆ w v u

!,^t ∙ x

− − ∙ $% Y \y| {

(19)

z

In this work, the GED method was applied in two ways. First, the heat capacities of the amorphous and crystalline API were measured as a function of temperature and used for the solubility-advantage calculations (see Eqs. (15)- (18); further referred to as GED I). Second, the difference in the heat capacity of the amorphous API below and above the glass transition Tg was determined and used according to Eq. (19) to improve the calculations (henceforth referred to as GED II).8 Finally, results of both, GED I and GED II, were compared with the PC-SAFT predictions, as well as with reported experimental data.

MATERIALS AND METHODS Materials Glibenclamide, γ-indomethacin and itraconazole with a purity of ≥ 98.5% were purchased from TCI Deutschland GmbH (Eschborn, Germany). Hydrochlorothiazide and griseofulvin with a purity of ≥ 98% were purchased from Alfa Aesar (Karlsruhe, Germany). Water was used as obtained from a Millipore purification system (Merck KGaA, Darmstadt, Germany).



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Measurement of API Solubility For the solubility measurements of itraconazole and hydrochlorothiazide, an excess of the crystalline API was added to water (100 ml). The aqueous solution was mixed using a magnetic stirrer with a rotation speed of 600 rpm. The temperature of the solution was measured by a PT100 element (accuracy of ± 0.1 K) and kept constant by using a glass vessel with a heating jacket. After at least 48 hours (thermodynamic equilibrium was assumed after the API concentration stopped changing), samples were taken from the solution. Syringes and filter materials (mesh size of 0.2 µm) were preheated prior to use to prevent API crystallization during sampling. After appropriate dilution (if necessary), the API concentration was determined by measuring the

API

absorbance

using

UV-Vis

spectrometry

(Analytic Jena

Specord 210 Plus

spectrophotometer, Jena, Germany). The absorbances of hydrochlorothiazide and itraconazole were measured at 317 nm and 263 nm, respectively. Calibration curves were determined for each API at these wavelengths, and the coefficient of determination R2 was higher than 0.99 for each calibration curve. To convert the measured API concentration in mg/l into mole fractions, a reported correlation for the temperature-dependent molar density of water was used.39 All solubility measurements were performed in triplicate, and average values of the measured data are reported. Measurement of Thermal Properties To calculate the solubility of a crystalline API according to Eq. (2), the melting

temperature , the melting enthalpy ∆ℎ and the difference between the solid and

liquid heat capacities ∆

!

of griseofulvin, hydrochlorothiazide and itraconazole were

measured using differential scanning calorimetery (DSC) Q2000 (TA Instruments GmbH, Eschborn, Germany). The DSC was calibrated for cell constant and temperature against the


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enthalpy of fusion and melting temperature of pure indium. API samples with masses of 5-15 mg were weighed in hermetically-sealed aluminum pans (Tzero low-mass pans) and heated at a heating rate of 2 K/min to approximately 20 K above their melting temperatures (except griseofulvin and hydrochlorothiazide; these APIs were heated only approximately 10 K above their melting temperatures to avoid degradation). During the measurement, the cell was purged with nitrogen at a flow rate of 50 ml/min. All results were analyzed using TA Universal Analysis software 2000 (TA Instruments GmbH, Eschborn, Germany). For the determination of the difference in solid and liquid API heat capacities, a modulated mode was choosen. An oscillation period of 60 s and an amplitude of 0.318 K were applied during these measurements, as recommended in the operation manual for oscillating temperature profiles. Prior to use, the instrument was calibrated for heatcapacity measurements. The heat capacities of the solid and liquid API were measured at different temperatures below and above the melting temperature and then extrapolated to the melting point by regression, which is a common method used in the literature.40 To generate amorphous API, each crystalline API was melted just above its melting temperature using the same DSC settings as described above. After the temperature was held constant for 5 min, the molten API was quench-cooled (cooling rate 20 K/min) to a temperature of 283.15 K. Before reheating the samples at a heating rate of 2 K/min, the temperature was kept constant for 5 min. The heat capacities of the crystalline and amorphous API were measured as function of temperature. The latter was measured below and above the glass transition temperature of the API. The difference in the heat capacity of the amorphous API below and above the glass transition temperature was determined by extrapolating the heat capacity data to the glass transition temperature by regression.



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The standard deviations of the experimentally-determined properties were within a range of

, 0.01 kJ/g for ∆ℎ , and 0.1 J/(gK) and 0.2 J/(gK) for the heat-capacity 0.3 K for

difference ∆

!

of the crystalline and liquid API, respectively. The standard deviations

were within a range of 0.3 K for the glass transition temperatures of the amorphous APIs and within 0.1 J/(gK) for the heat capacity measurements. The heat capacities of the amorphous and crystalline API at temperatures ranging from 290 K to 360 K are summarized in the Supporting Information. Average values of triplicate measurements were linear regressed and used for all calculations performed in this work.


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RESULTS Determination of PC-SAFT parameters To predict the solubility advantage using PC-SAFT, pure-component parameters of the APIs and water, as well as the corresponding binary interaction parameters between APIs and water, are required. The pure-component parameters of the APIs are usually fitted to solubility data in pure organic solvents15-18. In this work, the pure-component parameters of glibenclamide and indomethacin were taken from previous works17, 41. The pure-component parameters of griseofulvin, hydrochlorothiazide and itraconazole were fitted to solubility data in organic solvents. Detailed information about the selected solvents, solubility data, fitting results and pure-component parameters of the solvents used for the parameter estimation are summarized in the Supporting Information (Figure S1 to Figure S3 as well as Table S1 and Table S2). The thermal properties including the glass-transition temperature and the difference in heat capacities of amorphous and crystalline API at the glass transition temperature, are summarized in Table 1. Table 1: Melting temperatures; melting enthalpies; heat capacity differences between solid and liquid APIs; glass transition temperatures; and differences between the heat capacities of amorphous and crystalline APIs at the glass transition temperature, for the APIs considered in this work.

∆

~

[J/g]

∆

Tg [K]

[K]

∆

[J/(gK)]

[K]

[J/(gK)]

glibenclamide

446.48*

107.1*

0.311*

330.64

0.348

griseofulvin

491.17

92.9

0.266

360.9

0.364

hydrochlorothiazide

539.59

129.8

0.214

393.81

0.244

indomethacin

433.25*

109.8*

0.327*

318.05

0.388

441.9

98.7

0.252

331.31

0.516

API

itraconazole *values were taken from

41


!,^t


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Page 18 of 36

All APIs were modeled as associating compounds. The association sites were defined according to the chemical structure of each API (see Figure 1). The association-volume was fixed to a value between 0.02 and 0.03, which is a common approach in literature.15 The purecomponent parameters of the APIs and water, which were further used in this work to predict the API/water phase diagrams, are given in Table 2. Table 2: PC-SAFT pure-component parameters of glibenclamide, hydrochlorothiazide, indomethacin, itraconazole and water as used in this work M

miseg

σi

ui/kB

[g/mol]

[-]

[Å]

[K]

glibenclamide

494

18.278

3.058

griseofulvin

352.77

14.174

hydrochlorothiazide

297.74

indomethacin

AiBi

AiBi

griseofulvin,

Niassoc

[K]

κ [-]

221.08

2181.88

0.02

3/3

3.372

221.261

1985.49

0.02

2/2

11.961

2.938

179.849

2173.62

0.03

4/4

357.79

14.283

3.535

262.791

886.44

0.02

3/3

itraconazole

705.63

26.109

2.166

252.346

1204.88

0.02

2/2

water

18.015

1.2047

2.7927*

353.95

2425.67

0.045

1/1

API

ε

/kB

42

*The expression σwater = 2.7927 + 10.11·exp(-0.01775·T) – 1.417·exp(-0.01146·T) was used .


Ref.

[-] 41

this work this work 17

this work 42

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Phase Diagrams of API/Water Systems For the generation of an API/water phase diagram, first the solubility of crystalline API in water was calculated based on the SLE relationship shown in Eq. (2); second the API concentrations in both, the solvent-rich and the API-rich amorphous phases were calculated based on the LLE relationships (Eqs. (3) and (4)). Solid-liquid equilibrium calculation in API/water systems The solubility of crystalline API was modeled as function of temperature in water according to Eq. (2) using activity coefficients of the API in water estimated from PC-SAFT.

The experimental solubility data for the crystalline APIs in water are shown in Figure 4 (a) – (e). The solubility of hydrochlorothiazide and itraconazole in water was measured in this work. Detailed results are summarized in the Supporting Information (Table S1 and Table S2). Solubility data for glibenclamide, griseofulvin, and indomethacin in water were taken from the literature.41, 43 As shown in Figure 4 (a) – (e), the solubilities of all the selected APIs increase with increasing temperature. At a fixed temperature, the solubility of the APIs in water decreases in the order hydrochlorothiazide > griseofulvin > indomethacin > glibenclamide > itraconazole. Furthermore, the solubilities of the crystalline APIs in water were modeled with PC-SAFT and these results are also shown in Figure 4 (a) – (e). For modeling the solubility data, binary interaction parameters kij of the systems griseofulvin/water, hydrochlorothiazide/water and itraconazole/water were fitted to the solubility data. For the systems glibenclamide/water and indomethacin/water, these parameters have already been estimated in a previous work 41. The binary interaction parameters kij are summarized in Table 4. To evaluate the accuracy of the modeling results, the average relative deviation (ARD) and maximum relative deviation



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(MRD) between calculated and experimental API solubilities were calculated according to Eqs. (20) and (17).

100 ×

1

%._!

/

b 1)

73,7,1 − ._!,1 ._!,1

100 × 921),/

(20)

73,7,1 − ._!,1 ._!,1

(21)

In Eqs. (16) and (17), %._! is the number of experimental solubility data points, 73,7,1 is the

calculated API solubility in water in mole fraction and ._!,1 is the experimental API solubility in water in mole fraction. The results are summarized in Table 3. Table 3: Binary interaction parameters kij between APIs and water, and the ARDs and MRDs of the solubilities calculated using PC-SAFT compared to experimental data. API in the binary system (API/water) glibenclamide

kij,slope·104

kij,intercept

ARD (%)

MRD (%)

1.299*

-0.0833*

9.26*

14.02

griseofulvin

2.641

-0.155

7.01

8.76

hydrochlorothiazide

1.614

-0.113

9.20

16.43

indomethacin

1.691*

-0.1099*

7.55*

11.63*

itraconazole

-1.210

0.022

10.62

18.07

* values were taken from 41

As shown in Figure 4 (a) – (e), the API solubilities in water as modeled with PC-SAFT are in good accordance with the experimental data for all APIs. This is also verified by the ARD and MRD values summarized in Table 4. The ARDs between the calculated API solubility values and the experimental data are below 10% in most cases, which shows the high accuracy of the PC-SAFT calculations.

Liquid-Liquid equilibrium prediction in API/water systems


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Based only on the PC-SAFT pure-component parameters (see Table 2) and the binary interaction parameters between the APIs and water (see Table 3), the liquid-liquid equilibrium for each API/water system was predicted according to Eqs. (3) and (4). No additional parameters were required. The results predicted for the solubility of the amorphous API

)

in the water-rich phase

L1 are also included in Figure 4 (a) – (e). From these figures, it is obvious that in all cases and at any temperature the solubility of the amorphous API is higher than that of the crystalline API. Like the solubility of the crystalline API, the solubility of the amorphous API depends on temperature and for all cases increases with increasing temperature.



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(a)

(b)

(c)

d)

(e) Figure 4: Phase diagrams of the API/water systems for glibenclamide (a), griseofulvin (b), hydrochlorothiazide (c), indomethacin (d) and itraconazole (e); symbols represent experimental solubilities of the crystalline APIs glibenclamide (black circles), griseofulvin (gray squares), hydrochlorothiazide (dark gray triangles), indomethacin (gray stars) and itraconazole (gray hexagons) in water. Lines are modeled with PC-SAFT. Full lines represent the calculated solubility lines for crystalline APIs in water; dashed lines represent the waterrich phase of the predicted LLE and thus the solubilities of the amorphous APIs.


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Solubility advantage calculation The solubility advantage of the APIs was calculated according to Eq. (1) using two different methods: PC-SAFT and the GED method. For PC-SAFT, the solubility advantage of amorphous API versus its crystalline form in water was determined as function of temperature based on the generated phase diagrams (as shown in Figure 4 (a) – (e)).The results are shown in Figure 5 (a) – (e) in a temperature range of 280 – 360 K. The GED was applied in the same temperature range. Here, the difference in heat capacity of the amorphous and crystalline API (GED I), as well as the simplified approximation ∆c!

∆

!,^t

(GED II), were used for the calculations. The detailed temperature-dependent heat

capacity values for each API are summarized in the Supporting Information (Tables S3- S7). The API solubility advantages predicted by both, the two GED approaches and PC-SAFT were compared with experimental data reported in literature. The reported experimental data and the predicted API solubility advantages at the same temperatures obtained using the two methods are summarized in Table 4. The predicted solubility advantages at 310.15 K (37°C) are also included in Table 4 because these values are of interest for in vivo drug solubilization. Additionally, Table 4 contains the activity coefficients required for the calculating the solubility of amorphous and crystalline APIs (see Eq. (2) and Eq. (3)). The temperaturedependent calculations for the solubility advantage as well as the reported experimental data are also shown in Figure 5 (a) – (e) for all API/water systems. From Table 4 and Figure 5, it becomes obvious that the solubility advantages of amorphous APIs versus their crystalline form predicted by GED I and GED II are much higher than the experimental data. Similar results were also found earlier by Hancock et al.,8 Gupta et al.12 and Matteucci et al..13 Moreover, in all cases, the solubility advantages predicted by PC-SAFT are in much better agreement with the experimental data (which will further be discussed in the next section) than the values predicted by GED I and GED II. ACS Paragon Plus Environment


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Table 4: Calculated solubilities and activity coefficients of crystalline and amorphous API using PC-SAFT; experimentally-obtained and predicted solubility advantages of amorphous versus crystalline API in water using PC-SAFT, GED I and GED II. API activity coefficients and solubilities calculated using PC-SAFT

API

glibenclamide

griseofulvin

hydrochlorothiazide

298.15

6.16·10-8

7.65·104

1.75·10-6

7.64·104

2.21·10-1

310.15

1.54·10-7

4.97·104

2.59·10-6

4.96·104

294.15

-7

4.78·10

4

5.74·10

-6

4.80·10

4

5.72·10

3.12·10

298.15

5.32·10-7

5.59·104

4.92·10-6

5.57·104

310.15

-7

7.54·10

4

4.99·10

-6

5.43·10

4

4.98·10

3.06·10

8.8210

298.15

4.37·10-5

1.13·102

6.45·10-4

9.901·101

1.34·10-1

310.15

-5

7.50·10

1

9.49·10

-3

1.10·10

7.68·10

-1

1.30·10

298.15

2.64·10-7

8.31·104

5.66·10-6

8.29·104

4.17·10-1

T [K]

)

)

*

1

*

Solubility advantage

Prediction using PCSAFT

Prediction using GED I

Prediction using GED II

Experimental value

6.10·10-1

28.48

835.58

172.57

22.6

2.14·10-1

5.99·10-1

16.81

368.44

110.76

-1

-1

8.81·10

10.03

93.13

19.03

1.4

3.11·10-1

8.82·10-1

9.24

82.01

18.24

1.4

-1

-1

7.20

56.65

15.92

4.75·10-1

14.75

325.72

161.93

-1

4.81·10

14.65

164.85

115.64

1.13

21.43

109.14

37.02

4.9

4.9 4.5

indomethacin

itraconazole

318.15

8.64·10-7

4.74·104

9.37·10-6

4.72·104

3.88·10-1

1.14

10.84

57.14

26.54

310.15

-7

5.33·10

4

5.99·10

-6

7.60·10

4

5.98·10

-1

4.00·10

1.14

14.25

38.75

21.27

310.15

1.28·10-7

1.13·104

3.35·10-6

1.12·104

1.01·10-1

3.75·10-1

26.24

1668.19

142.41


2.8 10 16

Prepar metho th amorp for quen coo n.a quen coo quen coo n.a quen coo n.a quen coo quen coo quen coo n.a spray lyophi

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(a)

(b)

(c)

(d)

(e) Figure 5: Solubility advantage of amorphous API versus its crystalline form as a function of temperature. Stars represent the experimentally- determined solubility advantages of glibenclamide (a), griseofulvin (b), hydrochlorothiazide (c), indomethacin (d) and itraconazole (e) in water (references given in Table 5). The lines show the modeling results obtained using PC-SAFT (full line) and from GED I (dotted line) and GED II (dashed line).



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For glibenclamide, the solubility advantage predicted by PC-SAFT is approximately 1.26 times as high as the experimentally-determined value (see Figure 5 (a) and Table 4) at 298.15 K, which shows very good accordance between the predicted and experimental results. In contrast, the results calculated using the methods GED I and GED II are approximately 40 and 8 times as high as the experimental value. As seen in Figure 5 (a), the solubility advantage predicted by GED I changes at the glass transition temperature because temperature-dependent values for the heat capacities of the amorphous and crystalline form are used. Due to the distinct increase in the heat capacity of the amorphous API at the glass transition temperature, which can be related to the change in the molecular mobility of the API,12 the Gibbs-energy difference between the amorphous and crystalline API decreases, resulting in a lower predicted solubility advantage. Using the difference in the heat capacities at the glass transition temperature instead, the calculated solubility advantage is considerably lower at temperatures below Tg resulting in better predictions for GED II than for GED I. The highest deviation among the PC-SAFT predictions was observed for griseofulvin/water (see Figure 5 (b) and Table 4). Here, the predicted value is approximately 7 times as high as the experimental value (see Table 4). However, the results calculated using the GED methods are even higher, 14 times to 67 times bigger than the experimental values. Amorphous griseofulvin was reported to rapidly recrystallize in water,5 which certainly leads to a high uncertainty in the solubility measurements and thereby in the experimentally-found solubility advantage. In the case of the hydrochlorothiazide/water system (see Figure 5 (c) and Table 4), the results predicted by PC-SAFT were found to be three times as high as the experimental data, while the results calculated by GED I and GED II were between 33 times and 66 times as high as the experimental data. This obviously shows that PC-SAFT predictions are much more ACS Paragon Plus Environment

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accurate than the GED results. As before, the use of temperature-dependent heat capacities of amorphous and crystalline APIs in GED I lead to a much higher calculated solubility advantage for hydrochlorothiazide compared to experimentally-observed values. For hydrochlorothiazide, the high deviation is observed over the whole temperature range. Here, the small difference in the heat capacity of amorphous and crystalline hydrochlorothiazide leads to high values for the corresponding GED and thus to high values for the solubility advantage below the glass transition temperature (393.81 K). The deviation between PCSAFT predictions and experimental data for the hydrochlorothiazide/water system (see Figure 5 (c)) may be due to the reported fast recrystallization of amorphous hydrochlorothiazide during solubility measurements.5 For the indomethacin/water system, the results predicted by PC-SAFT were found to be approximately four to five times as high as the experimental values, while the results calculated by the GED I and GED II were found approximately 8 times to 24 times as high as the experimental data (see Figure 5 (d) and Table 4). Here again, the use of temperaturedependent heat capacities for the amorphous and crystalline indomethacin in GED I leads to a much higher calculated solubility advantage than the experimentally reported values (see Table 4). Additionally, a sharp decrease in the calculated solubility advantage is observed at the glass transition temperature, indicating the sharp increase in the heat capacity of amorphous indomethacin above the glass transition temperature and the lower GED between amorphous and crystalline indomethacin. As for the hydrochlorothiazide/water system, the higher deviations between the PC-SAFT predictions and the experimental data for the indomethacin/water system (see Figure 5 (d) and Table 4) may be due to the reported fast recrystallization of indomethacin during solubility measurements.5, indomethacin was reported to recrystallize in water within 20 minutes.5, 6


6,

8

Amorphous


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For itraconazole, the predicted solubility advantage obtained using PC-SAFT is again in good agreement with the experimental data (values varied by a factor of 1.6 to 2.6) at 310.15 K (see Figure 5 (e)). Although the experimentally-observed solubility advantage for itraconazole was reported to depend on several parameters13 (e.g., crystallinity, preparation method, surface area of the amorphous API, etc.), the PC-SAFT prediction is in good accordance with the experimental data (see Table 4). In contrast, the calculated values obtained using the GED methods are up to 167 times as high as the experimental data.


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DISCUSSION Amorphous pharmaceuticals are advantageous compared to their crystalline forms in terms of bioavailability, solubility and dissolution rate. According to the general thermodynamic phase behavior of API/solvent systems, the solubility advantage of amorphous versus crystalline API can be directly calculated based on the solubility of the crystalline API and the amorphous demixing in the API/solvent system. As amorphous demixing is often metastable with respect to crystallization, the solubility of amorphous API and thus the solubility advantage of amorphous versus its crystalline API is very difficult to measure and can only be obtained with high uncertainty. However, by applying a suitable thermodynamic model that can describe both, API solubility and amorphous demixing, the solubility advantage can be predicted readily and without any further assumptions. As shown in Figure 5 (a)- (e) for all considered APIs, the solubility advantage predicted by PC-SAFT is much more accurate than the results obtained by GED I and GED II. In all cases, however, the predicted results (PC-SAFT and GED methods) were higher than the experimental data. The most obvious explanation for the difference between the predicted and experimental solubility advantages is the fast recrystallization of amorphous API in the presence of a solvent,5, 6, 8, 9 leading to an experimentally-determined solubility advantage that is in most cases lower than the real one. Amorphous glibenclamide is reported to be quite stable in water and thus recrystallization of amorphous glibenclamide in water is likely very slow.5 Amorphous itraconazole was reported to be stable without recrystallization over four hours.13 Experimental data for the solubility advantage of glibenclamide and itraconazole should therefore be more reliable than the results ACS Paragon Plus Environment


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for the other APIs investigated. As seen in Figure 5, PC-SAFT yields the best prediction performance for the solubility advantage of these APIs in water, while the results obtained using GED I and GED II are much too high compared to the experimental data. As noted by Murdande et al.,5, 6 amorphous APIs may absorb a significant amount of water. By performing an LLE calculation for the amorphous API/water system, the amount of water absorbed in the amorphous API-rich phase L2 is considered in a straight-forward manner. The API activity coefficients shown in Table 4 for saturated API solutions in equilibrium with the crystalline APIs as well as those in the two liquid phases

)

and

*

being in

liquid-liquid equilibrium differ significantly from one and thus need to be considered in the calculations. They depend on the solvent and on temperature and thus allow accounting for the influence of solvent and temperature on the solubility advantage. It is however worth mentioning that the solubility advantage is not simply obtained as the ratio of the API activity coefficients and

)

but by using them in Eqs. (3) and (4). Applying two different

equilibrium conditions accounts for the fact that in the first case the saturated solution is in equilibrium with the pure crystalline API (Eq. (3)) whereas in the second case, it is in equilibrium with a liquid API-rich phase that contains a certain amount of solvent (Eq. (4)). For the GED methods, the remarkably too- high predictions may be attributed to the following two aspects. First, GED I and GED II assume that the amorphous API in water is a purecomponent phase, which means that absorbed solvent is neglected and the solubility of the amorphous API is treated the same way as that of the crystalline API. The amorphous phase in the pure state however has a much higher Gibbs energy than the amorphous phase in the solution which might be the reason why the two Gibbs-energy-difference methods predict too high solubility advantages. Second, the activity coefficient of the API in solution is neglected by the GED methods.12 This leads to a calculated solubility advantage that does not depend on the solvent and solvent composition, which also contradicts experimental findings.8, 10, 11, 13 ACS Paragon Plus Environment

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Finally, also the assumption of using the heat capacity change of the amorphous API at the glass transition temperature for the determination of the solubility-advantage calculations according to the GED method8 is questionable. This assumption neglects several effects that occur when the amorphous API comes into contact with water (e.g., decrease in the glass transition temperature,6 change in molecular mobility of the amorphous API,12, 45 etc.).



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CONCLUSIONS In this work, the thermodynamic model PC-SAFT was used to calculate and predict the phase diagrams of API/water systems for glibenclamide, griseofulvin, hydrochlorothiazide, indomethacin and itraconazole. Predictions were performed based only on solubility data and thermal properties of the crystalline API. These data are commonly available because they are collected within the first stages of API formulation studies. Based on the solubility of the crystalline API in water, the liquid-liquid demixing in the API/water was predicted using PC-SAFT. Assuming that the API concentration in the waterrich phase of the liquid-liquid boundary equals the solubility of the amorphous API, the solubility advantage of each API in water was predicted as function of temperature. Although shown here for water, this approach is a general one and not restricted to aqueous systems but applicable to any solvent or solvent mixture. It considers the influence of the solvent on the solubility of both, crystalline and amorphous API, and moreover accounts for the presence of solvent absorbed in the amorphous API. To evaluate the prediction performance of this approach, the predicted solubility advantage was compared to experimental data and to values obtained by commonly-applied GED methods. It was shown for all of considered systems that PC-SAFT predictions of the solubility advantage are significantly more accurate than the results obtained from the GED methods.


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Acknowledgements The authors would like to acknowledge financial support from the Alexander von HumboldtFoundation (Y. Ji) and German Science Foundation (Leibniz Award to G. Sadowski). All PCSAFT calculations were performed using the software SolCalc developed at TU Dortmund.

SUPPORTING INFORMATION API solubility data, API parameter estimation, thermal properties of amorphous and crystalline API. This information is available free of charge via the Internet at http://pubs.acs.org/.

AUTHOR INFORMATION Corresponding Author Tel: +49-231-755-2635. Fax: +49-231-755-2572. E-mail: [email protected] Notes The authors declare no competing financial interest.



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References 1. Babu, N. J.; Nangia, A. Solubility Advantage of Amorphous Drugs and Pharmaceutical Cocrystals. Cryst Growth Des 2011, 11, (7), 2662-2679. 2. Mullins, J. D.; Macek, T. J. Some Pharmaceutical Properties of Novobiocin. J Am Pharm Assoc 1960, 49, (4), 245-248. 3. Imaizumi, H.; Nambu, N.; Nagai, T. Pharmaceutical Interaction in Dosage Forms and Processing .18. Stability and Several Physical-Properties of Amorphous and Crystalline Forms of Indomethacin. Chem Pharm Bull 1980, 28, (9), 2565-2569. 4. Murdande, S. B.; Pikal, M. J.; Shanker, R. M.; Bogner, R. H. Solubility Advantage of Amorphous Pharmaceuticals, Part 3: Is Maximum Solubility Advantage Experimentally Attainable and Sustainable? J Pharm Sci-Us 2011, 100, (10), 4349-4356. 5. 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 ResDordr 2010, 27, (12), 2704-2714. 6. Murdande, S. B.; Pikal, M. J.; Shanker, R. M.; Bogner, R. H. Solubility Advantage of Amorphous Pharmaceuticals: I. A Thermodynamic Analysis. J Pharm Sci-Us 2010, 99, (3), 12541264. 7. Egawa, H.; Maeda, S.; Yonemochi, E.; Oguchi, T.; Yamamoto, K.; Nakai, Y. Solubility Parameter and Dissolution Behavior of Cefalexin Powders with Different Crystallinity. Chem Pharm Bull 1992, 40, (3), 819-820. 8. Hancock, B. C.; Parks, M. What is the true solubility advantage for amorphous pharmaceuticals? Pharm Res-Dordr 2000, 17, (4), 397-404. 9. Murdande, S. B.; Pikal, M. J.; Shanker, R. M.; Bogner, R. H. Aqueous solubility of crystalline and amorphous drugs: Challenges in measurement. Pharm Dev Technol 2011, 16, (3), 187-200. 10. Parks, G. S., Huffmann H.M., and Cattoir F.R., . Studies on glass II: The transition between the glassy and liquid states in the case of glucose. J. Chem. Phys. 1928, 32, 1366-1379. 11. Parks, G. S.; Snyder, L. J.; Cattoir, F. R. Studies on Glass: XI. Some Thermodynamic Relations of Glassy and Alpha-Crystalline Glucose. The Journal of Chemical Physics 1934, 2, (9), 595. 12. Gupta, P.; Chawla, G.; Bansal, A. K. Physical stability and solubility advantage from amorphous celecoxib: The role of thermodynamic quantities and molecular mobility. Mol Pharmaceut 2004, 1, (6), 406-413. 13. Matteucci, M. E.; Miller, M. A.; Williams, R. O.; Johnston, K. P. Highly Supersaturated Solutions of Amorphous Drugs Approaching Predictions from Configurational Thermodynamic Properties. J Phys Chem B 2008, 112, (51), 16675-16681. 14. Gross, J.; Sadowski, G. Perturbed-chain SAFT: An equation of state based on a perturbation theory for chain molecules. Industrial & Engineering Chemistry Research 2001, 40, (4), 1244-1260. 15. Ruether, F.; Sadowski, G. Modeling the Solubility of Pharmaceuticals in Pure Solvents and Solvent Mixtures for Drug Process Design. J Pharm Sci-Us 2009, 98, (11), 4205-4215. 16. Ruther, F.; Sadowski, G. Thermodynamic Modeling of Solubility. Chem-Ing-Tech 2011, 83, (4), 496-502. 17. Prudic, A.; Ji, Y. H.; Sadowski, G. Thermodynamic Phase Behavior of API/Polymer Solid Dispersions. Mol Pharmaceut 2014, 11, (7), 2294-2304. 18. Prudic, A.; Kleetz, T.; Korf, M.; Ji, Y.; Sadowski, G. Influence of copolymer composition on the phase behavior of solid dispersions. Mol Pharmaceut 2014, 11, (11), 4189–4198. 19. Cassens, J.; Prudic, A.; Ruether, F.; Sadowski, G. Solubility of Pharmaceuticals and Their Salts As a Function of pH. Ind Eng Chem Res 2013, 52, (7), 2721-2731. 20. Laube, F. S.; Sadowski, G. Predicting the Extraction Behavior of Pharmaceuticals. Ind Eng Chem Res 2014, 53, (2), 865-870. 21. Kiesow, K.; Tumakaka, F.; Sadowski, G. Experimental investigation and prediction of oiling out during crystallization process. Journal of Crystal Growth 2008, 310, (18), 4163-4168. 22. Kiesow, K.; Ruether, F.; Sadowski, G. Solubility, crystallization and oiling-out behavior of PEGDME: 1. Pure-solvent systems. Fluid Phase Equilibr 2010, 298, (2), 253-261. ACS Paragon Plus Environment

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