Solubility of the Ketoconazole (an Antifungal Drug) in Supercritical Carbon Dioxide and Menthol as a Cosolvent (Ternary System): Experimental Data and Empirical correlations

One of the main steps in choosing the drug nanoparticle production processes by supercritical carbon dioxide (SC-CO2) is determining the solubility of the solid solute. For this purpose, the solubility of Ketoconazole (KTZ) in the SC-CO2, binary system, as well as in the SC-CO2menthol (cosolvent), ternary system, was measured at 308–338 K and 12-30 MPa using the static analysis method. The KTZ solubility in the SC-CO2 ranged between 1.70×10 -6 and 8.02×10, while drug solubility in the SC-CO2 with cosolvent varied from 2.7×10 -5 to 1.96×10 . This difference indicated the significant effect of menthol cosolvent on KTZ solubility in the SC-CO2. Moreover, KTZ solubilities in the two systems were correlated by several empirical and semiempirical models. Among them, Sodeifian et al., Bian et al., MST, and Bartle et al. models can more accurately correlate experimental data for the binary system than other used models. Also, the Sodeifian and Sajadian model well fitted the solubility data of the ternary system with AARD,%= 6.45, Radj= 0.995.

Serious fungal infections can increase due to the development of the human immunodeficiency virus (HIV), anti-cancer chemotherapy, and/or the greater utilization of the immunosuppressive treatments in transplanting the organs 1 . Ketoconazole (KTZ) is mainly applied as a synthetic imidazole antifungal drug to treat fungal infections in different forms (oral tablets, topical creams, and gels). It has been applied in immunocompromised patients and advanced prostatic carcinoma 1,2 . KTZ has very low solubility (17 µg/ml) in the water and higher penetrability; therefore, it has been considered as a class II drug in the biopharmaceutics classification system (BCS). Improving the solubility of pharmaceutical compounds is a challenging subject as it can significantly reduce the oral bioavailability and, thus, the therapeutic efficacy of drugs 2 .
Reducing particles' size and hence increasing the available surface area can enhance the solubility and bioavailability of pharmaceutical compounds with lower water solubility. Therefore, researchers have applied different processes (such as high-pressure homogenization, evaporation, milling, and sublimation) to reduce particle size in the pharmaceutical industry. Meanwhile, supercritical fluid (SCF) technology has received much attention in medicine to decrease the size of the particles, hence, increasing their dissolution rate and bioactivity. According to studies conducted in this field, the application of supercritical solution methods in particle formation has rapidly expanded. The solubility of drugs in SCFs should be experimentally measured for designing pharmaceutical processes 3 .
Numerous investigators have demonstrated that solute solubility in the SCFs can be substantially improved with the addition of cosolvents (polar or non-polar) [4][5][6][7][8][9][10] . Gurdial et al. 4 , measured the solubility of o-and m-hydroxy-benzoic acid in acetone -SC-CO2 and methanol-SC-CO2 binary mixtures at the temperature range of 318-328 K and the pressure range of 90-200 bar using a continual flow apparatus. Their results indicated that the addition of little amounts of the cosolvents to SC-CO2 largely enhanced o-and m-hydroxy-benzoic acid solubility. Huang et al. 11 evaluated the equilibrium mole fraction of aspirin in SC-CO2 with and without acetone cosolvent. Their results showed that acetone cosolvent could cause a 5fold increase in aspirin solubility. Also, Koga et al. 9 investigated influences of cosolvents (octane & ethanol) on the solubility of fatty acids, stearic acid, and stearyl alcohol in SC-CO2 using a flow-type apparatus and showed the higher effectiveness of ethanol on the solubilities of fatty acids than octane. Hosseini et al. 12 determined the solubility of clozapine and lamotrigine in SC-CO2 with menthol cosolvent at the temperature range of 313-323 K and the pressure range of 123-337 bar. The applied cosolvent enhanced the solubility of both solutes in SC-CO2. Consequently, the solubility of numerous compounds has been experimentally determined in the SCFs [13][14][15][16][17][18][19][20] . However, the measurement of the solubility of drugs in the SCFs under diverse pressure and temperature conditions is costly and laborious 21 . In this regard, thermodynamic models have been developed to decrease the number of required experimental measurements. Compared to the other SCFs, SC-CO2 has been widely employed in SCF processes due to its special thermodynamic and heat transfer properties. Additionally, CO2 is non-toxic, non-flammable, cost-effective, abundant at high levels of purity, and environmentally-friendly with comparatively lower critical pressures and temperatures (7.38 MPa & 304.1 K) [22][23][24][25][26][27] .
Several models have been applied to correlate and predict solids solubility at supercritical conditions, among which empirical and semiempirical methods [28][29][30][31][32][33][34] , equations of state (EoS) (including cubic and non-cubic models) [35][36][37][38][39][40][41][42][43] , intelligent computational techniques (e.g. artificial neural networks (ANN) and least square support vector machine (LS-SVM) networks), and combination of grey wolf optimizer and support vector machines (GWO-SVM) networks 27,44 can be mentioned. Some characteristics such as acentric factor, and molar volume, as well as the solid vapor pressures, are essential for the calculations of EoS based models. These parameters are, however, unavailable and thus must be estimated by the group contribution techniques leading to attenuated accuracy. To overcome this drawback, several researchers have developed different empirical and semiempirical models to correlate the solubility data 45-52 . In this study, a static analysis procedure was employed to determine the solubility of KTZ in SC-CO2 at different temperature and pressure conditions with and without cosolvent. The solubility of KTZ in the SC-CO2 with cosolvent has not been experimentally measured so far.
Moreover, drug solubility in the SC-CO2 (i.e., the binary system) was correlated by ten semiempirical models, including Chrastil 28 , Sparks et al. 34   The amount of menthol and drug in saturator cell 1 (S1) and saturator cell 2 (S2) were 5 and 2 g, respectively. A magnetic stirrer (100 rpm) was applied to accelerate the equilibration and improve saturation of the particles in cells. The sintered filter was put on the top of the column to prevent the escape of menthol particles (as either powder or liquid droplets). In this research,

Binary system
In our previous study, the reliability of the solubility setup was evaluated by determining the solubility of naphthalene and alpha-tocopherol in SC-CO2 at different pressures and temperatures and comparing them with the corresponding data in the literature 55 . In general, the authors systematically check and calibrate the device before testing naphthalene and alphatocopherol solubilities in SC-CO2. It should be mentioned that the mole fraction and solubility (S(g/L)) of KTZ in SC-CO2 were measured at different temperature and pressure conditions ( Table 2). Each experimental data was measured in triplicate to enhance the data reliability. The relative standard uncertainty of the solubility data was below 0.05. The relative standard uncertainty (Us) can be calculated by the following equation: respectively. n is the number of times each experimental data was measured (n=3, in this work). Expanded uncertainty is U =k* ucombined and the relative combined standard uncertainty is defined as ucombined / y = is the relative standard uncertainty of each input estimate (xi) and Pi is known positive or negative number having negligible uncertainties. y2 and S are mole fraction of solute in binary system and solubility of solute in SC-CO2, respectively.    An enhancement in the density also increased the solubility at the elevated pressures.
Generally, SC-CO2 density and solute vapor pressure are the two key factors contributing to the solubility of the solute in SC-CO2. The solubility showed an ascending trend with increasing density and solute vapor pressure. At pressures below the crossover region, where the influence of increased solvent density on the solute solubility dominates over decreased solute vapor pressure, the solid solute exhibited higher solubility at lower temperatures rather than higher ones. At the top of the crossover region, when temperature increased, the solubility incremented more rapidly with pressure enhancement, which might be due to the competing effects of the reduction of SC-CO2 density and the increase of solute vapor pressure. 21   8.16×10 -4 . The mean standard deviation between their experimental data and the present work was 2%. The effects of temperature and pressure on the solubility were the same for both works. Figure 2b and Table 3 report KTZ solubility in SC-CO2 with cosolvent (menthol) under different pressures and temperatures. Accordingly, solubility based on the solute mole fraction (y) ranged from 2.7×10 -5 to 1.96×10 -4 . Each experimental data was measured three times to enhance the reliability of the solubility data. Figure 2b presents an increase in KTZ solubility with the pressure increment at all isotherms. The increase of density with rising the pressure led to the more powerful solvation ability of SC-CO2 and thus enhanced the solid solubility.

Ternary systems
The largest increment in solubility with rising pressure was observed at the highest temperature, which can be assigned to the impacts of the temperatures and pressures on the solvent density and pressure of the solute vapor 10 . As stated previously, temperature influences the solvating power by two challenging factors: the solvent density and pressure of the solute vapor. Therefore, an increment in temperature will decrease the solubility below the crossover pressure area and also increased the solubility above the crossover pressure area. Finally, the crossover point in the ternary system was between 13 and 15 MPa.
In the ternary system (solute-SC-CO2-cosolvent), the enhancement factor has been considered to study the cosolvent effect. This factor is the ratio of the obtained solubility of solute within the ternary system to that of the binary system. By investigating the presented results in Table   3, it can be founded out that the solubility was increased by adding menthol to SC-CO2. The cosolvent effect "e" was applied to better evaluate the solubility enhancement 7,59 :  In general, the increase in the solubility of solids in ternary systems (CO2 +cosolvent) can be attributed to the increase in solvent density, dipole-dipole interactions, and also hydrogen bonding between the solute and the cosolvent 62 . In this case, upon adding menthol to the cell, the density of the SCF enhanced, leading to an increment in the solubility. The polarity of SC-CO2 can also be affected by the cosolvent. Menthol enhanced the solubility of KTZ in CO2 due to the presence of a hydroxyl (polar) group and a hydrocarbon group (nonpolar) in the respective structures. As a result, it can be concluded that stronger attractive polar interaction and hydrogen bonding could lead to greater solubility. Also, by comparing values of e in Table   3, it can be inferred that cosolvent effects decreased with the increment of the pressure, which is compatible with the published studies 4-6,11 .

Correlation of the binary system
The present study considered ten semiempirical equations for correlating KTZ solubility in SC-CO2, as listed in Table 4. Figure 3 depicts the outputs of the correlation at different temperatures. Then, statistical criteria were employed to investigate the abilities of semiempirical models. As a general rule, the more adjustable parameters lead to more accurate correlations. To provide a reliable accuracy criterion to compare the models with different numbers of adjustable parameters, AARD and Radj with the following equations were used 63 So that Z represents the number of the adjustable variables for each model.
where N refers to the numbers of data points in each set. Moreover, Q stands for the numbers of the independent variables in each equation. Radj can be used to compare models with different numbers of independent variables and R 2 represents the correlation coefficient 64 .
Where SSE is the error of the sum of squares and SST is the total sum of squares.
Correlation outputs and optimal values of the parameters are presented in
The correlation results of the KTZ-Menthol-CO2 system provided by the semi empirical models (AARD, Radj and a0-a6 are average absolute relative deviation, adjusted correlation coefficient and adjustable parameters, respectively).

Conclusions
In this research, the KTZ solubility in SC-CO2 (with and without menthol) was experimentally measured at the temperature range of 308-338 K and the pressure range of 12-30 MPa using spectrophotometric analysis. The tests were carried out in triplicates to enhance the reliability of the solubility data. Moreover, the mole fractions(y) and KTZ solubility (S (g/ L)) in SC-CO2 (binary system) ranged between 0.016 and 0.784 and 1.70×10 -6 and 8.02×10 -4 , while the mole fractions of the drug in the SC-CO2 with cosolvent (i.e., the ternary system) ranged in 2.7×10 -5 -1.96×10 -4 . Therefore, it can be concluded that the solubility increased in the presence of menthol. Several semi-empirical and empirical models were utilized for correlating experimental results of binary and ternary systems. Among them, Sodeifian et al. model managed to correlate the experimental data for the mentioned binary system at higher accuracy.
In the case of the ternary system, the highest accuracy was provided by the Sodeifian and Sajadian model.

Acknowledgment
Hereby, the researchers thank the great financial supports supplied by the research deputy of University of Kashan for supporting the present applied, beneficial, and worthwhile plan (Grant # Pajoohaneh-1398/9). Moreover, the researchers appreciate the Arasto Pharmaceutical Company.