Experimental solubility and thermodynamic modeling of empagliflozin in supercritical carbon dioxide

Predicting the solubility of drugs in supercritical carbon dioxide using machine learning and atomic contribution

The pharmaceutical sector is aware of supercritical CO2 (SC-CO2) as a possible replacement for problematic organic solvents. Using a novel artificial intelligence (AI) strategy to predict drug solubility using the SC-CO2 system mathematically has been deemed an intriguing approach. In this work, the atomic contribution (AC) method and machine learning (ML) models are combined to develop hybrid machine learning models to compute the solubility of several drugs, including anticoagulants, anti-cancers, calcium channel blockers, immunosuppressives, antihistamines, and others. The novelty of the approach lies in using the AC concept to capture molecular details at the atomic level. This enables the model to account for the specific contributions of individual atoms and to provide more precise input features for machine learning. The integration of these molecular insights with ML techniques results in significantly improved predictive performance over traditional ML methods. Throughout the modeling procedure, temperature, pressure, the density of SC-CO2, and the effect of constituent atoms of the drugs are the input variables, while the solubility of drugs is the output. This study looks into predicting the solubility of these drugs in SC-CO2 using the least square support vector machine (LSSVM) with radial basis function kernel (RBF) and multilayer perceptron artificial neural network (MLPANN). These models were developed using a database including 2358 experimental solubility data points from 86 solid drugs. The solubility of solid drugs in supercritical CO2 spans a remarkably wide range in this study, from as high as 3.9 × 10-2 to as low as 1 × 10-7. The results demonstrated that this innovative approach could estimate solid drug solubility in SC-CO2 with AARD% and R2 values of 7.20 and 0.99, respectively, under different pressure and temperature conditions. The ability of the models to capture a wide range of solubilities in SC-CO2 showcases their effectiveness in dealing with both highly and poorly soluble compounds. The developed models, considering their global prediction, accuracy, and being user-friendly, are the best options to be used by researchers for incorporating into software for enabling more efficient design of supercritical extraction processes and reducing the need for trial-and-error experimentation in manufacturing.

Application of machine learning approach to estimate the solubility of some solid drugs in supercritical CO2

Accurate estimation of the solubility of solid drugs (SDs) in the supercritical carbon dioxide (SC-CO2) plays an essential role in the related technologies. In this study, artificial intelligence models (AIMs) by gene expression programming (GEP) and adaptive neuro-fuzzy inference system (ANFIS) methods were applied to estimate the solubility of SDs in SC-CO2. Hence, a comprehensive database (1816 datasets) comprising operational conditions (T, P) in the wide ranges (308-348.2 K and 80-400 bar), SD's molecular weight (MWSDs), and melting point (MPSDs) were gathered. Investigation analysis of the models' strength showed that the model developed by ANFIS exhibited a more satisfactory approximation than the GEP model. According to the optimized ANFIS model, statistical parameters of R2, RMSE, MAE, and AARD% were obtained, equivalent to 0.991, 0.260, 0.167, and 13.890% for training and 0.990, 0.256, 0.157, and 15.273% for validation, in that order. Sensitivity analysis showed that the highest effect of independent variables on calculating SDs solubility in SC-CO2 belong to MWSDs, P, MPSDs, and T, respectively. Therefore, MWSDs is a key factor for modeling the solubility of various SDs in SC-CO2. Comparing the estimated results obtained from the optimized AIM with previous semi-empirical models showed that the AIMs could be more accurate in modeling the solubility of SDs in SC-CO2.

Solubility of gemcitabine (an anticancer drug) in supercritical carbon dioxide green solvent: Experimental measurement and thermodynamic modeling

In order to develop supercritical fluid (SCF) processes for the micro or nanosizing of solid solute components, such as pharmaceuticals, it is essential to assess their solubility in solvents including supercritical carbon dioxide (SC-CO2). This crucial step is fundamental for choosing and evaluating the processes in SCF technology. A statistical method was developed and used to determine the solubility of gemcitabine in SC-CO2. The solubility measurements at various pressures and temperatures were conducted using UV-vis analysis. Two model types were used to correlate the data: semi-empirical (with 3-6 parameters) and equation of state (EoS) models. The solubility of gemcitabine in SC-CO2 using a static method at temperatures of 308-338 K and pressures of 120-270 bar were measured and modeled for the first time. Solubility of gemcitabine ranged from 0.1274 × 10- 5 to 1.8128 × 10- 5 in mole fraction and 0.00295 to 0.08489 kg/L. The PR EoS model performed best at 308 K with an AARD of 12.58%, and SRK excelled at 318-338 K with AARDs between 12.93 and 15.68%. Application of the Joback method (AARD 12.04-27.13%) and COSMO-RS method (AARD 18.68-31.28%) in EoS models also were compared. The Bian et al. model showed the best fit among density-based models with an AARD of 16.62%.

Mesalazine solubility in supercritical carbon dioxide with and without cosolvent and modeling

In this study, the solubility of mesalazine in supercritical carbon dioxide with and without cosolvent was carried out for the first time at different temperatures and pressure values ranging from 308 to 338 K and 12 to 30 MPa, respectively. The determined experimental molar solubilities of mesalazine in supercritical carbon dioxide were in the range of 4.41 × 10-5 to 9.97 × 10-5 (308 K), 3.9 × 10-5 to 13.1 × 10-5 (318 K), 3.4 × 10-5 to 16 × 10-5 (328 K) and 3.3 × 10-5 to 18.4 × 10-5 (338 K). Meanwhile, the determined experimental molar solubilities in supercritical carbon dioxide using 2% dimethyl sulfoxide as cosolvent were in the range of 28.22 × 10-5 to 36.2 × 10-5 (308 K), 26.07 × 10-5 to 51.41 × 10-5 (318 K), 25.02 × 10-5 to 69.07 × 10-5 (328 K) and 25.86 × 10-5 to 82.6 × 10-5 (338 K). A novel association model was employed to simulate the solubility data of the binary and ternary systems. Various semiempirical correlations were utilized to calculate the solubility of mesalazine in supercritical carbon dioxide. The new association model was deemed the most superior model, achieving an average absolute relative deviation value of 4.13% without a cosolvent, and 3.36% when a cosolvent was included.

Determination of Regorafenib monohydrate (colorectal anticancer drug) solubility in supercritical CO2: Experimental and thermodynamic modeling

In this study, the solubilities of Regorafenib monohydrate (REG), a widely used as a colorectal anticancer drug, in supercritical carbon dioxide (ScCO2) were measured under various pressures and temperature conditions, for the first time. The minimum value of REG in mole fraction was determined to be 3.06×10-7, while the maximum value was found to be 6.44×10-6 at 338 K and 27 MPa. The experimental data for REG were correlated through the utilization of two types of models: (1) a set of 25 existing empirical and semi-empirical models that incorporated 3-8 parameters according to functional dependencies, (2) a model that relied on solid-liquid equilibrium (SLE) and the newly improved association models. All of the evaluated models were capable of generating suitable fits to the solubility data of REG, however, the average absolute relative deviation (AARD) of Gordillo et al. model (AARD=13.2%) and Reddy et al. model (AARD=13.5%) indicated their superiority based on AARD%. Furthermore, solvation and sublimation enthalpies of REG drug were estimated for the first time.

Studies on solubility measurement of codeine phosphate (pain reliever drug) in supercritical carbon dioxide and modeling

In this study, the solubilities of codeine phosphate, a widely used pain reliever, in supercritical carbon dioxide (SC-CO2) were measured under various pressures and temperature conditions. The lowest determined mole fraction of codeine phosphate in SC-CO2 was 1.297 × 10-5 at 308 K and 12 MPa, while the highest was 6.502 × 10-5 at 338 K and 27 MPa. These measured solubilities were then modeled using the equation of state model, specifically the Peng-Robinson model. A selection of density models, including the Chrastil model, Mendez-Santiago and Teja model, Bartle et al. model, Sodeifian et al. model, and Reddy-Garlapati model, were also employed. Additionally, three forms of solid-liquid equilibrium models, commonly called expanded liquid models (ELMs), were used. The average solvation enthalpy associated with the solubility of codeine phosphate in SC-CO2 was calculated to be - 16.97 kJ/mol. The three forms of the ELMs provided a satisfactory correlation to the solubility data, with the corresponding average absolute relative deviation percent (AARD%) under 12.63%. The most accurate ELM model recorded AARD% and AICc values of 8.89% and - 589.79, respectively.

A machine learning approach for thermodynamic modeling of the statically measured solubility of nilotinib hydrochloride monohydrate (anti-cancer drug) in supercritical CO2

Nilotinib hydrochloride monohydrate (NHM) is an anti-cancer drug whose solubility was statically determined in supercritical carbon dioxide (SC-CO2) for the first time at various temperatures (308-338 K) and pressures (120-270 bar). The mole fraction of the drug dissolved in SC-CO2 ranged from 0.1 × 10-5 to 0.59 × 10-5, corresponding to the solubility range of 0.016-0.094 g/L. Four sets of models were employed to evaluate the correlation of experimental data; (1) ten empirical and semi-empirical models with three to six adjustable parameters, such as Chrastil, Bartle, Sparks, Sodeifian, Mendez-Santiago and Teja (MST), Bian, Jouyban, Garlapati-Madras, Gordillo, and Jafari-Nejad; (2) Peng-Robinson equation of state (Van der Waals mixing rule, had an AARD% of 10.73); (3) expanded liquid theory (modified Wilson model, on average, the AARD of this model was 11.28%); and (4) machine learning (ML) algorithms (random forest, decision trees, multilayer perceptron, and deep neural network with respective R2 values of 0.9933, 0.9799, 0.9724 and 0.9701). All the models showed an acceptable agreement with the experimental data, among them, the Bian model exhibited excellent performance with an AARD% of 8.11. Finally, the vaporization (73.49 kJ/mol) and solvation (- 21.14 kJ/mol) enthalpies were also calculated for the first time.

Solubility measurement and modeling of hydroxychloroquine sulfate (antimalarial medication) in supercritical carbon dioxide

A supercritical fluid, such as supercritical carbon dioxide (scCO₂) is increasingly used for the micronization of pharmaceuticals in the recent past. The role of scCO₂ as a green solvent in supercritical fluid (SCF) process is decided by the solubility information of the pharmaceutical compound in scCO₂. The commonly used SCF processes are the rapid expansion of supercritical solution (RESS) and supercritical antisolvent precipitation (SAS). To implement micronization process, solubility of pharmaceuticals in scCO₂ is required. Present study is aimed at both measuring and modeling of solubilities of hydroxychloroquine sulfate (HCQS) in scCO₂. Experiments were conducted at various conditions (P = 12 to 27 MPa and T = 308 to 338 K), for the first time. The measured solubilities were found to be ranging between (0.0304 × 10^-4 and 0.1459 × 10^-4) at 308 K, (0.0627 × 10^-4 and 0.3158 × 10^-4) at 318 K, (0.0982 × 10^-4 and 0.4351 × 10^-4) at 328 K, (0.1398 × 10^-4 and 0.5515 × 10^-4) at 338 K. To expand the usage of the data, various models were tested. For the modelling task existing models (Chrastil, reformulated Chrastil, Méndez-Santiago and Teja (MST), Bartle et al., Reddy-Garlapati, Sodeifian et al., models) and new set of solvate complex models were considered. Among the all models investigated Reddy-Garlapati and new solvate complex models are able to fit the data with the least error. Finally, the total and solvation enthalpies of HCQS in scCO₂ were calculated with the help of model constants obtained from Chrastil, reformulated Chrastil and Bartle et al., models.

Utilization of CO2 in supercritical conditions for the synthesis of cyclic poly (N-isopropylacrylamide) via emulsion and homogeneous reactions

In this study, cyclic poly (N-isopropylacrylamide) (cPNIPAAM) was synthesized in supercritical carbon dioxide (SC-CO₂) using emulsion and homogeneous reactions for the first time. This was accomplished by applying free radical polymerization and nitroxide compounds to produce low molecular weight precursors in the SC-CO₂ solvent. The cyclization reaction occurred in a homogeneous phase in the SC-CO₂ solvent, with dimethylformamide (DMF) serving as a co-solvent for dissolving the linear precursor. This reaction was also conducted in emulsion of SC-CO₂ in water. The effects of pressure and time on the morphology, molecular weight, and yield of a difunctionalized chain were investigated, where a higher pressure led to a higher yield. The maximum yield was 64% at 23 MPa, and the chain molecular weight (M_w) was 4368 (gr/mol). Additionally, a lower pressure reduced the solubility of materials (particularly terminator) in SC-CO₂ and resulted in a chain with a higher molecular weight 9326 (gr/mol), leading to a lower conversion. Furthermore, the effect of cyclization reaction types on the properties of cyclic polymers was investigated. In cyclic reactions, the addition of DMF as a co-solvent resulted in the formation of a polymer with a high viscosity average molecular weight (M_v) and a high degree of cyclization (100%), whereas the CO₂/water emulsion resulted in the formation of a polymer with a lower M_v and increased porosity. Polymers were characterized by ¹HNMR, FTIR, DSC, TLC, GPC, and viscometry tests. The results were presented and thoroughly discussed.