Novel numerical simulation of drug solubility in supercritical CO2 using machine learning technique: Lenalidomide case study

In pharmaceutical industry, finding promising ways to enhance the solubility of disparate types of drugs is an important challenge for the orally administered drug delivery system. Disparate techniques based on drug characteristics, nature of dosage form and properties of excipients have recently been under extensive evaluation all over the world to improve the solubility of poorly water-soluble drugs. Among them, supercritical fluid carbon dioxide (SC-CO₂) has received paramount attentions due to having considerable advantages like cost-effectiveness and low flammability. Lenalidomide belongs is an orally administered anti-cancer agent, which has recently received indication for the treatment of adult patients with different bone marrow-related malignancies such as multiple myeloma, mantle cell lymphoma and follicular lymphoma. Predicting the optimized value of Lenalidomide inside the SC-CO₂ in a wide range of pressure and temperature via developing mathematical models based on artificial intelligence (AI) is the main objective of this paper. In this study, three different machine learning based models are selected to predict and optimized the drug solubility. The available data includes 28 rows of data with two inputs including temperature and pressure and two outputs including density and solubility. Selected models are Kernel Ridge Regression (KRR), least angle regression (LAR), and Multilayer Perceptron (MLP). After optimizing models and comparing the results, the MLP was selected as the primary model of this research. The models illustrated R-squared scores of 0.999 and 0.994 for density and solubility. The maximum errors are also 2.92 and 6.44 × 10^-2 for these outputs, which shows the accuracy and significant generality of the model.     

Solubility of amphenicol bacteriostats in CO2

The solubilities of three veterinary amphenicol bacteriostats, chloramphenicol, florfenicol and thiamphenicol, were measured in supercritical carbon dioxide (SC-CO₂) by a re-circulating method at temperatures of 313.15 and 333.15 K and pressures ranging from 11.0 to 49.0 MPa. These compounds displayed very limited solubility in SC-CO₂ (10⁻⁵ to 10⁻⁷ mole fraction) over the range of experimental conditions. Chloramphenicol had the highest observed solubility of the three amphenicols, while the solubilities of florfenicol and thiamphenicol were almost an order of magnitude lower. The experimental solubility data were correlated with seven known density-based models. The density models (ln y versus ln ρ or ln ρ_r) gave better correlation than the semi-log scale of ln y versus ρ_r. Four models for ln E versus density correlations also gave better correlation than the semi-log scale of ln y versus ρ_r by introducing the enhancement factor E. The correlation accuracy of all the seven models mainly depends on the system investigated, measured density and temperature range.     

Solubility enhancement of decitabine as anticancer drug via green chemistry solvent: Novel computational prediction and optimization

Nowadays, supercritical fluid technology (SFT) has been an interesting scientific subject in disparate industrial-based activities such as drug delivery, chromatography, and purification. In this technology, solubility plays an incontrovertible role. Therefore, achieving more knowledge about the development of promising numerical/computational methods of solubility prediction to validate the experimental data may be advantageous for increasing the quality of research and therefore, the efficacy of novel drugs. Decitabine with the chemical formula C₈H₁₂N₄O₄ is a chemotherapeutic agent applied for the treatment of disparate bone-marrow-related malignancies such as acute myeloid leukemia (AML) by preventing DNA methyltransferase and activation of silent genes. This study aims to predict the optimum value of decitabine solubility in CO₂SCF by employing different machine learning-based mathematical models. In this investigation, we used AdaBoost (Adaptive Boosting) to boost three base models such as Linear Regression (LR), Decision Tree (DT), and GRNN. We used a dataset that has 32 sample points to make solubility models. One of the two input features is P (bar) and the other is T (k). ADA-DT (Adaboost Algorithm-Decision Tree), ADA-LR (Adaboost Algorithm-Linear Regresion), and ADA-GRNN (Generative Regression Neural Network) models showed MAE of 6.54 × 10^?5, 4.66 × 10^?5, and 8.35 × 10^?5, respectively. Also, in terms of R-squared score, these models have 0.986, 0.983, and 0.911 scores, respectively. ADA-LR was selected as the primary model according to numerical and visual analysis. Finally, the optimal values are (P = 400 bar, T = 3.38 K × 102, Y = 1.064 × 10^?3 mol fraction) using this model.     

On the use of semiempirical models of (solid + supercritical fluid) systems to determine solid sublimation properties

Experimental solubility data of solid–supercritical fluids have significantly increased in the last few years, and semiempirical models are emerging as one of the best choices to fit this type of data. This work establishes a methodology to calculate sublimation pressures using this type of equations. It requires the use of Bartle’s equation to model equilibria data solid–supercritical fluids with the aim of determining the vaporization enthalpy of the compound. Using this method, low deviations were obtained by calculating sublimation pressures and sublimation enthalpies. The values of the sublimation pressures were subsequently used to successfully model different multiphasic equilibria, as solid–supercritical fluids and solid–solvent–supercritical fluids with the Peng–Robinson equation of state (without considering the sublimation pressure as an adjustable parameter). On the other hand, the sublimation pressures were also used to calculate solid sublimation properties and acetaminophen solvation properties in some solvents. Also, solubility data solid–supercritical fluids from 62 pharmaceuticals were fitted with different semiempirical equations (Chrastil, Kumar-Johnston and Bartle models) in order to present the values of solvation enthalpies in sc-CO₂ and vaporization enthalpies for these compounds. All of these results highlight that semiempirical models can be used for any other purpose as well as modeling (solid + supercritical fluids) equilibria.     

(Vapour + liquid) equilibria (VLE) of CO2 in aqueous solutions of 2-amino-2-methyl-1-propanol: New data and modelling using eNRTL-equation

This work presents new experimental results for carbon dioxide (CO₂) solubility in aqueous 2-amino-2-methyl-1-propanol (AMP) over the temperature range of (298 to 328) K and CO₂ partial pressure of about (0.4 to 1500) kPa. The concentrations of the aqueous AMP lie within the range of (2.2 to 4.9) mol · dm^?3. A thermodynamic model based on electrolyte non-random two-liquid (eNRTL) theory has been developed to correlate and predict the (vapour + liquid) equilibrium (VLE) of CO₂ in aqueous AMP. The model predictions have been in good agreement with the experimental data of CO₂ solubility in aqueous blends of this work as well as those reported in the literature. The current model can also predict speciation, heat of absorption, enthalpy of CO₂ loaded aqueous AMP, pH of the loaded solution, and AMP volatility.     

Solubility-dependent complexation of active pharmaceutical ingredients with trimethyl-β-cyclodextrin under supercritical fluid condition

The effect of the solubility of active pharmaceutical ingredients (APIs) in supercritical carbon dioxide (SC-CO₂) on their complexation behavior with trimethyl-β-cyclodextrin (TM-β-CD) has been investigated. Flurbiprofen or naproxen, the solubility of which is lower than that of ibuprofen, was mixed with TM-β-CD and the complexation phenomena on SC-CO₂ processing was evaluated using powder X-ray diffraction, differential scanning calorimetry and IR measurement. Drug complexation depended both on SC-CO₂ treatment time and on drug solubility in CO₂. The inclusion complex formation of flurbiprofen with TM-β-CD proceeded slowly compared with the case of ibuprofen. The slower complexation behavior was also observed when naproxen was used as the guest molecule. These results indicate that dissolution of drug molecules in SC-CO₂ is a rate-determining step for the inclusion complex formation with TM-β-CD and that complexation proceeds after dissolving the both components in SC-CO₂.     

Theoretical and experimental study on Chloroquine drug solubility in supercritical carbon dioxide via the thermodynamic,multi-layer perceptron neural network (MLPNN), and molecular modeling

The design and development of supercritical carbon dioxide (sc-CO₂) based processes for production of pharmaceutical micro/nanoparticles is one of the interesting research topics of pharmaceutical industries owing to its attractive advantages. The solubility of drugs in sc-CO₂ at different temperatures and pressures is an essential parameter which should be determined for this purpose. Chloroquine as a traditional antirheumatic and antimalarial agent is approved as an effective drug for the treatment of Covid-19. Pishnamazi et al. (2021) measured the solubility of this drug in sc-CO₂ at the pressure range of 120–400 bar and temperature range of 308–338 K, and correlated the obtained data using some empirical models. In this work, a comprehensive computational approach was developed to more accurately study the supercritical solubility of Chloroquine. The thermodynamic models include two equations-of-state based models (Peng-Robinson and Soave-Redlich-Kowang) and two activity coefficient-based models (modified Wilson's and UNIQUAC)), as well as, a multi-layer perceptron neural network (MLPNN)) were used for this purpose. Also, molecular modeling was performed to study the electronic structure of Chloroquine and identify the potential centers of intermolecular interactions during the dissolution process. According to the obtained results, all of the theoretical models can predict Chloroquine solubility in sc-CO₂ with acceptable accuracy. Among these models, the MLPNN model possesses the highest precision with the lowest average absolute relative deviation (AARD%) of 1.76 % and the highest R_adj value of 0.999.     

Measurement and correlation of antifungal drugs solubility in pure supercritical CO2 using semiempirical models

In the present study the solubilities of two antifungal drugs of ketoconazole and clotrimazole in supercritical carbon dioxide were measured using a simple static method. The experimental data were measured at (308 to 348) K, over the pressure range of (12.2 to 35.5) MPa. The mole fraction solubilities ranged from 0.2 · 10^?6 to 17.45 · 10^?5. In this study five density based models were used to calculate the solubility of drugs in supercritical carbon dioxide. The density based models are Chrastil, modified Chrastil, Bartle, modified Bartle and Mendez-Santiago and Teja (M–T). Interaction parameters for the studied models were obtained and the percentage of average absolute relative deviation (AARD%) in each calculation was displayed. The correlation results showed good agreement with the experimental data. A comparison among the five models revealed that the Bartle and its modified models gave much better correlations of the solubility data with an average absolute relative deviation (AARD%) ranging from 4.8% to 6.2% and from 4.5% to 6.3% for ketoconazole and clotrimazole, respectively. Using the correlation results, the heat of drug–CO₂ solvation and that of drug vaporization was separately approximated in the range of (?22.1 to ?26.4 and 88.3 to 125.9) kJ · mol^?1.     

Solubility of CO2 in 1-(2-hydroxyethyl)-3-methylimidazolium ionic liquids with different anions

The solubility of carbon dioxide in a series of 1-(2-hydroxyethyl)-3-methylimidazolium ([hemim]⁺) based ionic liquids (ILs) with different anions, viz. hexafluorophosphate ([PF₆]^?), trifluoromethanesulfonate ([OTf]^?), and bis-(trifluoromethyl)sulfonylimide ([Tf₂N]^?) at temperatures ranging from 303.15 K to 353.15 K and pressures up to 1.3 MPa were determined. The solubility data were correlated using the Krichevsky–Kasarnovsky equation and Henry’s law constants were obtained at different temperatures. Using the solubility data, the partial molar thermodynamic functions of solution such as Gibbs free energy, enthalpy, and entropy were calculated. Comparison showed that the solubility of CO₂ in the ILs studied follows the same behaviour as the corresponding conventional 1-ethyl-3-methylimidazolium ([emim]⁺) based ILs with the same anions, i.e. [hemim][NTf₂] > [hemim][OTf] > [hemim][PF₆] > [hemim][BF₄].     

Interaction parameters and (solid + liquid) equilibria calculation for KCl–H2O–HCl–C2H5OH,K2SO4–H2O–H2SO4 and K2SO4–H2O–C2H5OH mixed solvent-electrolyte systems

This work deals with the prediction and experimental measurements of the (solid + liquid) equilibrium (SLE) in acid medium for industrial purposes. Specific systems including KCl–ethanol–water–HCl and K₂SO₄–water–H₂SO₄ were analyzed. At first, a critical discussion of SLE calculations was given, based on the well-known UNIQUAC extended and LIQUAC models. Two new proposals were derived, considering the explicit necessity of a new reference state for SLE calculations for the studied (solvents + acid) mixtures. The solubility of KCl in water–ethanol–HCl mixed solvents was measured in the temperature range of 300.15 to 315.15 K using an analytical gravimetric method. These results combined with some other experimental data reported in the open literature let us to propose a set of parameters for the new models. They included the interaction parameters between ethanol and the H⁺ ion. The prediction capability of the new models, for calculations in acid medium, was illustrated. Experimentally, it was observed that the (K₂SO₄ + water + H₂SO₄) system presented the unusual behavior of increasing K₂SO₄ solubility with an increase in the sulfuric acid concentration. This was accurately predicted by the newly proposed models.     

Equilibrium solubility of sodium 2-naphthalenesulfonate in binary (sodium chloride + water), (sodium sulfate + water), and (ethanol + water) solvent mixtures at temperatures from (278.15 to 323.15) K

The equilibrium solubility of sodium 2-naphthalenesulfonate in binary (sodium chloride + water), (sodium sulfate + water), and (ethanol + water) solvent mixtures was measured at elevated temperatures from (278.15 to 323.15) K using a steady-state method. With increasing temperatures, the solubility increases in aqueous solvent mixtures. The results of these results were regressed by a modified Apelblat equation. The dissolution entropy and enthalpy determined using the method of the least-squares and the change of Gibbs free energy calculated with the values of Δ_diffS^o and Δ_diffH^o at T = 278.15 K.     

Phase behaviour of mixed-gas hydrate systems containing carbon dioxide

We describe a new apparatus suitable for measurements of the phase behaviour and phase properties of fluid mixtures under conditions of high-pressure. We propose a synthetic method for the determination of gas solubility, and present results for the system (CO₂ + H₂O). In addition, we report new measurements of the hydrate equilibrium curves in aqueous systems containing either pure carbon dioxide or mixed gases including CO₂. For hydrates formed in the (CO₂ + H₂O) system, we find an enthalpy of dissociation of 77 kJ · mol^?1. This value was unchanged by the addition of mass fraction 0.043 of NaCl to the water. Compared with pure CO₂, mixtures of CO₂ with air exhibited markedly different dissociation pressures at given temperature, but were characterised by the same enthalpy of dissociation. However, two mixtures containing either nitrogen or methane and hydrogen both exhibited a higher enthalpy of dissociation, 106 kJ · mol^?1, consistent with these systems forming structure II hydrates.     

Solubilities and partial molar volumes of three bis(2-ethoxyethyl) ethanedioate derivatives in supercritical carbon dioxide

Three new CO₂-philic bis(2-ethoxyethyl) ethanedioate derivatives, bis(2-(2-methoxyethoxy)ethyl) ethanedioate (compound 1), bis(2-(2-ethoxyethoxy)ethyl) ethanedioate (compound 2), and bis(2-(2-butoxyethoxy)ethyl) ethanedioate (compound 3), were designed and synthesized and their solubilities in supercritical carbon dioxide (scCO₂) were then measured at different temperatures (313, 323, 333) K over the pressure range (8.9 to 13.9) MPa. The measured solubility data were correlated with five different theoretical semi-empirical models (Chrastil, kJ, SS, MST, JCF) and satisfactory agreements were obtained. The JCF model provided the best fit and the lowest average absolute relative deviation (AARD) varied from (3.58 to 6.80)%. Furthermore, the partial molar volumes of three compounds in the supercritical phase were also calculated according to the Kumar and Johnston theory, and the values were between −(19105 and 3510) cm³ · mol⁻¹.     

Effect of supercritical CO2 on bulk hydrogenation of nitrile butadiene rubber catalyzed by RhCl(PPh3)3

The effect of supercritical (SC) CO₂ on the bulk hydrogenation of NBR entrapped with the catalyst (RhCl(PPh₃)₃) was investigated under various reaction times, reaction temperatures, hydrogen pressures and loadings of the catalyst and the thicknesses of the polymer films. CO₂ helps in improving the transport behaviour of catalyst in polymer matrices, as well as helping to move catalyst into or out of the polymer. A method for the measurement of the dissolution extent or the apparent solubility of the Rh based catalyst in SC-CO₂ was developed. It is found that high temperatures and high SC-CO₂ densities would enhance the apparent solubility. Cosolvents, such as acetone, are also found to increase the apparent solubility. Details on the hydrogenation process are also presented.     

Ibuprofen-Cyclodextrin Inclusion Complex Formation using Supercritical Carbon Dioxide

Supercritical carbon dioxide (SC-CO₂) processing was performed with mixtures of cyclodextrins (CDs) and ibuprofen (IBP) to create inclusion complexes of ibuprofen and CD. Mixtures of IBP and trimethyl-β-CD showed new powder X-ray diffraction peaks after SC-CO₂ processing, although samples after processing with β-CD showed identical X-ray diffraction patterns with the physical mixture. The differential scanning calorimetry curves of samples after processing with trimethyl-β-CD showed no fusion peak of IBP and a new melting peak at around 185 °C. The physicochemical properties are similar to the co-precipitated samples of IBP and trimethyl-β-CD. Therefore, inclusion complex between IBP and trimethyl-β-CD was successfully prepared using SC-CO₂ technique. No inclusion formation was found when nitrogen was used as the supercritical fluid. Complexation of IBP and CD would not occur only on a high-pressure condition. The solubility of cyclodextrin into SC-CO₂ might play an important role in the formation of the inclusion complex.     

Zirconium Dioxide Solubility in High Temperature Aqueous Solutions

The heat transport purification system of CANDU nuclear reactors is used to remove particulates and dissolved impurities from the heat transport coolant. Zirconium dioxide shows some potential as a high-temperature ion-exchange medium for cationic and anionic impurities found in the CANDU heat transport system (HTS). Zirconium in the reactor core can be neutron activated, and potentially can be dissolved and transported to out-of-core locations in the HTS. However, the solubility of zirconium dioxide in high-temperature aqueous solutions has rarely been reported. This paper reports the solubility of zirconium dioxide in 10⁻⁴ mol⋅kg⁻¹ LiOH solution, determined between 298 and 573 K, using a static autoclave. Over this temperature range, the measured solubility of zirconium dioxide is between 0.9 and 12×10⁻⁸ mol⋅kg⁻¹, with a minimum solubility around 523 K. This low solubility suggests that its use as a high-temperature ion-exchanger would not introduce significant concentrations of contaminants into the system. A thermodynamic analysis of the solubility data suggests that Zr(OH)₄⁰ likely is the dominant species over a wide pH region at elevated temperatures. The calculated Gibbs energies of formation of Zr(OH)₄⁰(aq) and Zr(OH)₄(am) at 298.15 K are −1472.6 kJ⋅mol⁻¹ and −1514.2 kJ⋅mol⁻¹, respectively. The enthalpy of formation of Zr(OH)₄⁰ has a value of −1695±11 kJ⋅mol⁻¹ at 298.15 K.     

Experimental determination of the rate constants of the reactions of HO2 + DO2 and DO2 + DO2

The rate constants of the reactions of DO₂ + HO₂ (R1) and DO₂ + DO₂ (R2) have been determined by the simultaneous, selective, and quantitative measurement of HO₂ and DO₂ by continuous wave cavity ring-down spectroscopy (cw-CRDS) in the near infrared, coupled to a radical generation by laser photolysis. HO₂ was generated by photolyzing Cl₂ in the presence of CH₃OH and O₂. Low concentrations of DO₂ were generated simultaneously by adding low concentrations of D₂O to the reaction mixture, leading through isotopic exchange on tubing and reactor walls to formation of low concentrations of CH₃OD and thus formation of DO₂. Excess DO₂ was generated by photolyzing Cl₂ in the presence of CD₃OD and O₂, small concentrations of HO₂ were always generated simultaneously by isotopic exchange between CD₃OD and residual H₂O. The rate constant k₁ at 295 K was found to be pressure independent in the range 25–200 Torr helium, but increased with increasing D₂O concentration k₁ = (1.67 ± 0.03) × 10⁻¹² × (1 + (8.2 ± 1.6) × 10⁻¹⁸ cm³ × [D₂O] cm⁻³) cm³ s⁻¹. The rate constant for the DO₂ self-reaction k₂ has been measured under excess DO₂ concentration, and the DO₂ concentration has been determined by fitting the HO₂ decays, now governed by their reaction with DO₂, to the rate constant k₁. A rate constant with insignificant pressure dependence was found: k₂ = (4.1 ± 0.6) × 10⁻¹³ (1 + (2 ± 2) × 10⁻²⁰ cm³ × [He] cm⁻³) cm³ s⁻¹ as well as an increase of k₂ with increasing D₂O concentration was observed: k₂ = (4.14 ± 0.02) × 10⁻¹³ × (1 + (6.5 ± 1.3) × 10⁻¹⁸ cm³ × [D₂O] cm⁻³) cm³ s⁻¹. The result for k₂ is in excellent agreement with literature values, whereas this is the first determination of k₁.     

Thermodynamic properties of soddyite from solubility and calorimetry measurements

The release of uranium from geologic nuclear waste repositories under oxidizing conditions can only be modeled if the thermodynamic properties of the secondary uranyl minerals that form in the repository setting are known. Toward this end, we synthesized soddyite ((UO₂)₂(SiO₄)(H₂O)₂), and performed solubility measurements from both undersaturation and supersaturation. The solubility measurements rigorously constrain the value of the solubility product of synthetic soddyite, and consequently its standard-state Gibbs free energy of formation. The log solubility product (lg K_sp) with its error (1σ) is (6.43 + 0.20/−0.37), and the standard-state Gibbs free energy of formation is (−3652.2 ± 4.2 (2σ)) kJ mol⁻¹. High-temperature drop solution calorimetry was conducted, yielding a calculated standard-state enthalpy of formation of soddyite of (−4045.4 ± 4.9 (2σ)) kJ · mol⁻¹. The standard-state Gibbs free energy and enthalpy of formation yield a calculated standard-state entropy of formation of soddyite of (−1318.7 ± 21.7 (2σ)) J · mol⁻¹ · K⁻¹. The measurements and associated thermodynamic calculations not only describe the T = 298 K stability and solubility of soddyite, but they also can be used in predictions of repository performance through extrapolation of these properties to repository temperatures.     

Excess molar enthalpies and excess molar volumes of (1,3-dimethyl-2-imidazolidinone + an aromatic hydrocarbon) atT = 298.15 K

Excess molar enthalpies H_m^Eand excess molar volumesV_m^E of (1,3-dimethyl-2-imidazolidinone  +  benzene, or methylbenzene, or 1,2-dimethylbenzene, or 1,3-dimethylbenzene, or 1,4-dimethylbenzene, or 1,3,5-trimethylbenzene, or ethylbenzene) over the whole range of compositions have been measured at T =  298.15 K. The excess molar enthalpy values were positive for five of the seven systems studied and the excess molar volume values were negative for six of the seven systems studied. The excess enthalpy ranged from a maximum of 435 J · mol ^− 1for (1,3-dimethyl-2-imidazoline  +  1,3,5-trimethylbenzene) to a minimum of  − 308 J · mol ^− 1for (1,3-dimethyl-2-imidazoline  +  benzene). The excess molar volume values ranged from a maximum of 0.95cm³mol ^− 1 for (1,3-dimethyl-2-imidazoline  +  ethylbenzene) and a minimum of  − 1.41 cm³mol ^− 1for (1,3-dimethyl-2-imidazoline  +  methylbenzene). The Redlich–Kister polynomial was used to correlate both the excess molar enthalpy and the excess molar volume data and the NRTL and UNIQUAC models were used to correlate the enthalpy of mixing data. The NRTL equation was found to be more suitable than the UNIQUAC equation for these systems. The results are discussed in terms of the polarizability of the aromatic compound and the effect of methyl substituents on the benzene ring.