Computational prediction of drug solubility in supercritical carbon dioxide: Thermodynamic and artificial intelligence modeling

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.

Measuring and modeling the solubility of sulfasalazine in supercritical carbon dioxide to select methods for producing nanoparticles

In the present study, the solubility of sulfasalazine in carbon dioxide was investigated at temperatures ranging from 313 K to 343 K and pressures ranging from 12 to 30 MPa. The experimentally determined molar solubilities of sulfasalazine in ScCO2 were found to be in the range of 4.08 × 10- 5 to 8.61 × 10- 5 at 313 K, 3.54 × 10- 5 to 11.41 × 10- 5 at 323 K, 3.04 × 10- 5 to 13.64 × 10- 5 at 333 K, and 2.66 × 10- 5 to 16.35 × 10- 5 at 343 K. The solubility values were correlated via a number of different types of equations, such as semi-empirical correlations, the Peng-Robinson, the PC-SAFT equation, and the regular solution. Furthermore, the findings demonstrate that semi-empirical, equation of state models, and the regular solution model possess the capability of precisely determining the solubility. Moreover, the solubility magnitude suggests that the gas anti-solvent method may be a viable approach for nanoparticle production.

Predicting the microalgae lipid profile obtained by supercritical fluid extraction using a machine learning model

In this study a Machine Learning model was employed to predict the lipid profile from supercritical fluid extraction (SFE) of microalgae Galdieria sp. USBA-GBX-832 under different temperature (40, 50, 60°C), pressure (150, 250 bar), and ethanol flow (0.6, 0.9 mL min-1) conditions. Six machine learning regression models were trained using 33 independent variables: 29 from RD-Kit molecular descriptors, three from the extraction conditions, and the infinite dilution activity coefficient (IDAC). The lipidomic characterization analysis identified 139 features, annotating 89 lipids used as the entries of the model, primarily glycerophospholipids and glycerolipids. It was proposed a methodology for selecting the representative lipids from the lipidomic analysis using an unsupervised learning method, these results were compared with Tanimoto scores and IDAC calculations using COSMO-SAC-HB2 model. The models based on decision trees, particularly XGBoost, outperformed others (RMSE: 0.035, 0.095, 0.065 and coefficient of determination (R2): 0.971, 0.933, 0.946 for train, test and experimental validation, respectively), accurately predicting lipid profiles for unseen conditions. Machine Learning methods provide a cost-effective way to optimize SFE conditions and are applicable to other biological samples.

Advanced modeling of pharmaceutical solubility in solvents using artificial intelligence techniques: assessment of drug candidate for nanonization processing

This research is an analysis of multiple regression models developed for predicting ketoprofen solubility in supercritical carbon dioxide under different levels of T(K) and P(bar) as input features. Solubility of the drug was correlated to pressure and temperature as major operational variables. Selected models for this study are Piecewise Polynomial Regression (PPR), Kernel Ridge Regression (KRR), and Tweedie Regression (TDR). In order to improve the performance of the models, hyperparameter tuning is executed utilizing the Water Cycle Algorithm (WCA). Among, the PPR model obtained the best performance, with an R2 score of 0.97111, alongside an MSE of 1.6867E-09 and an MAE of 3.01040E-05. Following closely, the KRR model demonstrated a good performance with an R2 score of 0.95044, an MSE of 2.5499E-09, and an MAE of 3.49707E-05. In contrast, the TDR model produces a lower R2 score of 0.84413 together with an MSE of 7.4249E-09 and an MAE of 5.69159E-05.

Computational intelligence modeling of hyoscine drug solubility and solvent density in supercritical processing: gradient boosting, extra trees, and random forest models

This work presents the results of using tree-based models, including Gradient Boosting, Extra Trees, and Random Forest, to model the solubility of hyoscine drug and solvent density based on pressure and temperature as inputs. The models were trained on a dataset of hyoscine drug with known solubility and density values, optimized with WCA algorithm, and their accuracy was evaluated using R², MSE, MAPE, and Max Error metrics. The results showed that Gradient Boosting and Extra Trees models had high accuracy, with R² values above 0.96 and low MAPE and Max Error values for both solubility and density output. The Random Forest model was less accurate than the other two models. These findings demonstrate the effectiveness of tree-based models for predicting the solubility and density of chemical compounds and have potential applications in determination of drug solubility prior to process design by correlation of solubility and density to input parameters including pressure and temperature.

Predicting the aggregation number of cationic surfactants based on ANN-QSAR modeling approaches: understanding the impact of molecular descriptors on aggregation numbers

In this work, a quantitative structure-activity relationship (QSAR) study is performed on some cationic surfactants to evaluate the relationship between the molecular structures of the compounds with their aggregation numbers (AGGNs) in aqueous solution at 25 °C. An artificial neural network (ANN) model is combined with the QSAR study to predict the aggregation number of the surfactants. In the ANN analysis, four out of more than 3000 molecular descriptors were used as input variables, and the complete set of 41 cationic surfactants was randomly divided into a training set of 29, a test set of 6, and a validation set of 6 molecules. After that, a multiple linear regression (MLR) analysis was utilized to build a linear model using the same descriptors and the results were compared statistically with those of the ANN analysis. The square of the correlation coefficient (R 2) and root mean square error (RMSE) of the ANN and MLR models (for the whole data set) were 0.9392, 7.84, and 0.5010, 22.52, respectively. The results of the comparison revealed the efficiency of ANN in detecting a correlation between the molecular structure of surfactants and their AGGN values with a high predictive power due to the non-linearity in the studied data. Based on the ANN algorithm, the relative importance of the selected descriptors was computed and arranged in the following descending order: H-047 > ESpm12x > JGI6> Mor20p. Then, the QSAR data was interpreted and the impact of each descriptor on the AGGNs of the molecules were thoroughly discussed. The results showed there is a correlation between each selected descriptor and the AGGN values of the surfactants.

Estimating the Dissolution of Anticancer Drugs in Supercritical Carbon Dioxide with a Stacked Machine Learning Model

Synthesizing micro-/nano-sized pharmaceutical compounds with an appropriate size distribution is a method often followed to enhance drug delivery and reduce side effects. Supercritical CO2 (carbon dioxide) is a well-known solvent utilized in the pharmaceutical synthesis process. Reliable knowledge of a drug's solubility in supercritical CO2 is necessary for feasible study, modeling, design, optimization, and control of such a process. Therefore, the current study constructs a stacked/ensemble model by combining three up-to-date machine learning tools (i.e., extra tree, gradient boosting, and random forest) to predict the solubility of twelve anticancer drugs in supercritical CO2. An experimental databank comprising 311 phase equilibrium samples was gathered from the literature and applied to design the proposed stacked model. This model estimates the solubility of anticancer drugs in supercritical CO2 as a function of solute and solvent properties and operating conditions. Several statistical indices, including average absolute relative deviation (AARD = 8.62%), mean absolute error (MAE = 2.86 × 10-6), relative absolute error (RAE = 2.42%), mean squared error (MSE = 1.26 × 10-10), and regression coefficient (R2 = 0.99809) were used to validate the performance of the constructed model. The statistical, sensitivity, and trend analyses confirmed that the suggested stacked model demonstrates excellent performance for correlating and predicting the solubility of anticancer drugs in supercritical CO2.

Design of predictive model to optimize the solubility of Oxaprozin as nonsteroidal anti-inflammatory drug

These days, many efforts have been made to increase and develop the solubility and bioavailability of novel therapeutic medicines. One of the most believable approaches is the operation of supercritical carbon dioxide fluid (SC-CO₂). This operation has been used as a unique method in pharmacology due to the brilliant positive points such as colorless nature, cost-effectives, and environmentally friendly. This research project is aimed to mathematically calculate the solubility of Oxaprozin in SC-CO₂ through artificial intelligence. Oxaprozin is a nonsteroidal anti-inflammatory drug which is useful in arthritis disease to improve swelling and pain. Oxaprozin is a type of BCS class II (Biopharmaceutical Classification) drug with low solubility and bioavailability. Here in order to optimize and improve the solubility of Oxaprozin, three ensemble decision tree-based models including random forest (RF), Extremely random trees (ET), and gradient boosting (GB) are considered. 32 data vectors are used for this modeling, moreover, temperature and pressure as inputs, and drug solubility as output. Using the MSE metric, ET, RF, and GB illustrated error rates of 6.29E-09, 9.71E-09, and 3.78E-11. Then, using the R-squared metric, they demonstrated results including 0.999, 0.984, and 0.999, respectively. GB is selected as the best fitted model with the optimal values including 33.15 (K) for the temperature, 380.4 (bar) for the pressure and 0.001242 (mole fraction) as optimized value for the solubility.

Experimental solubility and thermodynamic modeling of empagliflozin in supercritical carbon dioxide

The solubility of empagliflozin in supercritical carbon dioxide was measured at temperatures (308 to 338 K) and pressures (12 to 27 MPa), for the first time. The measured solubility in terms of mole faction ranged from 5.14 × 10^–6 to 25.9 × 10^–6. The cross over region was observed at 16.5 MPa. A new solubility model was derived to correlate the solubility data using solid–liquid equilibrium criteria combined with Wilson activity coefficient model at infinite dilution for the activity coefficient. The proposed model correlated the data with average absolute relative deviation (AARD) and Akaike’s information criterion (AIC_c), 7.22% and − 637.24, respectively. Further, the measured data was also correlated with 11 existing (three, five and six parameters empirical and semi-empirical) models and also with Redlich-Kwong equation of state (RKEoS) along with Kwak-Mansoori mixing rules (KMmr) model. Among density-based models, Bian et al., model was the best and corresponding AARD% was calculated 5.1. The RKEoS + KMmr was observed to correlate the data with 8.07% (correspond AIC_c is − 635.79). Finally, total, sublimation and solvation enthalpies of empagliflozin were calculated.