Comparison of double log-log,mixture response-surface and combined NIBS/Redlich-Kister solubility models

The accuracy and prediction capability of the linear double log-log (LDL-L), mixture response-surface (MR-S) and the combined nearly ideal binary solvent/Redlich-Kister (CNIBS/R-K) solubility equations have been compared using the model parameters calculated from either the whole data or a minimum number of data in an experimental set. The CNIBS/R-K model produced better prediction for some experimental sets than the other two models when the parameters obtained from the whole data in a set were employed, whereas the LDL-L model was superior to the other models when the parameters calculated from a minimum number of data were used, indicating its greatest prediction capability.     

Comparison of various cosolvency models for calculating solute solubility in water-cosolvent mixtures

Previously published cosolvency models are critically evaluated in terms of their ability to mathematically correlate solute solubility in binary solvent mixtures as a function of solvent composition. Computational results show that the accuracy of the models is improved by increasing the number of curve-fit parameters. However, the curve-fit parameters of several models are limited. The combined nearly ideal binary solvent/Redlich-Kister, CNIBS/R-K, was found to be the best solution model in terms of its ability to describe the experimental solubility in mixed solvents. Also resented is an extension of the mixture response surface model. The extension was found to improve the correlational ability of the original model.     

Deviations of drug solubility in water-cosolvent mixtures from the Jouyban-Acree model--effect of solute structure

Deviations of the predicted solubilities using the Jouyban-Acree model from experimental data were correlated to the structural descritptors of the drugs computed by HyperChem software. The proposed models are able to predict the solubility in water-cosolvent mixtures and reduced the mean percentage deviations (MPD) of predicted solubilities from 24%, 48%, and 53% to 16%, 33% and 38%, respectively for water-propylene glycol, water-ethanol and water-polyethylene glycol 400 mixtures, with the overall improvement in prediction capability of the model being approximately 13%.     

Solubility prediction of salicylic acid in water-ethanol-propylene glycol mixtures using the Jouyban-Acree model

To show the applicability of a solution model, i.e. the Jouyban-Acree model, for predicting the solubility of a solute in ternary solvent systems based on model constants computed using solubility data of the solute in binary solvent systems, the solubility of salicylic acid in water-ethanol, water-propylene glycol, ethanol-propylene glycol mixtures was determined. A minimum number of three data points from each binary system was used to calculate the binary interaction parameters of the model. Then the solubility in other binary solvent compositions and also in a number of ternary solvents was predicted, and the mean percentage deviation (MPD) was calculated as an accuracy criterion. The overall MPD (+/-SD) was 7.3 (+/-7.3)% and those of a similar predictive model was 15.7 (+/-11.5)%. The mean difference between the proposed and a previous model was statistically significant (paired t-test, p < 0.004).     

Prediction of the optimized solvent composition for solubilization of drugs in water-cosolvent mixtures

The capability of the Jouyban-Acree model for predicting the optimized solvent composition of binary solvents for solubilization of drugs is shown employing solubility of drugs in aqueous mixtures of dioxane, ethanol and polyethylene glycol 400. The established model constants of the Jouyban-Acree model and solubility of drugs in water and cosolvent are used to predict the maximum solubility of in the binary solvent mixture (log Xm(max)) and the corresponding solvent composition (f1,max). The accuracy of the predicted log Xm(max) and f1,max is studied using average absolute error (AAE) of predicted and observed values. The AAEs were 0.10 +/- 0.12 and 0.08 +/- 0.10, respectively for log Xm(max) and f1,max. The method provided acceptable predictions and is recommended for practical applications. The main advantage of the proposed method is its extension to temperatures higher/lower than room temperature.     

Modeling drug solubility in water-cosolvent mixtures using an artificial neural network

Application of the artificial neural network (ANN) to calculate the solubility of drugs in water-cosolvent mixtures was shown using 35 experimental data sets. The networks employed were feedforward backpropagation errors with one hidden layer. The topology of neural network was optimized and the optimum topology achieved was a 6-5-1 architecture. All data points in each set were used to train the ANN and the solubilities were back-calculated employing the trained networks. The differences between calculated solubilities and experimental values was used as an accuracy criterion and defined as mean percentage deviation (MPD). The overall MPD (OMPD) and its S.D. obtained for 35 data sets was 0.90 +/- 0.65%. To assess the prediction capability of the method, five data points in each set were used as training set and the solubility at other solvent compositions were predicted using trained ANNs whereby the OMPD (+/-S.D.) for this analysis was 9.04 +/- 3.84%. All 496 data points from 35 data sets were used to train a general ANN model, then the solubilities were back-calculated using the trained network and MPD (+/-S.D.) was 24.76 +/- 14.76%. To test the prediction capability of the general ANN model, all data points with odd set numbers from 35 data sets were employed to train the ANN model, the solubility for the even data set numbers were predicted and the OMPD (+/-S.D.) was 55.97 +/- 57.88%. To provide a general ANN model for a given cosolvent, the experimental data points from each binary solvent were used to train ANN and back-calculated solubilities were used to calculate MPD values. The OMPD (+/-S.D.) for five cosolvent systems studied was 2.02 +/- 1.05%. A similar numerical analysis was used to calculate the solubility of structurally related drugs in a given binary solvent and the OMPD (+/-S.D.) was 4.70 +/- 2.02%. ANN model also trained using solubility data from a given drug in different cosolvent mixtures and the OMPD (+/-S.D.) obtained was 3.36 +/- 1.66%. The results for different numerical analyses using ANN were compared with those obtained from the most accurate multiple linear regression model, namely the combined nearly ideal binary solvent/Redlich-Kister equation, and the ANN model showed excellent superiority to the regression model.     

Solubilization behavior of a poorly soluble drug under combined use of surfactants and cosolvents.

The solubilization behavior of a poorly soluble model drug, phenytoin (PHT), under combined use of surfactants (sodium dodecyl sulfate (SDS), Tween 80) and cosolvents (dimethylacetoamide (DMA), ethanol, poly(ethylene glycol) 400 (PEG), glycerol) was examined. The solubility of PHT in the aqueous surfactant solutions increased linearly with increase of the surfactant concentration. The solubility of PHT in water-cosolvent mixtures roughly followed the log-linear model, which is widely accepted to explain the solubilization behavior of poorly soluble compounds in water-cosolvent mixtures, except for the case of glycerol, in which the solubility was minimal at 10% (w/v) of glycerol. When the cosolvents were added to the aqueous surfactant solutions, their effect on the solubility depended on the combination of the surfactant and the cosolvent. The most striking increase in solubility was observed with DMA, regardless of the type of surfactant. When ethanol was added, an increase in the solubility was observed with the Tween 80 solution, while a dramatic decrease was found with the SDS solution. The addition of glycerol or PEG to the surfactant solutions had only a minor impact on the solubility. These solubilization behaviors of PHT in the surfactant-cosolvent mixtures were partially explained by the solubility model introduced in our previous paper [Kawakami, K., Miyoshi, K., Ida, Y., 2004. Solubilization behavior of poorly soluble drugs with combined use of Gelucire 44/14 and cosolvent. J. Pharm. Sci. 93, 1471-1479]. Addition of the cosolvents to the surfactant solutions generally offered only a small advantage from the viewpoint of improving solubility because of the decrease in the solubilization capacity of the micelles.     

A new definition of solubilization power of a cosolvent

The solubilization power of a cosolvent is defined based on the maximum solubility of a solute in the water-cosolvent mixtures (X(m,max)) and the corresponding solvent composition (f(c,max)) predicted by trained versions of the Jouyban-Acree model. The applicability of the proposed definition was checked using solubility data of three cosolvent systems where the solubilization power was ordered as: dioxane > ethanol > polyethylene glycol 400. Using this definition, one could select the most appropriate cosolvent for solubilization of a poorly water soluble drug. There are linear relationships between the solubilization power of a cosolvent and the solute's logarithm of partition coefficients.     

A novel method for improvement of predictability of the CNIBS/R-K equation

A new method for obtaining the model constants of the combined nearly ideal binary solvent/Redlich-Kister (CNIBS/R-K) equation, via least square analysis has been presented. Predictability of CNIBS/R-K in a previous method and the new one of least square analysis has been compared using some experimental solubility data sets. The results have indicated that the new method improved the predictability of the CNIBS/R-K equation about 63%.     

Solubility prediction of solutes in aqueous mixtures of ethylene glycols

The applicability of a trained version of the Jouyban-Acree model, for predicting the solubility of solutes in aqueous mixtures of ethylene glycol and its polymerized forms was shown. The solubilities of 8 drugs in binary mixtures were determined and the mean percentage deviation (MPD) was calculated as a prediction accuracy criterion and the overall MPD (+/- SD) was 23.2 (+/- 13.1)%.     

Measurement and correlation of solubility data for albendazole in ten pure solvents and two binary solvent systems from 278.15 K to 323.15 K

The equilibrium solubility of albendazole (ABZ) in ten single solvents and two binary solvent mixtures of different ratio was measured by a typical static method combined with ultraviolet (UV) spectrophotometry within the temperature range from 278.15 K to 323.15 K. Meanwhile, the modified Apelblat model, Van't Hoff equation and λh equation were used to correlate the solubility data of ABZ in pure solvent, the modified Apelblat model, λh equation, Sun model, GSM equation and NRTL model were used to correlate the solubility data of ABZ in binary mixed solvent, the 100RD, 100ARD, 103RMSD and 103ORMSD values of the above models were calculated respectively. The results show that the experimental data of six models have a good correlation with the calculated data. Especially, the Van't Hoff equation in pure solvent has the best fitting effect, and the GSM equation in binary mixed solvent has the best fitting effect. Additionally, the Van't Hoff equation was used to calculate and evaluate the thermodynamic properties of the ABZ dissolution process, including enthalpy (ΔdisH), entropy (ΔdisS) and Gibbs free energy (ΔdisG).     

Extended hildebrand solubility approach: satranidazole in mixtures of dioxane and water

The extended Hildebrand solubility parameter approach is used to estimate the solubility of satranidazole in binary solvent systems. The solubility of satranidazole in various dioxane-water mixtures was analyzed in terms of solute-solvent interactions using a modified version of Hildebrand-Scatchard treatment for regular solutions. The solubility of satranidazole in the binary solvent, dioxane-water shows a bell-shaped profile with a solubility maximum well above the ideal solubility of the drug. This is attributed to solvation of the drug with the dioxane-water mixture, and indicates that the solute-solvent interaction energy is larger than the geometric mean (δ(1)δ(2)) of regular solution theory. The new approach provides an accurate prediction of solubility once the interaction energy is obtained. In this case, the energy term is regressed against a polynomial in δ(1) of the binary mixture. A quartic expression of W in terms of solvent solubility parameter was found for predicting the solubility of satranidazole in dioxane-water mixtures. The method has potential usefulness in preformulation and formulation studies during which solubility prediction is important for drug design.     

Mathematical representation of apparent dissociation constants in aqueous-organic solvent mixtures

A mathematical model for calculating apparent acid dissociation constants (pK(a)) in hydroorganic mixtures with respect to the concentration of organic solvent in a binary mixture is proposed. The correlation ability of the proposed model is evaluated by employing pK(a) value of 75 different weak acids in 13 water-cosolvent systems. The results show that the equation is able to correlate the pK(a) values with an overall mean percentage differences (MPD) of 0.52+/-0.43%. In order to test the prediction capability of the model, four experimental pK(a) values for each data set have been employed to train the model, then the pK(a) values at other solvent compositions predicted and the overall MPD obtained is 1.41+/-1.15%. The applicability of the model to correlate/predict pK(a) values of structurally related drugs in a given binary solvent has been shown. The obtained overall MPD for correlation and prediction capabilities are 1.60+/-2.16 and 2.89+/-3.22%, respectively.     

Mathematical representation of solubility of amino acids in binary aqueous-organic solvent mixtures at various temperatures using the Jouyban-Acree model

Applicability of a solution model for calculating solubility of amino acids in binary aqueous-organic solvent mixtures at various temperatures was shown. The accuracy of the proposed model was evaluated by computing mean percentage deviation (MPD) employing available solubility data of amino acids in binary solvents at various temperatures from the literature. The overall MPD (+/- SD) for correlation of solubility data was 16.5 +/- 8.8%. In addition, the equations calculating solubility of amino acids in binary solvent mixtures at a fixed temperature was revisited.     

Solubility prediction of clonazepam in aqueous mixtures of ethanol,polyethylene glycol 200 and propylene glycol at 30 °C

Solubility of clonazepam in aqueous binary mixtures of ethanol, polyethylene glycol 200 and propylene glycol was determined at 30 °C using the shake flask method. The maximum solubility of clonazepam was observed at volume fraction of 0.90 of ethanol, whereas for aqueous mixtures of polyethylene glycol 200 and propylene glycol, the maximum values were observed in the neat cosolvents. The generated data was fitted to the Jouyban-Acree model and its constants were computed, then the back-calculated solubilities were compared with the corresponding experimental values by calculating the mean percentage deviation (MPD) in which the overall MPD for three cosolvent systems was 7.0 %. The solubility data in cosolvent + water mixtures was predicted using previously trained versions of the Jouyban-Acree model and the prediction MPDs were 13.4, 54.2 and 24.9 %, respectively for ethanol, polyethylene glycol 200 and propylene glycol mixtures and the overall MPD was 30.8 %.     

Extended Hildebrand solubility approach: sulfonamides in binary and ternary solvents

The extended Hildebrand solubility approach is used to estimate the solubility of sulfonamides in binary and ternary solvent systems. The solubility of sulfisomidine in the binary solvent, dioxane-water, shows a bell-shaped profile with a solubility maximum well above the ideal solubility of the drug. This is attributed to solvation of the drug with the dioxane-water solvent, and indicates that the solute-solvent interaction energy (W) is larger than the geometric mean (delta 1 delta 2) of regular solution theory. The solubilities of sulfadiazine, sulfisomidine, sulfathiazole, and sulfamethoxazole were determined in mixtures of dimethylacetamide, glycerol, and water, and the solubility profiles were well reproduced by use of the extended Hildebrand solubility approach. Since the solubility parameter (delta 1 = 11) of the solvent (dimethylacetamide) was approximately equal to the solubility parameters of the sulfonamides, and because of the powerful solvating power of dimethylacetamide, the solubility profiles did not exhibit peaks as observed for sulfisomidine in dioxane-water. When sulfisomidine was dissolved in a ternary mixture, i.e., butyl acetate (delta 1 = 8.5), dimethylacetamide (delta 1 congruent to 11), and methanol (delta 1 = 14.5), a spike was produced in the solubility profile at the solubility parameter of dimethylacetamide. This sharply peaked profile suggests that the two branches be treated as separate solubility curves, which are then independently well reproduced by the extended Hildebrand solubility approach. None of the four sulfonamides yielded log-linear relationships in the ternary mixtures.     

Solubility Prediction of Satranidazole in Propylene Glycol-Water Mixtures Using Extended Hildebrand Solubility Approach

Extended Hildebrand solubility approach is used to estimate the solubility of satranidazole in binary solvent systems. The solubility of satranidazole in various propylene glycol-water mixtures was analyzed in terms of solute-solvent interactions using a modified version of Hildebrand-Scatchard treatment for regular solutions. The solubility equation employs term interaction energy (W) to replace the geometric mean (δ₁δ₂), where δ₁ and δ₂ are the cohesive energy densities for the solvent and solute, respectively. The new equation provides an accurate prediction of solubility once the interaction energy, W, is obtained. In this case, the energy term is regressed against a polynomial in δ₁ of the binary mixture. A quartic expression of W in terms of solvent solubility parameter was found for predicting the solubility of satranidazole in propylene glycol-water mixtures. The expression yields an error in mole fraction solubility of ~3.74%, a value approximating that of the experimentally determined solubility. The method has potential usefulness in preformulation and formulation studies during which solubility prediction is important for drug design.     

Solubility Prediction of Satranidazole in Aqueous N,N-dimethylformamide Mixtures Using Extended Hildebrand Solubility Approach

The solubility of satranidazole in several water–N,N-dimethylformamide mixtures was analysed in terms of solute–solvent interactions and data were treated on the basis of extended Hildebrand solubility approach. The solubility profile of satranidazole in water–N,N-dimethylformamide mixtures shows a curve with a solubility maxima well above the ideal solubility of drug. This is attributed to solvation of the drug with the water–N,N-dimethylformamide mixture, and indicates that the solute–solvent interaction energy (W) is larger than the geometric mean (δ₁δ₂) of regular solution theory. The new approach provides an accurate prediction of solubility once the interaction energy (W) is obtained. In this case, the energy term is regressed against a polynomial in δ₁ of the binary solvent mixture. A quartic expression of W in terms of solvent solubility parameter was found for predicting the mole fraction solubility of satranidazole in the studied mixtures. The method has potential usefulness in preformulation and formulation studies during which solubility prediction is important for drug design.     

Study of Mesalazine Solubility in Ternary Mixtures of Ethanol,Propylene Glycol,and Water at Various Temperatures

Mesalazine is a low-permeable and low-soluble drug, which makes it a class IV drug in the Biopharmaceutics Classification System. Hence, its solubilization can be helpful for various stages of formulation development. The purpose of this study was to investigate the solubilization manner and thermodynamics of mesalazine in ternary solvent combinations of {ethanol (1) + propylene glycol (2) + water (3)} using the shake-flask technique at (298.2–313.2) K. In the following, the mathematical representation of the acquired solubility data using some popular models was evaluated. The accuracies of the applied models were described by percentages of mean relative deviation (MRD%). Based on obtained results (MRD% < 10.0), it can be concluded that the trained models can adequately predict the solubility of mesalazine in the investigated ternary solvent combinations. The findings also revealed that the solution composition and temperatures greatly influence the solubility of mesalazine. In addition, the thermodynamic characteristics of the mesalazine dissolution process indicate that the mesalazine dissolution process is endothermic and entropy-driven. The generating data in the current work also expands the available solubility database for mesalazine in the solvent mixtures.