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.     

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).     

Solubility of pioglitazone hydrochloride in ethanol,N-methyl pyrrolidone,polyethylene glycols and water mixtures at 298.20 °K

Background and the purpose of the study

Solubility of pharmaceuticals is still a challenging subject and solubilization using cosolvents is the most common technique used in the pharmaceutical industry. The purpose of this study was reporting and modeling the experimental molar solubility of pioglitazone hydrochloride (PGZ-HCl) in binary and ternary mixtures of ethanol (EtOH), N-methyl pyrrolidone (NMP), polyethylene glycols (PEGs) 200, 400, 600 and water along with the density of saturated solutions at 298.2 °K.

Methods

To provide a computational method, the Jouyban-Acree model was fitted to the solubilities of the binary solvents, and solubilities of the ternary solvents were back-calculated by employing the solubility data in mono-solvents. In the next step, the ternary interaction terms were added to the model and the prediction overall mean percentage deviation (MPD) of the ternary data was reduced. Also a previously proposed version of the model was used to predict the solubility of PGZ-HCl in binary and ternary mixtures employing the experimental solubility data in mono-solvents.

Results

The overall MPD of the model for fitting the binary data and predicted data of ternary solvents were 2.0 % and 50.5 %, respectively. The overall MPD of the predicted solubilities in ternary solvents using the ternary interaction terms in the model was 34.2 %, and by using the proposed version of the Jouyban-Acree model for binary and ternary data the overall correlation and prediction errors were 18.0 and 15.0 %, respectively.

Conclusion

The solubility of PGZ-HCl was increased by addition of EtOH, NMP, PEGs 200, 400 and 600 to aqueous solutions. The reported data extended the available solubility data of pharmaceuticals which are crucial in formulation of liquid dosage forms. The constants of the Jouyban-Acree model using the generated data are also reported which provides the possibility of solubility prediction in other solvent mixtures and temperatures.     

Estimation of the ethanol/water solubility profile from the octanol/water partition coefficient

While the ethanol/water solubility profiles of very polar and very non-polar drugs are monotonic, many semi-polar drugs show a maximum solubility at an ethanol volume fraction (f(max)) between 0 and 1. A sigmoidal relationship was observed between the value of f(max) and the log of the octanol/water partition coefficient (logK(ow)) of the solute. This relationship reasonably predicts the value of the volume fraction of ethanol that gives maximum solubility (f(max)). Combining this sigmoidal relationship with the previously reported linear relationship between the logK(ow) and the initial slope of the plot of log solubility versus ethanol composition [Li, A., Yalkowsky, S.H., 1994. Solubility of organic solutes in ethanol/water mixtures. J. Pharm. Sci. 83, 1735-1740] enables the estimation of the total ethanol/water solubility profile.     

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.     

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)%.     

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 %.     

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%.     

Correlation of retention factor of analytes in quaternary solvent mobile phases using the Jouyban-Acree model

The Jouyban-Acree model has been used for the mathematical representation of retention factors of phenobarbital, phenytoin and carbamazepine in quaternary aqueous-organic solvent mobile phases. The accuracy of the proposed model is evaluated using average percentage deviation (APD) of experimental and calculated values as an accuracy criterion. The obtained mean and standard deviation of APDs of the model is 4.2 +/- 0.5%. The results showed that the Jouyban-Acree model provided accurate calculations and could be used in practice to speed up the method development process in which quaternary solvent mobile phases are required.     

Prediction of drug solubility in water-propylene glycol mixtures using Jouyban-Acree model

A trained version of the Jouyban-Acree model was presented to predict drug solubility in water-propylene glycol mixtures at various temperatures. The model is able to predict the solubility in various solubility units and requires the experimental solubility of a solute in mono-solvent systems. The mean percentage deviation (MPD) of predicted solubilities was computed to show the accuracy of the predicted data and 24% was found as the average MPD for 27 data sets studied. The proposed model enables the researchers to predict solubiliy in water-propylene glycol mixtures at various temperatures and reduces the number of required experimental data from five to two points.     

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 of drugs in aqueous solutions. Part 4. Drug solubility by the dilute approximation

As in our previous publications in this journal [Int. J. Pharm. 258 (2003a) 193; Int. J. Pharm. 260 (2003b) 283; Int. J. Pharm. 267 (2003c) 121], this paper is concerned with the solubility of poorly soluble drugs in aqueous mixed solvents. In the previous publications, the solubilities of drugs were assumed to be low enough for the so-called infinite dilution approximation to be applicable. In contrast, in the present paper, the solubilities are considered to be finite and the dilute solution approximation is employed. As before, the fluctuation theory of solutions is used to express the derivatives of the activity coefficient of a solute in a ternary solution (dilute solute concentrations in a binary solvent) with respect to the concentrations of the solvent and cosolvent. The expressions obtained are combined with a theoretical equation for the activity coefficient of the solute. As a result, the activity coefficient of the solute was expressed through the activity coefficients of the solute at infinite dilution, solute mole fraction, some properties of the binary solvent (composition, molar volume and activity coefficients of the components) and parameters reflecting the nonidealities of binary species. The expression thus obtained was used to derive an equation for the solubility of poorly soluble drugs in aqueous binary solvents which was applied in two different ways. First, the nonideality parameters were considered as adjustable parameters, determined from experimental solubility data. Second, the obtained equation was used to correct the solubilities of drugs calculated via the infinite dilution approximation. It was shown that both procedures provide accurate correlations for the drug solubility.     

Solubility of drugs in aqueous solutions. Part 3: multicomponent mixed solvent

The results obtained previously by Ruckenstein and Shulgin [Int. J. Pharm. 258 (2003a) 193; Int. J. Pharm. 260 (2003b) 283] via the fluctuation theory of solutions regarding the solubility of drugs in binary aqueous mixed solvents were extended in the present paper to multicomponent aqueous solvents. The multicomponent mixed solvent was considered to behave as an ideal solution and the solubility of the drug was assumed small enough to satisfy the infinite dilution approximation.An expression derived for the activity coefficient of a solid solute in a multicomponent solvent was used to obtain an equation for the solubility of a drug in terms of its solubilities in two subsystems of the multicomponent solvent and their molar volumes. Ultimately the solubility can be expressed in terms of those in binary or even in individual solvents and their molar volumes.The method was applied to the solubility of tioconazole and 19-Nor-1alpha,25-dihydrovitamin D(2) in several ternary and in a quaternary aqueous mixed solvents. The predicted solubilities were compared with experimental data and good agreement was found.     

In silico prediction of drug solubility in water-dioxane mixtures using the Jouyban-Acree model

A numerical method based on the Jouyban-Acree model was presented for prediction of drug solubility in water-dioxane mixtures at various temperatures. The method requires drug solubility in monosolvent systems, i.e. two data points for each temperature of interest. The mean percentage deviation (MPD) of predicted solubilities was calculated to show the accuracy of the predicted data and 27% was found as the average MPD for 36 data sets studied. The proposed numerical method reduced the number of required experimental data from five to two points and could also be extended to predict solubility at various temperatures.     

Use of solubility parameter to design dry suspension of cefaclor as a dual pack system

One of the important methods to improve the solubility of a less water-soluble drug is by the use of co solvents. The solubility enhancement produced by two binary blends with a common co solvent (water-propylene glycol and propylene glycol-ethyl acetate) was studied against the solubility parameter of solvent blends (δ(1)) to evaluate the solubility parameter of drug (δ(2)). The binary blend water:propylene glycol (20:80) gave maximum solubility with an experimental δ(2) value of 16.52 (Cal/cm(3))(0.5) that was comparable to the theoretical value of 16.52 (Cal/cm(3))(0.5) determined by molar volume method and 16.35 (Cal/cm(3))(0.5) when determined by method proposed by Lin and Nash. The solvent blend water:propylene glycol (20:80) in which the drug exhibited maximum solubility was used as the reconstituting medium for formulation of dry suspension of cefaclor. The percentage cumulative drug release of cefaclor from the formulation F7 was compared to the marketed formulation by calculating the f1 (dissimilarity factor) and f2 (similarity factor) factors. A higher f1 value and f2 value below 50 indicates difference between the two dissolution profiles.     

Mathematical representation of analyte's capacity factor in binary solvent mobile phases using the Jouyban-Acree model

Applicability of a solution model, namely the Jouyban-Acree model, for mathematical representation of capacity factors of phenobarbital, phenytoin and carbamazepine in mobile phases containing water and the organic modifiers: methanol, acetonitrile, acetone and tetrahydrofuran and also a number of data sets collected from the literature has been shown. The accuracy of the proposed model is compared with those of the linear model and the quadratic equation using average percentage deviation (APD) as an accuracy criterion. The obtained mean and standard deviation of APDs of the Jouyban-Acree, linear and quadratic models are 8.1 +/- 8.4, 25.2 +/- 18.0 and 14.5 +/- 16.2%, respectively. The results showed that the Jouyban-Acree model provided more accurate calculations than the previously published models and the mean differences were statistically significant (p < 0.002).