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.