From Heuristic to Mathematical Modeling of Drugs Dissolution Profiles: Application of Artificial Neural Networks and Genetic Programming.

The purpose of this work was to develop a mathematical model of the drug dissolution (Q) from the solid lipid extrudates based on the empirical approach. Artificial neural networks (ANNs) and genetic programming (GP) tools were used. Sensitivity analysis of ANNs provided reduction of the original input vector. GP allowed creation of the mathematical equation in two major approaches: (1) direct modeling of Q versus extrudate diameter (d) and the time variable (t) and (2) indirect modeling through Weibull equation. ANNs provided also information about minimum achievable generalization error and the way to enhance the original dataset used for adjustment of the equations' parameters. Two inputs were found important for the drug dissolution: d and t. The extrudates length (L) was found not important. Both GP modeling approaches allowed creation of relatively simple equations with their predictive performance comparable to the ANNs (root mean squared error (RMSE) from 2.19 to 2.33). The direct mode of GP modeling of Q versus d and t resulted in the most robust model. The idea of how to combine ANNs and GP in order to escape ANNs' black-box drawback without losing their superior predictive performance was demonstrated. Open Source software was used to deliver the state-of-the-art models and modeling strategies.

Application of artificial neural networks (ANNs) and genetic programming (GP) for prediction of drug release from solid lipid matrices.

The aim of the present study was to develop a semi-empirical mathematical model, which is able to predict the release profiles of solid lipid extrudates of different dimensions. The development of the model was based on the application of ANNs and GP. ANNs' abilities to deal with multidimensional data were exploited. GP programming was used to determine the constants of the model function, a modified Weibull equation. Differently dimensioned extrudates consisting of diprophylline, tristearin and polyethylene glycol were produced by the use of a twin-screw extruder and their dissolution behaviour was studied. Experimentally obtained dissolution curves were compared to the calculated release profiles, derived from the semi-empirical mathematical model.

Drug release from extruded solid lipid matrices: theoretical predictions and independent experiments.

The aim of this study was to use a mechanistically realistic mathematical model based on Fick's second law to quantitatively predict the release profiles from solid lipid extrudates consisting of a ternary matrix. Diprophylline was studied as a freely water-soluble model drug, glycerol tristearate as a matrix former and polyethylene glycol or crospovidone as a pore former (blend ratio: 50:45:5%w/w/w). The choice of these ratios is based on former studies. Strains with a diameter of 0.6, 1, 1.5, 2.7 and 3.5mm were prepared using a twin-screw extruder at 65 °C and cut into cylinders of varying lengths. Drug release in demineralised water was measured using the USP 32 basket apparatus. Based on SEM pictures of extrudates before and after exposure to the release medium as well as on DSC measurements and visual observations, an analytical solution of Fick's second law of diffusion was identified in order to quantify the resulting diprophylline release kinetics from the systems. Fitting the model to one set of experimentally determined diprophylline release kinetics from PEG containing extrudates allowed determining the apparent diffusion coefficient of this drug (or water) in this lipid matrix. Knowing this value, the impact of the dimensions of the cylinders on drug release could be quantitatively predicted. Importantly, these theoretical predictions could be confirmed by independent experimental results. Thus, diffusion is the dominant mass transport mechanism controlling drug release in this type of advanced drug delivery systems. In contrast, theoretical predictions of the impact of the device dimensions in the case of crospovidone containing extrudates significantly underestimated the real diprophylline release rates. This could be attributed to the disintegration of this type of dosage forms when exceeding a specific minimal device diameter. Thus, mathematical modelling can potentially significantly speed up the development of solid lipid extrudates, but care has to be taken that none of the assumptions the mathematical theory is based on is violated.

Dissolution from solid lipid extrudates containing release modifiers.

The influence of different types of release modifiers on the dissolution from solid lipid extrudates was investigated. Diprophylline was extruded together with 45% tristearin and 5% (w/w) of a release modifier to suitable extrudates. Three groups of release modifiers were defined: Hydrocolloids, disintegrants and pore formers. All of the release modifier-containing extrudates showed a faster release compared to the reference extrudate, which contained 50% (w/w) of each, API and lipid. Increasing the amount of diprophylline in the binary mixture up to 55% (w/w) also increased its release rate. Compared to this new reference, not all of the release modifier-containing extrudates exhibited an increased dissolution rate. Within the group of pore formers, there was a great discrepancy concerning the dissolution rates. Extrudates containing polyethylene glycol (PEG) exhibited a much higher release rate compared with extrudates containing sodium chloride or mannitol. This behaviour was assumed to be based on the extrusion temperature of 65°C at which PEG exists in the molten state. The hypothesis was tested using different PEGs and another solid lipid.