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Comput Math Methods Med. 2015;2015:863874. doi: 10.1155/2015/863874. Epub 2015 May 26.

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

### Author information

1
Department of Pharmaceutical Technology and Biopharmaceutics, Jagiellonian University Medical College, Medyczna 9 Street, 30-688 Krakow, Poland.
2
Institute of Pharmaceutics and Biopharmaceutics, Heinrich-Heine University of Düsseldorf, Universitätsstraße 1, 40225 Duesseldorf, Germany.
3
Department of Pharmacoepidemiology and Pharmacoeconomics and Department of Social Pharmacy, Faculty of Pharmacy, Jagiellonian University Medical College, Medyczna 9 Street, 30-688 Krakow, Poland ; Simcyp (a Certara Company) Limited, Blades Enterprise Centre, John Street, Sheffield S2 4SU, UK.
4
Department of Pharmacoepidemiology and Pharmacoeconomics and Department of Social Pharmacy, Faculty of Pharmacy, Jagiellonian University Medical College, Medyczna 9 Street, 30-688 Krakow, Poland.

### Abstract

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.

PMID:
26101544
PMCID:
PMC4460208
DOI:
10.1155/2015/863874
[Indexed for MEDLINE]
Free PMC Article