Journal of Sol-Gel Science and Technology

, Volume 86, Issue 1, pp 112–125 | Cite as

Prediction of hydroxyapatite crystallite size prepared by sol–gel route: gene expression programming approach

  • Mehrdad Mahdavi Jafari
  • Gholam Reza Khayati
Original Paper: Sol-gel and hybrid materials for biological and health (medical) applications


Excellent biocompatibility and its similar biological characteristics to bone apatite, extensively expand the hydroxyapatite (HA) usage in bioimplant applications. The crystallite size of HA is one of the most administrated parameter for determination of reaction rate at the interface of artificial/natural bones. This study tried to propose a new predictive model by employment of the gene expression programming (GEP), i.e., a powerful soft computing technique, to estimate the crystallite size of HA that were prepared by sol–gel route. Firstly, 37 different reliable experiments were carried out considering the type of phosphor precursor, pH, drying temperature, aging time, temperature and time of calcination as practical parameters as input variables, and HA crystallite size as output variable. Absolute fraction of variance (R2), mean absolute percentage error (MAPE), root relative squared error (RRSE), and mean squared error (MSE) were considered to validate the most appropriate GEP model/s. The experiment results were divided randomly into 29 training sets and 8 testing sets. Finally, the best model was selected in R2 = 0.9929, MAPE = 2.8, RRSE = 0.0956, and MSE = 1.7. The results of simulation confirmed the unique features of GEP for the determination of HA crystallite size prepared by sol–gel route.

Predicted vs. experimental HA crystallite size through GEP-3, GEP-8 and GEP-6 models in (a) training phase, and (b) testing phase.


Hydroxyapatite Crystallite size Sol–gel Process parameters Modeling Gene expression programming 



This work was supported by the Iranian National Science Foundation (INSF).

Compliance with ethical standards

Conflicts of interest

The authors declare that they have no conflict of interest.


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Materials Science and EngineeringShahid Bahonar University of KermanKermanIran

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