Kinetic Parameter Estimation of Calcium Phosphate Coating Using Particle Swarm Optimization

Abstract

Metallic surface coated with calcium phosphate combines the excellent mechanical properties of metal with the calcium phosphate bioactivity. Therefore, these materials have been largely used for biomedical applications. The aim of this work was to study the biomimetic deposition process kinetics by using two solutions with different chemical compositions. The biomimetic process consists of substrate immersion into a Simulated Body Fluid (SBF). Many papers describe this process; however, few works have focused on the process of the kinetic parameter estimation. In the experimental procedure, titanium samples were soaked into solutions, called as Simulated Body Fluid (SBF) and Solution for Bioactivity Evaluation (SBE); calcium and phosphorous concentration were quantified during the biomimetic exposure. In the present work, Lagergren models were tested to fit the experimental data. In order to find the best model and consequently obtain the kinetic parameters, with confidence intervals, a computational package based on Particle Swarm Optimization (PSO) was used. Pseudo-first and second order kinetics were tested with experimental data. However, the best fit for both SBE and SBF was obtained with the first order. The estimated SBE deposition rate was higher than the SBF one and this result can be corroborated by more intense deposition of simplified fluid.
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