Integrating classical and fractional calculus rheological models in developing hydroxyapatite-enhanced hydrogels

Abstract

This study presents a novel method for comprehending the rheological behavior of biomaterials utilized in bone regeneration. The focus is on gelatin, alginate, and hydroxyapatite nanoparticle composites to enhance their mechanical properties and osteoconductive potential. Traditional rheological models are insufficient for accurately characterizing the behavior of these composites due to their complexity and heterogeneity. To address this issue, we utilized fractional calculus rheological models, such as the Scott-Blair, Fractional Kelvin-Voigt, Fractional Maxwell, and Fractional Kelvin-Zener models, to accurately represent the viscoelastic properties of the hydrogels. Our findings demonstrate that the fractional calculus approach is superior to classical models in describing the intricate, time-dependent behaviors of the hydrogel-hydroxyapatite composites. Furthermore, the addition of hydroxyapatite not only improves the mechanical strength of hydrogels but also enhances their bioactivity. These findings demonstrate the potential of these composites in bone tissue engineering applications. The study highlights the usefulness of fractional calculus in biomaterials science, providing new insights into the design and optimization of hydrogel-based scaffolds for regenerative medicine.