Mathematical modeling of bioactive glass degradation

Bioactive glasses (BGs) are promising for bone tissue engineering (BTE). Mathematical modeling is a powerful tool for understanding BTE scaffold degradation. We developed mathematical functions based on chemical reaction equations governing dissolution and diffusion processes to model the degradation of 45S5 BGs. An empirical mathematical model was employed to characterize the formation process of hydroxycarbonate apatite (HCA). Two sets of numerical simulations with BG powder and bulk samples immersed in simulated body fluid were compared with in vitro experiments to validate and parameterize the model. The model could accurately predict BG degradation and HCA formation. Our findings indicate that the proposed parameters K ₁=2600 mm/(μmol·h), K ₂=2.0 mm/h and K ₃=0.001 mm/h are suitable for simulating the degradation of silicate-based BGs, specifically 45S5 BG. The proposed model successfully predicted the degradation behavior and subsequent HCA formation over 21 days. The proposed mathematical model serves as a valuable tool for designing degradable BG-containing scaffolds.