Mathematical and Computational Models for Osseointegration in Titanium Dental Implants: A Systematic Review of Current Approaches and Future Directions.

Purpose: To identify, compare, and critically evaluate the main mathematical and computational models used to study osseointegration in titanium dental implants. It focuses on the models' predictive accuracy, biological and mechanical integration, and clinical relevance, highlighting their contributions and limitations in simulating implant stability and bone remodeling.

Materials and methods: A systematic literature search was conducted in MEDLINE/PubMed, Scopus, and SpringerLink databases up to February 2025. Studies were included if they employed mathematical or computational models-such as finite element analysis, mechanobiological frameworks, or reaction-diffusion systems-to investigate osseointegration in titanium dental implants. A quality assessment of included studies was performed using the GRADE approach to ensure methodological rigor.

Results: A total of 42 studies met the inclusion criteria. Finite element analysis (FEA) was the most commonly used technique, primarily addressing mechanical aspects such as stress distribution and implant geometry. Mechanobiological and reaction-diffusion models incorporated biological and biochemical processes but lacked standardization and clinical validation. The integration of mechanical and biological factors remains limited, hindering real-world applicability. Despite progress, few models included patient-specific parameters or were validated experimentally.

Conclusion: Mathematical and computational models have substantially advanced our understanding of osseointegration in titanium dental implants. However, their translation into clinical practice is still constrained by validation gaps, heterogeneity in model parameters, and limited biological integration. Future research should emphasize hybrid models, incorporate robust validation protocols, and leverage artificial intelligence to enable personalized and clinically meaningful simulations.