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Mathematical Modelling and Examination of Interactions between Bone Substitute, Mandibular Living Tissue and Tooth Implant
- Speaker(s)
- Yunuhen Hernandez Rodriguez
- Date
- June 5, 2024, 2:15 p.m.
- Room
- room 5070
- Title in Polish
- Modelowanie matematyczne i badanie interakcji między substytutem kości, żywą tkanką żuchwy i implantem zęba
- Seminar
- Seminar of Biomathematics and Game Theory Group
Objective: This presentation aims to introduce a novel mathematical model of bone remodelling that closely mirrors the natural behavior of cancellous bone. By translating cellular functions into mathematical equations, we have developed new relationships that mimic bone's natural processes.
Key Points:
1) Understanding Bone Failure Mechanics:
* Initial investigation into cancellous bone failure mechanisms.
* Empirical data collected to inform the new model.
2) Novel Mathematical Approach:
* Separation of mechanical loading stimulus from bone growth and absorption signals.
* Introduction of an exponentially decaying signal over distance and time.
3) Model Validation:
* Comparison with X-ray photographs of healthy mandibles and edentulous cases.
* Accurate prediction of bone synthesis and resorption areas.
4) Simulation Studies:
* Testing the model with bone tissue, bone substitute materials, and dental implants.
* Development of a dynamic moving border concept between bone tissue and substitute material.
* Successful replacement of bone substitute material with normal bone tissue over time.
4) Implications for Implant Desing:
* Dynamic interactions between bone tissue and implants.
* Potential improvements in implant design for various conditions, including bone diseases.
Conclusion: This innovative model provides a robust framework for understanding and predicting bone remodelling, with significant implications for dental implant design and other orthopedic applications. Future studies will explore its application in disease cases.
