INTRODUCTION: Orthopedic surgical procedures such as osteotomy, in which cutting of the tibia bone is performed, are very common and should be very well performed in order to yield good results. Under this scenario, the study on how the bone reacts to the cutting process is a relevant topic for studies. The goal of this work is to present a mathematical model of the cutting process in the human tibia bone using the Bond Graph method. METHODS: Based on a previous work, a model for the reaction force to the cutting action of the saw has been developed. Moreover, a bond graph based model for determining the bone response to the cutting action of the saw has also been developed. Frequency domain analyses were performed for evaluating the stability of the system. RESULTS: The results of the simulations described were obtained and presented. The results were in good agreement with the expected behavior for the reaction force to the saw, and with respect to the response of the bone material to the cutting process. Moreover, the frequency domain analyses showed that the proposed modelling method has promising characteristics regarding system stability. CONCLUSION: The results suggest that the method has good potential for use, in the near future, for analyses of the cutting process before the surgical procedures. However, additional studies on stability, as well as a proper project of a velocity controller, are still necessary.
Mathematical modeling; Bond Graph; Human bone; Osteoarthritis; Osteotomy
