Identification of tissue differentiation rates in a mechanobiological model of fracture healing

Abstract

As a basis for model-based analysis of the processes in secondary fracture healing, a dynamical model is presented that characterises the physiological status in the fracture area by the location-dependent composition of tissues. Five types of tissue are distinguished: connective tissue, cartilage, bone, haematoma and avascular bone. A rule base is given that describes dynamical tissue differentiation processes. The rules consider not only a mechanical stimulus but also osteogenic and a vasculative factors as biological stimuli. Within this model structure, it is possible, e.g., to distinguish intramembranous from endochondral ossification processes. An objective function is introduced to assess accordance between the model-based simulation results and reference healing stages. By minimising this objective function, relevant tissue differentiation rates can be determined. For a reference process of secondary fracture healing it could be shown that the intramembranous ossification rate of 0.313%/day (from connective tissue to bone) is much smaller than the endochondral ossification rate of 1.136%/day (from cartilage to bone). In order to verify the model approach, it is transferred to simulate long bone distraction. Results show that healing patterns of bone distraction can be predicted. Using this method, it is possible to identify model parameters for individual subjects. This will allow a patient-specific analysis of tissue healing processes in future.

Keywords::

• secondary fracture healing
• bone distraction
• mechanobiological model
• fuzzy logic
• parameter identification

Acknowledgements

The authors would like to thank Prof. L. Claes (University of Ulm, Germany) and his team, as well as Prof. E.P. Hofer (University of Ulm, Germany) for their support in the development of the model. Part of the work was supported by the German Science Foundation (DFG).