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Abstract
In cranio-maxillofacial surgical simulation, many difficulties occur in building a realistic biomechanical model of soft tissue deformation, e.g. constitutive properties of the living tissues, geometry description, and kinematics of the facial soft tissues. This paper presents a nonlinear finite mixed-element model (NFM-EM) to enhance the tissue behaviour in the simulation. A novel geometric description method based on the mixed elements is first designed to allow the skin and the internal tissues (muscles and fat) to be discretised with different volumetric elements and assigned unique material properties. Moreover, it provides C 1-continuity at the facial surface and leaves C 0-continuity in the interior elements. In addition, this approach employs the Lagrange principle of virtual work to compute the deformation of the soft tissues. Six Crouzon syndrome patients who underwent mid-face distraction surgery are tested by the proposed approach. The comparative results of different models and the quantitative validation demonstrated the effectiveness of this approach. The total map errors (L2-norm) between the predicted results and the actual post-operative results stay below 30 mm and the variance of the map errors proves to be the least in all methods.
Acknowledgements
The authors would like to thank the anonymous reviewers and editors for their comments and suggestions, which helped to improve the quality of this work greatly. The research was supported by Shanghai Leading Academic Discipline Project (No. S30602) and Shanghai Science Foundation of China (No. 08ZR1409300). The authors would like to thank Prof. Xiongzheng Mu and Dr Zheyuan Yu in the Shanghai 9th People's Hospital for their assistance in acquiring patients' dataset and validating the results.