Simulating cranio-maxillofacial surgery based on mixed-element biomechanical modelling.

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 C¹-continuity at the facial surface and leaves C⁰-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.