Gradient field based inhomogeneous volumetric mesh deformation for maxillofacial surgery simulation

This paper presents a novel inhomogeneous volumetric mesh deformation approach by gradient field manipulation, and uses it for maxillofacial surgery simulation. The study is inspired by the state-of-the-art surface deformation techniques based on differential representations. Working in the volumetric domain instead of on only the surface can preserve the volumetric details much better, avoid local self-intersections, and achieve better deformation propagation because of the internal mesh connections. By integrating the mesh cell material stiffness parameter into our new discrete volumetric Laplacian operator, it is very convenient to incorporate inhomogeneous materials into the deformation framework. In addition, the system matrix for solving the volumetric harmonic field to handle the local transformation problem is the same used for Poisson reconstruction equation, thus it requires solving essentially only one global linear system. The system is easy to use, and can accept explicit rotational constraints, or only translational constraints to drive the deformation. One typical maxillofacial surgery case was simulated by the new methodology with inhomogeneous material estimated directly from CT data, and compared to the commonly used finite element method (FEM) approach. The results demonstrated that the deformation methodology achieved good accuracy, as well as interactive performance. Therefore, the usage of our volumetric mesh deformation approach is relevant and suitable for daily clinical practice.