虚拟膝关节镜手术中保持单元质量的体网格形变方法

Quality-Preserving Deformation of Tetrahedral Meshes in Virtual Knee Arthroscopic Surgery

在虚拟膝关节手术中,需要对膝关节进行大范围形变的实时模拟。本文针对四面体网格的膝关节模型,提出了采用LSD度量建立形变能量,然后将带约束的最优化问题转化为不带约束的最优化问题,最后通过带Armijo线性查找的非精确牛顿法求解最优化问题。在求解过程中,通过预估未知点的位置,减少迭代步数,提高了算法的效率。这种方法具有较好的保体积性,同时保证形变后的四面体网格不出现体元翻转和退化。该方法也能推广应用于其它类似的关节弯曲运动的变形中。

In the virtual knee arthroscopic surgery, a real-time large deformation of the knee joint model is required. Towards the tetrahedral model, we firstly employ the LSD metric to build the deformation energy. By converting the constrained optimization problem into an unconstrained one, the optimization can be performed by using the inexact Newton method with an Armijo line search method, Through estimating the unknown vertices, we reduce the iterations and enhance the efficiency of the algorithm. This approach can produce volume preserving and flip-free tetrahedral mesh results. The proposed method can also be applied to other applications involving join〉like deformations.