Research On Improved LSD Metric Tetrahedral Meshes Bending Deformation Methods

With the rapid development of modern science and technology, the computer application technology seeps rapidly to each domain of social life. The combination of virtual reality technology and modern medicine gives rise to virtual surgery techniques. As the traditional surgery training with low efficiency, high-price, long time, and other shortcomings, the virtual surgery system, as a medical education and surgical training system, has got prompt development and promotion in recent years.Practical virtual surgery system must provide with vivid visual feedback of the operation scene. There are a large number of deformations in human soft tissues, both include the small scope elastic deformation caused by medical instruments contact with human organs, such as sinking or bulging of muscles, and include the bending deformation caused by limb movement, such as the movement of elbow and knee. The deformation simulation of tissues is one of the fundamental problems in virtual surgery, and it plays an important role in enhancing the authenticity of the virtual surgery system and strengthening the immersion of the users. In Virtual Knee Arthroscopic Surgery, because we need to calculate force feedback after the deformation of the knee, so it is necessary to ensure the quality of the tetrahedral element after deformation and meet the requirement of the real-time system.There are a lot of methods on the deformation of human soft tissues, and most of them study the deformation of the surface meshes, only a few papers study the deformation of the tetrahedral meshes in the literature. With the background of the Virtual Arthroscopic Surgery system, this paper studied the problem of the tetrahedral bending deformation of the knee. The followings are the main contributions of this paper.1. We put forward to the improved LSD quality metric. In this paper, we start with the quality metric of the tetrahedral meshes, and introduce several commonly used tetrahedral quality metrics, then analyze and compare with their strengths and weaknesses. Combined with the practical needs of the system, we modify the LSD quality metric and enhance the accuracy of the metric.2. We put forward to the tetrahedral bending deformation method based on the improved LSD quality metric. Towards the tetrahedral model, we firstly employ the improved LSD metric to build the deformation energy. By converting the constrained optimization problem into the unconstrained one, the optimization can be performed by using inexact Newton method with an Armijo line search method. According to the character of the bending deformation, estimating the unknown vertices by the controlled vertices, we reduce the iterations and enhance the efficiency of the algorithm.3. We put forward to the implement of bending deformation based on tetrahedral meshes in the Virtual Knee Arthroscopic Surgery in detail. The results show that this module is a very good solution to knee bending deformation problem, and meet the accuracy and real-time requirements of the system. The proposed method can also be applied to other applications involving joint-like bending deformations.In the last, combining the experience and the defects of our methods, we conclude our work and propose the future work and improvement.