旋转切割有限元方法用于实时手术模拟：应用于针刺插入模拟
Corotational Cut Finite Element Method for real-time surgical simulation: application to needle insertion simulation
AI总结：
本文提出了一种旋转切割有限元方法用于实时手术模拟，通过多级嵌入算法考虑表面细节，避免复杂网格生成，提高模拟精度。
摘要：
本文描述了旋转切割有限元方法（FEM）在实时手术模拟中的应用。用户只需提供一个不必要符合模拟对象边界/界面的背景网格。通过多级嵌入算法将从二值图像直接获得的表面细节考虑进背景网格被表面切割的元素中。通过拉格朗日乘数隐式施加边界条件。通过收敛研究验证了实现的最优收敛率。该算法应用于各种针刺插入模拟（如活检或近距离放射治疗）到脑部和肝脏中以验证方法的可靠性，数值结果表明该方法可以使得离散化与几何描述无关，并能避免复杂几何的网格生成复杂性，同时保持标准FEM的准确性。使用所提出的方法非常适合实时和患者特定的模拟，因为它通过自动且适当地考虑模拟几何来提高模拟精度。
英文摘要：
This paper describes the use of the corotational cut Finite Element Method (FEM) for real-time surgical simulation. Users only need to provide a background mesh which is not necessarily conforming to the boundaries/interfaces of the simulated object. The details of the surface, which can be directly obtained from binary images, are taken into account by a multilevel embedding algorithm applied to elements of the background mesh that cut by the surface. Boundary conditions can be implicitly imposed on the surface using Lagrange multipliers. The implementation is verified by convergence studies with optimal rates. The algorithm is applied to various needle insertion simulations (e.g. for biopsy or brachytherapy) into brain and liver to verify the reliability of method, and numerical results show that the present method can make the discretisation independent from geometric description, and can avoid the complexity of mesh generation of complex geometries while retaining the accuracy of the standard FEM. Using the proposed approach is very suitable for real-time and patient specific simulations as it improves the simulation accuracy by taking into account automatically and properly the simulated geometry.
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