Total Lagrangian explicit dynamics finite element algorithm for computing soft tissue deformation
Total Lagrangian explicit dynamics finite element algorithm for computing soft tissue deformation
复制标题
DOI：
10.1002/cnm.887
复制
发表时间：
2007-02-01
影响因子：
--
通讯作者：
Wittek, Adam
中科院分区：
文献类型：
--
作者：
Miller, Karol;Joldes, Grand;Wittek, Adam
我们提出了一种有效的数值算法，用于计算“非常”软组织（如大脑，肝脏，肾脏等）的变形，应用于实时手术模拟。该算法是基于有限元法，使用总拉格朗日公式，其中的应力和应变测量相对于原始配置。这种选择允许在时间步进过程开始之前预先计算大多数空间导数。我们使用显式时间积分，消除了时间步进过程中迭代求解方程的需要。该算法能够处理几何和材料的非线性。采用八节点六面体欠积分单元的全拉格朗日显式动力学（TLED）算法比采用相同单元的更新拉格朗日显式算法每步的浮点运算量减少约35%。算法的稳定性分析表明，由于非常软的组织的刚度比典型的工程材料低得多，与工程模拟中常用的积分时间步长相比，TLED算法的积分时间步长可以大几个数量级，数值算例验证了TLED算法的准确性和有效性。版权所有（C）2006约翰威利父子有限公司
We propose an efficient numerical algorithm for computing deformations of 'very' soft tissues (such as the brain, liver, kidney etc.), with applications to real-time surgical simulation. The algorithm is based on the finite element method using the total Lagrangian formulation, where stresses and strains are measured with respect to the original configuration. This choice allows for pre-computing of most spatial derivatives before the commencement of the time-stepping procedure.We used explicit time integration that eliminated the need for iterative equation solving during the time-stepping procedure. The algorithm is capable of handling both geometric and material non-linearities. The total Lagrangian explicit dynamics (TLED) algorithm using eight-noded hexahedral under-integrated elements requires approximately 35% fewer floating-point operations per element, per time step than the updated Lagrangian explicit algorithm using the same elements.Stability analysis of the algorithm suggests that due to much lower stiffness of very soft tissues than that of typical engineering materials, integration time steps a few orders of magnitude larger than what is typically used in engineering simulations are possible.Numerical examples confirm the accuracy and efficiency of the proposed TLED algorithm. Copyright (C) 2006 John Wiley & Sons, Ltd.