Arikatla Venkata S, Ortiz Ricardo, Thompson David, Sasaki-Adams Deanna, Enquobahrie Andinet, De Suvranu
Center for Modeling, Simulation and Imaging in Medicine, Rennselaer Polytechnic Institute, 110, 8th street, Troy, NY, 12180.
Kitware Inc., Carrboro, NC, 27510.
Int Conf Comput Math Biomed Eng. 2015 Jun-Jul;2015:332-335.
Modeling interaction between deformable and rigid objects efficiently and accurately is one of the most important tasks for interactive surgical simulation. The Finite Element Method (FEM) has become very popular in this context due to its versatility in representing elastic bodies with irregular geometric features and diverse material properties. In this work we propose a hybrid FEM approach to simulating realistic tissue behavior that uses a non-linear formulation in the vicinity of the interaction while employing a less accurate and inexpensive linear formulation elsewhere. A semi-implicit time stepping is used for the non-linear portion of the domain. This avoids expensive domain decomposition strategies required to maintain consistency at the interface and allows for regular system assembly using a non-overlapping interface and single solver for both domains. This study demonstrates the advantages of our novel approach, especially for the case of real-time surgical simulation.
高效且准确地对可变形物体与刚性物体之间的相互作用进行建模是交互式手术模拟最重要的任务之一。有限元方法（FEM）在这方面变得非常流行，因为它在表示具有不规则几何特征和多样材料特性的弹性体方面具有通用性。在这项工作中，我们提出了一种混合有限元方法来模拟逼真的组织行为，该方法在相互作用附近使用非线性公式，而在其他地方采用不太精确且成本较低的线性公式。对于域的非线性部分使用半隐式时间步长。这避免了在界面处保持一致性所需的昂贵域分解策略，并允许使用非重叠界面和单个求解器对两个域进行常规系统组装。本研究展示了我们新方法的优势，特别是在实时手术模拟的情况下。
