Tan Yunhao, Hua Jing, Qin Hong
Department of Computer Science, Wayne State University, Detroit, MI 48202, USA.
Comput Aided Des. 2010 Feb 1;42(2):95. doi: 10.1016/j.cad.2009.02.014.
In this paper, we present a novel computational modeling and simulation framework based on dynamic spherical volumetric simplex splines. The framework can handle the modeling and simulation of genus-zero objects with real physical properties. In this framework, we first develop an accurate and efficient algorithm to reconstruct the high-fidelity digital model of a real-world object with spherical volumetric simplex splines which can represent with accuracy geometric, material, and other properties of the object simultaneously. With the tight coupling of Lagrangian mechanics, the dynamic volumetric simplex splines representing the object can accurately simulate its physical behavior because it can unify the geometric and material properties in the simulation. The visualization can be directly computed from the object's geometric or physical representation based on the dynamic spherical volumetric simplex splines during simulation without interpolation or resampling. We have applied the framework for biomechanic simulation of brain deformations, such as brain shifting during the surgery and brain injury under blunt impact. We have compared our simulation results with the ground truth obtained through intra-operative magnetic resonance imaging and the real biomechanic experiments. The evaluations demonstrate the excellent performance of our new technique.
在本文中，我们提出了一种基于动态球形体积单纯形样条的新型计算建模与仿真框架。该框架能够处理具有真实物理特性的零亏格物体的建模与仿真。在此框架下，我们首先开发了一种精确高效的算法，用球形体积单纯形样条重建真实世界物体的高保真数字模型，这些样条能够同时精确表示物体的几何、材料及其他特性。通过拉格朗日力学的紧密耦合，代表物体的动态体积单纯形样条能够精确模拟其物理行为，因为它能在仿真中统一几何和材料特性。在仿真过程中，可视化可以直接基于动态球形体积单纯形样条从物体的几何或物理表示中计算得出，无需插值或重采样。我们已将该框架应用于大脑变形的生物力学仿真，如手术过程中的脑移位和钝器撞击下的脑损伤。我们将仿真结果与通过术中磁共振成像获得的地面真值以及实际生物力学实验结果进行了比较。评估结果证明了我们新技术的卓越性能。
