基于改进弹簧振子模型的软组织形变仿真

Simulation of Soft Tissue Deformation Based on Improved Mass-Spring Model

研究虚拟手术中软组织形变的特定性优化问题。传统弹簧振子模型由于采用线弹力方程及显示欧拉积分法求解,导致的真实性低、计算复杂、实时性差的问题。为解决形变动特性问题,提出一种改进弹簧振子模型的形变方法,采用四面体网格弹簧振子模型进行建模,并通过定义质点间弹簧的非线性弹力方程以及作用于质点的体积力方程,来减弱超弹性现象的发生,提高真实性。模型求解时,采用一种改进显式欧拉积分的动态局部算法来求解形变方程。实验结果表明,所提算法提高了形变仿真的真实性、实时性和稳定性,可为软组织形变动态仿真系统的设计提供参考。

In this paper, the specific nature optimization problem of soft tissue deformation in virtual surgery was studied. Because linear elastic equation and explicit Euler integration method are implemented in traditional mass spring model, its authenticity and real-time characteristic are too low. A deformation simulation algorithm based on improved mass spring model was proposed to improve the authenticity and real-time characteristic. Tetrahedral mass spring model was constructed, in which nonlinear spring mechanics equations between particles and volume force e- quations applied to particles were defined to cut down the probability of super elasticity and improve the precision of simulation. Based on the improved explicit Euler integration method, a dynamic partial simulation solution algorithm was employed to work out the deformation equation. Experiment result shows that this proposed method improves the authenticity, real-time and stability of soft tissue deformation simulation, so it can be implemented to dynamic simulation of soft tissue deformation.