基于质点-弹簧模型的血管变形研究

Research on vascular deformation based on mass-spring model

针对目前血管介入手术培训系统中将血管作为刚体的现状，提出一种基于质点．弹簧模型的柔性体建模方法，用于模拟血管介入手术培训中血管的形变。为了提高模拟精度，利用有限元模型确定弹簧弹性系数。首先，血管被离散为若干个四节点四面体单元，建立四面体三维实体元素的位移向量，并通过位移向量确定应变矩阵，建立基于应变矩阵的四面体有限元单元刚度矩阵，然后推导出基于质点．弹簧模型的四面体变形矩阵，最后通过有限元刚体矩阵确定弹簧系数。仿真和动物实验表明，建立的血管模型满足血管介入手术培训要求。

In view of the fact that at present blood vessels are generally considered as a rigid body in vascular interventional surgery training, the author of the paper presents a novel soft tissue modeling method based on the mass-spring model for simulation of vascular deformation. The spring coefficient is determined by finite element model. First, blood vessels are discretized into many tetrahedrons, then the displacement vectors of the tetrahedral 3D object are deduced and the strain matrix is determined using the vectors, and the stiffness matrix of the finite element is deduced; finally, the stiffness matrix of the mass-spring model is obtained, and the spring coefficient is derived from the stiffness matrix of the finite element. The simulation and experimental results show that the vascular modeling can meet the demand of surgery training.