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1、华北水利水电学院 硕士学位论文 基于无网格方法的软组织形变模型 姓名：毛磊 申请学位级别：硕士 专业：计算机应用技术 指导教师：刘雪梅 2011-05 华北水利水电学院硕士学位论文 I 基于无网格方法的软组织形变模型 摘 要 随着虚拟现实与计算机技术的不断发展， 虚拟手术在医疗卫生领域发挥的作用越来 越大，不仅可用于手术技能培训，还可用于手术规划、手术预演、手术导航等。在虚拟 手术中，软组织形变仿真是最为关键的技术，其基本任务是模拟手术器械与软组织接触 时的形变情况。虽然软组织形变模型已从非物理模型发展为基于物理特性的形变模型， 但现有的大多数形变模型是基于网格的模型，在发生大变形或切割、缝合
2、等拓扑结构改 变时容易出现网格畸变或者需要重构网格，严重影响形变仿真的精度和效率。本文主要 针对现有模型的不足，对虚拟手术中的软组织形变仿真进行较为深入的研究，主要研究 内容是：基于粘弹性力学模型，构建无网格伽辽金与质点弹簧耦合的软组织形变模型， 实现软组织的形变仿真。 采用无网格伽辽金与质点弹簧耦合的软组织模型来描述软组织， 针对手术操作过程 的局部性，将接受手术的软组织分为两部分来处理，即手术区域和非手术区域。在手术 区域采用无网格伽辽金法获取精确模拟，在非手术区域采用质点弹簧法提高模拟效率。 由于无网格伽辽金法对离散模型的边界定义较为模糊， 本文提出确定无网格边界的搜索 算法。该算法适应
3、性强，并为后续过渡单元近似位移函数的建立奠定坚实的基础。 为有效建立无网格区域与质点弹簧区域之间的光滑过渡，因此，需要在两个区域之 间建立近似位移函数。本文提出了在无网格区域与质点弹簧区域之间建立过渡单元，并 在过渡单元内建立过渡节点；设计了过渡单元搜索算法，根据过渡节点必须满足的位移 和力平衡条件建立过渡单元的近似位移函数。 为了验证本文实现变形的有效性，以肝脏数据作为测试样本进行形变模拟，实验表 明采用基于 Kelvin 粘弹性力学模型的无网格伽辽金与质点弹簧耦合模型， 可有效表现软 组织在形变过程中所具有的蠕变和松弛特性；既提高计算精度，又降低了计算复杂度， 提高了运行效率。 关键词：虚
4、拟手术；无网格伽辽金模型；粘弹性模型；形变仿真；耦合模型 华北水利水电学院硕士学位论文 II THE MODEL OF SOFT TISSUE DEFORMATION BASED ON THE METHOD OF MESHFREE ABSTRACT With the development of virtual reality and computer technology, virtual surgery has played a more and more important role in the field of medical treatment and public health.
5、 It can be utilized in the training of operation skills, operation planning, rehearsal of operations, and navigation of operation etc. In a virtual surgery the key technique is the simulation of soft tissue deformation whose basic function is to stimulate the deformation which occurs when the operat
6、ion instruments get to contact the soft tissues. Although the model of soft tissue deformation has evolved from non-physical model into deformation model in accordance with its physical characteristics, most existing deformation models are models based upon gridding, which easily lead to gridding di
7、stortions or reconstructing gridding and severely affect preciseness and efficiency of the deformation stimulation once changes of topological structure, like material distortion, cutting or suturing happen. Aiming at the lack of existing models, this dissertation carries out a deep research into th
8、e stimulation of soft tissue deformation in the virtual surgery. The main contributions of the paper are as follows: Build a compling of Galerkin-based Meshfree and Mass-Spring Models based Viscoelastic model, achieve deformation simulation of soft tissue. Based on limitations existing during the op
9、eration process, the soft tissues is described by the soft tissue coupling of Galerkin-based Meshfree Methods and Mass-Spring Models. The soft tissues to be operated on are divided into two parts: operation area and non-operation area. In the operation area, Galerkin-based Meshfree Methods are appli
10、ed to obtain a precise stimulation, while in the non-operation area, Mass-Spring Models are employed to make stimulation more efficient. Since the definition of discrete model boundary in Galerkin-based Meshfree Methods are relatively vague, in this dissertation a search algorithm to determine the m
11、eshfree boundary is put forward. This kind of algorithm is very adaptable, and lays a sound foundation for the establishment of the approximate displacement function of following transitional unit. In order to establish a smooth transition between Meshfree domain and Mass-Spring 华北水利水电学院硕士学位论文 III d
12、omain effectively, the approximate displacement function between the two areas needs to be built. In this dissertation a transitional unit is proposed between Meshfree domain and Mass-Spring domain. Also transitional joint point is built in transitional unit. A search algorithm of transitional unit
13、is devised, and the approximate displacement function of transitional unit is built according to the balance conditions about forces and displacements that should be satisfied by transitional joint point. The liver data are sampled to conduct the deformation model in order to prove the effectiveness
14、 of the deformation realized in this dissertation. The experiment shows the models based on Kelvin Viscoelastic model of coupling model which Galerkin-based Meshfree methods and Mass-Spring methods can present creep as well as looseness occurring in the deformation process of soft tissues effectivel
15、y. Not only does it increase the calculation accuracy, but also reduces complication of calculation and improves operating efficiency. Key Words: Virtual surgery; Galerkin-based Meshfree methods; Viscoelastic model; Deformation simulation; Coupling models 独立完成与诚信声明 本人郑重声明：所提交的学位论文，是本人在指导教师的指导下，独立进行研
16、究 工作所取得的研究成果并撰写完成的。没有剽窃、抄袭等违反学术道德、学术规范的侵 权行为。文中除已经标注引用的内容外，本学位论文中不包含其他人或集体已经发表或 撰写过的研究成果， 也不包含为获得华北水利水电学院或其它教育机构的学位或证书所 使用过的材料。对本文的研究做出重要贡献的个人和集体，均已在文中作了明确的说明 并表示了谢意。本人完全意识到本声明的法律后果由本人承担。 学位论文作者签名： 保证人（导师）签名： 签字日期： 签字日期： 学位论文版权使用授权书 本人完全了解华北水利水电学院有关保管、使用学位论文的规定。特授权华北水 利水电学院可以将学位论文的全部或部分内容公开和编入有关数据库提供检索， 并采用 影印、缩印或扫描等复制手段复制、保存、汇编以供查阅和借阅。同意学校向国家有关 部门或机构送交论文原件或复印件和电子文档。 （涉密的学位论文在
