碰撞接触问题中软组织形变的建模与应用
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摘要
从计算机诞生至今,其应用已经遍布人类生活的方方面面,从原始的科学计算到如今的日常娱乐都有计算机的影子。计算机的发展加速了不同学科交流融合,如今数学、物理、生物、医学等都与计算机科学有着密切联系,而医学领域中的虚拟手术模拟系统更是将这些学科全部有机地结合在一起。近几年来,随着计算机技术的发展,医学领域迫切需要开发出能够模拟手术进行的虚拟手术系统,以应用于教学、培训、诊断、术前计划等多个领域。一个完整的虚拟手术系统,涉及计算机图形学、数字图像处理、计算机人机交互、软组织形变计算等多方面的技术。
虚拟手术系统作为虚拟现实技术的一种,与人体软组织的三维建模都已经成为是计算机图形学的重要研究课题。而其中结构复杂的软组织形变计算研究也是实时虚拟手术系统和人机交互系统中最具挑战性的内容。
本文讨论了虚拟脊柱手术系统的需求分析及模块设计,并对其中的软组织形变仿真及其在脊柱手术系统中的应用展开详细分析和实验。考虑到人体脊柱软组织(椎间盘)的环-核结构及其强接触非线性特性,为了兼顾计算的准确性和计算效率,重点研究讨论了接触有限元模型的实现及其改进方案。
本研究在传统有限元计算的基础上,根据研究对象在结构和材料上的特点,提出创新性的混合与简化计算方案,结合非线性的准确性和简化模型的效率计算软组织形变,并实验验证其可行性和效率;同时介绍了特殊结构的三维网格重建算法、图形处理单元的并行计算加速、人机交互技术等相关内容。
本文的主要工作和创新点如下:
1.详细讨论了有限元方法、相关的力学概念以及对应的数值解法,并重点针对接触碰撞中的强非线性问题对有限元求解算法进行整理简化和优化。
2.讨论了有限元分析中特殊结构网格模型的建立与选取,以及不同网格划分方法在具体使用中的区别和注意事项。
3.本文对传统碰撞接触状态下强非线性有限元的计算进行了简化和改进,满足了人体脊柱软组织的特点,提升了算法的计算效率。
4.利用图形显示卡的并行计算特性进行计算加速。
5.建立验证手术形变模拟结果的较合理的机制,通过在真实医疗数据上进行实验来验证该形变模拟的真实性和有效性。
6.根据实际实验的结果和结论,选取并结合使用不同合适的网格模型生成算法,对算法中的参数和材料参数的设定进行调整优化,以达到计算效率和模拟真实性的最优平衡。
7.本论文的新型算法成功地将碰撞接触非线性有限元分析应用于脊柱手术模拟中,并对软组织不同部位的形变模拟结果进行应力分析。
Since the birth of the computer, it has been applied in every aspect of people’s daily life. Computers can be easily seen in the areas from scientific computing to the common entertainment. The development of computer speeds up the integration among different disciplines. Mathematics, physics, biology, medicine and computer science are having close contact now. In recent years, as the fast development of computer science, the field of medicine has an urgent requirement of a virtual surgery system that can perform virtual surgery. This system will be applied to teaching, training, diagnosis, surgical pre-planning and many other areas. A complete medical virtual surgery simulation system involves multiple technologies such as computer graphics, digital image process, human-computer interaction and soft issue deformation computation.
Virtual surgery system, as a kind of virtual Reality technology, and the three-dimensional modeling of human soft tissue have become important research topics in Computer Graphics. The study of soft tissue deformation with complex structure is also one of the most challenging aspects in virtual surgery and human-computer interaction systems.
In this article, we discuss the requirement analysis and module design of virtual spine surgery system, and propose detailed analysis and experiments on the soft tissue deformation and simulation. The soft tissue in human spine (inter-vertebral disks) has severe non-linear characteristics in contact and collision status. So we focus on discussing the contact Finite Element Method (CFEM) and its improvement in order to achieve a good balance of both accuracy and efficiency of the calculation.
In this research, we propose a novel simplified approach to calculate annulus-core structure soft tissue’s deformation. It’s based on classic contact FEM, combines the accuracy of non-linear model and the efficiency of the simplified model. Experimental results have been given to evaluate the feasibility and efficiency. Besides, it includes the introduction of complex structure three-dimensional meshing algorithm, parallel computing by Graphics Processing Unit (GPU) to accelerate, as well as human-computer interaction technology.
The main works and innovation points are described as follows:
1. The detailed overview of the FEM, related mechanics theories, and numerical algorithm. Optimize the organization of solution for problems with severe non-linear deformation in the contact and collision status.
2. Discussion on different meshing algorithms and the selection among them according to the specific requirements.
3. We propose improved and simplified algorithm considering severe contact non-linearity. And with the proper contact vertices approximation, we could increase the efficiency of CFEM solution.
4. Optimizing the speed of CFEM calculation with the help of GPU parallel computing.
5. We propose a rational mechanism to evaluate the simulation results. And validate the authenticity and feasibility on real human spine data.
6. Find a balance between efficiency and accuracy by selecting and combing different meshing methods and adjusting program coefficients, material parameters based on practical experiments.
7. Our proposed novel algorithm is successfully applied for human spine surgery simulation. Strain and stress analysis on different structures of the inter-vertebral disks are conducted.
虚拟手术系统作为虚拟现实技术的一种,与人体软组织的三维建模都已经成为是计算机图形学的重要研究课题。而其中结构复杂的软组织形变计算研究也是实时虚拟手术系统和人机交互系统中最具挑战性的内容。
本文讨论了虚拟脊柱手术系统的需求分析及模块设计,并对其中的软组织形变仿真及其在脊柱手术系统中的应用展开详细分析和实验。考虑到人体脊柱软组织(椎间盘)的环-核结构及其强接触非线性特性,为了兼顾计算的准确性和计算效率,重点研究讨论了接触有限元模型的实现及其改进方案。
本研究在传统有限元计算的基础上,根据研究对象在结构和材料上的特点,提出创新性的混合与简化计算方案,结合非线性的准确性和简化模型的效率计算软组织形变,并实验验证其可行性和效率;同时介绍了特殊结构的三维网格重建算法、图形处理单元的并行计算加速、人机交互技术等相关内容。
本文的主要工作和创新点如下:
1.详细讨论了有限元方法、相关的力学概念以及对应的数值解法,并重点针对接触碰撞中的强非线性问题对有限元求解算法进行整理简化和优化。
2.讨论了有限元分析中特殊结构网格模型的建立与选取,以及不同网格划分方法在具体使用中的区别和注意事项。
3.本文对传统碰撞接触状态下强非线性有限元的计算进行了简化和改进,满足了人体脊柱软组织的特点,提升了算法的计算效率。
4.利用图形显示卡的并行计算特性进行计算加速。
5.建立验证手术形变模拟结果的较合理的机制,通过在真实医疗数据上进行实验来验证该形变模拟的真实性和有效性。
6.根据实际实验的结果和结论,选取并结合使用不同合适的网格模型生成算法,对算法中的参数和材料参数的设定进行调整优化,以达到计算效率和模拟真实性的最优平衡。
7.本论文的新型算法成功地将碰撞接触非线性有限元分析应用于脊柱手术模拟中,并对软组织不同部位的形变模拟结果进行应力分析。
Since the birth of the computer, it has been applied in every aspect of people’s daily life. Computers can be easily seen in the areas from scientific computing to the common entertainment. The development of computer speeds up the integration among different disciplines. Mathematics, physics, biology, medicine and computer science are having close contact now. In recent years, as the fast development of computer science, the field of medicine has an urgent requirement of a virtual surgery system that can perform virtual surgery. This system will be applied to teaching, training, diagnosis, surgical pre-planning and many other areas. A complete medical virtual surgery simulation system involves multiple technologies such as computer graphics, digital image process, human-computer interaction and soft issue deformation computation.
Virtual surgery system, as a kind of virtual Reality technology, and the three-dimensional modeling of human soft tissue have become important research topics in Computer Graphics. The study of soft tissue deformation with complex structure is also one of the most challenging aspects in virtual surgery and human-computer interaction systems.
In this article, we discuss the requirement analysis and module design of virtual spine surgery system, and propose detailed analysis and experiments on the soft tissue deformation and simulation. The soft tissue in human spine (inter-vertebral disks) has severe non-linear characteristics in contact and collision status. So we focus on discussing the contact Finite Element Method (CFEM) and its improvement in order to achieve a good balance of both accuracy and efficiency of the calculation.
In this research, we propose a novel simplified approach to calculate annulus-core structure soft tissue’s deformation. It’s based on classic contact FEM, combines the accuracy of non-linear model and the efficiency of the simplified model. Experimental results have been given to evaluate the feasibility and efficiency. Besides, it includes the introduction of complex structure three-dimensional meshing algorithm, parallel computing by Graphics Processing Unit (GPU) to accelerate, as well as human-computer interaction technology.
The main works and innovation points are described as follows:
1. The detailed overview of the FEM, related mechanics theories, and numerical algorithm. Optimize the organization of solution for problems with severe non-linear deformation in the contact and collision status.
2. Discussion on different meshing algorithms and the selection among them according to the specific requirements.
3. We propose improved and simplified algorithm considering severe contact non-linearity. And with the proper contact vertices approximation, we could increase the efficiency of CFEM solution.
4. Optimizing the speed of CFEM calculation with the help of GPU parallel computing.
5. We propose a rational mechanism to evaluate the simulation results. And validate the authenticity and feasibility on real human spine data.
6. Find a balance between efficiency and accuracy by selecting and combing different meshing methods and adjusting program coefficients, material parameters based on practical experiments.
7. Our proposed novel algorithm is successfully applied for human spine surgery simulation. Strain and stress analysis on different structures of the inter-vertebral disks are conducted.
引文
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[2] Ayache N, Cotin, S. Delingette, et al. Simulation of Endoscopic Surgery [J]. Journal of Minimally Invasive Therapy and Allied Technologies (MI-TAT), 1998, 7:71–77.
[3] Tuchschmid S, Grassi M, Bachofen D, et al. A Flexible Frame-work for Highly - Modular Surgical Simulation Systems. [C].
[4] Harders M., Székely G. 2006. Lecture Notes in Computer Science, vol. 4072, 2006-06-26, http://dblp.uni-trier.de/db/conf/isbms/isbms2006.html#TuchschmidGBFTSH06.
[5] Heng P. A., Wong T. T., Leung K. M., et al. A haptic needle manipulation simulator for Chinese acupuncture learning and training [C]. VRCAI’04: Proceedings of the 2004 ACM SIGGRAPH international conference on Virtual Reality continuum and its applications in industry. New York, NY, USA: ACM, 2004:57–64.
[6] Shao-Xiang, Zhang Z., J. Liang, Pheng-Ann Heng. Chinese visible human project [J]. Clinical Anatomy, 2006, 19:204– 215.
[7] A. M. Chiu, D. Dey. Port Placement Simulation in a Virtual 3-D Thoracic Model[C]. Minimally Invasive Cardiac Surgery Symposium. Key West, California: [s.n.], 2000.
[8] Liu A., Tendick F., Cleary K., et al. A survey of surgical simulation: applications, technology, and education [J]. Presence: Teleoper. Virtual Environment, 2003, 12(6):599–614.
[9] Ursino, Tasto JL. Cath Sim: An intravascular catheterization simulator on a PC [J]. Stud Health Technol Inform, 1999, 62:360–366
[10] Chao Liu, Zu-Hua Jiang, Yu-Long Liu (2009) Standardized Representation Model and Case Application of TCM Massage Therblig. Computer Engineering Vol. 35, no. 11, pp 20-22, 25
[11] Daniel C Cherkin, David Eisenberg, Karen J Sherman, William Barlow, Ted J Kaptchuk, Janet Street, Richard A Deyo (2001) Randomized Trial Comparing Traditional Chinese Medical Acupuncture, Therapeutic Massage, and Self-care Education for Chronic Low Back Pain. Arch Intern Med. vol 161, pp 1081-1088
[12] Andrew Nealen, Matthias Müller, Richard Keiser, Eddy Boxerman, Mark Carlson (2005) Physically Based Deformable Models in Computer Graphics. In: EUROGRAPHICS 2005.
[13] Gentaro Hirota, Susan Fisher, Andrei State (2003) An improved finite-element contact model for anatomical simulations. The Visual Computer 2003, vol 19, pp 291–309
[14] Antonius Rohlmann, Anke Mann, Thomas Zander, Georg Bergmann (2009) Effect of an artificial disc on lumbar spine biomechanics: a probabilistic finite element study. European Spine Journal, vol 18, no 1, page 89-97, January 2009
[15] Joachim Georgii, Rudiger Westermann (2005) Mass-Spring Systems on the GPU. In: Simulation Modelling Practice and Theory, Volume 13, Issue 8, November 2005, Pages 693-702
[16] Youquan Liu, Shaohui Jiao, Wen Wu, Suvranu De (2008) GPU Accelerated Fast FEM Deformation Simulation. Circuits and Systems, APCCAS 2008, IEEE Asia Pacific Conference, vol., no., pp.606-609, Nov. 30 2008-Dec. 3 2008
[17] P Nanakorn, W Tharanon, J Vander Sloten. A finite element study of the effect of contact forces between an implant-retained crown and its adjacent teeth on bone stresses. Journal of Mechanics, Vol. 25, No. 4, pp 441-450
[18] G Ranzuglia, P Cignoni, F Ganovelli, R Scopigno (2006) Implementing mesh-based approaches for deformable objects on GPU. In: Fourth EurographicsItalian Chapter, Eurographics Association, pp. 213-218, feb. 2006
[19] Georgii, J, Echtler, F, Westermann, R (2005) Interactive simulation of deformable bodies on GPUs. in: Simulation and Visualisation 2005, pp. 247–258
[20] Sizhe Lv, Lixu Gu, Lei Pan (2009) Delaunay Mesh Reconstruction From 3D Medical Images Based On Centroidal Voronoi Tessellations. In: Proceedings of The International Conference on Computational Intelligence and Software Engineering, pp 1-4
[21] Jeff Bolz, Ian Farmer, Eitan Grinspun, Peter Schroder (2003) Sparse Matrix Solvers on the GPU: Conjugate Gradients and Multigrid. In: International Conference on Computer Graphics and Interactive Techniques, ACM SIGGRAPH 2003 Papers, Pages: 917 - 924
[22] H Lin, D Sucato (2004) Identification of Lenke Spine Deformity Classification By Simplified 3D Spine Model. Engineering in Medicine and Biology Society, 2004. IEMBS '04. 26th Annual International Conference of the IEEE, Volume: 2, page(s): 3144– 3146
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