改进布尔方法及其在虚拟膝关节手术中的应用研究
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摘要
虚拟手术作为虚拟现实的重要应用之一,其发展对促进医学水平的提高具有重要意义。近年来,随着微创手术技术的发展,研究和开发具有逼真视觉和力学反馈的内窥镜手术仿真系统已成为虚拟手术的主要发展方向,膝关节手术是内窥镜手术之一,虚拟膝关节手术系统实现的是对膝关节微创伤外科手术的模拟。
几何网格模型的切割技术作为虚拟手术系统的重要组成部分,必须满足实时性和真实感特性。在虚拟手术中,切割模拟分为对软组织器官模型切割模拟和对刚性骨骼模型切割模拟两种,本文的背景即是基于对骨骼的几何网格模型进行切割操作的布尔方法研究。
布尔方法在计算机图形学中的应用具体表现在三个方面:构造实体几何模型、生成纹理样本、对几何网格模型的操作。本文从计算机图形学角度出发,首先介绍了布尔方法的基本原理、布尔运算中的相交检测方法,并给出布尔方法的实现过程。之后,本文概括总结了三维空间中几何网格模型布尔运算的一般方法,并针对该方法中存在的不足,提出在几种常见的模型布尔操作中的改进方法。其中,针对包含几何图元的布尔运算,改进布尔方法能够充分利用图元参数方程的函数性质,提高相交检测的效率。
本文的核心在于提出了基于隐含模型空间排序的预处理过程,从而实现的对几何网格模型进行切割操作的改进布尔方法。该方法针对利用曲线或多边形对模型沿某一方向矢量进行切割操作的情况,研究提高对模型进行切割操作的布尔运算效率的改进方法。该方法能够将三维相交检测问题转化为二维相交检测问题,省略了布尔操作的预处理过程——即对模型进行空间排序的过程,并提出了基于保持位移矢量的平滑处理方法来代替三维空间中较为复杂的平滑处理方法,实现了对布尔操作后的几何网格模型的平滑处理。
在本文最后,基于几何网格模型切割操作的改进布尔方法,我们应用该方法实现了虚拟膝关节手术中的双隧道钻孔模拟,并针对虚拟膝关节手术的特殊性要求,对算法进行了进一步完善,比如:“T”型点的消除、隧道的动态模拟等。
Virtual Surgery is an important application of Virtual Reality in medicine, and its development has tremendous impact on modern surgery level. Recently years, as the development of endoscopic surgery, the research on endoscopic surgery system with both reality and force feedback has become the main orientation of Virtual Surgery. Arthroscopic surgery is a kind of endoscopic surgery, and its virtual system is a simulation of the arthroscopic operation process.
Cutting operation is an important part of virtual surgery, and both its efficiency and reality must be ensured during the simulation. Cutting on organs and cutting on bones are the two kind of Cutting operations in virtual surgery. Our research is based on the cutting operation on bones which is expressed as a geometry mesh model.
Since Boolean method has widely used in Computer Graphics, there are three kind of applications: constructive solid geometry models, texture synthesis, and operations on geometry mesh models. This thesis is mainly based on Computer Graphics. In the first part of thesis we discussed the essential theory of Boolean method, how it detects the intersected elements, and how it implements different operations on models. In this thesis we also discussed the normal Boolean method on geometry mesh models in 3D space. We present an improvement method according to several kinds of widely used Boolean operations, especially when the geometry mesh model is a kind of basic geometry element. We may use the geometry's variable function to accelerate the inside-outside test step.
The mainly part of this thesis is that we present a fast improved Boolean method for cutting operation on geometry mesh models. This improved method is based on overleap the step of re-sequence for mesh models, which is time costing in normal methods. Our fast improved method is often used in the case when we need to cut a geometry mesh model use a curve or a polygon in straight direction. The mainly improvement of our method is that we overleap some time-costing step in Boolean operations and simplify 3D operation to 2D operation. We omit re-sequence operation of models, and the work of inside-outside test of 3D models is finished in 2D coordinate. We implement a smooth strategy after Boolean operation by keeping the vertices' vector, thus smooth operation is also time-saving compare to 3D smooth method.
In the last part of this thesis, we further discussed how to simulate the drill operation and how to express the two tunnel meshes. For the trait of virtual endoscopic surgery, we made a further improvement to our method, such as eliminate T points in meshes, dynamic simulation of drill process, and so on.
几何网格模型的切割技术作为虚拟手术系统的重要组成部分,必须满足实时性和真实感特性。在虚拟手术中,切割模拟分为对软组织器官模型切割模拟和对刚性骨骼模型切割模拟两种,本文的背景即是基于对骨骼的几何网格模型进行切割操作的布尔方法研究。
布尔方法在计算机图形学中的应用具体表现在三个方面:构造实体几何模型、生成纹理样本、对几何网格模型的操作。本文从计算机图形学角度出发,首先介绍了布尔方法的基本原理、布尔运算中的相交检测方法,并给出布尔方法的实现过程。之后,本文概括总结了三维空间中几何网格模型布尔运算的一般方法,并针对该方法中存在的不足,提出在几种常见的模型布尔操作中的改进方法。其中,针对包含几何图元的布尔运算,改进布尔方法能够充分利用图元参数方程的函数性质,提高相交检测的效率。
本文的核心在于提出了基于隐含模型空间排序的预处理过程,从而实现的对几何网格模型进行切割操作的改进布尔方法。该方法针对利用曲线或多边形对模型沿某一方向矢量进行切割操作的情况,研究提高对模型进行切割操作的布尔运算效率的改进方法。该方法能够将三维相交检测问题转化为二维相交检测问题,省略了布尔操作的预处理过程——即对模型进行空间排序的过程,并提出了基于保持位移矢量的平滑处理方法来代替三维空间中较为复杂的平滑处理方法,实现了对布尔操作后的几何网格模型的平滑处理。
在本文最后,基于几何网格模型切割操作的改进布尔方法,我们应用该方法实现了虚拟膝关节手术中的双隧道钻孔模拟,并针对虚拟膝关节手术的特殊性要求,对算法进行了进一步完善,比如:“T”型点的消除、隧道的动态模拟等。
Virtual Surgery is an important application of Virtual Reality in medicine, and its development has tremendous impact on modern surgery level. Recently years, as the development of endoscopic surgery, the research on endoscopic surgery system with both reality and force feedback has become the main orientation of Virtual Surgery. Arthroscopic surgery is a kind of endoscopic surgery, and its virtual system is a simulation of the arthroscopic operation process.
Cutting operation is an important part of virtual surgery, and both its efficiency and reality must be ensured during the simulation. Cutting on organs and cutting on bones are the two kind of Cutting operations in virtual surgery. Our research is based on the cutting operation on bones which is expressed as a geometry mesh model.
Since Boolean method has widely used in Computer Graphics, there are three kind of applications: constructive solid geometry models, texture synthesis, and operations on geometry mesh models. This thesis is mainly based on Computer Graphics. In the first part of thesis we discussed the essential theory of Boolean method, how it detects the intersected elements, and how it implements different operations on models. In this thesis we also discussed the normal Boolean method on geometry mesh models in 3D space. We present an improvement method according to several kinds of widely used Boolean operations, especially when the geometry mesh model is a kind of basic geometry element. We may use the geometry's variable function to accelerate the inside-outside test step.
The mainly part of this thesis is that we present a fast improved Boolean method for cutting operation on geometry mesh models. This improved method is based on overleap the step of re-sequence for mesh models, which is time costing in normal methods. Our fast improved method is often used in the case when we need to cut a geometry mesh model use a curve or a polygon in straight direction. The mainly improvement of our method is that we overleap some time-costing step in Boolean operations and simplify 3D operation to 2D operation. We omit re-sequence operation of models, and the work of inside-outside test of 3D models is finished in 2D coordinate. We implement a smooth strategy after Boolean operation by keeping the vertices' vector, thus smooth operation is also time-saving compare to 3D smooth method.
In the last part of this thesis, we further discussed how to simulate the drill operation and how to express the two tunnel meshes. For the trait of virtual endoscopic surgery, we made a further improvement to our method, such as eliminate T points in meshes, dynamic simulation of drill process, and so on.
引文
[1]曾建超,俞志和.虚拟现实的技术及其应用.北京:清华大学出版社,1996.
[2]汪成为,高文等.灵境(虚拟现实)技术的理论、实现及应用.北京:清华大学出版,1996.
[3] Isdale J. What is Virtual Reality? http://www.cms.dmu.ac.uk/-cph/
[4]杨轶璐,胡英,刘纪红,徐心和.虚拟现实技术及其在现代医学中的应用.信息与控制, 2003,32(03):512-517.
[5]杨棉华,陈丹芸.虚拟现实技术在医学中的发展与应用.医学教育探索, 2005,4(6):410-412.
[6]罗伟,李珊珊.虚拟现实技术在医疗中的应用.生堡医院管理杂志, 2005,21(12):17-21.
[7]朱彦军,姜国华.虚拟现实中虚拟人体模型概述.计算机仿真, 2004, 21:11-13.
[8] Juli Y, Yasushi Y, Masaaki M, Yukio F, Kazunori Y. Real-time 3-D model-based navigation system for endoscopic paranasal sinus surgery. IEEE Transactions on Biomedical Engineering, 1999,46(1):107-116.
[9] Kuhn C, Kühnapfel U G, Krumm H G, Neisius B. A Virtual Reality Based Training System for Minimally Invasive Surgery. In Proceedings of Computer Assisted Radiology, Elsevier, 1996:764-769.
[10] Kühnapfel U, ?akmak H K, Maass H. Endoscopic surgery training using virtual reality and deformable tissue simulation. Computers & Graphics, 2000,24(5):671-682.
[11] Aulignac D, Laugier C, Cavusoglu M C. Towardsa realistic echographic simulator with force feedback. In the Proceedings Of the IEEE/RSJ International Conference on Intelligent Robots and Systems, Kyongju, Korea, 1999:727-732.
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[18]孙剑,柴建云,唐泽圣.手术模拟中软组织变形的实时有限元新算法.系统仿真学报, 2000,12(05):82-87.
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[20]钟云飞,熊岳山,谭珂,郭光友. FASTRAK数据滤波校正及在虚拟手术中的应用.系统仿真学报, 2006,18(5):1243-1246.
[21]熊岳山,罗军,谭珂,王彦臻,郭光友.一种新的基于体元剖分的软组织切割算法.计算机研究与发展, 2005,42(12):2132-2136.
[22] Lorensen W E, Cline H E. Marching Cubes:A High Resolution 3D Surface Construction Algorithm. Computer Graphics, 1987,21(4):163-169.
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[24]王志强,洪嘉振,杨辉.碰撞检测问题研究综述.软件学报,1999,10(5):545-551.
[25]魏迎梅,吴泉源,石教英.碰撞检测中的固定方向凸包包围盒的研究.软件学报, 2001,12(7):1056-1063.
[26] Cover S A, Ezquerra N F, O’Brien J F, Rowe R, Gadacz T,Palm E. Interactively Deformable Models for Surgery Simulation. IEEE Computer Graphics & Applications, 1993,11: 68-75.
[27] Boden B, Griffin L, Garret W. Etiology and prevention of noncontact ACL injury. The Physician and Sports Medicine, 2000,28:1-14.
[28] Freedman K B, Amato M J, Nedeff DD. Arthroscopic anterior cruciate ligament reconstruction: a metaanalysis comparing patellar tendon and hamstring tendon autografts. Am J Sports Med, 2003,31:2-11.
[29] Adachi N, Ochi M, Uchio Y. Reconstruction of the anteriors doubled semitendinosus and gracilis tendons for anterior cruciate ligament reconstraction. Am J SportsMed, 1999,22:211-217.
[30] Fithian D C, Paxton M W, Stone M L. Prospective trial of a treatment algorithm for the management of the anterior cruciate ligament-injured knee. Am J Sports Med, 2005,33:335-346.
[31] Norwood L A, Cross M J. Anterior cruciate ligament: functional anatomy of its bundles in rotatory instabilities. The American Journal of Sports Medicine, 1979,7:23-26.
[32] Hefzy M S, Grood E S. Sensitivity of insertion locations on length patterns of anterior cruciate ligament fibers. Journal of Biomechanical Engineering, 1986, 108(1):73-82.
[33] Fu F A, narner C D, Johnson D L. Biomechanics of knee ligaments. BoneJoint Surg(Am), 1993,75:1716-1725.
[34]张文强,王成琪,唐胜建.单束单隧道与双束双隧道重建膝前交叉韧带的生物力学对比研究.中国矫形外科杂志, 2006,10:757-759.
[35]陈百成,毛远青,高石军.双束股骨双隧道法重建后十字韧带的实验研究.中华骨科杂志, 2005,23(5):308-312.
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[2]汪成为,高文等.灵境(虚拟现实)技术的理论、实现及应用.北京:清华大学出版,1996.
[3] Isdale J. What is Virtual Reality? http://www.cms.dmu.ac.uk/-cph/
[4]杨轶璐,胡英,刘纪红,徐心和.虚拟现实技术及其在现代医学中的应用.信息与控制, 2003,32(03):512-517.
[5]杨棉华,陈丹芸.虚拟现实技术在医学中的发展与应用.医学教育探索, 2005,4(6):410-412.
[6]罗伟,李珊珊.虚拟现实技术在医疗中的应用.生堡医院管理杂志, 2005,21(12):17-21.
[7]朱彦军,姜国华.虚拟现实中虚拟人体模型概述.计算机仿真, 2004, 21:11-13.
[8] Juli Y, Yasushi Y, Masaaki M, Yukio F, Kazunori Y. Real-time 3-D model-based navigation system for endoscopic paranasal sinus surgery. IEEE Transactions on Biomedical Engineering, 1999,46(1):107-116.
[9] Kuhn C, Kühnapfel U G, Krumm H G, Neisius B. A Virtual Reality Based Training System for Minimally Invasive Surgery. In Proceedings of Computer Assisted Radiology, Elsevier, 1996:764-769.
[10] Kühnapfel U, ?akmak H K, Maass H. Endoscopic surgery training using virtual reality and deformable tissue simulation. Computers & Graphics, 2000,24(5):671-682.
[11] Aulignac D, Laugier C, Cavusoglu M C. Towardsa realistic echographic simulator with force feedback. In the Proceedings Of the IEEE/RSJ International Conference on Intelligent Robots and Systems, Kyongju, Korea, 1999:727-732.
[12]罗春光,谭欧,吕旭东. Visual Human图像数据集的自动匹配方法.中国生物医学工程学报, 2001,20(2):202-205.
[13]罗述谦.拟人体研究与医学图像处理方法学.医疗设备信息, 2002,5:1-3.
[14] Sagar M A, Bullivant D, Mallinson G D, Hunter P J, Hunter I. A Virtual Environment and Model of the Eye for Surgical Simulation. In Proceedings of SIGGRAPH’94, 1994:205-212.
[15] Pieper S D, Laub D R, Rosen J M. A Finite-element Facial Model for Simulating Plastic Surgery. Plastic and Reconstructive Surgery, 1995,96(5): 1100-1105.
[16] Satava R. Medical Virtual Reality: The Current status of the future. In Proc.4th Conference Medicine Meet Virtual Reality, San Diego, 1996:100-106.
[17] Satava R M, Jones S B, Shaun B. Advanced Technologies for Surgical Practice. New York, 1997:75-96.
[18]孙剑,柴建云,唐泽圣.手术模拟中软组织变形的实时有限元新算法.系统仿真学报, 2000,12(05):82-87.
[19]阎丽霞.虚拟手术关键技术研究.浙江大学博士生学位论文, 2002.
[20]钟云飞,熊岳山,谭珂,郭光友. FASTRAK数据滤波校正及在虚拟手术中的应用.系统仿真学报, 2006,18(5):1243-1246.
[21]熊岳山,罗军,谭珂,王彦臻,郭光友.一种新的基于体元剖分的软组织切割算法.计算机研究与发展, 2005,42(12):2132-2136.
[22] Lorensen W E, Cline H E. Marching Cubes:A High Resolution 3D Surface Construction Algorithm. Computer Graphics, 1987,21(4):163-169.
[23] J D Boissonnat. Shape Reconstruction from Planar Cross-Sections. Computer Vision, Graphics, and Image Processing, 1988.44:1-29.
[24]王志强,洪嘉振,杨辉.碰撞检测问题研究综述.软件学报,1999,10(5):545-551.
[25]魏迎梅,吴泉源,石教英.碰撞检测中的固定方向凸包包围盒的研究.软件学报, 2001,12(7):1056-1063.
[26] Cover S A, Ezquerra N F, O’Brien J F, Rowe R, Gadacz T,Palm E. Interactively Deformable Models for Surgery Simulation. IEEE Computer Graphics & Applications, 1993,11: 68-75.
[27] Boden B, Griffin L, Garret W. Etiology and prevention of noncontact ACL injury. The Physician and Sports Medicine, 2000,28:1-14.
[28] Freedman K B, Amato M J, Nedeff DD. Arthroscopic anterior cruciate ligament reconstruction: a metaanalysis comparing patellar tendon and hamstring tendon autografts. Am J Sports Med, 2003,31:2-11.
[29] Adachi N, Ochi M, Uchio Y. Reconstruction of the anteriors doubled semitendinosus and gracilis tendons for anterior cruciate ligament reconstraction. Am J SportsMed, 1999,22:211-217.
[30] Fithian D C, Paxton M W, Stone M L. Prospective trial of a treatment algorithm for the management of the anterior cruciate ligament-injured knee. Am J Sports Med, 2005,33:335-346.
[31] Norwood L A, Cross M J. Anterior cruciate ligament: functional anatomy of its bundles in rotatory instabilities. The American Journal of Sports Medicine, 1979,7:23-26.
[32] Hefzy M S, Grood E S. Sensitivity of insertion locations on length patterns of anterior cruciate ligament fibers. Journal of Biomechanical Engineering, 1986, 108(1):73-82.
[33] Fu F A, narner C D, Johnson D L. Biomechanics of knee ligaments. BoneJoint Surg(Am), 1993,75:1716-1725.
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