基于无网格方法的软组织形变模型
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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。
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. 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 operation 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 distortions 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 the 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 operation 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 applied 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 meshfree 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 domain 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 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 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 effectively. Not only does it increase the calculation accuracy, but also reduces complication of calculation and improves operating efficiency.
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。
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. 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 operation 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 distortions 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 the 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 operation 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 applied 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 meshfree 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 domain 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 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 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 effectively. Not only does it increase the calculation accuracy, but also reduces complication of calculation and improves operating efficiency.
引文
[1]张秋葵.手术仿真系统的关键技术研究[D],南京:东南大学,2008.
[2]王征.虚拟手术中的软组织形变仿真算法研究[D].南京:东南大学,2006.
[3]李建英.虚拟手术中软组织形变仿真研究出处[D].山东:山东大学,2009.
[4]程立英.虚拟手术若干关键技术研究[D].东北:东北大学,2006.
[5] S. Cotin, H. Delingette, N. Ayache. Real-time elastic deformations of soft tissues for surgery simulation[J]. Visualization and Computer Graphics, 1999, 5(1): 62-73.
[6] U Kühnapfel, H.K. ?akmak and H.Maa?. Endoscopic surgery training using virtual reality and deformable tissue simulation[J]. Computers & Graphics, 2000, 24(5): 671-682.
[7]张青.虚拟手术中人体软组织变形仿真[D].青岛大学,2003.
[8] G. Szekely, M. Bajka, C. Brechbuehler. Virtual reality-based simulation of endoscopic surgery resence[J]. Teleoperators and virtual environments, 2000, 3(3): 310–333.
[9]李振明等.基于非线性力反馈模型的软组织变形仿真[J].计算机仿真,2007,1:76-82.
[10]Joel Brown, Kevin Montgomery, Jean-Claude Latombe, Michael Stephanides. A Microsurgery Simulation System[J]. Medical Image Computing and Computer-Assisted Intervention-MICCAI 2001, Lecture Notes in Computer Science, 2001, Volume 2208/2001, 137-144.
[11]Meier U,Garcia F,Parr N. 3D Surgery Trainer with Force Feedback in Minimally Invasive Surgery[Z]. 2001.
[12]Brian Wheeler, Philip C.Doyle, Shamir Chandarana. Interactive computer-based simulator for training in blade navigation and targeting in myringotomy[J]. Computer Methods and Programs in Biomedicine, 2010, 98: 130-139.
[13]王延臻.改进的弹簧振子模型及其在虚拟手术中的应用研究[D].长沙:国防科学技术大学,2006.
[14]熊岳山,徐凯,王彦臻等.虚拟膝关节镜手术仿真系统的关键技术研究.国防科技大学学报,2007,29(1):76-80.
[15]黄鹏飞.医学数据可视化及软组织建模[D].上海:同济大学,2005.
[16]谭曦.基于三维重建的软组织变形模型研究[D].广州:中山大学,2007.
[17]于健.虚拟手术中支持实时切割的混合弹性模型.山东:青岛,2006.
[18]张勇.医学图像可视化技术及其在虚拟骨折手术中的应用[D].大连:大连理工大学,2002.
[19]朱志有.基于触觉编程和面模型的弹性形变及虚拟切割研究[D].广州:华南师范大学,2008.
[20]薛清.虚拟手术中的软组织建模与应用[D].上海:上海交通大学,2006.
[21]魏迎梅,王涌,吴泉源等.手术仿真中的碰撞检测研究[J].计算机研究与发展,2002,39(1):114-119.
[22]蒋春涛.人体软组织弹性模型的研究[D].南京:东南大学,2004.
[23]龚楷楠.基于内部压力方法的人体软组织弹性模型研究[D].南京:东南大学,2008.
[24]张小萍等.软组织虚拟手术仿真的关键技术探析[J].南通职业大学学报,2008,3:38-43.
[25]乔冰.基于质点—弹簧模型的人体软组织形变技术的研究[D].哈尔滨工程大学,2008.
[26]Cotin S, Delingette H. Real-time elastic deformations of soft tissues for surgery simulation[J]. Visualization and Computer Graphics, 1999, 5(1): 62～73.
[27]Zhu Q L, Francis J K. Dynamic biphasic poroviscoelastic model simulation of hydrated soft tissues and itspotential applications for brain impact study[C]. Bioengineering Conference ASME, 2001, 50: 835～836.
[28]Pieper S, Rosen J. Interactive graphics for plastic surgery: A task-level analysis and implementation[J]. Computer Graphics, 1992, 25(2): 127～134.
[29]Sascha S, Oliver B. Deformable modeling of the cervical spine for neurosurgical navigation[C]. International Congress Series, 2004, 1268: 455～460.
[30]G.R.LIU,Y.T.GU著,王建明,周学军译.无网格法理论及程序设计[M].山东:山东大学出版社,2007:75
[31]Bernard PS. A deterministic vortex sheet method for boundary layer flow. J. of Computational Physics, 1995, 117: 132-145.
[32]Yi-Je Lim, Suvranu De. Real time simulation of nonlinear tissue response in virtual surgery using the point collocation-based method of finite spheres[J]. Computer methods in applied mechanicw and engineering, 2007, 196: 3011-3024.
[33]Lin C. C. An iterative finite element-boundary element algorithm[J]. Comput-ers & Structures, 1996, 59 (5): 899~909.
[34]Belytschko T, Krongauz Y, Organ D, Fleming M and Krysl P. Meshless Method: an overview and recent development[J]. Computational Methods in Applied Mechanics and Engineering, 1996, 139:3-47.
[35]Belytschko T, Lu YY and Gu L. Element-free Galerkin methods[J]. 1994, 229-256
[36]Chen WH and Guo XM. Element Free Galerkin Method for three-dimensional structural analysis. Computer Modeling in Engineering & Science, 2001, 4(2):497-508.
[37]宋卫峰.基于径向基点插值无网格法(RPIM法)研究及应用[D].西安:西安理工大学,2009.
[38]张文婧.径向基函数及径向点插值无网格法(RPIM法)的研究[D].秦皇岛:燕山大学,2008.
[39]姬威.若干边界条件下的无网格伽辽金法及其改进[D].秦皇岛:燕山大学,2009.
[40]李冬梅.无网格局部Petrov-Galerkin法的改进及应用[D].秦皇岛:燕山大学,2009.
[41]程江华.基于无网格伽辽金法疲劳裂纹扩展的数值模拟[D].沈阳:东北大学,2008.
[42]周家杰.三维弹塑性大变形接触问题的无网格分析[D].湖南:湖南大学,2003.
[43]Lu Y Y, Belytschko T, Tabbara M. Element-free Galerkin methods for wave propagation and dynamic fracture[C]. Comput. Methods Appl. Mech. Engrg., 1995, 126:131~153.
[44]Gu YT and Liu GR.. A boundary point interpolation method for stress analysis of solids[J]. Computational Mechanics, 2002, 28, 47-54.
[45]Krongauz Y and Belytschko T. Enforcement of essential boundary conditions in meshless approximations using finite element[J]. Comput. Methods in Appl. Mech. And Engrg, 1996, 131, 133-145.
[46]杨梃青.粘弹性力学[M].武汉:华中理工大学出版社,1990:35.
[47]刘威龙.粘弹性柱体问题的对偶体系研究[D].大连:大连理工大学,2002.
[48]陈相概.虚拟手术中软组织形变过程研究与实现[D].长沙:中南大学,2010.
[49]Michael Macri, Suvranu De. Towards an automatic discretization scheme for the method of finite spheres and its coupling with the finite element method[J]. Computers & Structures. 2005, 83,1429-1447.
[50]S. De, K. J. Bathe. The method of finite spheres[J]. Computational Mechanics. 2000, 25, 329-345.
[51]Suvranu De, Klaus-Jurgen Bathe. The method of finite spheres with improved numerical integration[J]. Computers & Structures. 2001, 79, 2183-2196.
[52]Hong JW, Bathe KJ. Coupling and enrichment schemes for finite sphere discretizations[J]. Comput Struct. 2005, 83, 1386–95.
[53]Brown J.Real-time Soft Tissue and Suture Simulation[D]. California, USA:Stanford University, 2003.
[54]Xuemei Liu, Lei Mao. Visual Simulation of Soft Tissue Deformation[C]. 2010 International Conference on Computer and Communication Technologies in Agriculture Engineering. June 12-13, 2010: 548-551.
[2]王征.虚拟手术中的软组织形变仿真算法研究[D].南京:东南大学,2006.
[3]李建英.虚拟手术中软组织形变仿真研究出处[D].山东:山东大学,2009.
[4]程立英.虚拟手术若干关键技术研究[D].东北:东北大学,2006.
[5] S. Cotin, H. Delingette, N. Ayache. Real-time elastic deformations of soft tissues for surgery simulation[J]. Visualization and Computer Graphics, 1999, 5(1): 62-73.
[6] U Kühnapfel, H.K. ?akmak and H.Maa?. Endoscopic surgery training using virtual reality and deformable tissue simulation[J]. Computers & Graphics, 2000, 24(5): 671-682.
[7]张青.虚拟手术中人体软组织变形仿真[D].青岛大学,2003.
[8] G. Szekely, M. Bajka, C. Brechbuehler. Virtual reality-based simulation of endoscopic surgery resence[J]. Teleoperators and virtual environments, 2000, 3(3): 310–333.
[9]李振明等.基于非线性力反馈模型的软组织变形仿真[J].计算机仿真,2007,1:76-82.
[10]Joel Brown, Kevin Montgomery, Jean-Claude Latombe, Michael Stephanides. A Microsurgery Simulation System[J]. Medical Image Computing and Computer-Assisted Intervention-MICCAI 2001, Lecture Notes in Computer Science, 2001, Volume 2208/2001, 137-144.
[11]Meier U,Garcia F,Parr N. 3D Surgery Trainer with Force Feedback in Minimally Invasive Surgery[Z]. 2001.
[12]Brian Wheeler, Philip C.Doyle, Shamir Chandarana. Interactive computer-based simulator for training in blade navigation and targeting in myringotomy[J]. Computer Methods and Programs in Biomedicine, 2010, 98: 130-139.
[13]王延臻.改进的弹簧振子模型及其在虚拟手术中的应用研究[D].长沙:国防科学技术大学,2006.
[14]熊岳山,徐凯,王彦臻等.虚拟膝关节镜手术仿真系统的关键技术研究.国防科技大学学报,2007,29(1):76-80.
[15]黄鹏飞.医学数据可视化及软组织建模[D].上海:同济大学,2005.
[16]谭曦.基于三维重建的软组织变形模型研究[D].广州:中山大学,2007.
[17]于健.虚拟手术中支持实时切割的混合弹性模型.山东:青岛,2006.
[18]张勇.医学图像可视化技术及其在虚拟骨折手术中的应用[D].大连:大连理工大学,2002.
[19]朱志有.基于触觉编程和面模型的弹性形变及虚拟切割研究[D].广州:华南师范大学,2008.
[20]薛清.虚拟手术中的软组织建模与应用[D].上海:上海交通大学,2006.
[21]魏迎梅,王涌,吴泉源等.手术仿真中的碰撞检测研究[J].计算机研究与发展,2002,39(1):114-119.
[22]蒋春涛.人体软组织弹性模型的研究[D].南京:东南大学,2004.
[23]龚楷楠.基于内部压力方法的人体软组织弹性模型研究[D].南京:东南大学,2008.
[24]张小萍等.软组织虚拟手术仿真的关键技术探析[J].南通职业大学学报,2008,3:38-43.
[25]乔冰.基于质点—弹簧模型的人体软组织形变技术的研究[D].哈尔滨工程大学,2008.
[26]Cotin S, Delingette H. Real-time elastic deformations of soft tissues for surgery simulation[J]. Visualization and Computer Graphics, 1999, 5(1): 62～73.
[27]Zhu Q L, Francis J K. Dynamic biphasic poroviscoelastic model simulation of hydrated soft tissues and itspotential applications for brain impact study[C]. Bioengineering Conference ASME, 2001, 50: 835～836.
[28]Pieper S, Rosen J. Interactive graphics for plastic surgery: A task-level analysis and implementation[J]. Computer Graphics, 1992, 25(2): 127～134.
[29]Sascha S, Oliver B. Deformable modeling of the cervical spine for neurosurgical navigation[C]. International Congress Series, 2004, 1268: 455～460.
[30]G.R.LIU,Y.T.GU著,王建明,周学军译.无网格法理论及程序设计[M].山东:山东大学出版社,2007:75
[31]Bernard PS. A deterministic vortex sheet method for boundary layer flow. J. of Computational Physics, 1995, 117: 132-145.
[32]Yi-Je Lim, Suvranu De. Real time simulation of nonlinear tissue response in virtual surgery using the point collocation-based method of finite spheres[J]. Computer methods in applied mechanicw and engineering, 2007, 196: 3011-3024.
[33]Lin C. C. An iterative finite element-boundary element algorithm[J]. Comput-ers & Structures, 1996, 59 (5): 899~909.
[34]Belytschko T, Krongauz Y, Organ D, Fleming M and Krysl P. Meshless Method: an overview and recent development[J]. Computational Methods in Applied Mechanics and Engineering, 1996, 139:3-47.
[35]Belytschko T, Lu YY and Gu L. Element-free Galerkin methods[J]. 1994, 229-256
[36]Chen WH and Guo XM. Element Free Galerkin Method for three-dimensional structural analysis. Computer Modeling in Engineering & Science, 2001, 4(2):497-508.
[37]宋卫峰.基于径向基点插值无网格法(RPIM法)研究及应用[D].西安:西安理工大学,2009.
[38]张文婧.径向基函数及径向点插值无网格法(RPIM法)的研究[D].秦皇岛:燕山大学,2008.
[39]姬威.若干边界条件下的无网格伽辽金法及其改进[D].秦皇岛:燕山大学,2009.
[40]李冬梅.无网格局部Petrov-Galerkin法的改进及应用[D].秦皇岛:燕山大学,2009.
[41]程江华.基于无网格伽辽金法疲劳裂纹扩展的数值模拟[D].沈阳:东北大学,2008.
[42]周家杰.三维弹塑性大变形接触问题的无网格分析[D].湖南:湖南大学,2003.
[43]Lu Y Y, Belytschko T, Tabbara M. Element-free Galerkin methods for wave propagation and dynamic fracture[C]. Comput. Methods Appl. Mech. Engrg., 1995, 126:131~153.
[44]Gu YT and Liu GR.. A boundary point interpolation method for stress analysis of solids[J]. Computational Mechanics, 2002, 28, 47-54.
[45]Krongauz Y and Belytschko T. Enforcement of essential boundary conditions in meshless approximations using finite element[J]. Comput. Methods in Appl. Mech. And Engrg, 1996, 131, 133-145.
[46]杨梃青.粘弹性力学[M].武汉:华中理工大学出版社,1990:35.
[47]刘威龙.粘弹性柱体问题的对偶体系研究[D].大连:大连理工大学,2002.
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