生物软组织建模仿真方法研究
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摘要
随着计算机科学与技术的快速发展,医学仿真已经从单一的视觉仿真逐渐向物理仿真和生理仿真发展。以虚拟手术仿真为代表的基于物理的医学仿真的基础问题是生物软组织建模仿真,其主要任务是生物软组织的几何建模、物理建模、变形计算、碰撞检测、交互操作、视觉绘制、触觉反馈等。文章首先对这些关键技术和应用情况做了一个比较全面的概述,指出当前研究的焦点是折中仿真的实时性和真实性。文章主要以厦门大学的国家自然基金项目—虚拟眼建模仿真课题为依托,以白内障手术仿真、肝脏手术仿真为背景,系统的研究了生物软组织建模仿真的方法,并以福建省自然基金项目—虚拟手术仿真基础平台研究为基础,分析设计了一个可扩展的基础框架。
生物软组织仿真是多学科融合的应用研究领域,文章系统的论述了生物软组织建模仿真的一些基础理论和方法,包括几何模型的数据结构—半边数据结构和半面结构;网格剖分和插值细分的基础理论;生物软组织的生物力学特性和典型的物理建模方法;CT图像的基本原理。
白内障手术仿真的第一步是撕囊。囊膜是附着在晶状体上的一层富有弹性的透明薄膜。文章系统地研究了囊膜建模仿真的全过程。用裂隙灯测量的数据拟合的多项式建立了晶状体的轮廓曲线,然后经旋转离散建立了囊膜的三角面模型并用半边结构表示。使用准静态求解的线弹性质点弹簧模型和碰撞检测技术,建立了具有附着特性的囊膜物理仿真模型。通过一种渐进动态切割方法,实现了囊膜切割操作。依据断裂力学的基本原理,分析、设计了囊膜撕裂的基本算法,实现了囊膜定向撕裂。虚拟器械与囊膜的交互不仅在视觉上给出反馈,作者还建立了具有黏滞性摩擦反馈的触力觉仿真模型,使交互触摸、拉伸、切割和撕裂等更具有真实感。
白内障手术仿真的另一重要步骤是碎核乳化过程即把膜下的皮质和晶状体核吸出体外。文章以三角面模型为限定,依Delaunay准则对皮质和核进行了四面体剖分,并用半面数据结构表示。对四面体剖分建立了对应的质点弹簧模型,提出了一种基于半面结构的劈核仿真算法。把分核的结果视为类刚体,采用一种无网格的光滑粒子流体动力学模型SPH建模,在吸食器接触的一定的范围内的粒子采用随机删除机制删除,以仿真乳化吸出过程。
基于医学图像的建模仿真是典型的医学仿真过程,文章从CT医学图像的预处理一分割方法,MC表面重构,QEM模型化简与平滑等,到有限元建模,作了比较系统的论述。以肝脏、鼻咽部为例应用了这些方法并作了一些改进,如多组织的鼻咽部建模,优化的QEM简化方法等,还探讨了黏弹性有限元建模问题。
文章针对面模型提出了一种局部自适应建模仿真方法,该方法以一个可以接受的比较稀疏的面模型为基础,通过蝶型插值细分方法建立了若干细节层次,借助于一个森林结构把它们组合起来,仿真时动态地局部加细分,这样在不增加模型整体复杂度的情况下,提高模型仿真的精度;在触觉反馈计算中,提出了一个层次半边碰撞检测方法,大大减少了触觉线程中碰撞检测的开销;为了加速物理仿真的计算,系统讨论了GPU用于通用计算的基本特征和方法,提出了基于GPU的质点弹簧建模方法,分析了基于GPU的有限元仿真加速的基本实现方法。
文章针对虚拟手术仿真的应用研究现状提出了建立一个虚拟手术仿真基础平台,搭建一个可扩展的基础框架的重要性和实际意义。基于面向对象的方法,从系统需求分析,功能分析出发,通过用例顺序图研究定义了与功能、场景相关的基础类,分析了虚拟手术仿真的一些可扩展点,给出了系统基础框架的层次结构体系模型。从框架设计实现的基本设计模式出发讨论了框架系统实现的基本策略,以及双线程的同步器共享的运行机制。
总之,文章在实时和真实的折中平衡方面提出了几种加速算法如自适应局部求精方法、层次半边碰撞检测方法、基于GPU的硬件加速方法;以白内障手术仿真为主线,系统地给出了晶状体囊膜、晶状体皮质、晶状体核的建模仿真方法;系统地论述了基于医学图像的建模仿真方法;系统地分析设计了一个虚拟手术仿真基础框架。尽管如此,本文所做的工作还远远不够,可以说仅仅是开始,每个问题都需要再深入研究。
With the fast development of computer science and technology, medical simulation has progressed from only visual simulation into physical and physiology simulation. The basic problems is the bio-soft tissue modeling and simulation in the field of physics-based medical simulation with the representation of virtual surgery simulation. The main tasks include geometry modeling, physical modeling, deformation calculating, collision detection, interactive operations, visual feedback and force feedback. A survey of these key techniques and applications was presented in the paper and pointed out the studying focus is balancing the realism and real-time. This paper origins mainly from the project of National Science Fund on virtual eye simulation of Xiamen University, backgrounds on the surgery simulation of cataract and liver, also bases on the project of Fujian province fund which is the study for basic framework of virtual surgery simulation to integrate the related algorithms serving for future studying and application.
The modeling and simulation for bio-soft tissue is a field in which multi-subject cooperate each other. The paper discussed the basic theory and methods about the bio-soft tissue modeling and simulation in 1) the data structure of geometry model, half-edge and half-face data structure; 2) the definition and methods about the mesh generation and subdivision; 3) the typical method of physical modeling; 4) the principle of medical image CT.
Tearing capsule of lens is the first step of cataract surgery. The capsule of lens is a rich elastic thin and transparent tissue attaching on the lens. The paper discussed a whole procedure about the capsule in modeling and simulation. The outline of lens was rotated and discretized to get the surface model of triangles and is represented by half edge structure. The physical simulation model of the capsule was created by use of the linear elastic mass spring model with quasi static solving method, combined with the collision detection techniques. The paper implemented a progress cutting algorithm for the capsule cutting, also designed a tearing algorithms for capsule of lens in terms of the fracture mechanics principle. The paper simulated the capsule of lens not only in visualization but also in force feedback by using force feedback device to simulate the visco-stick friction and to make the simulation more realistic.
Another important step of cataract surgery is breaking the kernel and aspirating it from eye. For this the paper investigated the tetrahedron dividing methods for virtual organ. It divided the cortex and lens into tetrahedron based on Delaunay rules and constrained with the triangle surface of lens capsule. Then an algorithm for breaking core of lens was presented based on half-face data structure. The process of emulsification and aspiration were simulated by means of the smooth particles hydrokinetics and the random deletion mechanism near the top of absorptiometer.
It is a typical of medical simulation based on medical images such as CT image. It contains the image preprocessing and image segmentation, surface reconstruction using MC(marching cube) method, model simplification by QEM and smooth by Laplace operator and Finite Element Modeling. The paper discussed these contents in details and modified some methods such as the modeling of the liver organ, nasopharynx with multiply tissues and the optimization for QEM simplification. It also explored the simulation of visco-elastic soft tissue with FEM.
The paper also presented an algorithm for surface model to simulate virtual organ in local adaptively. First we create a sparse mesh that can represents the organ in a allowable extent. Then we derived from it into a series level model by butterfly interpolate method. We integrated these levels model by a forest structure to implement dynamic subdividing simulation. This kind of method can enhance the precision of simulation in the case of not increasing the complexity of whole model. To lower computation complexity in the force/haptic feedback process a kind of collision detection method with hierarchical half-edge was presented. To make the simulation more faster, the paper discussed the basic principles and methods about GPGPU and the physical simulation by mass spring model and FEM on GPU.
The paper analysed the importance and practical sense for creating a framework system of virtual surgery simulation and created the function and scene class diagram by system analysis and design. It found out the extendable key points and presented the hierarchical architecture of the framework. It provided a basic implementing strategy from some basic design patterns and the run mechanics of the surgery simulation system including two thread with a shared information synchronizer.
In summary, the paper presented several methods such as adaptive dynamic local subdivision, collision detection by a hiberarchy-halfedge, GPU speeding methods and so on. Around the main line, the surgery simulation of cataract, the paper introduced the method of modeling and simulation about the lens capsule, cortex and kernel. The paper also disserted the modeling and simulation based on medical images systematically. At last, a basic software framework of surgery simulation was given. Still, the work what this paper has discussed is not enough. Author says he will study every part of the paper in future in more detail and more deeper.
生物软组织仿真是多学科融合的应用研究领域,文章系统的论述了生物软组织建模仿真的一些基础理论和方法,包括几何模型的数据结构—半边数据结构和半面结构;网格剖分和插值细分的基础理论;生物软组织的生物力学特性和典型的物理建模方法;CT图像的基本原理。
白内障手术仿真的第一步是撕囊。囊膜是附着在晶状体上的一层富有弹性的透明薄膜。文章系统地研究了囊膜建模仿真的全过程。用裂隙灯测量的数据拟合的多项式建立了晶状体的轮廓曲线,然后经旋转离散建立了囊膜的三角面模型并用半边结构表示。使用准静态求解的线弹性质点弹簧模型和碰撞检测技术,建立了具有附着特性的囊膜物理仿真模型。通过一种渐进动态切割方法,实现了囊膜切割操作。依据断裂力学的基本原理,分析、设计了囊膜撕裂的基本算法,实现了囊膜定向撕裂。虚拟器械与囊膜的交互不仅在视觉上给出反馈,作者还建立了具有黏滞性摩擦反馈的触力觉仿真模型,使交互触摸、拉伸、切割和撕裂等更具有真实感。
白内障手术仿真的另一重要步骤是碎核乳化过程即把膜下的皮质和晶状体核吸出体外。文章以三角面模型为限定,依Delaunay准则对皮质和核进行了四面体剖分,并用半面数据结构表示。对四面体剖分建立了对应的质点弹簧模型,提出了一种基于半面结构的劈核仿真算法。把分核的结果视为类刚体,采用一种无网格的光滑粒子流体动力学模型SPH建模,在吸食器接触的一定的范围内的粒子采用随机删除机制删除,以仿真乳化吸出过程。
基于医学图像的建模仿真是典型的医学仿真过程,文章从CT医学图像的预处理一分割方法,MC表面重构,QEM模型化简与平滑等,到有限元建模,作了比较系统的论述。以肝脏、鼻咽部为例应用了这些方法并作了一些改进,如多组织的鼻咽部建模,优化的QEM简化方法等,还探讨了黏弹性有限元建模问题。
文章针对面模型提出了一种局部自适应建模仿真方法,该方法以一个可以接受的比较稀疏的面模型为基础,通过蝶型插值细分方法建立了若干细节层次,借助于一个森林结构把它们组合起来,仿真时动态地局部加细分,这样在不增加模型整体复杂度的情况下,提高模型仿真的精度;在触觉反馈计算中,提出了一个层次半边碰撞检测方法,大大减少了触觉线程中碰撞检测的开销;为了加速物理仿真的计算,系统讨论了GPU用于通用计算的基本特征和方法,提出了基于GPU的质点弹簧建模方法,分析了基于GPU的有限元仿真加速的基本实现方法。
文章针对虚拟手术仿真的应用研究现状提出了建立一个虚拟手术仿真基础平台,搭建一个可扩展的基础框架的重要性和实际意义。基于面向对象的方法,从系统需求分析,功能分析出发,通过用例顺序图研究定义了与功能、场景相关的基础类,分析了虚拟手术仿真的一些可扩展点,给出了系统基础框架的层次结构体系模型。从框架设计实现的基本设计模式出发讨论了框架系统实现的基本策略,以及双线程的同步器共享的运行机制。
总之,文章在实时和真实的折中平衡方面提出了几种加速算法如自适应局部求精方法、层次半边碰撞检测方法、基于GPU的硬件加速方法;以白内障手术仿真为主线,系统地给出了晶状体囊膜、晶状体皮质、晶状体核的建模仿真方法;系统地论述了基于医学图像的建模仿真方法;系统地分析设计了一个虚拟手术仿真基础框架。尽管如此,本文所做的工作还远远不够,可以说仅仅是开始,每个问题都需要再深入研究。
With the fast development of computer science and technology, medical simulation has progressed from only visual simulation into physical and physiology simulation. The basic problems is the bio-soft tissue modeling and simulation in the field of physics-based medical simulation with the representation of virtual surgery simulation. The main tasks include geometry modeling, physical modeling, deformation calculating, collision detection, interactive operations, visual feedback and force feedback. A survey of these key techniques and applications was presented in the paper and pointed out the studying focus is balancing the realism and real-time. This paper origins mainly from the project of National Science Fund on virtual eye simulation of Xiamen University, backgrounds on the surgery simulation of cataract and liver, also bases on the project of Fujian province fund which is the study for basic framework of virtual surgery simulation to integrate the related algorithms serving for future studying and application.
The modeling and simulation for bio-soft tissue is a field in which multi-subject cooperate each other. The paper discussed the basic theory and methods about the bio-soft tissue modeling and simulation in 1) the data structure of geometry model, half-edge and half-face data structure; 2) the definition and methods about the mesh generation and subdivision; 3) the typical method of physical modeling; 4) the principle of medical image CT.
Tearing capsule of lens is the first step of cataract surgery. The capsule of lens is a rich elastic thin and transparent tissue attaching on the lens. The paper discussed a whole procedure about the capsule in modeling and simulation. The outline of lens was rotated and discretized to get the surface model of triangles and is represented by half edge structure. The physical simulation model of the capsule was created by use of the linear elastic mass spring model with quasi static solving method, combined with the collision detection techniques. The paper implemented a progress cutting algorithm for the capsule cutting, also designed a tearing algorithms for capsule of lens in terms of the fracture mechanics principle. The paper simulated the capsule of lens not only in visualization but also in force feedback by using force feedback device to simulate the visco-stick friction and to make the simulation more realistic.
Another important step of cataract surgery is breaking the kernel and aspirating it from eye. For this the paper investigated the tetrahedron dividing methods for virtual organ. It divided the cortex and lens into tetrahedron based on Delaunay rules and constrained with the triangle surface of lens capsule. Then an algorithm for breaking core of lens was presented based on half-face data structure. The process of emulsification and aspiration were simulated by means of the smooth particles hydrokinetics and the random deletion mechanism near the top of absorptiometer.
It is a typical of medical simulation based on medical images such as CT image. It contains the image preprocessing and image segmentation, surface reconstruction using MC(marching cube) method, model simplification by QEM and smooth by Laplace operator and Finite Element Modeling. The paper discussed these contents in details and modified some methods such as the modeling of the liver organ, nasopharynx with multiply tissues and the optimization for QEM simplification. It also explored the simulation of visco-elastic soft tissue with FEM.
The paper also presented an algorithm for surface model to simulate virtual organ in local adaptively. First we create a sparse mesh that can represents the organ in a allowable extent. Then we derived from it into a series level model by butterfly interpolate method. We integrated these levels model by a forest structure to implement dynamic subdividing simulation. This kind of method can enhance the precision of simulation in the case of not increasing the complexity of whole model. To lower computation complexity in the force/haptic feedback process a kind of collision detection method with hierarchical half-edge was presented. To make the simulation more faster, the paper discussed the basic principles and methods about GPGPU and the physical simulation by mass spring model and FEM on GPU.
The paper analysed the importance and practical sense for creating a framework system of virtual surgery simulation and created the function and scene class diagram by system analysis and design. It found out the extendable key points and presented the hierarchical architecture of the framework. It provided a basic implementing strategy from some basic design patterns and the run mechanics of the surgery simulation system including two thread with a shared information synchronizer.
In summary, the paper presented several methods such as adaptive dynamic local subdivision, collision detection by a hiberarchy-halfedge, GPU speeding methods and so on. Around the main line, the surgery simulation of cataract, the paper introduced the method of modeling and simulation about the lens capsule, cortex and kernel. The paper also disserted the modeling and simulation based on medical images systematically. At last, a basic software framework of surgery simulation was given. Still, the work what this paper has discussed is not enough. Author says he will study every part of the paper in future in more detail and more deeper.
引文
[1]Satava R.Medical virtual reality:The current status of the future.In Proc.of 4th conf.Medecine Meets Virtual Reality(MMVR Ⅳ),pages 100-106,1996.
[2]钟世镇.数字化虚拟人的研究和前景.见:香山科学会议,科学前沿与未来.北京:中国环境科学出版社,2002(6):171-175.
[3]钟世镇.“虚拟中国人”(VCH)切片建模研究进展.中国临床解剖学杂志,2002,20(5):323-326.
[4]Herman G T,Liu H K.Three-dimensional display of human organs from computed tomograms.Computer Graphics and Image Processing,1979,9(1):1-21.
[5]Keppel E.Approximating complex surfaces by triangulation of contour lines.IBM Journal of Research and Development,1975,19(1):2-11.
[6]Lorensen W,Cline H E.Marching cubes:a high resolution 3d surface construction algorithm.ACM Computer Graphics SIGGRAPH'87),21:163-169,1987.
[7]Nielson G M,Hamann B.The Asymptotic Decider:Resolving the Ambiguity in Marching Cubes.IEEE Proceedings of Visualization' 91,83-91.1991.
[8]Sullivan J M,Wu Z,Kulkarni A.3d volume mesh generation of human organs using surface geometries created from the visible human data set.In:Banvard R A,editor,The Third Visible Human Project Conference Proceedings.National Institutes of Health,Oct.2000.
[9]Loehner R,Parikh P.Three-dimensional grid generation via the advancing-front method.Int.J.Numer.Meth.Fluids,vol.8,pp.1135-1149,1988.
[10]Cebral J,Lohner R.From medical images to cfd meshes.In Proceedings of the 8th International Meshing Roundtable,pages 321-331,1999.
[11]Robert Bridson.adaptive physics based tetrahedral mesh geration using level sets.Stanford,technique reports,2005.2.
[12]Montagnat J,Delingette H.Globally constrained deformable models for 3d object reconstruction.Signal Processing,pages 173-186,1998.8.
[13]Shantz M.Surface Definition for Branching Contour Defined Objects[J],Computer Graphics,1981,15(2).
[14]Garland M,Heckbert P S.Simplifying surfaces with color and texture using quadric error metrics[C].In:IEEE Visualization '98,1998:263-270.
[15]Xu X G,Chao T C,Bozkurt A.VIP-Man:an image-based wholebody adult male model constructed from color photographs of the visible human project for multi-particle Monte Carlo calculations.Health Physics,2000,78(5):476-480.
[16]秦笃烈.可视人真实可视化的突出进展-Voxel-Man.中国医疗器械信息,2004,10(4):43-47.
[17]Joel Brown,Stephen Sorkin,Cynthia Bruyns.Real-Time Simulation of Deformable Objects:Tools and Application,2001.
[18]Wagner C,Schill M,Manner R.Collision Detection and Tissue Modelling in a VR-Simulator for Eye Surgery.In:ACM International Conference Proceeding Series,Proceedings of the workshop on Virtual environments,pp.27-36.
[19]Mollemans W,et al.Tetrahedral Mass Spring Model for Fast Soft Tissue Deformation,Proceedings of the International Symposium on Surgery Simulation and Soft-Tissue Modeling,2003.
[20]Bro-Nielsen M.Finite element modeling in surgery simulation.In:Proceedings of the IEEE,1998,86(3):490-503.
[21]Cotin S,Delingette H,Ayache N.Real Time Volumetric Deformable Models for Surgery Simulation[M].Hohne K,Kikinis R,editors,Vizualisation in Biomedical Computing,volume 1131 of Lecture Notes in Computer Science,Springer,1996:535-540.
[22]Wu X,et al.Adaptive Nonlinear Finite Elements for deformable body simulation using dynamic progressive Meshes.Computer graphics forum,2001,20(3).
[23]Berkley J,Turkiyyah G,Berg D,Ganter M,Weghorst S.Real-Time Finite Element Modeling for Surgery Simulation:An Application to Virtual Suturing.IEEE Transactions On Visualization And Computer Graphics,Vol.10,No.3,May/June,2004.
[24]Zachmann G.Real time and exact collision detection for interactive virtual prototyping.In Proceedings of DETC'97,1997:1-10.
[25]Gottschalk S,Lin M,Manocha D.OBB-Tree:A Hierarchical Structure for Rapid Interference Detection,the Proceedings of ACM SIGGRAPH'96,1996:171-180.
[26]Klosowski J,Held M,Mitchell JSB,Sowizral H,Zikan K.Efficient collision detection using bounding volume hierarchies of k-DOPs.IEEE Transaction On Visualization and Computer Graphics,1998,4(1):21-37.
[27]Turk G,Interactive collision detection for molecular graphics.Tech.Rep.TR90-014,University of North Carolina at Chapel Hill,1990.
[28]Raghupathi L,Grisoni L,et al.An intestine surgery simulator:Real-time collision processing and visualization.IEEE Transactions on Visualization and Computer Graphics (2004).
[29]Baciu G,Wong S K W,Sun H.RECODE:An image-based collision detection algorithm,Journal of Visualization and Computer Animation,1999,10(4):181-192.
[30]范昭炜,万华根,高曙明.基于图像的快速碰撞检测算法.计算机辅助设计与图形学学报,2002,14(9):805-809.
[31]Shade J.S Gortler et al.Layered depth images.In:Proceedings of SIGGRAPH ' 98(1998):231-242.
[32]Heidelberger B,Teschner M,Gross M.Volumetric collision detection for deformable objects.TR395 in Computer Science Department ETH Zurich,Switzerland,April 2003.
[33]Mor A B,Kanade T.Modifying soft tissue models:Progressive cutting with minimal new element creation,ln:CVRMed-Proceedings,volume 19,pages 598-607,2000.
[34]Bielser D,Glardon P,Teschner M,Gross M H.A State Machine for Real-Time Cutting of Tetrahedral Meshes,Proceedings of Pacific Graphics(PG' 03),October 8-10,Canmore,Alberta,Canada,pp.377-386.
[35]Bielser D,Maiwald V A,Gross M H.Interactive Cuts Through 3-Dimensional Soft Tissue.In:Proc.of the Eurographics' 99,Computer Graphics Forum,18,3,pp.C31-C38.
[36]Matt LeDuc,Shahram Payandeh,John Dill.Toward Modeling of a suturing Task.Graphic Interface 2003.
[37]Jeffrey Berkley,George Turkiyyah,Daniel Berg,Mark Ganter,and Suzanne Weghorst,Real-Time Finite Element Modeling for Surgery Simulation:An Application to Virtual Suturing.IEEE Transactions On Visualization And Computer Graphics,Vol.10,No.3,May/June,2004.
[38]唐泽圣.三维数据场可视化.清华大学出版社,1999.
[39]3Dmed(3-Dimensional Medical Image Processing and Analyzing System).http://www.3dmed.net
[40]Zilles C,Salisbury J K.A Constraint-Based God-Object Method for Haptic Display.In:Proc.IEE/RSJ Int' 1 Conf.Intelligent Robots and Systems,Human Robot Interaction,and Cooperative Robots,vol.3,IEEE CS Press,1995:146-151.
[41]Ruspini D C,Kolarov K,Khatib O.The Haptic Display of Complex Graphical Environments.Proc.ACM Siggraph,ACM Press,1997:345-352.
[42]鞠颖.中国人虚拟眼形态和功能的建模研究:(博士学位论文).西安:西安交通大学,2003.
[43]黄晓阳.人眼组织切片图像的配准、三维重建的研究与实现:(硕士学位论文).厦门:厦门大学,2003.
[44]鞠颖,王博亮,谢杰镇等.基于裂隙灯显微图像的眼前节特征提取的新方法.中国生物医学工程学报,2004,23(3):193-198.
[45]Loop C.Smooth subdivision surfaces based on triangles.Master' s thesis,University of Utah,August 1987.
[46]DYN N,LEVIN D,GREGORY J A.A Butterfly Subdivision Scheme for Surface Interpolation with Tension Control.ACM TOG 9,2(April),160-169.
[47]Denis Zorin,Peter Schroeder,Wim Sweldens.Interpolating Subdivision for Meshes with Arbitrary Topology.In:Proceedings of SIGGRAPH 1996:189-192.
[48]杨钦.限定Delaunay三角剖分:(博士学位论文).北京:北京航空航天大学,2003.
[49]Jonathan Richard Shewchuk.Lecture Notes on Delaunay Mesh Generation,1999.
[50]徐永安.约束Delaunay三角化的关键问题研究与算法实现及应用:(博士学位论文).杭州: 大学,1999.
[51]杨挺青等.黏弹性理论与应用.科学出版社,2004.
[52]CT Image.http://medical.nema.org.
[53]曾攀.有限元分析及应用.清华大学出版社,2004.
[54]Provot X.Deformation Constrains in a mass spring Model to Describe Rigid Cloth Behavior.Graphics Interface' 95:147-154.
[55]Nedel L,Thalmann D.Real time muscle deformation using mass-spring systems.CG Int.1998:156-165.
[56]Lee Y C,rerzopoulos D,Waters K.Realistic face modeling for animation.Siggraph proceedings,1995:55-62.
[57]Hutchinson D,Preston M,Hewitt T.Adaptive Refinement for Mass/Spring Simulations,In:Proc.Of the Eurographics Workshop on Computer Animation and Simulation,pages 31-45,Sep.1996.
[58]Vasily Volkov,Li Ling.Adaptive Local Refinement and Simplification of Cloth Meshes.In:Proceedings of ist International conference on Information Technology &Applications(ICITA 2002).Bathurst,Australia,November 25-28,2002.
[59]Xunlei Wu,Micahel S.Dowries,Tolga Goktekin,Frank Tendick.Adaptive Nonlinear Finite Elements for Deformable Body Simulation Using Dynamic Progressive Meshes,EUROGRAPHICS 2001,Volume 20(2001),Number 3.
[60]蔡及时等.应用于网上虚拟手术的自适应变形模型.软件学报,Vol.13,No.9,2002.
[61]O' Brien J,Hodgins J.Graphical model and animation of brittle fracture.In:Proceedings of SIGGRAPH 1999:137-146.
[62]Xia J C,EiSana J,Varshney A.Adaptive Real-Time Level-of-Detail-Based Rendering for Polygonal Models,IEEE Trans.Visualization and Computer Graphics,vol.3,no.2,171-183,Apr.-June 1997.
[63]Hoppe H.View-Dependent Refinement of Progressive Meshes,Proc.SIGGRAPH' 97,189-198,1997.
[64]Grinspun E,Krysl P,et al.Charms:a simple framework for adaptive simulation.In:Proceedings of the 29th annual conference on Computer graphics and interactive techniques,pages 281-290.ACM Press,2002.
[65]李鸣凤.眼科全书.北京:人民卫生出版社,1996.
[66]Burd H J,Judge S J,Cross JA,Numerical Modeling of the Accommodating Lens.Vision Research,2002,42:2235-2251.
[67]Rafael I.Barraquer,1 Ralph Michael,l Rodrigo Abreu,1 José Lamarca,1 and Francisco Tresserra2.Human Lens Capsule Thickness as a Function of Age and Location along the Sagittal Lens Perimeter.Investigative Ophthalmology and Visual Science.2006,47:2053-2060.
[68]Fisher,R F,The elastic constants of the human lens capsule.Journal of Physiology.1971,212:147-180.
[69]Ronald A Schachar,Roger W Chan,Min Fu.Viscoelastic shear properties of the fresh porcine lens,British Journal of Ophthalmology.2007,91:366-368.
[70]Krag S,Olsen T,Anderassen T T.Biomechanical characteristics of the human anterior lens capsule in relation to age.Investigative Ophthalmology and Visual Science,1997b.38:357-363.
[71]Krag S,T.Olsen T,Anderassen T T.Thermal and mechanical stability of the lens capsule.Current Eye Research,1998,17:470-477.
[72]Krag S,Anderassen T T.Mechanical properties of the human lens capsule.Progress in Retinal and Eye Research,2003,22:749-767.
[73]Johannes PW,Wagner G,Manner R.Interactive Real-Time Simulation of the Internal Limiting Membrane.Lecture Notes in Computer Science,Springer-Verlag Heidelberg,2004,3078:153-160.
[74]庄茁等.工程断裂与损伤.机械工业出版社,2004.
[75]林振德,李绍珍.小切口白内障手术.人民卫生出版社,2002.
[76]张雄,刘岩.无网格法.清华大学出版社/Springer出版社,2004.
[77]MULLER M,HEIDELBERGER B,TESCHNER M,GROSS M.Meshless deformations based on shape matching.ACM Trans.Graph.24,3(2005),471-478.
[78]Ruspini D C,Kolarov K,Khatib O.The Haptic Display of Complex Graphical Environments.In:Proc.ACM Siggraph,ACM Press,1997:345-352.
[79]Balaniuk R.Using fast local modeling to buffer haptic data.In:Proceedings of 4th PHANToM Users Group Workshop,Boston,Massachusetts,October 1999.
[80]Mendoza C A,Laugier C.Realistic haptic rendering for highly deformable virtual objects.In:Proceedings,IEEE Virtual Reality,Yokohama,Japan,March 2001.
[81]Park J G,Niemeyer G.Haptic Rendering with Predictive Representation of Local Geometry.In:Proceedings of 10th Symposium on Haptic Interfaces for Virtual Environment and Teleoperator Systems,March 2002:201-208.
[82]Chih-Hao Ho,Basdogan C,Srinicasan M A.Efficient Point-Based Rendering Techniques for Haptic Display of Virtual Objects.Presence(S1054-7460),1999,8(5):447-491.
[83]Zachmann G.Real-time and exact collision detection for interactive virtual prototyping.In:Proceedings of DETC'97,1997:1-10.
[84]Richard C,Cutkosky M R,MacLean K.Friction Identification for Haptic Display.In:Proceedings of the ASME Dynamic Systems and Control Division,1999,67:327-334.
[85]Richard C,et al.Friction modeling and display in haptic applications involving user performance.In:Proceedings of the 2002 IEEE International Conference on Robotics & Automation,May 2002:605-611.
[86]吴恩华.图形处理器用于通用计算的技术现状及其挑战.软件学报,2004年10月,15(10):206-214.
[87]John D.Owens,David Luebke,et al.A Survey of General-Purpose Computation on Graphics Hardware.EUROGRAPHICS 2005.
[88]Mosegaard J,Sorensen T S,GPU Accelerated Surgical Simulators for Complex Morphology,IEEE Virtual Reality Conference 2005(VR'05).2005,323:47-154.
[89]Guido Ranzuglia,Paolo Cignoni et al.Implementing mesh-based approaches for deformable objects on GPU.http://vcg.isti.cnr.it/Publications/2006/RCGS06/gpgpu.pdf
[90]KRUGER J,WESTERMANN R.:Linear algebra operators for GPU implementation of numerical algorithms.ACM Transactions on Graphics 22,3(July 2003),908-916.
[91]BOLZ J,FARMER I,GRINSPUN E,SCHRODER P.Sparse matrix solvers on the GPU:Conjugate gradients and multigrid.ACM Transactions on Graphics 22,3(July2003):917-924.
[92]BUCK I.GPGPU:General-purpose computation on graphics hardware-GPU computation strategies & tricks.ACM SIGGRAPH Course Notes(Aug.2004).
[93]章毓晋.图像分割.北京:科学出版社,2001.
[94]罗述谦,周果宏.医学图象处理与分析.北京:科学出版社,2003.
[95]Osher S,Sethian J.Fronts propagating with curvature dependent speed:algorithms based on the Hamilton-Jacobi formulation.Journal of Computational Physics,1988,79:12-49.
[96]沈毅.基于CT数据的肝脏及其内部管道的可视化和虚拟手术研究:(硕士学位论文).厦门:厦门大学,2005.
[97]戴培山.虚拟眼三维建模与仿真技术研究:(博士学位论文).长沙:国防科技大学,2007.
[98]Hoppe H,DeRose T,Duchamp T,et al.Piecewise smooth surface reconstruction.In:Andrew Glassner SIGGRAPH'94.Orlando:ACM Press,1994:295-302.
[99]Garland M,Heckbert P S.Surface simplification using quadric error metrics,In:Proceedings of SIGGRAPH 97,Computer Graphics Proceedings,Annual Conference Series.Los Angeles:Addison Wesley,1997:209-216.
[100]吴伟力,王博亮等.一种改进的基于二次误差测度的网格简化算法.厦门大学学报,2007.03.
[101]阎丽霞.虚拟手术关键技术研究:(博士学位论文).杭州:浙江大学,2001.
[102]XIN CHEN.应用框架的设计与实现:.NET平台.电子工业出版社,2005.
[103]Erich Gamma,Richard Helm,Ralph Johnson,John Vlissides.Design Pattern:Elements of reuseable object-oriented software.Addison-Wesley,1995.
[2]钟世镇.数字化虚拟人的研究和前景.见:香山科学会议,科学前沿与未来.北京:中国环境科学出版社,2002(6):171-175.
[3]钟世镇.“虚拟中国人”(VCH)切片建模研究进展.中国临床解剖学杂志,2002,20(5):323-326.
[4]Herman G T,Liu H K.Three-dimensional display of human organs from computed tomograms.Computer Graphics and Image Processing,1979,9(1):1-21.
[5]Keppel E.Approximating complex surfaces by triangulation of contour lines.IBM Journal of Research and Development,1975,19(1):2-11.
[6]Lorensen W,Cline H E.Marching cubes:a high resolution 3d surface construction algorithm.ACM Computer Graphics SIGGRAPH'87),21:163-169,1987.
[7]Nielson G M,Hamann B.The Asymptotic Decider:Resolving the Ambiguity in Marching Cubes.IEEE Proceedings of Visualization' 91,83-91.1991.
[8]Sullivan J M,Wu Z,Kulkarni A.3d volume mesh generation of human organs using surface geometries created from the visible human data set.In:Banvard R A,editor,The Third Visible Human Project Conference Proceedings.National Institutes of Health,Oct.2000.
[9]Loehner R,Parikh P.Three-dimensional grid generation via the advancing-front method.Int.J.Numer.Meth.Fluids,vol.8,pp.1135-1149,1988.
[10]Cebral J,Lohner R.From medical images to cfd meshes.In Proceedings of the 8th International Meshing Roundtable,pages 321-331,1999.
[11]Robert Bridson.adaptive physics based tetrahedral mesh geration using level sets.Stanford,technique reports,2005.2.
[12]Montagnat J,Delingette H.Globally constrained deformable models for 3d object reconstruction.Signal Processing,pages 173-186,1998.8.
[13]Shantz M.Surface Definition for Branching Contour Defined Objects[J],Computer Graphics,1981,15(2).
[14]Garland M,Heckbert P S.Simplifying surfaces with color and texture using quadric error metrics[C].In:IEEE Visualization '98,1998:263-270.
[15]Xu X G,Chao T C,Bozkurt A.VIP-Man:an image-based wholebody adult male model constructed from color photographs of the visible human project for multi-particle Monte Carlo calculations.Health Physics,2000,78(5):476-480.
[16]秦笃烈.可视人真实可视化的突出进展-Voxel-Man.中国医疗器械信息,2004,10(4):43-47.
[17]Joel Brown,Stephen Sorkin,Cynthia Bruyns.Real-Time Simulation of Deformable Objects:Tools and Application,2001.
[18]Wagner C,Schill M,Manner R.Collision Detection and Tissue Modelling in a VR-Simulator for Eye Surgery.In:ACM International Conference Proceeding Series,Proceedings of the workshop on Virtual environments,pp.27-36.
[19]Mollemans W,et al.Tetrahedral Mass Spring Model for Fast Soft Tissue Deformation,Proceedings of the International Symposium on Surgery Simulation and Soft-Tissue Modeling,2003.
[20]Bro-Nielsen M.Finite element modeling in surgery simulation.In:Proceedings of the IEEE,1998,86(3):490-503.
[21]Cotin S,Delingette H,Ayache N.Real Time Volumetric Deformable Models for Surgery Simulation[M].Hohne K,Kikinis R,editors,Vizualisation in Biomedical Computing,volume 1131 of Lecture Notes in Computer Science,Springer,1996:535-540.
[22]Wu X,et al.Adaptive Nonlinear Finite Elements for deformable body simulation using dynamic progressive Meshes.Computer graphics forum,2001,20(3).
[23]Berkley J,Turkiyyah G,Berg D,Ganter M,Weghorst S.Real-Time Finite Element Modeling for Surgery Simulation:An Application to Virtual Suturing.IEEE Transactions On Visualization And Computer Graphics,Vol.10,No.3,May/June,2004.
[24]Zachmann G.Real time and exact collision detection for interactive virtual prototyping.In Proceedings of DETC'97,1997:1-10.
[25]Gottschalk S,Lin M,Manocha D.OBB-Tree:A Hierarchical Structure for Rapid Interference Detection,the Proceedings of ACM SIGGRAPH'96,1996:171-180.
[26]Klosowski J,Held M,Mitchell JSB,Sowizral H,Zikan K.Efficient collision detection using bounding volume hierarchies of k-DOPs.IEEE Transaction On Visualization and Computer Graphics,1998,4(1):21-37.
[27]Turk G,Interactive collision detection for molecular graphics.Tech.Rep.TR90-014,University of North Carolina at Chapel Hill,1990.
[28]Raghupathi L,Grisoni L,et al.An intestine surgery simulator:Real-time collision processing and visualization.IEEE Transactions on Visualization and Computer Graphics (2004).
[29]Baciu G,Wong S K W,Sun H.RECODE:An image-based collision detection algorithm,Journal of Visualization and Computer Animation,1999,10(4):181-192.
[30]范昭炜,万华根,高曙明.基于图像的快速碰撞检测算法.计算机辅助设计与图形学学报,2002,14(9):805-809.
[31]Shade J.S Gortler et al.Layered depth images.In:Proceedings of SIGGRAPH ' 98(1998):231-242.
[32]Heidelberger B,Teschner M,Gross M.Volumetric collision detection for deformable objects.TR395 in Computer Science Department ETH Zurich,Switzerland,April 2003.
[33]Mor A B,Kanade T.Modifying soft tissue models:Progressive cutting with minimal new element creation,ln:CVRMed-Proceedings,volume 19,pages 598-607,2000.
[34]Bielser D,Glardon P,Teschner M,Gross M H.A State Machine for Real-Time Cutting of Tetrahedral Meshes,Proceedings of Pacific Graphics(PG' 03),October 8-10,Canmore,Alberta,Canada,pp.377-386.
[35]Bielser D,Maiwald V A,Gross M H.Interactive Cuts Through 3-Dimensional Soft Tissue.In:Proc.of the Eurographics' 99,Computer Graphics Forum,18,3,pp.C31-C38.
[36]Matt LeDuc,Shahram Payandeh,John Dill.Toward Modeling of a suturing Task.Graphic Interface 2003.
[37]Jeffrey Berkley,George Turkiyyah,Daniel Berg,Mark Ganter,and Suzanne Weghorst,Real-Time Finite Element Modeling for Surgery Simulation:An Application to Virtual Suturing.IEEE Transactions On Visualization And Computer Graphics,Vol.10,No.3,May/June,2004.
[38]唐泽圣.三维数据场可视化.清华大学出版社,1999.
[39]3Dmed(3-Dimensional Medical Image Processing and Analyzing System).http://www.3dmed.net
[40]Zilles C,Salisbury J K.A Constraint-Based God-Object Method for Haptic Display.In:Proc.IEE/RSJ Int' 1 Conf.Intelligent Robots and Systems,Human Robot Interaction,and Cooperative Robots,vol.3,IEEE CS Press,1995:146-151.
[41]Ruspini D C,Kolarov K,Khatib O.The Haptic Display of Complex Graphical Environments.Proc.ACM Siggraph,ACM Press,1997:345-352.
[42]鞠颖.中国人虚拟眼形态和功能的建模研究:(博士学位论文).西安:西安交通大学,2003.
[43]黄晓阳.人眼组织切片图像的配准、三维重建的研究与实现:(硕士学位论文).厦门:厦门大学,2003.
[44]鞠颖,王博亮,谢杰镇等.基于裂隙灯显微图像的眼前节特征提取的新方法.中国生物医学工程学报,2004,23(3):193-198.
[45]Loop C.Smooth subdivision surfaces based on triangles.Master' s thesis,University of Utah,August 1987.
[46]DYN N,LEVIN D,GREGORY J A.A Butterfly Subdivision Scheme for Surface Interpolation with Tension Control.ACM TOG 9,2(April),160-169.
[47]Denis Zorin,Peter Schroeder,Wim Sweldens.Interpolating Subdivision for Meshes with Arbitrary Topology.In:Proceedings of SIGGRAPH 1996:189-192.
[48]杨钦.限定Delaunay三角剖分:(博士学位论文).北京:北京航空航天大学,2003.
[49]Jonathan Richard Shewchuk.Lecture Notes on Delaunay Mesh Generation,1999.
[50]徐永安.约束Delaunay三角化的关键问题研究与算法实现及应用:(博士学位论文).杭州: 大学,1999.
[51]杨挺青等.黏弹性理论与应用.科学出版社,2004.
[52]CT Image.http://medical.nema.org.
[53]曾攀.有限元分析及应用.清华大学出版社,2004.
[54]Provot X.Deformation Constrains in a mass spring Model to Describe Rigid Cloth Behavior.Graphics Interface' 95:147-154.
[55]Nedel L,Thalmann D.Real time muscle deformation using mass-spring systems.CG Int.1998:156-165.
[56]Lee Y C,rerzopoulos D,Waters K.Realistic face modeling for animation.Siggraph proceedings,1995:55-62.
[57]Hutchinson D,Preston M,Hewitt T.Adaptive Refinement for Mass/Spring Simulations,In:Proc.Of the Eurographics Workshop on Computer Animation and Simulation,pages 31-45,Sep.1996.
[58]Vasily Volkov,Li Ling.Adaptive Local Refinement and Simplification of Cloth Meshes.In:Proceedings of ist International conference on Information Technology &Applications(ICITA 2002).Bathurst,Australia,November 25-28,2002.
[59]Xunlei Wu,Micahel S.Dowries,Tolga Goktekin,Frank Tendick.Adaptive Nonlinear Finite Elements for Deformable Body Simulation Using Dynamic Progressive Meshes,EUROGRAPHICS 2001,Volume 20(2001),Number 3.
[60]蔡及时等.应用于网上虚拟手术的自适应变形模型.软件学报,Vol.13,No.9,2002.
[61]O' Brien J,Hodgins J.Graphical model and animation of brittle fracture.In:Proceedings of SIGGRAPH 1999:137-146.
[62]Xia J C,EiSana J,Varshney A.Adaptive Real-Time Level-of-Detail-Based Rendering for Polygonal Models,IEEE Trans.Visualization and Computer Graphics,vol.3,no.2,171-183,Apr.-June 1997.
[63]Hoppe H.View-Dependent Refinement of Progressive Meshes,Proc.SIGGRAPH' 97,189-198,1997.
[64]Grinspun E,Krysl P,et al.Charms:a simple framework for adaptive simulation.In:Proceedings of the 29th annual conference on Computer graphics and interactive techniques,pages 281-290.ACM Press,2002.
[65]李鸣凤.眼科全书.北京:人民卫生出版社,1996.
[66]Burd H J,Judge S J,Cross JA,Numerical Modeling of the Accommodating Lens.Vision Research,2002,42:2235-2251.
[67]Rafael I.Barraquer,1 Ralph Michael,l Rodrigo Abreu,1 José Lamarca,1 and Francisco Tresserra2.Human Lens Capsule Thickness as a Function of Age and Location along the Sagittal Lens Perimeter.Investigative Ophthalmology and Visual Science.2006,47:2053-2060.
[68]Fisher,R F,The elastic constants of the human lens capsule.Journal of Physiology.1971,212:147-180.
[69]Ronald A Schachar,Roger W Chan,Min Fu.Viscoelastic shear properties of the fresh porcine lens,British Journal of Ophthalmology.2007,91:366-368.
[70]Krag S,Olsen T,Anderassen T T.Biomechanical characteristics of the human anterior lens capsule in relation to age.Investigative Ophthalmology and Visual Science,1997b.38:357-363.
[71]Krag S,T.Olsen T,Anderassen T T.Thermal and mechanical stability of the lens capsule.Current Eye Research,1998,17:470-477.
[72]Krag S,Anderassen T T.Mechanical properties of the human lens capsule.Progress in Retinal and Eye Research,2003,22:749-767.
[73]Johannes PW,Wagner G,Manner R.Interactive Real-Time Simulation of the Internal Limiting Membrane.Lecture Notes in Computer Science,Springer-Verlag Heidelberg,2004,3078:153-160.
[74]庄茁等.工程断裂与损伤.机械工业出版社,2004.
[75]林振德,李绍珍.小切口白内障手术.人民卫生出版社,2002.
[76]张雄,刘岩.无网格法.清华大学出版社/Springer出版社,2004.
[77]MULLER M,HEIDELBERGER B,TESCHNER M,GROSS M.Meshless deformations based on shape matching.ACM Trans.Graph.24,3(2005),471-478.
[78]Ruspini D C,Kolarov K,Khatib O.The Haptic Display of Complex Graphical Environments.In:Proc.ACM Siggraph,ACM Press,1997:345-352.
[79]Balaniuk R.Using fast local modeling to buffer haptic data.In:Proceedings of 4th PHANToM Users Group Workshop,Boston,Massachusetts,October 1999.
[80]Mendoza C A,Laugier C.Realistic haptic rendering for highly deformable virtual objects.In:Proceedings,IEEE Virtual Reality,Yokohama,Japan,March 2001.
[81]Park J G,Niemeyer G.Haptic Rendering with Predictive Representation of Local Geometry.In:Proceedings of 10th Symposium on Haptic Interfaces for Virtual Environment and Teleoperator Systems,March 2002:201-208.
[82]Chih-Hao Ho,Basdogan C,Srinicasan M A.Efficient Point-Based Rendering Techniques for Haptic Display of Virtual Objects.Presence(S1054-7460),1999,8(5):447-491.
[83]Zachmann G.Real-time and exact collision detection for interactive virtual prototyping.In:Proceedings of DETC'97,1997:1-10.
[84]Richard C,Cutkosky M R,MacLean K.Friction Identification for Haptic Display.In:Proceedings of the ASME Dynamic Systems and Control Division,1999,67:327-334.
[85]Richard C,et al.Friction modeling and display in haptic applications involving user performance.In:Proceedings of the 2002 IEEE International Conference on Robotics & Automation,May 2002:605-611.
[86]吴恩华.图形处理器用于通用计算的技术现状及其挑战.软件学报,2004年10月,15(10):206-214.
[87]John D.Owens,David Luebke,et al.A Survey of General-Purpose Computation on Graphics Hardware.EUROGRAPHICS 2005.
[88]Mosegaard J,Sorensen T S,GPU Accelerated Surgical Simulators for Complex Morphology,IEEE Virtual Reality Conference 2005(VR'05).2005,323:47-154.
[89]Guido Ranzuglia,Paolo Cignoni et al.Implementing mesh-based approaches for deformable objects on GPU.http://vcg.isti.cnr.it/Publications/2006/RCGS06/gpgpu.pdf
[90]KRUGER J,WESTERMANN R.:Linear algebra operators for GPU implementation of numerical algorithms.ACM Transactions on Graphics 22,3(July 2003),908-916.
[91]BOLZ J,FARMER I,GRINSPUN E,SCHRODER P.Sparse matrix solvers on the GPU:Conjugate gradients and multigrid.ACM Transactions on Graphics 22,3(July2003):917-924.
[92]BUCK I.GPGPU:General-purpose computation on graphics hardware-GPU computation strategies & tricks.ACM SIGGRAPH Course Notes(Aug.2004).
[93]章毓晋.图像分割.北京:科学出版社,2001.
[94]罗述谦,周果宏.医学图象处理与分析.北京:科学出版社,2003.
[95]Osher S,Sethian J.Fronts propagating with curvature dependent speed:algorithms based on the Hamilton-Jacobi formulation.Journal of Computational Physics,1988,79:12-49.
[96]沈毅.基于CT数据的肝脏及其内部管道的可视化和虚拟手术研究:(硕士学位论文).厦门:厦门大学,2005.
[97]戴培山.虚拟眼三维建模与仿真技术研究:(博士学位论文).长沙:国防科技大学,2007.
[98]Hoppe H,DeRose T,Duchamp T,et al.Piecewise smooth surface reconstruction.In:Andrew Glassner SIGGRAPH'94.Orlando:ACM Press,1994:295-302.
[99]Garland M,Heckbert P S.Surface simplification using quadric error metrics,In:Proceedings of SIGGRAPH 97,Computer Graphics Proceedings,Annual Conference Series.Los Angeles:Addison Wesley,1997:209-216.
[100]吴伟力,王博亮等.一种改进的基于二次误差测度的网格简化算法.厦门大学学报,2007.03.
[101]阎丽霞.虚拟手术关键技术研究:(博士学位论文).杭州:浙江大学,2001.
[102]XIN CHEN.应用框架的设计与实现:.NET平台.电子工业出版社,2005.
[103]Erich Gamma,Richard Helm,Ralph Johnson,John Vlissides.Design Pattern:Elements of reuseable object-oriented software.Addison-Wesley,1995.