心脏三维及四维数学建模
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摘要
心脏是人体循环系统的动力源,是人体中最重要的器官之一。它是集电生理学、动力学、血液流体力学以及神经、生化控制等于一身的极其复杂的综合系统。建模是研究复杂生物学问题的有效手段,利用计算机强大的计算能力和图形处理显示能力,建立心脏的三维模型并最终使其可视化是深入研究心脏的有效途径。模型不仅要从形态上仿真心脏,而且应能模拟真实心脏的运动过程,为研究动态心脏提供模型基础。
本文主要建立了心脏的三维静态模型及四维动态模型,并设计显示界面对其进行显示和操作。所建心脏模型一方面根据冠状动脉依附在心脏表面的特性,可以对冠状动脉建模进行约束和指导,建立冠状动脉血管的静态及动态模型;另一方面经过X射线投影,得到二维图像可用于冠状动脉衰减投影图像的分析。
本文通过构造心脏的心包和腔室的三维曲面的方法来进行静态心脏建模。在对人体心脏的解剖切片进行手工分割提取心包和各腔室的轮廓并用高斯滤波器对其进行平滑后,使用均匀取样的方法对轮廓进行取样,得到的样点作为心包和腔室的拟合点。在曲面拟合方面本文使用的是一种非均匀有理B样条(NURBS)曲面拟合法,这种方法在曲面拟合上具有准确和控制自由度高的优点。心脏静态模型是动态模型建立的基础,通过构造并连接一系列的由静态的心脏模型构成的时间帧来建立动态的心脏模型。根据心脏生理学特性,将一个心脏周期分成七个时期,并假定每一个时期内的心脏为线性运动,根据心脏运动的定量描述构造出7个时间帧并将其连接起来。
显示方面使用的是显示工具VTK(Visual Toolkit),它不光可以对建立好的静态和动态模型进行显示,还可以对它们进行操作,增加了观察的灵活性。显示结果表明静态模型形态上比较接近真实心脏,动态模型也能很好的体现心脏的运动规律。
The heart, which is the power source of human circulatory system, is one of the most important organs of human bodies. It is such a complex integrated system that includes Physiology, Dynamics, Blood Hydrodynamics and neurological, biochemical control. Modeling is an efficient tool to analyze the complex problems of biology.
In this paper, we build 3D static and 4D dynamic models of heart and design visual interface to observe and operate it. The heart models are used on one hand to restrict and instruct coronary artery modeling as a result of coronary artery above the heart interface, the other hand to get 2D images through X-Ray for analyzing angiogram image of coronary artery.
In this paper, constructing 3D surfaces of pericardium and antrum is used to model 3D static heart. First we manually segment the slice ups of human heart to get profiles and smooth them by Gaussian filters. Then the uniform sampling algorithm is used to sample points from the profiles. After it, a 3D surface model is constructed from the sampled points applying a surface fitting algorithm. Nonuniform Rational B-Spline (NURBS)is represented to fit surface as its accuracy and manageability. Static heart is the foundation of dynamic heart. After constructing and connecting a series of time frames of static heart models, a dynamic heart model has been constructed. Cardiac circle is divided into 7 time segments based on physiology knowledge and the movement between each segment is supposed linear. In accordance of description of heart movement, 7 time frames are constructed and connected together to form the dynamic heart model.
Visual Toolkit (VTK)is used as the visualization tool. It can not only show the static and dynamic heart models, but also handle them freely.
The result indicates the static heart model constructed looks like real heart and the dynamic heart model built expresses heart movement well.
本文主要建立了心脏的三维静态模型及四维动态模型,并设计显示界面对其进行显示和操作。所建心脏模型一方面根据冠状动脉依附在心脏表面的特性,可以对冠状动脉建模进行约束和指导,建立冠状动脉血管的静态及动态模型;另一方面经过X射线投影,得到二维图像可用于冠状动脉衰减投影图像的分析。
本文通过构造心脏的心包和腔室的三维曲面的方法来进行静态心脏建模。在对人体心脏的解剖切片进行手工分割提取心包和各腔室的轮廓并用高斯滤波器对其进行平滑后,使用均匀取样的方法对轮廓进行取样,得到的样点作为心包和腔室的拟合点。在曲面拟合方面本文使用的是一种非均匀有理B样条(NURBS)曲面拟合法,这种方法在曲面拟合上具有准确和控制自由度高的优点。心脏静态模型是动态模型建立的基础,通过构造并连接一系列的由静态的心脏模型构成的时间帧来建立动态的心脏模型。根据心脏生理学特性,将一个心脏周期分成七个时期,并假定每一个时期内的心脏为线性运动,根据心脏运动的定量描述构造出7个时间帧并将其连接起来。
显示方面使用的是显示工具VTK(Visual Toolkit),它不光可以对建立好的静态和动态模型进行显示,还可以对它们进行操作,增加了观察的灵活性。显示结果表明静态模型形态上比较接近真实心脏,动态模型也能很好的体现心脏的运动规律。
The heart, which is the power source of human circulatory system, is one of the most important organs of human bodies. It is such a complex integrated system that includes Physiology, Dynamics, Blood Hydrodynamics and neurological, biochemical control. Modeling is an efficient tool to analyze the complex problems of biology.
In this paper, we build 3D static and 4D dynamic models of heart and design visual interface to observe and operate it. The heart models are used on one hand to restrict and instruct coronary artery modeling as a result of coronary artery above the heart interface, the other hand to get 2D images through X-Ray for analyzing angiogram image of coronary artery.
In this paper, constructing 3D surfaces of pericardium and antrum is used to model 3D static heart. First we manually segment the slice ups of human heart to get profiles and smooth them by Gaussian filters. Then the uniform sampling algorithm is used to sample points from the profiles. After it, a 3D surface model is constructed from the sampled points applying a surface fitting algorithm. Nonuniform Rational B-Spline (NURBS)is represented to fit surface as its accuracy and manageability. Static heart is the foundation of dynamic heart. After constructing and connecting a series of time frames of static heart models, a dynamic heart model has been constructed. Cardiac circle is divided into 7 time segments based on physiology knowledge and the movement between each segment is supposed linear. In accordance of description of heart movement, 7 time frames are constructed and connected together to form the dynamic heart model.
Visual Toolkit (VTK)is used as the visualization tool. It can not only show the static and dynamic heart models, but also handle them freely.
The result indicates the static heart model constructed looks like real heart and the dynamic heart model built expresses heart movement well.
引文
[1]石教英,蔡文立.科学计算可视化算法与系统.第一版.北京:科学出版社, 1996
[2] Shantz M, Surface Definition for Branching Contour Defined Objects. Computer Graphics, 1981, 15(2)
[3]周辉,李涛,邢启江.欧宗瑛.数字曲线的线性逼近和分段识别.大连理工大学学报, 1997, 37(5): 576-580
[4] Keppel E., Approximating Complex Surfaces by Triangulation of Contour Lines, IBM J. Res. Dev, 1975, 19
[5] Fuchs H., Kedem Z., et al. Optimal Surface Reconstruction from planar Contours, CACM, 1977, 20
[6] Christiansen H.N., Sederberg T.W., Construction of Complex Contours Line Definition into Polygonal Element Mosaics, Computer Graphics, 1978, 12(3): 187-192
[7] Cook L.T., Dwyer S., et al, A Three Dimensional Display system for Diagnostic Imaging Applications, IEEE Computer Graphics and Apprication, 1983, 3(4)
[8] Ganapathy S., Dennely T.G., A New General Triangulation Method for Planar Contours, Computer Graphics, 1982, 16(3)
[9] Lin W C. A new surface interpolation technique for reconstruction3D objects from serial cross-sections[J], Computer Vision &Graph Image Process 1989, 48(1): 124~143
[10] Boissonnat J.D., Shape Reconstruction from planar cross Section. CVGIP, 1988, 44
[11] Herman G.T., Liu H.K., Three-Dimensional Display of Human Organs from Computed Tomograms, Computer Graphics Image Processing, 1979, 9
[12] Lorensen W.E., Cline H.E., Marching Cubes: A High Resolution 3D Surface Construction Algorithm, Computer Graphics,1987, 21(4) : 163-169
[13] Nielson G., Hamann B., The Asymptotic Decider: Resolving the Ambiguity in Marching Cube. Visualization, 1991, 91 : 83-91
[14] Wilhelms J., Von Gelder A., Topological Considerations in IsoSurface Generation,San Diego Workshop on Volume Visualization, 1990
[15] Wu K., Hesselink L., Computer Display of Reconstructed 3D Scalar over Data, Applied Optics, 1988, 27(2)
[16] Cline H., Lerensen W. Tow, Algorithms for the 3D Reconstruction of Tomograms, Medical Physics, 1988, 15(3)
[17] Miller J. V., Breen D. E., et al. Extracting Geometric Models through Constraint Minimization, Visualization, 1990, 90
[18] Miller J. V., Breen D. E., et al. Geometrically Deformed Models: A Method for Extracting closed Geometric Models from Volume Data, Computer Graphics, 1991, 25(3)
[19]管伟光.体视化技术及其应用.北京:电子工业出版社, 1998
[20]沈宗文.实用人体断层解剖学.上海医科大学出版社, 1997
[21] (美)布朗威.心脏病学——心血管内科学教科书.人民卫生出版社, 2000
[22] The Visible Human Project, http : //www .nlm.nih.gov/research/visible/visible human.htm
[23] M. Sonka, M. D. Winniford, S. M. Collins. Robust simultaneous detection of coronary borders in complex images. IEEE Trans. Med. Imaging, 1995, 14(1): 151-161
[24] Kitware, Inc. The VTK user’s guide, http: //www.vtk.org
[25] Carole Blanc and Christophe Schlick, University of Bordeaux, Accurate parametrization of conics by NURBS, IEEE Transactions on Computer Graphics and Applications, 1996. 11, 16(6): 64 - 71
[26] Jiang Dan . Wang Lancheng, An algorithm of NURBS surface fitting for reverse engineering, Springer-Verlag London Limited, 2006
[27] Nicholas J. Tustison and Amir A. Amini*, Senior Member, IEEE, Biventricular myocardial strains via nonrigid registration of AnFigatomical NURBS models, IEEE Transactions On Medical Imaging, 2006, 25(1)
[28] M. Pourazady and X. Xu, Direct manipulations of B-spline and NURBS curves, Advances in Engineering Software 31 Elsevier, 2000: 107-118
[29] M. Pourazady and X. Xu, Direct manipulations of NURBS surfaces subjected to geometric constraints, Computers & Graphics 30 (2006)598–609, Elsevier
[30] Les Piegl, On NURBS: A Survey, Jan 01, IEEE Computer Graphics and Applications, 1991, 11(1): 55
[31] Kathi Hogshead Davis and Peter H. Aiken, Data Reverse Engineering: A Historical survey, Reverse Engineering, 2000. Proceedings. Seventh Working Conference on , 2000, 11(23-25): 70– 78
[32] SUN Zheng , YU Dao-Yin , CHEN Xiao-Dong , XU Zhi , HUANG Jia-Xiang , XIE Hong-Bo, 3D Heart Motion Model Based on Coronary Artery Angiographic Image Sequence, Chinese Journal of Biomedical Engineering, 2005(2)
[33] W. Ma and J.-P. Kruth, NURBS Curve and Surface Fitting for Reverse Engineering, Int J Adv Manuf Technol, 1998, 14: 918-927
[34] L.A. Piegl, W. Tiller, Parametrization for surface fitting in reverse engineering, Computer-Aided Design, 2001, 33: 593-603
[35]施法中.计算机辅助几何设计与非均匀有理B样条.北京:北京航空航天大学出版社, 1994
[36] [美]奥佩(Opie, L.H.).心脏生理学:从细胞到循环.高天祥,高天礼译.北京:科学出版社, 2001
[37]席焕久.人体解剖学.北京:高等教育出版社, 2003.8
[38]李广生,王凡.心肌病理学.上海:上海科学技术出版社, 1985
[39]心脏的临床检查
[40] MeierG, Ziskin M, Santamore W , et al.Kinematics ofthe beating heart[J].IEEE Transactions Biomedical Engineering, 1980, 27: 319-329
[41] Potel MJ, MacKey SA, Rubin Jm, et al.Three-dimensional left ventricular wall motion is maIl coordinate systems for representing wall movement direction[J].Investigative Radiol, 1984, 19: 499-509
[42] Jinah Park, Dimitri Metaxas and Leon Axel, Analysis of left ventricular wall motion based on volumetric deformable models and MRI-SPAMM, Medical Image Analysis volume 1, number 1, Oxford University Press, 1996: 53-71
[43] Tad W. Taylor, Yoichi Goto, and Hiroyuki Suga, Cardiac muscle fiber force versus length determined by a cardiac muscle crossbridge model, Heart Vessels, 1992, 7: 200-205
[44] M. Sermesant, C. Forest, X. Pennec, H. Delingette and N. Ayache, Deformable biomechanical models: Application to 4D cardiac image analysis, Medical Image Analysis 7 (2003)475–488, Elesvier
[45] Wolfram-Hubertus Zimmermann *, Michael Didie′, Stephan Do¨ker, Ivan Melnychenko, Hiroshi Naito, Christina Rogge, Malte Tiburcy, Thomas Eschenhagen, Heart muscle engineering: An update on cardiac muscle replacement therapy, Cardiovascular Research 71 (2006)419– 429, Elsevier
[46] J. Sainte-Marie a, b, D. Chapelle a, *, R. Cimrman c, M. Sorine, Modeling and estimation of the cardiac electromechanical activity, Computers and Structures 84 (2006)1743–1759, Elsevier
[47] K. B. Campbell, Y. Wu, A. M. Simpson, R. D. Kirkpatrick, S. G. Shroff, H. L. Granzier and B. K. Slinker, Dynamic myocardial contractile parameters from left ventricular pressure-volume measurements, Am J Physiol Heart Circ Physiol 289: 114-130, 2005
[48] Xenophon Papademetris*, Albert J. Sinusas, Donald P. Dione, R. Todd Constable, and James S. Duncan, Estimation of 3-D Left Ventricular Deformation From Medical Images Using Biomechanical Models, IEEE Transactions On Medical Imaging, 2002. 7, 21(7)
[49] Chang Wen Chen, Member, IEEE, Thomas S. Huang, Fellow, IEEE. and Matthew Arrott, Modeling, Analysis, and Visualization of Left Ventricle Shape and Motion by Hierarchical Decomposition, IEEE Transactions On Pattern Analysis and Machine Intelligence, 1994. 4, 16(4)
[50]张泽宝.医学影像物理学,人民卫生出版社, 2000
[51] Ingal V N. Phase Radiography. A new technique of X ray imaging[OL].2000, http: //www.xraysite.com/knowbase/phasradiology-html
[52] J. C. Cauvin, J. Y. Boire, M. Zanca, J. M. Bonny, J. Maublant, and A. Veyre,“3D modeling in myocardial 201TL SPECT,”Comput. Med. Imag. Graph., 1993,17(4-5): 345-350
[53] J. Park, D. N. Metaxas, A. A. Young, and L. Axel,“Deformable models with parameter functions for cardiac motion analysis from tagged MRI data,”IEEE Trans. Med. Imag.1996.6, 15: 278-289
[54] L. H. Staib and J. S. Duncan,“Model-based deformable surface finding for medical images,”IEEE Trans. Med. Imag. 1996, 15: 720-731
[55] P. Shi, A. J. Sinusas, R. T. Constable, E. Ritman, and J. S. Duncan,“Point-tracked quantitative analysis of left ventricular surface motion from 3D image sequences: Algorithms and validation,”IEEE Trans. Med. Imag, 2000. 1, 19: 36-50
[56] D. F. Watson,“Computing the n-dimensional Delaunay tessellation with application to Voronoi polytopes,”Comput. J., 1981,24(2): 167-172
[57] C.W. Chen, T. S. Huang, and M. Arrott,“Modeling, analysis, and visualization of left ventricle shape, and motion by hierarchical decomposition,”IEEE Trans. Pattern Anal. Machine Intell., Apr. 1994, 16: 342–356
[58] E. Bardinet, L. D. Cohen, and N. Ayache,“A parametric deformable model to fit unstructured 3D data,”Comput. Vis. Image Underst., July 199871(1): 39–54
[59] T. Gustavsson, R. Pascher, and K. Caidahl,“Model based dynamic 3D reconstruction and display of the left ventricle from 2D cross-sectional echocardiograms,”Comput. Med. Imag. Graph., July 1993, 17(4–5): 273–278
[60] Byong Hwan Son, Byeong il Lee, Heung Kook Choi,“Cardiac Modeling Using the Parameterized Super-Quadric and the Contractility”, Visualization, Image-Guided Procedures, and Display, Robert L. Galloway, Jr., Editor, Proceedings of SPIE Vol. 5029 (2003).
[61] Nicholas J. Tustison and Amir A. Amini*,“Biventricular Myocardial Strains via Nonrigid Registration of AnFigatomical NURBS Models”, IEEE TRANSACTIONS ON MEDICAL IMAGING, JANUARY 2006, 25(1)
[62] A. Pentland and B. Horowitz,“Recovery of nonrigid motion and structure,”IEEE Trans. Pattern Anal. Machine Intell., July 1991 13: 730–742
[63] D. Friboulet, I. E. Magnin, and D. Revel,“Assessment of a model for overall left ventricular three-dimensional motion from MRI data,”Int. J. Card. Imag., Sept. 1992, 8(3): 175–190
[2] Shantz M, Surface Definition for Branching Contour Defined Objects. Computer Graphics, 1981, 15(2)
[3]周辉,李涛,邢启江.欧宗瑛.数字曲线的线性逼近和分段识别.大连理工大学学报, 1997, 37(5): 576-580
[4] Keppel E., Approximating Complex Surfaces by Triangulation of Contour Lines, IBM J. Res. Dev, 1975, 19
[5] Fuchs H., Kedem Z., et al. Optimal Surface Reconstruction from planar Contours, CACM, 1977, 20
[6] Christiansen H.N., Sederberg T.W., Construction of Complex Contours Line Definition into Polygonal Element Mosaics, Computer Graphics, 1978, 12(3): 187-192
[7] Cook L.T., Dwyer S., et al, A Three Dimensional Display system for Diagnostic Imaging Applications, IEEE Computer Graphics and Apprication, 1983, 3(4)
[8] Ganapathy S., Dennely T.G., A New General Triangulation Method for Planar Contours, Computer Graphics, 1982, 16(3)
[9] Lin W C. A new surface interpolation technique for reconstruction3D objects from serial cross-sections[J], Computer Vision &Graph Image Process 1989, 48(1): 124~143
[10] Boissonnat J.D., Shape Reconstruction from planar cross Section. CVGIP, 1988, 44
[11] Herman G.T., Liu H.K., Three-Dimensional Display of Human Organs from Computed Tomograms, Computer Graphics Image Processing, 1979, 9
[12] Lorensen W.E., Cline H.E., Marching Cubes: A High Resolution 3D Surface Construction Algorithm, Computer Graphics,1987, 21(4) : 163-169
[13] Nielson G., Hamann B., The Asymptotic Decider: Resolving the Ambiguity in Marching Cube. Visualization, 1991, 91 : 83-91
[14] Wilhelms J., Von Gelder A., Topological Considerations in IsoSurface Generation,San Diego Workshop on Volume Visualization, 1990
[15] Wu K., Hesselink L., Computer Display of Reconstructed 3D Scalar over Data, Applied Optics, 1988, 27(2)
[16] Cline H., Lerensen W. Tow, Algorithms for the 3D Reconstruction of Tomograms, Medical Physics, 1988, 15(3)
[17] Miller J. V., Breen D. E., et al. Extracting Geometric Models through Constraint Minimization, Visualization, 1990, 90
[18] Miller J. V., Breen D. E., et al. Geometrically Deformed Models: A Method for Extracting closed Geometric Models from Volume Data, Computer Graphics, 1991, 25(3)
[19]管伟光.体视化技术及其应用.北京:电子工业出版社, 1998
[20]沈宗文.实用人体断层解剖学.上海医科大学出版社, 1997
[21] (美)布朗威.心脏病学——心血管内科学教科书.人民卫生出版社, 2000
[22] The Visible Human Project, http : //www .nlm.nih.gov/research/visible/visible human.htm
[23] M. Sonka, M. D. Winniford, S. M. Collins. Robust simultaneous detection of coronary borders in complex images. IEEE Trans. Med. Imaging, 1995, 14(1): 151-161
[24] Kitware, Inc. The VTK user’s guide, http: //www.vtk.org
[25] Carole Blanc and Christophe Schlick, University of Bordeaux, Accurate parametrization of conics by NURBS, IEEE Transactions on Computer Graphics and Applications, 1996. 11, 16(6): 64 - 71
[26] Jiang Dan . Wang Lancheng, An algorithm of NURBS surface fitting for reverse engineering, Springer-Verlag London Limited, 2006
[27] Nicholas J. Tustison and Amir A. Amini*, Senior Member, IEEE, Biventricular myocardial strains via nonrigid registration of AnFigatomical NURBS models, IEEE Transactions On Medical Imaging, 2006, 25(1)
[28] M. Pourazady and X. Xu, Direct manipulations of B-spline and NURBS curves, Advances in Engineering Software 31 Elsevier, 2000: 107-118
[29] M. Pourazady and X. Xu, Direct manipulations of NURBS surfaces subjected to geometric constraints, Computers & Graphics 30 (2006)598–609, Elsevier
[30] Les Piegl, On NURBS: A Survey, Jan 01, IEEE Computer Graphics and Applications, 1991, 11(1): 55
[31] Kathi Hogshead Davis and Peter H. Aiken, Data Reverse Engineering: A Historical survey, Reverse Engineering, 2000. Proceedings. Seventh Working Conference on , 2000, 11(23-25): 70– 78
[32] SUN Zheng , YU Dao-Yin , CHEN Xiao-Dong , XU Zhi , HUANG Jia-Xiang , XIE Hong-Bo, 3D Heart Motion Model Based on Coronary Artery Angiographic Image Sequence, Chinese Journal of Biomedical Engineering, 2005(2)
[33] W. Ma and J.-P. Kruth, NURBS Curve and Surface Fitting for Reverse Engineering, Int J Adv Manuf Technol, 1998, 14: 918-927
[34] L.A. Piegl, W. Tiller, Parametrization for surface fitting in reverse engineering, Computer-Aided Design, 2001, 33: 593-603
[35]施法中.计算机辅助几何设计与非均匀有理B样条.北京:北京航空航天大学出版社, 1994
[36] [美]奥佩(Opie, L.H.).心脏生理学:从细胞到循环.高天祥,高天礼译.北京:科学出版社, 2001
[37]席焕久.人体解剖学.北京:高等教育出版社, 2003.8
[38]李广生,王凡.心肌病理学.上海:上海科学技术出版社, 1985
[39]心脏的临床检查
[40] MeierG, Ziskin M, Santamore W , et al.Kinematics ofthe beating heart[J].IEEE Transactions Biomedical Engineering, 1980, 27: 319-329
[41] Potel MJ, MacKey SA, Rubin Jm, et al.Three-dimensional left ventricular wall motion is maIl coordinate systems for representing wall movement direction[J].Investigative Radiol, 1984, 19: 499-509
[42] Jinah Park, Dimitri Metaxas and Leon Axel, Analysis of left ventricular wall motion based on volumetric deformable models and MRI-SPAMM, Medical Image Analysis volume 1, number 1, Oxford University Press, 1996: 53-71
[43] Tad W. Taylor, Yoichi Goto, and Hiroyuki Suga, Cardiac muscle fiber force versus length determined by a cardiac muscle crossbridge model, Heart Vessels, 1992, 7: 200-205
[44] M. Sermesant, C. Forest, X. Pennec, H. Delingette and N. Ayache, Deformable biomechanical models: Application to 4D cardiac image analysis, Medical Image Analysis 7 (2003)475–488, Elesvier
[45] Wolfram-Hubertus Zimmermann *, Michael Didie′, Stephan Do¨ker, Ivan Melnychenko, Hiroshi Naito, Christina Rogge, Malte Tiburcy, Thomas Eschenhagen, Heart muscle engineering: An update on cardiac muscle replacement therapy, Cardiovascular Research 71 (2006)419– 429, Elsevier
[46] J. Sainte-Marie a, b, D. Chapelle a, *, R. Cimrman c, M. Sorine, Modeling and estimation of the cardiac electromechanical activity, Computers and Structures 84 (2006)1743–1759, Elsevier
[47] K. B. Campbell, Y. Wu, A. M. Simpson, R. D. Kirkpatrick, S. G. Shroff, H. L. Granzier and B. K. Slinker, Dynamic myocardial contractile parameters from left ventricular pressure-volume measurements, Am J Physiol Heart Circ Physiol 289: 114-130, 2005
[48] Xenophon Papademetris*, Albert J. Sinusas, Donald P. Dione, R. Todd Constable, and James S. Duncan, Estimation of 3-D Left Ventricular Deformation From Medical Images Using Biomechanical Models, IEEE Transactions On Medical Imaging, 2002. 7, 21(7)
[49] Chang Wen Chen, Member, IEEE, Thomas S. Huang, Fellow, IEEE. and Matthew Arrott, Modeling, Analysis, and Visualization of Left Ventricle Shape and Motion by Hierarchical Decomposition, IEEE Transactions On Pattern Analysis and Machine Intelligence, 1994. 4, 16(4)
[50]张泽宝.医学影像物理学,人民卫生出版社, 2000
[51] Ingal V N. Phase Radiography. A new technique of X ray imaging[OL].2000, http: //www.xraysite.com/knowbase/phasradiology-html
[52] J. C. Cauvin, J. Y. Boire, M. Zanca, J. M. Bonny, J. Maublant, and A. Veyre,“3D modeling in myocardial 201TL SPECT,”Comput. Med. Imag. Graph., 1993,17(4-5): 345-350
[53] J. Park, D. N. Metaxas, A. A. Young, and L. Axel,“Deformable models with parameter functions for cardiac motion analysis from tagged MRI data,”IEEE Trans. Med. Imag.1996.6, 15: 278-289
[54] L. H. Staib and J. S. Duncan,“Model-based deformable surface finding for medical images,”IEEE Trans. Med. Imag. 1996, 15: 720-731
[55] P. Shi, A. J. Sinusas, R. T. Constable, E. Ritman, and J. S. Duncan,“Point-tracked quantitative analysis of left ventricular surface motion from 3D image sequences: Algorithms and validation,”IEEE Trans. Med. Imag, 2000. 1, 19: 36-50
[56] D. F. Watson,“Computing the n-dimensional Delaunay tessellation with application to Voronoi polytopes,”Comput. J., 1981,24(2): 167-172
[57] C.W. Chen, T. S. Huang, and M. Arrott,“Modeling, analysis, and visualization of left ventricle shape, and motion by hierarchical decomposition,”IEEE Trans. Pattern Anal. Machine Intell., Apr. 1994, 16: 342–356
[58] E. Bardinet, L. D. Cohen, and N. Ayache,“A parametric deformable model to fit unstructured 3D data,”Comput. Vis. Image Underst., July 199871(1): 39–54
[59] T. Gustavsson, R. Pascher, and K. Caidahl,“Model based dynamic 3D reconstruction and display of the left ventricle from 2D cross-sectional echocardiograms,”Comput. Med. Imag. Graph., July 1993, 17(4–5): 273–278
[60] Byong Hwan Son, Byeong il Lee, Heung Kook Choi,“Cardiac Modeling Using the Parameterized Super-Quadric and the Contractility”, Visualization, Image-Guided Procedures, and Display, Robert L. Galloway, Jr., Editor, Proceedings of SPIE Vol. 5029 (2003).
[61] Nicholas J. Tustison and Amir A. Amini*,“Biventricular Myocardial Strains via Nonrigid Registration of AnFigatomical NURBS Models”, IEEE TRANSACTIONS ON MEDICAL IMAGING, JANUARY 2006, 25(1)
[62] A. Pentland and B. Horowitz,“Recovery of nonrigid motion and structure,”IEEE Trans. Pattern Anal. Machine Intell., July 1991 13: 730–742
[63] D. Friboulet, I. E. Magnin, and D. Revel,“Assessment of a model for overall left ventricular three-dimensional motion from MRI data,”Int. J. Card. Imag., Sept. 1992, 8(3): 175–190