荧光分子断层成像中的三维网格优化
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摘要
光学分子成像是医学成像领域的一个新兴分支,它可以在细胞和分子水平上检测人体新陈代谢和功能方面的疾病。因为红外光线或可见光可以穿透人体若干厘米并能够在人体表层被检测,我们在外部放置光源照射实验体,光线穿透人体到达荧光染剂位置(荧光染剂事先被注射到人体内),荧光染剂被激发,发出另一个波长的光波并在人体表面被检测到,荧光断层重建算法根据体外检测到的光波信息便能够重建出体内荧光染料的位置。为了能够精确的计算出荧光染剂的位置,数值分析方法(比如有限元)常用来求解描述光在组织内传播的偏微分方程。本文的目的就是提供一个基于荧光断层重建算法特点的三维网格优化算法,这个算法得到的网格是一个荧光断层重建算法的有效网格。算法结合了网格简化和网格细化两个过程,并根据体内器官组织的光照属性提出了相应的网格代价函数。算法结果证明了新网格较原网格(Digimouse)在质量上和密度上都有了非常大的提高,并能够应用在荧光分子断层重建算法中。
Optical Molecular Imaging technique is a novel branch of medical imaging that has the potential to diagnose the metabolic and functional state of tissue at the cellular and molecular level. Light in the visible or near infrared spectrum penetrates several centimeters inside the body and can be measured on the surface. External light illuminating a body penetrates the tissues up to injected fluorescent molecules which absorb and reemit light at a different wavelength. Detection of the emitted light on the surface of the body can be coupled to a Fluorescence Tomography Reconstruction (FTR) algorithm to recover the location of fluorescent concentration inside the body. In order to precisely localize the fluorescent sources, numerical techniques (e.g. Finite Element Method) are used to solve the mathematical formulation which describes photon propagation in tissues. Specifically, we have developed a remeshing module to generate valid meshes for FEM in the application of FTR, this algorithm combines tetrahedron collapse operation with refinement operation,driven by cost functions specific to Fluorescence Tomography Reconstruction. Results show an increase of mesh quality and density on the final mesh which becomes a valid mesh for Fluorescence Tomography Reconstruction.
Optical Molecular Imaging technique is a novel branch of medical imaging that has the potential to diagnose the metabolic and functional state of tissue at the cellular and molecular level. Light in the visible or near infrared spectrum penetrates several centimeters inside the body and can be measured on the surface. External light illuminating a body penetrates the tissues up to injected fluorescent molecules which absorb and reemit light at a different wavelength. Detection of the emitted light on the surface of the body can be coupled to a Fluorescence Tomography Reconstruction (FTR) algorithm to recover the location of fluorescent concentration inside the body. In order to precisely localize the fluorescent sources, numerical techniques (e.g. Finite Element Method) are used to solve the mathematical formulation which describes photon propagation in tissues. Specifically, we have developed a remeshing module to generate valid meshes for FEM in the application of FTR, this algorithm combines tetrahedron collapse operation with refinement operation,driven by cost functions specific to Fluorescence Tomography Reconstruction. Results show an increase of mesh quality and density on the final mesh which becomes a valid mesh for Fluorescence Tomography Reconstruction.
引文
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[30] Rossignac J,Borrel P.Multi-Resolution 3D Approximation for Rendering Complex Scenes. Proceedings of the 2nd conference Modeling in Computer Graphics:Methods and Application. 1993
[31] Kalvin, A.D, Taylor,R.H. Surperfaces:polygonal mesh simplification with bouned error. IEEE Computer Graphics and Applications.1996
[32] K.J.Renze and J.H Oliver. Generalized unstructured decimation. IEEE Computer graphics,1996
[33] Natarajan V.,Edelsbrunner H. Simplification of three-dimensional density maps. IEEE Transactions on Visualization and Computer Graphics.2004
[34] C.L Lawson. Software for C1 surface interporlation Mathematical Software III.1977
[35] J. R. Shewchuk,Talk slides: Constrained Delaunay Tetrahedralizations, Bistellar Flips, and Provably Good Boundary Recovery.
[36] J.R. Shewchuk, Constrained Delaunay Tetrahedralizations and Provably Good Boundary Recovery. Eleventh International Meshing roundtable(Ithaca,New York). 2002.
[37]古成中,吴新跃.有限元网格划分及发展趋势.计算机科学与探索. 2008.
[38]刘力,吴晓锋.正电子断层扫描仪与PET图像重建概述. CT理论与应用研究. 2003
[39]董方敏,张蕊,刘勇,周学君.网格模型简化算法综述.三峡大学学报. 2007.
[40] MC Rivara. Mesh refinement processes based on the generalized bisection of simplices.SIAM.Numer.Anal.2.1984
[2] P. Banerjee and R. Butterfield, Boundary Element Methods in Engineer-ing Science. McGraw-Hill, 1981.
[3] C. Brebbia, J. Telles, and L. Wrobel, Boundary element techniques: Theory and applications in engineering. Springer-Verlag, 1984.
[4] J. Ripoll and V. Ntziachristos,“Iterative boundary method for diffuse optical tomography,”J.Opt.Soc.Am. A, vol. 20, no. 1103-10, 2003.
[5] O. Zienkiewicz, The Finite Element Method, 3rd ed. McGraw-Hill, 1977.
[6] R. Ackroyd, Finite element methods for particle transport:Applications to reactor and radiation physics. Taunton,United Kingdom: Research Studies Press, 1997.
[7] M. Schweiger and S. Arridge,“The finite-element method for the propagation of light in scattering media:frequency domain case,”Med Phys, vol. 24, pp. 895–902, March 1997.
[8] A. Joshi, W. Bangerth, and E. M.Sevick-Muraca,“Adaptive finite element based tomography for fluorescence optical imaging in tissue,”Optics Express, vol. 12, pp. 5402–5417, 2004.
[9] B. Dogdas, D. Stout, A.Chatziioannou, and R.M.leahy,“Digimouse a 3d whole body mouse atlas from ct and cryosection data,”Phys Med Biol, vol. 3, no. 52, pp. 577–587, Feb 2007.
[10] D. Stout, P. Silverman, R. M. Leahy, X. Lewis, S.Gambhir, and A. Chatziiaonnou,“Creating a whole body digital mouse atlas with pet,ct and cryosection images,”Molecular Imaging and Biology, vol. 4, no. 4, p. 27, 2002.
[11] G. Alexandrakis, F. Rannou, and A. F. Chatziioannou,“Tomographic bioluminescence imaging by use of a combined optical-pet (opet) system: a computer simulation feasibility study,”Phys. Med.Biol, 2005.
[12] M. Kraus and T. Ertl,“Simplification of nonconvex tetrahedral meshes,”Visualization and Interactive Systems Group,Germany, 2000.
[13] O. G. Staadt and M. H.Gross,“Progressive tetrahedralizations,”IEEE, vol. 555, pp. 397–402, Oct 1998.
[14] P. Chopra and J. Meyer,“Tetfusion: An algorithm for rapid tetrahedral mesh simplification,”Proceedings of IEEE Visualization 2002, pp. 133– 140, 2002.
[15] B. Cutler, J. Dorsey, and L. McMillan,“Simplification and improvement of tetrahedral models for simulation,”Eurographics Symposium on Geometry Processing, pp. 93–102, 2004.
[16] P.Cignoni, D. Constanza, C. Montani, C.Rocchini, and R. Scopigno,“Simplification of tetrahedral meshes with accurate error evaluation,”Proceedings of the conference on visualization 2000, pp. 85–92, Oct. 2000.
[17] R. Klein, G. Liebich, and W. Straber,“Mesh reduction with error control,”Visualization 96. ACM, pp. 311–318, Oct. 1996.
[18] J. Bey,“Tetrahedral grid refinement,”Computing, vol. 55, no. 4, pp. 355–378, 1995.
[19] J. R. Shewchuk,“Tetrahedral mesh generation by delaunay refinement,”Proceedings of the fourteenth annual symposium on Computational geometry, pp. 86–95, June 1998.
[20] E. B?nsch. Local mesh refinement in 2 and 3 dimensions. Impact of Comp.in Sci and Engrg.1991
[21] Issac J.Trotts, Bernd Hamann, Kenneth I. Joy, David F. Wiley. Simplification of Tetrahedral Meshes. Proc.IEEE Visualization 98.
[22] Issac J.Trotts, Bernd Hamann, Kenneth I. Joy, David F. Wiley. Simplification of Tetrahedral Meshes with error bounds. Proc.IEEE Visualization 99
[23] Alexandrakis G. et al. Tomographic bioluminescence imaging by use of a combined optical-PET (OPET) system: a computer simulation feasibility study Phys Med Biol. 50(17) 4225–4241 (2005).
[24] Jim Ruppert. A Delaunay Refinement Algorithm for Quality 2-Dimensional Mesh Generation. Journal of Algorithms 18(3):548-585, May 1995
[25] J. R. Shewchuk. Delaunay Refinement Mesh Generation, Ph.D. thesis, Technical Report CMU-CS-97-137, School of Computer Science, Carnegie Mellon University, Pittsburgh, Pennsylvania, 18 May 1997.
[26] Schroeder,william,Zarge J,et al. Decimation of Triangle Meshes. Computer Graphics,1992
[27] Turk,G Re-tiling polygonal surfaces. Computer Graphics(SIGGRAPH’92 Proceeding),1992
[28] Hugues Hoppe. Progressive meshes. Computer Graphics(SIGGRAPH’96 Proceeding),1996
[29] Garland,M,Heckbert, P.S. Surface simplification using quadric error metric. Proceedings of the SIGGRAPH’97
[30] Rossignac J,Borrel P.Multi-Resolution 3D Approximation for Rendering Complex Scenes. Proceedings of the 2nd conference Modeling in Computer Graphics:Methods and Application. 1993
[31] Kalvin, A.D, Taylor,R.H. Surperfaces:polygonal mesh simplification with bouned error. IEEE Computer Graphics and Applications.1996
[32] K.J.Renze and J.H Oliver. Generalized unstructured decimation. IEEE Computer graphics,1996
[33] Natarajan V.,Edelsbrunner H. Simplification of three-dimensional density maps. IEEE Transactions on Visualization and Computer Graphics.2004
[34] C.L Lawson. Software for C1 surface interporlation Mathematical Software III.1977
[35] J. R. Shewchuk,Talk slides: Constrained Delaunay Tetrahedralizations, Bistellar Flips, and Provably Good Boundary Recovery.
[36] J.R. Shewchuk, Constrained Delaunay Tetrahedralizations and Provably Good Boundary Recovery. Eleventh International Meshing roundtable(Ithaca,New York). 2002.
[37]古成中,吴新跃.有限元网格划分及发展趋势.计算机科学与探索. 2008.
[38]刘力,吴晓锋.正电子断层扫描仪与PET图像重建概述. CT理论与应用研究. 2003
[39]董方敏,张蕊,刘勇,周学君.网格模型简化算法综述.三峡大学学报. 2007.
[40] MC Rivara. Mesh refinement processes based on the generalized bisection of simplices.SIAM.Numer.Anal.2.1984