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Finite Element Modeling for Fluorescence Molecular Tomography

Received: 25 October 2021    Accepted: 23 November 2021    Published: 24 November 2021
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Abstract

Non-contact Fluorescence Molecular Tomography (FMT) and Bioluminescence Tomography (BLT) has attracted more and more attention due to its unique advantages. For real experiments, how to obtain the 3D model of an object and the surface fluorescence distribution is one of the main obstacles. In this paper, an effective method to obtain the Finite Element Model is presented. We discuss the geometric and mathematical principles in detail. We prove that the FEM model generated by the method has enough quality for reconstruction. We demonstrate the quality of the model through a series of examples. This method can realize the whole process only by using a single-mode optical system. Firstly, a series of white light and fluorescence images are collected along the object in white light flat field illumination mode and excitation fluorescence mode respectively. The white light illumination images are used to reconstruct the 3D model contour of the object. After voxelization with appropriate resolution, we use the Delaunay algorithm to divide the model into tetrahedral finite elements. For the fluorescence image, we proposed a method based on vertex normal vector to realize the photon flux density mapping from 2D fluorescence image to 3D Finite Element Method (FEM) mesh nodes of the surface. The experimental results prove the accuracy of the model and the mapping, and the FEM obtained can meet the needs of FMT/ BLT reconstruction.

Published in American Journal of Biomedical and Life Sciences (Volume 9, Issue 6)
DOI 10.11648/j.ajbls.20210906.17
Page(s) 307-314
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

FMT, BLT, 3D Modeling, FEM

References
[1] Vls K K, Kjelgaard-Hansen M, Ley C D, et al. In vivo fluorescence molecular tomography of induced haemarthrosis in haemophilic mice: link between bleeding characteristics and development of bone pathology. BMC Musculoskeletal Disorders, 21: 1 (2020).
[2] Meng H, Gao Y, Yang X, et al. K-nearest Neighbor Based Locally Connected Network for Fast Morphological Reconstruction in Fluorescence Molecular Tomography. IEEE Transactions on Medical Imaging, 99: 1-1 (2020).
[3] V. Ntziachristos, J. Ripoll, L. V. Wang, and R. Weissleder, Looking and listening to light: the evolution of whole-body photonic imaging, Nat. Biotechnol. 23, 313-320 (2005).
[4] B. W. Rice, M. D. Cable, and M. B. Nelson, In vivo imaging of light-emitting probes, J. Biomed. Opt. 6, 432-440 (2001).
[5] Strangman, Gary, D. A. Boas, and J. P. Sutton, Non-invasive neuroimaging using near-infrared light, Biological Psychiatry 52, 679-693 (2002).
[6] Dianwen Zhu, Yue Zhao, Reheman Baikejiang, Zhen Yuan, and Changqing Li. Comparison of regularization methods in fluorescence molecular tomography. Photonics, 1 (2): 95–109 (2014).
[7] L. Yin, K. Wang, T. Tong, Q. Wang, J Tian, Adaptive Grouping Block Sparse Bayesian Learning Method for Accurate and Robust Reconstruction in Bioluminescence Tomography. IEEE Transactions on Biomedical Engineering, 99, 1-1 (2021).
[8] Wang G, Li Y, Jiang M. Uniqueness theorems in bioluminescence tomography. Medical Physics. 31 (8), 2289-2299 (2004).
[9] Feng JC, Jia KB, Yan GR, et al. An optimal permissible source region strategy for multispectral bioluminescence tomography. Optics Express. Sep 29, 16 (20), 15640-15654 (2008).
[10] Zhang Z. A Flexible New Technique for Camera Calibration. IEEE Transactions on Pattern Analysis and Machine Intelligence, 22 (11), 1330-1334 (2000).
[11] H Wang, Bian C, Kong L, et al. A Novel Adaptive Parameter Search Elastic Net Method for Fluorescent Molecular Tomography. IEEE Transactions on Medical Imaging, p. 99 (2021).
[12] Ntziachristos, Vasilis, et al. "Fluorescence molecular tomography resolves protease activity in vivo." Nature Medicine 8.7, 757-761 (2002).
[13] Cong A X, Wang G. A finite-element-based reconstruction method for 3D fluorescence tomography. Optics Express, 13 (24): 9847-9857 (2005).
[14] Chen D, Liang J, Yao L, et al. A Sparsity-Constrained Preconditioned Kaczmarz Reconstruction Method for Fluorescence Molecular Tomography [J]. BioMed Research International, 2016: 1-15 (2016).
[15] A. Ale, V. Ermolayev, E. Herzog, C. Cohrs, M. H. de Angelis, and V. Ntziachristos, FMT-XCT: in vivo animal studies with hybrid fluorescence molecular tomography-X-ray computed tomography, Nat Methods 9, 615-U140 (2012).
[16] M. Saxena, P. M. Finnigan, C. M. Graichen, A. F. Hathaway, and V. N. Parthasarathy. Octree-based automatic mesh generation for nonmanifold domains. Engineering with Computers. 11, 1–14 (1995).
[17] M. S. Shephard and M. K. Georges. Three-dimensional mesh generation by finite octree technique. International Journal for Numerical Methods in Engineering, 32, 709–749 (1991).
[18] K. Tchon, K. Mohammed, G. Francois, C. Ricardo, Constructing anisotropic geometric metrics using octrees and skeletons, in: Proceedings of the 12th International Meshing Roundtable. p. 293–304 (2003).
[19] P. Frey, L. Marechal, Fast adaptive quadtree mesh generation, in: Proceedings of the Seventh International Meshing Roundtable. p. 211–222 (1998).
[20] Sevick EM, Lakowicz JR, Szmacinski H, Nowaczyk K, Johnson ML. Frequency domainimaging of absorbers obscured by scattering. Journal of photochemistry and photobiology. B, Biology. 16, 169-185 (1992).
[21] Martin WN. Aggarwal J K. Volumetric descriptions of objects from multiple views. IEEE Trans onPattern Analysis and Machine Intelligence, (1983).
[22] Qianqian Fang and David Boas, "Tetrahedral mesh generation from volumetric binary and gray-scale images," Proceedings of IEEE International Symposium on Biomedical Imaging. p. 1142-1145 (2009).
[23] R. Lohner. Progress in grid generation via the advancing front technique. Engineering with Computers. 12, 186–210 (1996).
[24] S. H. Lo. Volume discretization into tetrahedra-I. Verification and orientation of boundary surfaces. Computers and Structures. 39 (5), 493–50 0 (1991).
[25] R. Lohner, P. Parikh, and C. Gumbert. Interactive generation of unstructured grid for three dimensional problems. In Numerical Grid Generation in Computational Fluid Mechanics. (Pineridge Press, 1988), p. 687–697.
[26] C. Lee, Automatic metric advancing front triangulation over curved surfaces, Eng. Comput. 17, 48–74 (2000).
[27] R. Lohner, C. Juan, Generation of non-isotropic unstructured grids via directional enrichment, Internat. J. Numer. Methods Engrg. 49 (1), 219–232 (2000).
[28] S. Lo, Volume discretization into tetrahedra-I, Verification and orientation of boundary surfaces, Comput. Structures. 36, 493–500 (1991).
[29] R. Lohner, Progress in grid generation via the advancing front technique, Engrg. Comput. 12, 186–199 (1996).
[30] D. Marcum, N. Weatherill, Unstructured grid generation using iterative point insertion and local reconnection, AIAA J. 33 (9), 1625 (1995).
[31] K. Nakahashi, D. Sharov, Direct surface triangulation using the advancing front method, AIAA, p. 95-1686-CP (1995).
[32] Q. Du, D. Wang, Boundary recovery for three dimensional conforming Delaunay triangulation, Comput. Methods Appl. Mech. Engrg. 193, 2547-2563 (2004).
[33] Q. Du, D. Wang, Tetrahedral mesh generation and optimization based on centroidal Voronoi tessellations, Internat. J. Numer. Methods Engrg. 56, 1355–1373 (2003).
[34] X. Li, Sliver-free three dimensional Delaunay mesh generation, Ph.D thesis, (2000), UIUC.
[35] N. Weatherill, O. Hassan, Efficient three dimensional Delaunay triangulation with automatic point creation and imposed boundary constraints, Internat. J. Numer. Methods Engrg. 37, 2005-2039 (1994).
[36] Q. Du, D. Wang, Constrained boundary recovery for three dimensional Delaunay triangulation, Internat. J. Numer. Methods Engrg. 61, 1471–1500 (2004).
[37] P. George, Gamanic3d, adaptive anisotropic tetrahedral mesh generator, Technical Report, (2002), INRIA.
[38] Hang Si, TetGen, a Delaunay-based quality tetrahedral mesh generator, ACM Transactions on Mathematical Software. 41, 36 (2015).
Cite This Article
  • APA Style

    Zhaolu Zuo, Shaobin Dou, Deyi Kong, Kai Wu. (2021). Finite Element Modeling for Fluorescence Molecular Tomography. American Journal of Biomedical and Life Sciences, 9(6), 307-314. https://doi.org/10.11648/j.ajbls.20210906.17

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    ACS Style

    Zhaolu Zuo; Shaobin Dou; Deyi Kong; Kai Wu. Finite Element Modeling for Fluorescence Molecular Tomography. Am. J. Biomed. Life Sci. 2021, 9(6), 307-314. doi: 10.11648/j.ajbls.20210906.17

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    AMA Style

    Zhaolu Zuo, Shaobin Dou, Deyi Kong, Kai Wu. Finite Element Modeling for Fluorescence Molecular Tomography. Am J Biomed Life Sci. 2021;9(6):307-314. doi: 10.11648/j.ajbls.20210906.17

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  • @article{10.11648/j.ajbls.20210906.17,
      author = {Zhaolu Zuo and Shaobin Dou and Deyi Kong and Kai Wu},
      title = {Finite Element Modeling for Fluorescence Molecular Tomography},
      journal = {American Journal of Biomedical and Life Sciences},
      volume = {9},
      number = {6},
      pages = {307-314},
      doi = {10.11648/j.ajbls.20210906.17},
      url = {https://doi.org/10.11648/j.ajbls.20210906.17},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajbls.20210906.17},
      abstract = {Non-contact Fluorescence Molecular Tomography (FMT) and Bioluminescence Tomography (BLT) has attracted more and more attention due to its unique advantages. For real experiments, how to obtain the 3D model of an object and the surface fluorescence distribution is one of the main obstacles. In this paper, an effective method to obtain the Finite Element Model is presented. We discuss the geometric and mathematical principles in detail. We prove that the FEM model generated by the method has enough quality for reconstruction. We demonstrate the quality of the model through a series of examples. This method can realize the whole process only by using a single-mode optical system. Firstly, a series of white light and fluorescence images are collected along the object in white light flat field illumination mode and excitation fluorescence mode respectively. The white light illumination images are used to reconstruct the 3D model contour of the object. After voxelization with appropriate resolution, we use the Delaunay algorithm to divide the model into tetrahedral finite elements. For the fluorescence image, we proposed a method based on vertex normal vector to realize the photon flux density mapping from 2D fluorescence image to 3D Finite Element Method (FEM) mesh nodes of the surface. The experimental results prove the accuracy of the model and the mapping, and the FEM obtained can meet the needs of FMT/ BLT reconstruction.},
     year = {2021}
    }
    

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  • TY  - JOUR
    T1  - Finite Element Modeling for Fluorescence Molecular Tomography
    AU  - Zhaolu Zuo
    AU  - Shaobin Dou
    AU  - Deyi Kong
    AU  - Kai Wu
    Y1  - 2021/11/24
    PY  - 2021
    N1  - https://doi.org/10.11648/j.ajbls.20210906.17
    DO  - 10.11648/j.ajbls.20210906.17
    T2  - American Journal of Biomedical and Life Sciences
    JF  - American Journal of Biomedical and Life Sciences
    JO  - American Journal of Biomedical and Life Sciences
    SP  - 307
    EP  - 314
    PB  - Science Publishing Group
    SN  - 2330-880X
    UR  - https://doi.org/10.11648/j.ajbls.20210906.17
    AB  - Non-contact Fluorescence Molecular Tomography (FMT) and Bioluminescence Tomography (BLT) has attracted more and more attention due to its unique advantages. For real experiments, how to obtain the 3D model of an object and the surface fluorescence distribution is one of the main obstacles. In this paper, an effective method to obtain the Finite Element Model is presented. We discuss the geometric and mathematical principles in detail. We prove that the FEM model generated by the method has enough quality for reconstruction. We demonstrate the quality of the model through a series of examples. This method can realize the whole process only by using a single-mode optical system. Firstly, a series of white light and fluorescence images are collected along the object in white light flat field illumination mode and excitation fluorescence mode respectively. The white light illumination images are used to reconstruct the 3D model contour of the object. After voxelization with appropriate resolution, we use the Delaunay algorithm to divide the model into tetrahedral finite elements. For the fluorescence image, we proposed a method based on vertex normal vector to realize the photon flux density mapping from 2D fluorescence image to 3D Finite Element Method (FEM) mesh nodes of the surface. The experimental results prove the accuracy of the model and the mapping, and the FEM obtained can meet the needs of FMT/ BLT reconstruction.
    VL  - 9
    IS  - 6
    ER  - 

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Author Information
  • Hefei Institutes of Physical Science, Chinese Academy of Sciences, Hefei, China

  • Hefei Institutes of Physical Science, Chinese Academy of Sciences, Hefei, China

  • Hefei Institutes of Physical Science, Chinese Academy of Sciences, Hefei, China

  • Hefei Institutes of Physical Science, Chinese Academy of Sciences, Hefei, China

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