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High-Quality Model Generation for Finite Element Simulation of Tissue Deformation

  • Orcun Goksel
  • Septimiu E. Salcudean
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5762)

Abstract

In finite element simulation, size, shape, and placement of the elements in a model are significant factors that affect the interpolation and numerical errors of a solution. In medical simulations, such models are desired to have higher accuracy near features such as anatomical boundaries (surfaces) and they are often required to have element faces lying along these surfaces. Conventional modelling schemes consist of a segmentation step delineating the anatomy followed by a meshing step generating elements conforming to this segmentation. In this paper, a one-step energy-based model generation technique is proposed. An objective function is minimized when each element of a mesh covers similar image intensities while, at the same time, having desirable FEM characteristics. Such a mesh becomes essential for accurate models for deformation simulation, especially when the image intensities represent a mechanical feature of the tissue such as the elastic modulus. The use of the proposed mesh optimization is demonstrated on synthetic phantoms, 2D/3D brain MR images, and prostate ultrasound-elastography data.

References

  1. 1.
    Alliez, P., Cohen-Steiner, D., Yvinec, M., Desbrun, M.: Variational tetrahedral meshing. ACM Trans. on Graphics (procs. of SIGGRAPH) 24(3), 617–625 (2005)CrossRefGoogle Scholar
  2. 2.
    Shewchuk, J.R.: What is a good linear element? interpolation, conditioning, and quality measures. In: Eleventh International Meshing Roundtable (2002)Google Scholar
  3. 3.
    Chen, L., Xu, J.: Optimal Delaunay triangulation. Journal of Computational Mathematics 22(2), 299–308 (2004)zbMATHMathSciNetGoogle Scholar
  4. 4.
    Zienkiewicz, O.C., Taylor, R.L.: The Finite Element Method. Butterworth-Heinemann (2000)Google Scholar
  5. 5.
    Greenleaf, J.F., Fatemi, M., Insana, M.: Selected Methods for Imaging Elastic Properties of Biological Tissues. Annual Review of Biomed. Eng. 5, 57–78 (2000)CrossRefGoogle Scholar
  6. 6.
    Ophir, J., Céspedes, I., Ponnekanti, H., Yazdi, Y., Li, X.: Elastography: a method for imaging the elasticity of biological tissues. Ultrasonic Img. 13(2), 111–134 (1991)CrossRefGoogle Scholar
  7. 7.
    Chan, T.F., Vese, L.A.: Active contours without edges. IEEE Trans. Image Processing 10(2), 266–277 (2001)zbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Orcun Goksel
    • 1
  • Septimiu E. Salcudean
    • 1
  1. 1.Department of Electrical and Computer EngineeringUniversity of British ColumbiaVancouverCanada

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