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Computation of a finite element-conformal tetrahedral mesh approximation for simulated soft tissue deformation using a deformable surface model

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Abstract

In this article, we present a new method for the generation of surface meshes of biological soft tissue. The method is based on the deformable surface model technique and is extended to histological data sets. It relies on an iterative adjustment towards polygonal segments describing the histological structures of the soft tissue. The generated surface meshes allow for the construction of volumetric meshes through a standard constrained Delaunay approach and, thus, for the application in finite element methods. The geometric properties of volumetric meshes have an immediate influence on the numerical conditioning and, therewith, on the stability of the finite element method and the convergence of iterative solvers. In this article, the influence of the surface meshes on the quality of the volumetric meshes is analysed in terms of the spectral condition number of the stiffness matrices, which are assembled within Newton’s method. The non-linear material behavior of biological soft tissue is modeled by the Mooney–Rivlin material law. The subject is motivated by the requirements of virtual surgery.

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Acknowledgements

The authors would like to thank Karl Meller, Philipp Geis, Katrin Wernstedt and Anja Wilde for processing the tissues as well as Christoph Ewerlin and Olaf Schulz for their assistance in implementing code. This work was kindly supported by the HOMFOR Forschungsförderung 2008, Homburg Saar, Germany.

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Authors and Affiliations

  1. Department of Computer Science VII, TU Dortmund University, Dortmund, Germany

    Frank Weichert, Lars Walczak & Heinrich Müller

  2. Department of Mathematics, Humboldt-Universität zu Berlin, Berlin, Germany

    Andreas Schröder

  3. Maxillofacial and Facial Plastic Surgery, Johann Wolfgang Goethe-University Medical Center, Frankfurt, Germany

    Constantin Landes

  4. Department of Oral Biology, Al Minia University Dental School, Al Minia, Egypt

    Ali Shamaa

  5. Department of Maxillofacial Surgery, University of Mansoura Dental School, Mansura, Egypt

    Said Kamel Awad

  6. Department of Pathology, University of Saarland, Homburg Campus, Homburg Saar, Germany

    Mathias Wagner

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  1. Frank Weichert
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  2. Andreas Schröder
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  3. Constantin Landes
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  4. Ali Shamaa
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  5. Said Kamel Awad
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  7. Heinrich Müller
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  8. Mathias Wagner
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Correspondence to Frank Weichert.

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Weichert, F., Schröder, A., Landes, C. et al. Computation of a finite element-conformal tetrahedral mesh approximation for simulated soft tissue deformation using a deformable surface model. Med Biol Eng Comput 48, 597–610 (2010). https://doi.org/10.1007/s11517-010-0607-0

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  • DOI: https://doi.org/10.1007/s11517-010-0607-0

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