An Immersed Boundary Method for Detail-Preserving Soft Tissue Simulation from Medical Images

  • Christoph J. Paulus
  • Roland Maier
  • Daniel Peterseim
  • Stéphane CotinEmail author
Conference paper


Simulating the deformation of the human anatomy is a central element of Medical Image Computing and Computer-Assisted Interventions. Such simulations play a key role in nonrigid registration, augmented reality, and several other applications. Although the Finite Element Method is widely used as a numerical approach in this area, it is often hindered by the need for an optimal meshing of the domain of interest. The derivation of meshes from imaging modalities such as CT or MRI can be cumbersome and time-consuming. In this paper, we use the Immersed Boundary Method (IBM) to bridge the gap between these imaging modalities and the fast simulation of soft tissue deformation on complex shapes represented by a surface mesh directly retrieved from binary images. A high-resolution surface, which can be obtained from binary images using a marching cubes approach, is embedded into a hexahedral simulation grid. The details of the surface mesh are properly taken into account in the hexahedral mesh by adapting the Mirtich integration method. In addition to not requiring a dedicated meshing approach, our method results in higher accuracy for less degrees of freedom when compared to other element types. Examples on brain deformation demonstrate the potential of our method.


Immersed Boundary Method (IBM) Hexahedral Mesh Surface Mesh Corotational Approach Compression Example 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



Daniel Peterseim was supported by DFG-SPP 1748 under the project Adaptive isogeometric modeling of discontinuities in complex-shaped heterogeneous solids.


  1. 1.
    Benzley SE, Perry E, Merkley K, Clark B, Sjaardama G (1995) A comparison of all hexagonal and all tetrahedral finite element meshes for elastic and elasto-plastic analysis. In: Proceedings, 4th international meshing roundtable, vol 17, pp 179–191Google Scholar
  2. 2.
    Burman E, Claus S, Hansbo P, Larson MG, Massing A (2015) Cutfem: discretizing geometry and partial differential equations. Int J Numer Methods Eng 104(7):472–501Google Scholar
  3. 3.
    Cotin S, Delingette H, Ayache N (1999) Real-time elastic deformations of soft tissues for surgery simulation. IEEE Trans Vis Comput Graph 5(1):62–73Google Scholar
  4. 4.
    Faure F, Duriez C, Delingette H, Allard J, Gilles B, Marchesseau S, Talbot H, Courtecuisse H, Bousquet G, Peterlik I et al (2012) Sofa: a multi-model framework for interactive physical simulation. In: Soft tissue biomechanical modeling for computer assisted surgery. Springer, pp 283–321Google Scholar
  5. 5.
    Geuzaine C, Remacle J-F (2009) GMSH: A 3-d finite element mesh generator with built-in pre-and post-processing facilities. Int J Numer Methods Eng 79(11): 1309–1331Google Scholar
  6. 6.
    Hackbusch W, Sauter SA (1997) Composite finite elements for the approximation of PDEs on domains with complicated micro-structures. Numer Math 75(4):447–472Google Scholar
  7. 7.
    Ji S, Ford JC, Greenwald RM, Beckwith JG, Paulsen KD, Flashman LA, McAllister TW (2011) Automated subject-specific, hexahedral mesh generation via image registration. Finite Elem Anal Des 47(10):1178–1185Google Scholar
  8. 8.
    Liseikin VD (2009) Grid generation methods. Springer, BerlinGoogle Scholar
  9. 9.
    Massing A, Larson MG, Logg A (2013) Efficient implementation of finite element methods on nonmatching and overlapping meshes in three dimensions. SIAM J Sci Comput 35(1): C23–C47Google Scholar
  10. 10.
    Miller K (1999) Constitutive model of brain tissue suitable for finite element analysis of surgical procedures. J Biomech 32(5):531–537Google Scholar
  11. 11.
    Mirtich B (1996) Fast and accurate computation of polyhedral mass properties. J Graph Tools 1(2):31–50Google Scholar
  12. 12.
    Nitsche J (1971) Über ein variationsprinzip zur lösung von dirichlet-problemen bei verwendung von teilräumen, die keinen randbedingungen unterworfen sind, vol 36. Springer, Berlin, pp 9–15Google Scholar
  13. 13.
    Owen SJ (1998) A survey of unstructured mesh generation technology. In: International Meshing Roundtable, pp 239–267Google Scholar
  14. 14.
    Parvizian J, Düster A, Rank E (2007) Finite cell method. Comput Mech 41(1):121–133MathSciNetCrossRefGoogle Scholar
  15. 15.
    Paulus CJ, Haouchine N, Kong S-H, Soares RV, Cazier D, Cotin S (2016) Handling topological changes during elastic registration: application to augmented reality in laparoscopic surgery. Int J Comput Assist Radiol Surg 12(3):461–470CrossRefGoogle Scholar
  16. 16.
    Peskin CS (1972) Flow patterns around heart valves: a numerical method. J Comput Phys 10(2):252–271MathSciNetCrossRefGoogle Scholar
  17. 17.
    Peskin CS (2002) The immersed boundary method. Acta Numer 11:479–517MathSciNetCrossRefGoogle Scholar
  18. 18.
    Peterseim D, Sauter SA (2008) The composite mini element - coarse mesh computation of stokes flows on complicated domains. SIAM J Numer Anal 46(6):3181–3206MathSciNetCrossRefGoogle Scholar
  19. 19.
    Rech M, Sauter S, Smolianski A (2006) Two-scale composite finite element method for Dirichlet problems on complicated domains. Numer Math 102(4):681–708MathSciNetCrossRefGoogle Scholar
  20. 20.
    Rüberg T, Cirak F, García Aznar JM (2016) An unstructured immersed finite element method for nonlinear solid mechanics. AMSES 3(1):22Google Scholar
  21. 21.
    Wriggers P (2008) Nonlinear finite element methods. Springer, New YorkzbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  • Christoph J. Paulus
    • 1
    • 2
  • Roland Maier
    • 1
    • 3
  • Daniel Peterseim
    • 3
  • Stéphane Cotin
    • 1
    • 2
    Email author
  1. 1.Inria Nancy Grand EstVillers-lès-NancyFrance
  2. 2.Université de StrasbourgICube Lab, CNRSIllkirchFrance
  3. 3.University of AugsburgAugsburgGermany

Personalised recommendations