Image Guidance and Surgery Simulation Using Inverse Nonlinear Finite Element Methods

  • Philip Pratt
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5104)


Nonlinear finite element methods are described in which cyclic organ motion is implied from 4D scan data. The equations of motion corresponding to an explicit integration of the total Lagrangian formulation are reversed, such that the sequence of node forces which produces known changes in displacement is recovered. The forces are resolved from the global coordinate system into systems local to each element, and at every simulation time step are expressed as weighted sums of edge vectors. In the presence of large deformations and rotations, this facilitates the combination of external forces, such as tool-tissue interactions, and also positional constraints. Applications in the areas of surgery simulation and minimally invasive robotic interventions are proposed, and the methods are illustrated using CT images of a pneumatically-operated beating heart phantom.


Image Guidance Global Coordinate System Node Force Surgery Simulation Simulation Time Step 
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  1. 1.
    Pratt, P., Bello, F., Edwards, E., Rueckert, D.: Interactive finite element simulation of the beating heart for image-guided robotic cardiac surgery. In: Medicine Meets Virtual Reality, vol. 16, pp. 378–383. IOS Press, Amsterdam (2008)Google Scholar
  2. 2.
    Bathe, K.J.: Finite element procedures, 1st edn. Prentice-Hall, Englewood Cliffs (2007)Google Scholar
  3. 3.
    Miller, K., Joldes, G., Lance, D., Wittek, A.: Total lagrangian explicit dynamics finite element algorithm for computing soft tissue deformation. Communications in Numerical Methods in Engineering 23, 121–134 (2007)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Berti, G.: Image-based unstructured 3D mesh generation for medical applications. In: European Congress on Computational Methods in Applied Sciences and Engineering - ECCOMAS 2004, University of Jyväskylä, Department of Mathematical Information Technology (2004)Google Scholar
  5. 5.
    Rueckert, D., Sonoda, L.I., Hayes, C., Hill, D.L.G., et al.: Non-rigid registration using free-form deformations: Application to breast MR images. IEEE Transactions on Medical Imaging 18(8), 712–721 (1999)CrossRefGoogle Scholar
  6. 6.
    Schnabel, J.A., Rueckert, D., Quist, M., Blackall, J.M., et al.: A generic framework for non-rigid registration based on non-uniform multi-level free-form deformations. In: Niessen, W.J., Viergever, M.A. (eds.) MICCAI 2001. LNCS, vol. 2208, pp. 573–581. Springer, Heidelberg (2001)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Philip Pratt
    • 1
  1. 1.Institute of Biomedical EngineeringImperial College of Science, Technology and MedicineLondonUnited Kingdom

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