Numerical Algorithms and Visualization in Medical Treatment Planning

  • Rudolf Beck
  • Peter Deuflhard
  • Hans-Christian Hege
  • Martin Seebaß
  • Detlev Stalling


After a short summary on therapy planning and the underlying technologies we discuss quantitative medicine by giving a short overview on medical image data, summarizing some applications of computer based treatment planning, and outlining requirements on medical planning systems. Then we continue with a description of our medical planning system HyperPlan. It supports typical working steps in therapy planning, like data aquisition, segmentation, grid generation, numerical simulation and optimization, accompanying these with powerful visualization and interaction techniques.


Volume Render Medical Planning Active Contour Model Therapy Planning Computer Tomography Image 
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.


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  1. 1.
    H. Battke, D. Stalling, and H.-C. Hege, Fast Line Integral Convolution for Arbitrary Surfaces in 3D, In H.-C. Hege and K. Polthier (eds.), Visualization and Mathematics, Springer Verlag (1996), 181–195.Google Scholar
  2. 2.
    R. Bendl, J. Pross, M. Keller, J. Bürkelbach, and W. Schlegel, VIRTUOS - A program for VIRTUal radiOtherapy Simulation,in: H.U. Lemke et al. (eds), Computer Assisted Radiology, Berlin, Springer, (1993) 676–682.Google Scholar
  3. 3.
    F. Bornemann, An Adaptive Multilevel Approach to Parabolic Equations, part III: 2D-error estimation and multilevel preconditioning, IMPACT Comput. Sci. Engrg. 4 (1992), 1–45.MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    A. Bossavit, Whitney forms: a class of finite elements for three-dimensional computation in electromagnetism, Inst. Elec. Eng. Proc., Part A, 135:8 (1988), 493–500.Google Scholar
  5. 5.
    F. Bornemann, B. Erdmann, and R. Kornhuber, Adaptive multilevel-methods in three space dimensions, Int. J. Numer. Meth. Eng. 36 (1993), 3187–3203.MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    B. CabraL, N. Cam, and J. Foran, Accelerated Volume Rendering and Tomographic Reconstruction Using Texture Mapping Hardware, in: Proceedings of the Symposium on Volume Visualization, 1994, 91–98.Google Scholar
  7. 7.
    P. Deuflhard, P. Leinen, and H. Yserentant, Concepts for an adaptive hierarchical finite element code, IMPACT Comput. Sci. Engrg. 1 (1989), 3–35.zbMATHCrossRefGoogle Scholar
  8. 8.
    R.A. Drebin, L. Carpenter, and P. Hanrahan, Volume Rendering, Computer Graphics 22:4 (1988), 65–74.CrossRefGoogle Scholar
  9. 9.
    R. Ďurokovič, K. Kaneda, and H. Yamashita, Dynamic contour: A texture approach and contour operations, The Visual Comp. 11 (1995), 277–289.Google Scholar
  10. 10.
    P. A. Van Den Elsen, E. Pol, and M.A. Viergever, Medical image matching — A review with classification, IEEE Engineering in Medicine and Biology, 12:1 (1993), 26–39.CrossRefGoogle Scholar
  11. 11.
    B. Geiger, Three-dimensional modeling of human organs and its application to diagnosis and surgical planning, Technical Report 2105, Institut National de Recherche en Informatique et Automatique, (France), Dec 1993.Google Scholar
  12. 12.
    H.C. Hege, T. Höllerer, and D. Stalling, Volume Rendering: Mathematical Models and Algorithmic Aspects, ZIB Techn. Rep. TR 93–7 (May 1994), 36 p.Google Scholar
  13. 13.
    H. Jin and R. Tanner, Generation of three-dimensional unstructured grids by the advancing front technique, Int. J. Num. Meth. Eng. 36 (1993), 1805–1823.zbMATHCrossRefGoogle Scholar
  14. 14.
    V.N. Kannelopoulos and J.P. Webb, Numerical study of vector absorbing boundary conditions for the finite element solution of Maxwell’s equations, IEEE Microwave Guided Wave Lett., 1 (1991), 325–327.CrossRefGoogle Scholar
  15. 15.
    M. Kass, A. Witkin, and D. Terzopoulos, Snakes: active contour models, Int. J. Comput. Vis. 4 (1987), 321–331.Google Scholar
  16. 16.
    W.E. Lorensen and H.E. Cline, Marching cubes: A high resolution 3D surface construction algorithm,Computer Graphics 21:4 (1987), 163–169.CrossRefGoogle Scholar
  17. 17.
    W.E. Lorensen, Extracting Surfaces from Medical Volumes, in: Visualization ‘84, Course Notes: Volume 13, Visualization Algorithms and Applications (1994), 26–45.Google Scholar
  18. 18.
    D. Laur and P. Hanrahan, Hierachical Splatting: A Progressive Refinement Algorithm for Volume Rendering, Computer Graphics (SIGGRAPH ‘81 Proceedings) 25:4 (1991), 285–288.CrossRefGoogle Scholar
  19. 19.
    M. Levoy, Display of Surfaces from Volume Data, IEEE Computer Graphics and Applications 8:3 (1988), 29–37.CrossRefGoogle Scholar
  20. 20.
    C. Montani, R. Scateni, and R. Scopigno, A modified look-up table for implicit disambiguation of marching cubes, The Visual Comp., 10:6 (1994), 353–355.CrossRefGoogle Scholar
  21. 21.
    D. Moore and J. Warren, Mesh Displacement: An Improved Contouring Method for Trivariate Data, Technical Report TR-91–166, Rice University, Department of Computer Science, 1991.Google Scholar
  22. 22.
    D. Meyer, Multiresolution Tiling, Proceedings of Graphics Interface ‘84, Canadian Information Processing Society, May 1994, Banff, Alberta (Canada) 1994, 25–32.Google Scholar
  23. 23.
    J.-M. Morel and S. Solimini, Variational Methods in Image Segmentation, Progress in Nonlinear Differential Equations and Their Applications, Vol. 14, Birkhäuser, Boston, 1995.CrossRefGoogle Scholar
  24. 24.
    E.N. Mortensen and W.A. Barrett, Intelligent Scissors for Image Composition, in: R. Cook (ed.), SIGGRAPH 95 Conference Proceedings, Annual Conference Series, 1995, 191–198.CrossRefGoogle Scholar
  25. 25.
    H. H. Pennes, Analysis of tissue and arterial blood temperatures in the resting human forearm, Journal of Applied Physiology 1 (1948), 93–122.Google Scholar
  26. 26.
    K.D. Paulsen, X. Jia, and J.M. Sullivan, Finite element computations of specific absorption rates in anatomically conforming full-body models for hyperthermia treatment analysis, IEEE Trans. Biomed. Engrg., 40:9 (1993), 933–945.CrossRefGoogle Scholar
  27. 27.
    R. B. Roemer and A. W. Dutton, A new tissue convective energy balance equation for predicting tissue temperature distributions, presented at: ICHO VII, Rome, Italy, April 9–13, 1996; Univ. at Utah preprint 1996, Mechan. Eng. Dept. and Radiation Oncology Dept., Salt Lake City, Utah.Google Scholar
  28. 28.
    P. Shirley and A. Tuchman, A Polygonal Approximation to Direct Scalar Volume Rendering, Computer Graphics 24:5 (1990), 63–70.CrossRefGoogle Scholar
  29. 29.
    D. Stalling and H.C. Hege, Fast and Resolution Independent Line Integral Convolution„ Proceedings of SIGGRAPH ‘85, (Los Angeles, California, August 6–11,1995). In Computer Graphics Annual Conference Series, 1995, 249–256.Google Scholar
  30. 30.
    D. Stalling and H.-C. Hege, Intelligent Scissors for Medical Image Segmentation, in: B. Arnolds, H. Müller, D. Saupe, T. Tolxdorff (eds), Tagungsband zum 4. Freiburger Workshop “Digitale Bildverarbeitung in der Medizin”, Freiburg, 14.-15. März, 1996, 32–36.Google Scholar
  31. 31.
    P.S. Strauss and R. Carey, An object-oriented 3D graphics toolkit, Computer Graphics (SIGGRAPH ‘82 Proceedings) 26:4 (1992), 341–349.CrossRefGoogle Scholar
  32. 32.
    J.K. Udupa and R.J. Gonçalves, Imaging Transforms for Volume Visualization,in: R. H. Taylor, S. Lavallée, G.C. Burdea, and Ralph Mösges (eds.), Computer-Integrated Surgery, MIT-Press, Cambridge MA, 1996.Google Scholar
  33. 33.
    C. Upson and M. Keeler, V-Buffer: Visible Volume Rendering, Computer Graphics 22:4 (1988), 59–64.CrossRefGoogle Scholar
  34. 34.
    O. Wilson, A. Van Gelder, and J. Wilhelms, Direct Volume Rendering via 3D-Textures, Technical Report UCSC-CRL-94–19, University of California, Santa Cruz, 1994.Google Scholar
  35. 35.
    S. Webb, The Physics of Medical Imaging, (Medical Science Series) Bristol, UK, 1988, IOP Publishing.CrossRefGoogle Scholar
  36. 36.
    S. Wegner, T. Harms, H. Oswald, and E. Fleck, The Watershed Transformation on Graphs for the Segmentation of CT Images, Proc. of 13th International Conference on Pattern Recognition, Vienna 96, 1996, 498–502.Google Scholar
  37. 37.
    L. Westover, Footprint Evaluation for Volume Rendering, Computer Graphics 24:4 (1990), 367–376.CrossRefGoogle Scholar
  38. 38.
    P. Wust, J. Nadobny, R. Felix, P. Deuflhard, A. Louis, and W. John, Strategies for optimized application of annular-phased-array systems in clinical hyperthermia, Int. J. Hyperthermia 7 (1991), 157–173.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Rudolf Beck
    • 1
  • Peter Deuflhard
    • 1
  • Hans-Christian Hege
    • 1
  • Martin Seebaß
    • 1
  • Detlev Stalling
    • 1
  1. 1.Konrad-Zuse-Zentrum für Informationstechnik Berlin (ZIB)Germany

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