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Numerical Algorithms and Visualization in Medical Treatment Planning

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Visualization and Mathematics

Summary

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.

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References

  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. 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. 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.

    Article  MathSciNet  MATH  Google Scholar 

  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. F. Bornemann, B. Erdmann, and R. Kornhuber, Adaptive multilevel-methods in three space dimensions, Int. J. Numer. Meth. Eng. 36 (1993), 3187–3203.

    Article  MathSciNet  MATH  Google Scholar 

  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. P. Deuflhard, P. Leinen, and H. Yserentant, Concepts for an adaptive hierarchical finite element code, IMPACT Comput. Sci. Engrg. 1 (1989), 3–35.

    Article  MATH  Google Scholar 

  8. R.A. Drebin, L. Carpenter, and P. Hanrahan, Volume Rendering, Computer Graphics 22:4 (1988), 65–74.

    Article  Google Scholar 

  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. 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.

    Article  Google Scholar 

  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. 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. 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.

    Article  MATH  Google Scholar 

  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.

    Article  Google Scholar 

  15. M. Kass, A. Witkin, and D. Terzopoulos, Snakes: active contour models, Int. J. Comput. Vis. 4 (1987), 321–331.

    Google Scholar 

  16. W.E. Lorensen and H.E. Cline, Marching cubes: A high resolution 3D surface construction algorithm,Computer Graphics 21:4 (1987), 163–169.

    Article  Google Scholar 

  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. D. Laur and P. Hanrahan, Hierachical Splatting: A Progressive Refinement Algorithm for Volume Rendering, Computer Graphics (SIGGRAPH ‘81 Proceedings) 25:4 (1991), 285–288.

    Article  Google Scholar 

  19. M. Levoy, Display of Surfaces from Volume Data, IEEE Computer Graphics and Applications 8:3 (1988), 29–37.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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. D. Meyer, Multiresolution Tiling, Proceedings of Graphics Interface ‘84, Canadian Information Processing Society, May 1994, Banff, Alberta (Canada) 1994, 25–32.

    Google Scholar 

  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.

    Book  Google Scholar 

  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.

    Chapter  Google Scholar 

  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. 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.

    Article  Google Scholar 

  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. P. Shirley and A. Tuchman, A Polygonal Approximation to Direct Scalar Volume Rendering, Computer Graphics 24:5 (1990), 63–70.

    Article  Google Scholar 

  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. 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. P.S. Strauss and R. Carey, An object-oriented 3D graphics toolkit, Computer Graphics (SIGGRAPH ‘82 Proceedings) 26:4 (1992), 341–349.

    Article  Google Scholar 

  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. C. Upson and M. Keeler, V-Buffer: Visible Volume Rendering, Computer Graphics 22:4 (1988), 59–64.

    Article  Google Scholar 

  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. S. Webb, The Physics of Medical Imaging, (Medical Science Series) Bristol, UK, 1988, IOP Publishing.

    Book  Google Scholar 

  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. L. Westover, Footprint Evaluation for Volume Rendering, Computer Graphics 24:4 (1990), 367–376.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

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© 1997 Springer-Verlag Berlin Heidelberg

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Beck, R., Deuflhard, P., Hege, HC., Seebaß, M., Stalling, D. (1997). Numerical Algorithms and Visualization in Medical Treatment Planning. In: Hege, HC., Polthier, K. (eds) Visualization and Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-59195-2_20

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  • DOI: https://doi.org/10.1007/978-3-642-59195-2_20

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-63891-6

  • Online ISBN: 978-3-642-59195-2

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