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Research Article

Study of Ill-conditioning of Linac Stereotactic Irradiation Subspaces using Singular Values Decomposition Analysis

Pages 581-590 | Published online: 08 Jul 2009

REFERENCES

  • Kallman P. Optimization of radiation therapy planning using physical and biological objective functions, Doctoral Disserta-tion, Edsbruck: Academitryck AB, ISBN 91 7153 011 8, 1992.
  • Webb S. Treatment plan optimization. In: Thieme G, ed. Stereotaxic atlas of the human brain. New York: Verlag, 1988.
  • Bahr GK, Kereikes JK, Horwitz H, et al. The method of linear programming applied to radiation treatment planning. Radiology 1968; 91: 686–93.
  • Brahme A, Lind BK. Inverse radiation therapy planning as a tool for 3D dose optimization. Phys Med 1990; 6: 53–63.
  • Cooper REM. A gradient methode of optimizing external beam radiotherapy treatment plans. Radiology 1978; 128: 235–43.
  • Holmes T, Mackie R. A filtered backprojection dose calcula-tion method for inverse treatment planning. Med Phys 1994; 21: 303–13.
  • Lind BK, Brahme A. Photon field quantities and units for kernel based radiation therapy planning and treatment opti-mization. Phys Med Biol 1992; 37: 891–909.
  • Redpath AT, Vickery BL, Wright DH. A new technique for radiotherapy planning using quadratic programming. Phys Med Biol 1976; 21: 781–91.
  • Webb S. Optimization by simulated annealing of three- di-mensional conformal treatment planning for radiation fields defined by a multileaf collimator: II. Inclusion of two dimen-sional modulation of x-ray intensity. Phys Med Biol 1992; 37: 1689–704.
  • Rosen I, Lane R, Mori11 M, et al. Treatment plan optimisa-tion using linear programming. Med Phys 1991; 18: 141–52.
  • Lefkopoulos D, Devaux J-Y, Roucayrol J-C. Methode gen-erale d'optimisation de la distribution des isodoses en radio-therapie par faisceaux de petites dimensions. Proc Intern Symposium on: Dosimetry in radiotherapy, Vienna, 31 Au-gust-4 September 1987, IAEA: 365–378.
  • Lefkopoulos D, Levier M, Bendada S, et al. A general optimizationprocedure for stereotactic small beam multi-isocentric radiotherapy. Int J Imaging Sci Tech 1995; 6: 114–23.
  • Lefkopoulos D, Grandjean P, Laouar A, et al. Study of the degree of ill-conditioning of phase space of pencil beam radiotherapy using singular value decomposition. Int J Imag-ing Sci Tech 1995; 6: 104–13.
  • Andrew HC, Patterson C. Singular value decomposition and digital image processing. IEEE Trans Acoust Speech Signal Proc 1976; 24: 1.
  • Smith MF, Floyd CE, Jaszczak RJ, et al. Reconstruction of SPECT images using generalized matrix INVERSE. IEEE Trans Med Imaging 1992; 11: 2.
  • Colombo F, Francescon P, Cora S, et al. Evaluation of linear accelerator radiosurgical techniques using biophysical para-meters (NTCP and TCP). Int .1- Rad Oncol Biol Phys 1995; 31: 617–28.
  • Betti O, Derechinsky VE. Hyperselective encephalic irradiation with linear accelerator. Acta Neurol 1984; 33: 385–90.
  • Talairach J, Tournaux P. Coplanar stereotaxic atlas of the human brain. Stuttgart: Thieme Verlag, 1988.
  • Lefkopoulos D, Schlienger M, Merienne L, et al. The associ-ated targets methodology and the multi-isocenters radio-surgery treatment planning system ARTEMIS-3D. Bull Cancer/Radiother 1994; 81: 1 1 1–25.
  • Colub G, Greenbaum A, Luskin M. Computing the sparse singular value decomposition via SVDPACK, recent advances in iterative methods. New York: Springer-Verlag, 1994: 13–29.
  • Horn AR, Johnson CA. Norms for vectors and matrices, matrix analysis. Cambridge: Cambridge University, 1985: 257–342.
  • Grandjean P, Platoni K, Lefkopoulos D, et al. Use of a general inverse technique for the conformational stereotactic treatment of complex intracranial lesions. Int J Rad Oncol Biol Phys 1998; 41: 69–76.

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