Skip to main content
SpringerLink
Log in

Development of a 3-D convolution / superposition algorithm for precise dose calculation in the skull

  • Scientific Papers
  • Published:
Australasian Physics & Engineering Sciences in Medicine Aims and scope Submit manuscript

Abstract

In this paper an algorithm for calculating 3-D dose distributions within the brain is introduced and adapted to the demands of modern radiosurgery. The dose calculation with this model is based on a 3-D distribution of the primary photon intensity which is calculated with a ray casting algorithm. A prelocated matrix takes into account field sizes as well as modifying elements as collimator positions (MLC), blocks, wedges and compensators. Monte Carlo precalculated monoenergetic kernels from 0.1 MeV to 50 MeV were at our disposal. The components of the spectrum were either determined by deconvoluting depth dose curves measured in water or analyzed with a Ge-Li detector system in the case of60Co. The calculated fluence distribution has to be superposed to the complete kernel containing the spatial energy deposition. Inhomogeneities and tissue interface phenomena (σe, Z) have been investigated. The divergence of the rays and the curved surface of the patient are taken into account. Assuming homogenous media, it is possible to shorten the computation time by using the Fast Fourier Transformation (FFT) delivering a first overview within seconds.The algorithm was evaluated and verified under specific conditions of small fields as used in radiosurgery and compared to dose measurements and Monte Carlo calculations. In using both the fast algorithm (FFT) for mainly homogenous conditions on one hand and the very precise superposition for inhomogeneous cases on the other, this algorithm can be a very helpful instrument especially for critical locations in the skull.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. McNutt, T. R., Mackie, T. R., Paliwal B. R.Analysis and convergence of the iterative convolution/superposition dose reconstruction technique for multiple treatment beams and tomotherapy. Med. Phys., 24(9): (1465–1476), 1997.

    Article  CAS  PubMed  Google Scholar 

  2. Boyer, A., Dosobry, G., Wells, N.Potential and limitations of invariant kernel conformal therapy. Med. Phys., 18(4): (703–712), 1991.

    Article  CAS  PubMed  Google Scholar 

  3. Eklöf, A., Ahnesjö, A., Brahme, A.Photon Beam Energy Deposition Kernels for inverse Radiotherapy Planning. Acta Radiol. Oncol., 29: (447–454), 1990.

    Article  Google Scholar 

  4. Siebers, J. V., Lauterbach, M., Tong, S., Wu, Q., Mohan, R.Reducing dose calculation time for accurate iterative IMRT planning. Med. Phys. 29(2): (231–237), 2002.

    Article  PubMed  Google Scholar 

  5. Siebers, J. V., Tong, S., Lauterbach, M., Wu, Q., Mohan R.Acceleration of dose calculations for intensity-modulated radiotherapy. Med. Phys., 28(6): (903–910), 2001.

    Article  CAS  PubMed  Google Scholar 

  6. Liu, H.H., McCullough, E.C., Mackie T.R.Calculating output factors for photon beam radiotherapy using a convolution/superposition method based on a dual source beam model. Med. Phys., 24(12): (1975–1985), 1997.

    Article  CAS  PubMed  Google Scholar 

  7. Liu, H. H., McCullough, E. C., Mackie, T. R.Calculating dose and output factors for wedged photon radiotherapy fields using a convolution/superposition method. Med. Phys., 24(11): (1714–1728), 1997.

    Article  CAS  PubMed  Google Scholar 

  8. Mack, A., Mack, G., Weltz, D., Czempiel, H., Kreiner, H.J.Vertification of dose plans using film dosimetry for quality assurance in radiosurgery. D. Kondziolka (ed): Radiosurgery, Basel, Karger, vol 4, pp 213–227, 2002.

    Article  Google Scholar 

  9. Mack, A., Scheib, S., Major, J., Gianolini S., Pazmandi, G., Feist, H., Czempiel, H., Kreiner, H.J.Precicsion dosimetry for narrow photon beams used in radiosurgery — Determination of Gamma Knife output factors. Med Phys 29 (9): 2080–2089, 2002.

    Article  PubMed  Google Scholar 

  10. Keall, P. J., Hoban, P. W.Superposition dose calculation incorporating Monte Carlo generated electron track kernels. Med. Phys., 23(4): (479–485), 1996.

    Article  CAS  PubMed  Google Scholar 

  11. Murray, D.C., Hoban, P.W., Round, W.H., Graham, I.D., Metcalfe, P.E.Superposition on a multicomputer system. Med. Phys., 18(3): (468–473), 1991.

    Article  CAS  PubMed  Google Scholar 

  12. Ostapiak, O. Z., Zhu, Y., Van, D.Refinements of the finite-size pencil beam model of three-dimensional photon dose calculation. Med. Phys., 24(5): (743–750), 1997.

    Article  CAS  PubMed  Google Scholar 

  13. Aspradakis, M. M., Redpath A. T.A technique for the fast calculation of three-dimensional photon dose distributions using the superposition model. Phys. Med. Biol., 42(8): (1475–1489), 1997.

    Article  CAS  PubMed  Google Scholar 

  14. Bortfeld, T., Schlegel, W., Rhein, B.Decomposition of pencil beam kernels for fast dose calculations in three-dimensional treatment planning. Med. Phys., 20(2): (311–318), 1993.

    Article  CAS  PubMed  Google Scholar 

  15. Bourland, J. D., Chaney, E. L.A finite-size pencil beam model for photon dose calculations in three dimensions. Med. Phys., 19(6): (1401–1412), 1992.

    Article  CAS  PubMed  Google Scholar 

  16. Redpath, A., Twaites, D.A 3-dimensional scatter correction algorithm for photon beams. Phys. Med. Biol., 36(6): (779–798), 1991.

    Article  Google Scholar 

  17. Woo, M., Cunningham, J., Jezioranski, J.Extending the concept of primary and scatter separation to the condition of electronic disequilibrium. Med. Phys., 17(4): (588–595), 1990.

    Article  CAS  PubMed  Google Scholar 

  18. Photon treatment planning collaborative working group.Role of inhomogeneity corrections in three-dimensional photon treatment planning. Rad. Onc. Biol. Phys., 21(1): (59–69) 1991.

    Google Scholar 

  19. Wong, J., Purdy, J.On methods of inhomogeneity corrections for photon transport. Med. Phys., 17(5): (807–814), 1990.

    Article  CAS  PubMed  Google Scholar 

  20. Thomas, S.A modified power-law formula for inhomogeneity corrections in beams of high-energy x-rays. Med. Phys., 18(4): (719–723), 1991.

    Article  CAS  PubMed  Google Scholar 

  21. Condor, J. O’.The density scaling theorem applied to lateral electronic equilibrium. Med. Phys., 11(5): (678–680), 1984.

    Article  Google Scholar 

  22. Iwasaki, A.Calculation of three-dimensional photon primary absorbed dose using forward and backward spread dose distribution functions. Med. Phys., 17(29): (195–202), 1990.

    Article  CAS  PubMed  Google Scholar 

  23. Liu, H. H., McCullough, E. C., Mackie, T. R.Calculating dose distributions and wedge factors for photon treatment fields with dynamic wedges based on an convolution/superposition method. Med. Phys., 25(1): (56–63), 1998.

    Article  CAS  PubMed  Google Scholar 

  24. Lydon, J.M.Photon dose calculations in homogeneous media for treatment planning system using a collapsed cone superposition convolution algorithm. Phys. Med. Biol. 43(6): (1813–1822), 1998.

    Article  CAS  PubMed  Google Scholar 

  25. Arnfield, M. R., Siantar, C. H., Siebers, J., Garmon, P., Cox, L., Mohan, R.The impact of electron transport on the accuracy of computed dose. Med. Phys., 27(6): (1266–1274), 2000.

    Article  CAS  PubMed  Google Scholar 

  26. Mack, A.Entwicklung von Verfahren zur Optimierung der räumlichen Dosisverteilung in der Therapie mit hochenergetischen Photonenstrahlenbündeln. PhD Thesis, University of Tübingen, 1996.

  27. Mackie, T., Bielajew, A., Rogers, W., Battista, J.Generation of photon energy kernels using the EGS Monte Carlo Code. Phys. Med. Biol., 33: (1–20), 1988.

    Article  CAS  PubMed  Google Scholar 

  28. Liu, H. H., McCullough, E. C., Mackie, T. R.A dual source photon beam model used in convolution/superposition dose calculations for clinical megavoltage x-ray beams. Med. Phys., 24(12): (1960–1974), 1997.

    Article  CAS  PubMed  Google Scholar 

  29. Liu, H.H., McCullough, E.C., Mackie, T.R.Correcting kernel tilting and hardening in convolution/superposition dose calculations for clinical divergent and polychromatic photon beams. Med. Phys., 24(11): (1729–1741), 1997.

    Article  CAS  PubMed  Google Scholar 

  30. Metcalfe, P., Hoban, P., Murray, D., Round, W.Beam hardening of 10MV radiotherapy X-rays; analysis using a convolution/superposition method. Phys. Med. Biol., 35(11): (1533–1549), 1990.

    Article  CAS  PubMed  Google Scholar 

  31. Treuer, H., Boesecke, R., Schlegel, W.The source-density function: determination from lateral dose distributions and use for convolution dosimetry. Phys. Med. Biol., 38: (1895–1993), 1993.

    Article  Google Scholar 

  32. Ahnesjö, A., Trepp, A.Acquisition of the effective lateral energy fluence distribution for photon beam dose calculations by convolution models. Phys. Med. Biol., 36 (7): (973–985), 1991.

    Article  Google Scholar 

  33. Sauer, O.Dosisverteilungen an Material-Grenzflächen bei energiereichen Röntgenstrahlen. Dissertation, Universität Würzburg, 1994.

    Google Scholar 

  34. Werner, B.Dose perturbations at interfaces in photon beams: Annihilation radiation. Med. Phys., 18: (713–718), 1991.

    Article  CAS  PubMed  Google Scholar 

  35. Sharpe, M. B., Battista, J. J.Dose calculations using convolution and superposition principles: the orientation of dose spread kernels in divergent x-ray beams. Med. Phys., 20(6): (1685–1694), 1993.

    Article  CAS  PubMed  Google Scholar 

  36. Ahnesjö, A., Andreo, P.Determination of effective bremsstrahlung spectra and electron contamination for photon dose calculations. Phys. Med. Biol., 34: (1451–1464), 1989.

    Article  PubMed  Google Scholar 

  37. Chui, C., Mohan, R.Extraction of pencil beam kernels by the deconvolution method. Med. Phys., 15(2): (138–144), 1988.

    Article  CAS  PubMed  Google Scholar 

  38. Sauer, O., Neumann, M.Reconstruction of high-energy bremsstrahlung spectra by numerical analysis of depth dose data. Rad. and Onc., 18: (39–47), 1990.

    Article  CAS  Google Scholar 

  39. Boyer, A., Wackwitz, R., Mok, E.A comparison of the speeds of three convolution algorithms. Med. Phys., 15(2): (224–227), 1988.

    Article  CAS  PubMed  Google Scholar 

  40. Butts, J. R., Foster, A. E.Comparison of commercially available three-dimensional treatment planning algorithms for monitor unit calculations in the presence of heterogeneities. J. Appl. Clin. Med. Phys., 2(1): ( 32–41). 2001.

    Article  CAS  PubMed  Google Scholar 

  41. Boyer, A., Zhu, Y., Wang, L., Francois, P.Fast Fourier Transform convolution calculations of x-ray isodose distributions in homogeneous media. Med. Phys., 16(2): (248–253), 1989.

    Article  CAS  PubMed  Google Scholar 

  42. Miften, M., Wiesmeyer, M., Monthofer, S., Krippner, K.Implementation of FFT convolution and multigrid superposition models in the FOCUS RTP system. Phys. Med. Biol., 45(4): (817–833), 2000.

    Article  CAS  PubMed  Google Scholar 

  43. Murray, D. C., Hoban, P. W., Metcalfe, P. E., Round, W. H.3-D superposition for radiotherapy treatment planning using fast Fourier transforms. Australas Phys. Eng. Sci. Med., 12(3): (128–137), 1989.

    CAS  PubMed  Google Scholar 

  44. Zhu, Y., Boyer, A.X-ray dose computations in heterogeneous media using 3-dimensional FFT convolution. Phys. Med. Biol., 35(3): (351–368), 1990.

    Article  Google Scholar 

  45. Schulze, C.,3-D-Dosisberechnung(II)-Inhomogenitatskorrekturen. 3-D-Workshop 95, DKFZ Heidelberg: (73-88), 1995.

Download references

Author information

Authors and Affiliations

  1. Gamma Knife Center Frankfurt, Schleusenweg 2-16, NG 95, 60528, Frankfurt, Germany

    A. Mack

  2. EDV-Consulting, Metzingen, Germany

    D. Weltz

  3. Department of Medical Radiation Physics, Klinik Im Park, Zürich, Switzerland

    S. G. Scheib

  4. Gamma Knife Center Munich, Germany

    B. Wowra

  5. Department of Radiotherapy, University Hospital Frankfurt, Frankfurt, Germany

    H. Böttcher

  6. Department of Neurosurgery, University Hospital Frankfurt, Frankfurt, Germany

    V. Seifert

Authors
  1. A. Mack
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. D. Weltz
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S. G. Scheib
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. B. Wowra
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. H. Böttcher
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. V. Seifert
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. Mack.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Mack, A., Weltz, D., Scheib, S.G. et al. Development of a 3-D convolution / superposition algorithm for precise dose calculation in the skull. Australas. Phys. Eng. Sci. Med. 29, 1 (2006). https://doi.org/10.1007/BF03178822

Download citation

  • Received:

  • Accepted:

  • DOI: https://doi.org/10.1007/BF03178822

Key words

Search

Navigation