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A Fourier analysis on the maximum acceptable grid size for discrete proton beam dose calculation
Abstract
We developed an analytical method for determining the maximum acceptable grid size for discrete dose calculation in proton therapy treatment plan optimization, so that the accuracy of the optimized dose distribution is guaranteed in the phase of dose sampling and the superfluous computational work is avoided. The accuracy of dose sampling was judged by the criterion that the continuous dose distribution could be reconstructed from the discrete dose within a 2% error limit. To keep the error caused by the discrete dose sampling under a 2% limit, the dose grid size cannot exceed a maximum acceptable value. The method was based on Fourier analysis and the Shannon-Nyquist sampling theorem as an extension of our previous analysis for photon beam intensity modulated radiation therapy [J. F. Dempsey, H. E. Romeijn, J. G. Li, D. A. Low, and J. R. Palta, Med. Phys. 32, 380-388 (2005)]. The proton beam model used for the analysis was a near mono-energetic (of width about 1% the incident energy) and monodirectional infinitesimal (nonintegrated) pencil beam in water medium. By monodirection, we mean that the proton particles are in the same direction before entering the water medium and the various scattering prior to entrance to water ismore »
- Authors:
-
- Department of Radiation Oncology, University of Florida College of Medicine, Gainesville, Florida 32610-0385 (United States)
- Publication Date:
- OSTI Identifier:
- 20853469
- Resource Type:
- Journal Article
- Journal Name:
- Medical Physics
- Additional Journal Information:
- Journal Volume: 33; Journal Issue: 9; Other Information: DOI: 10.1118/1.2241996; (c) 2006 American Association of Physicists in Medicine; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0094-2405
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 62 RADIOLOGY AND NUCLEAR MEDICINE; ACCURACY; BRAGG CURVE; COULOMB SCATTERING; DOSIMETRY; ERRORS; FOURIER ANALYSIS; GAUSS FUNCTION; MODULATION; OPTIMIZATION; PHANTOMS; PHOTON BEAMS; PROTON BEAMS; RADIATION DOSE DISTRIBUTIONS; RADIATION DOSES; RADIOTHERAPY; SAMPLING; SPATIAL RESOLUTION
Citation Formats
Li, Haisen S, Romeijn, H Edwin, Dempsey, James F, Department of Radiation Oncology, University of Florida College of Medicine, Gainesville, Florida 32610-0385 and Department of Industrial and Systems Engineering, University of Florida, Gainesville, Florida 32610-0385, and Department of Radiation Oncology, University of Florida College of Medicine, Gainesville, Florida 32610-0385. A Fourier analysis on the maximum acceptable grid size for discrete proton beam dose calculation. United States: N. p., 2006.
Web. doi:10.1118/1.2241996.
Li, Haisen S, Romeijn, H Edwin, Dempsey, James F, Department of Radiation Oncology, University of Florida College of Medicine, Gainesville, Florida 32610-0385 and Department of Industrial and Systems Engineering, University of Florida, Gainesville, Florida 32610-0385, & Department of Radiation Oncology, University of Florida College of Medicine, Gainesville, Florida 32610-0385. A Fourier analysis on the maximum acceptable grid size for discrete proton beam dose calculation. United States. https://doi.org/10.1118/1.2241996
Li, Haisen S, Romeijn, H Edwin, Dempsey, James F, Department of Radiation Oncology, University of Florida College of Medicine, Gainesville, Florida 32610-0385 and Department of Industrial and Systems Engineering, University of Florida, Gainesville, Florida 32610-0385, and Department of Radiation Oncology, University of Florida College of Medicine, Gainesville, Florida 32610-0385. 2006.
"A Fourier analysis on the maximum acceptable grid size for discrete proton beam dose calculation". United States. https://doi.org/10.1118/1.2241996.
@article{osti_20853469,
title = {A Fourier analysis on the maximum acceptable grid size for discrete proton beam dose calculation},
author = {Li, Haisen S and Romeijn, H Edwin and Dempsey, James F and Department of Radiation Oncology, University of Florida College of Medicine, Gainesville, Florida 32610-0385 and Department of Industrial and Systems Engineering, University of Florida, Gainesville, Florida 32610-0385 and Department of Radiation Oncology, University of Florida College of Medicine, Gainesville, Florida 32610-0385},
abstractNote = {We developed an analytical method for determining the maximum acceptable grid size for discrete dose calculation in proton therapy treatment plan optimization, so that the accuracy of the optimized dose distribution is guaranteed in the phase of dose sampling and the superfluous computational work is avoided. The accuracy of dose sampling was judged by the criterion that the continuous dose distribution could be reconstructed from the discrete dose within a 2% error limit. To keep the error caused by the discrete dose sampling under a 2% limit, the dose grid size cannot exceed a maximum acceptable value. The method was based on Fourier analysis and the Shannon-Nyquist sampling theorem as an extension of our previous analysis for photon beam intensity modulated radiation therapy [J. F. Dempsey, H. E. Romeijn, J. G. Li, D. A. Low, and J. R. Palta, Med. Phys. 32, 380-388 (2005)]. The proton beam model used for the analysis was a near mono-energetic (of width about 1% the incident energy) and monodirectional infinitesimal (nonintegrated) pencil beam in water medium. By monodirection, we mean that the proton particles are in the same direction before entering the water medium and the various scattering prior to entrance to water is not taken into account. In intensity modulated proton therapy, the elementary intensity modulation entity for proton therapy is either an infinitesimal or finite sized beamlet. Since a finite sized beamlet is the superposition of infinitesimal pencil beams, the result of the maximum acceptable grid size obtained with infinitesimal pencil beam also applies to finite sized beamlet. The analytic Bragg curve function proposed by Bortfeld [T. Bortfeld, Med. Phys. 24, 2024-2033 (1997)] was employed. The lateral profile was approximated by a depth dependent Gaussian distribution. The model included the spreads of the Bragg peak and the lateral profiles due to multiple Coulomb scattering. The dependence of the maximum acceptable dose grid size on the orientation of the beam with respect to the dose grid was also investigated. The maximum acceptable dose grid size depends on the gradient of dose profile and in turn the range of proton beam. In the case that only the phantom scattering was considered and that the beam was aligned with the dose grid, grid sizes from 0.4 to 6.8 mm were required for proton beams with ranges from 2 to 30 cm for 2% error limit at the Bragg peak point. A near linear relation between the maximum acceptable grid size and beam range was observed. For this analysis model, the resolution requirement was not significantly related to the orientation of the beam with respect to the grid.},
doi = {10.1118/1.2241996},
url = {https://www.osti.gov/biblio/20853469},
journal = {Medical Physics},
issn = {0094-2405},
number = 9,
volume = 33,
place = {United States},
year = {Fri Sep 15 00:00:00 EDT 2006},
month = {Fri Sep 15 00:00:00 EDT 2006}
}
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