Analytical theory for the fluence,planar fluence,energy fluence,planar energy fluence and absorbed dose of primary particles and their fragments in broad therapeutic light ion beams |
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| Authors: | J Kempe A Brahme |
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| Institution: | 1. Radiation Oncology Branch, National Cancer Institute, National Institutes of Health, Bethesda, MD;2. Division of Radiation Oncology, Department of Radiology, Walter Reed National Military Medical Center, Bethesda, MD;3. Department of Radiation Oncology, University of Pennsylvania, Philadelphia, PA;4. Department of Radiation Oncology, University of Washington, Seattle, WA;1. Department of Physics, Ryerson University, 350 Victoria St, Toronto, ON M5B 2K3, Canada;2. Department of Radiation Physics, Princess Margaret Cancer Center, 610 University Ave, Toronto, ON M5G 2M9, Canada;3. Department of Radiation Oncology, University of Toronto, 150 College St, Toronto, ON M5S 3E2, Canada;4. Carleton Laboratory for Radiotherapy Physics, Department of Physics, Carleton University, 1125 Colonel By Drive, Ottawa, ON K1S 5B6, Canada;5. Department of Medical Physics, Odette Cancer Center, Sunnybrook Health Sciences Center, 2075 Bayview Ave, Toronto, ON M4N 3M5, Canada;1. 1050 Harriet St., Palo Alto, CA 94301, USA;2. Rapiscan Laboratories Inc., 520 Almanor Ave., Sunnyvale, CA 94085, USA;1. Department of Radiation Oncology, Washington University School of Medicine, Saint Louis, Missouri;2. Philips Healthcare, Cleveland, Ohio;3. Department of Radiation Oncology, Henry Ford Health System, Detroit, Michigan;4. Department of Radiation Oncology, University of California-Los Angeles, Los Angeles, California;6. Department of Radiation Oncology, Mayo Clinic in Arizona, Phoenix, Arizona;2. Department of Biomedical Engineering, Seoul National University, Seoul, Korea;3. Department of Radiation Oncology, Soonchunhyang University Hospital, Seoul, Korea;4. Department of Radiation Oncology, Virginia Commonwealth University, Richmond, VA;1. National Centre for Oncological Hadrontherapy (CNAO), Clinical Department, Pavia, Italy;2. Clinical Cooperation Unit Translational Radiation Oncology, National Center for Tumor Diseases (NCT), Heidelberg University Hospital (UKHD) and German Cancer Research Center (DKFZ), Heidelberg, Germany;3. Division of Molecular and Translational Radiation Oncology, Department of Radiation Oncology, Heidelberg Faculty of Medicine (MFHD) and Heidelberg University Hospital (UKHD), Heidelberg Ion-Beam Therapy Center (HIT), Heidelberg, Germany;4. German Cancer Consortium (DKTK) Core-Center Heidelberg, German Cancer Research Center (DKFZ), Heidelberg, Germany;5. Clinical Cooperation Unit Radiation Oncology, Heidelberg Institute of Radiation Oncology (HIRO), National Center for Radiation Oncology (NCRO), Heidelberg University and German Cancer Research Center (DKFZ), Heidelberg, Germany;6. Faculty of Physics and Astronomy, Heidelberg University, Germany;7. Heidelberg Ion-Beam Therapy Center (HIT), Department of Radiation Oncology, Heidelberg University Hospital, Heidelberg, Germany |
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| Abstract: | The purpose of the present work is to develop analytical expressions for the depth variation of the fluence, planar fluence, the energy fluence, planar energy fluence, the mean energy and absorbed dose of primary ions and their associated fragments in tissue-like media with ranges of clinical interest. The analytical expressions of the primary ions and associated fragments take into account nuclear interactions, energy losses, range straggling and multiple scattering. The analytical models of the radiation field quantities were compared with the results of the modified Monte Carlo (MC) code SHIELD-HIT+. The results show that the shape of the depth absorbed dose distribution of the primary particles is characterized by an increasingly steep exponential fluence decrease with depth as the charge and atomic weight increase. This is accompanied by a compensating increased energy loss towards the Bragg peak as the charge of the ion increases. These largely compensating mechanisms are the main reason that the depth absorbed dose curve of all light ions is surprisingly similar. In addition, a rather uniform dose in the plateau region is obtained since the increasing fragment production almost precisely compensates the loss of primaries. The dominating light fragments such as protons and alpha particles are characterized by longer ranges than the primaries and their depth dose curves to some extent coincide well with the depth fluence curves due to a rather slow variation of mean stopping powers. In contrast, the heavier fragments are characterized by the build up of a slowing down spectrum similar to that of the primaries but with initially slightly shorter or longer ranges depending on their mass to atomic number ratio. The presented analytical theory for the light ion penetration in matter agree quite well with the MC and experimental data and may be very useful for fast analytical calculations of quantities like mean energy, fluence, energy fluence, absorbed dose, and LET. |
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