Analytical investigation of magnetic field effects on Proton lateral deflection and penetrating depth in the water phantom
A relativistic approach
Keywords:
Proton radiation therapy, Penetration depth, Lateral deflection, Magnetic fieldAbstract
Background: Integrated proton therapy - MRI systems are capable of delivering high doses to the target tissues near sensitive organs and achieve better therapeutic results; however, the applied magnetic field for imaging, influences the protons path, changes the penetration depth and deflects the particles, laterally, leading to dose distribution variations. Objective: To determine the effects of a magnetic field on the range and the lateral deflection of protons, analytically. Methods: An analytical survey based on protons energy and range power law relation, without using small angle assumption was done. The penetration depth and lateral deflection of protons with therapeutic energy ranges 60-250 MeV in the presence of uniform magnetic fields of 0-10T intensities, were calculated analytically. Calculations were done for relativistic conditions with Mathematica software version 7.0, and MATLAB 7.0 was applied to plot curves and curve fittings. Results: In the presence of a magnetic field, the depth of Bragg peak was decreased and it was shifted laterally. A second order polynomial model with power equation for its coefficients and a power model with quadratic polynomial coefficients predicted the maximum lateral deflection (ymax) and maximum penetration depth (zmax) variations with energy and magnetic field intensity, respectively. Conclusion: The applied correction for deflection angle will give more reliable results in initial energy of 250 MeV and 3T magnetic field intensity. For lower energies and magnetic field intensities the differences are negligible, clinically.
References
Price P, Sikora K. Treatment of Cancer. 5th ed. London: Arnold Hodder; 2008.
Chu WT, Ludewigt BA, Renner TR. Instrumentation for treatment of cancer using proton and light-ion
beams. Rev Sci Instrum. 1993; 64(8): 2055-2122. doi: 10.1063/1.1143946.
Brahme A. Design Principles and Clinical Possibilities With a new Generation of Radiation Therapy
Equipment. Acta Oncologia. 1987; 26(6): 403-12. doi: 10.3109/02841868709113708. PMID: 3328620.
Khan Fhaiz M. the physics of the radiation therapy. 4th ed. Wolters Kluwer Health; 2010.
Hollmark M, Uhrdin J, Belkic Dz, Gudowska I, Brahme A. Influence of multiple scattering and energy loss
straggling on the absorbed dose distribution of therapeutic light ion beams: I. Analytical pencil beam model.
Phys Med Biol. 2004; 49(14): 3247-65. doi: 10.1088/0031-9155/49/14/016.
Scifoni E, Surdutovich E, Solov’yov A, Pshenichnov I, Mishustin I, Greiner W. Ion-beam therapy: from
electron production in tissue like media to DNA damage estimations. Biological Physics. 2008; 104: 104-10.
doi: 10.1063/1.3058968.
DePauw N, Dias MF, Rosenfeld A, Seco JC. Ion Radiography as a Tool for Patient Set-up & Image Guided
Particle Therapy: A Monte Carlo Study. Technology in Cancer Research & Treatment. 2014; 13(1): 69-79.
doi: 10.7785/tcrt.2012.500357.
You S, Gou Ch, Wu Zh, Hou Q. A semi-analytical model for calculating the penetration depth of a High
energy electron beam in a water phantom with a magnetic field. Physica Medica. 2015; 31(5): 463-7. doi:
1016/j.ejmp.2015.04.013.
Schulte R, Bashkirov V, Li T, Liang Zh, Mueller K, Heimann J, et al. Conceptual Design of a Proton
Computed Tomography System for Applications in Proton Radiation Therapy. IEEE Transaction On Nuclear
Science. 2004; 51(3): 866-72. doi: 10.1109/TNS.2004.829392.
Pedroni E, Bacher R, Blattmann H, Böhringer T, Coray A, Lomax A, et al. The 200 MeV proton therapy
project at the Paul Scherrer Institute: Conceptual design and practical realization. Medical Physics. 1995;
(1): 37-53. doi: 10.1118/1.597522.
Pedroni E. Latest Development in Proton Therapy. Proceedings of EPAC 2000, Vienna, Austria.
Riboldi M, Orecchia R, Baroni G. Real-time tumour tracking in particle therapy: technological developments
and future perspectives. The lancet oncology. 2012; 13(9): 383-91. doi: 10.1016/S1470-2045(12)70243-7.
Vander Heide UA, Houweling AC, Groenendaal G, Beets-Tan RGH, Lambin Ph. Functional MRI for
radiotherapy dose painting. Magn Reson Imaging. 2012; 30(9): 1216-23. doi: 10.1016/j.mri.2012.04.010.
Raaymakers BW, Raaijmakers AJE, Kotte ANTJ, Jette D, Lagendijk JJW. Integrating a MRI scanner with a
MV radiotherapy accelerator: dose deposition in a transverse magnetic field. Phys Med Biol. 2004; 49(17):
–18. doi: 10.1088/0031-9155/49/17/019.
Keyvanloo A, Burke B, Warkentin B, Tadic T, Rathee S, Kirkby C, et al. Skin dose in longitudinal and
transverse linac-MRIs using Monte Carlo and realistic 3D MRI field models. Med Phys. 2012; 39(10): 6509-
doi: 10.1118/1.4754657. PMID: 23039685.
Haliday D, Resnick R, Walker J. fundamentals of physics extended. Wiley; 2010.
Fuchs H, Moser P, Groschl M, Georg D. Magnetic field effects on particle beams and their implications for
dose calculation in MR guided particle therapy. 2017.
Bol GH, Issoiny SH, Lagendijk JJW, Raaymakers BW. Fast online Monte Carlo-based IMRT planning for
the MRI linear accelerator. Phys Med Biol. 2012; 57(5): 1375–85. doi: 10.1088/0031-9155/57/5/1375.
Yang YM, Geurts M, Smilowitz JB, Sterpin E, Bednarz BP. Monte Carlo simulations of patient dose
perturbations in rotational-type radiotherapy due to a transverse magnetic field: A tomotherapy investigation.
Med Phys. 2015; 42(2): 715-25. doi: 10.1118/1.4905168.
Ghila A, Fallone BG, Rathee S. Influence of standard RF coil material on surface and build up dose from a
MV photon beam in magnetic field. Med Phys. 2016; 43(11): 5808-16. doi: 10.1118/1.4963803. PMID:
Chen X, Prior P, Chen G, Schuitz CJ, Li XA. Technical Note: Dose effects of 1.5 T transverse magnetic field
on tissue interfaces in MRI- guided radiotherapy. Med Phys. 2016; 43(8): 4797-802. doi: 10.1118/1.4959534.
PMID: 27487897.
Paganetti H, Jiang H, Trofimov A. 4D Monte Carlo simulation of proton beam scanning: modelling of
variations in time and space to study the interplay between scanning pattern and time-dependent patient
geometry. Phys Med Biol. 2005; 50(5): 983–90. doi: 10.1088/0031-9155/50/5/020.
Koehler AM, Schneider RJ, Sisterson JM. Flattening of proton dose distribution for large field radiotherapy.
Medical Physics. 1977; 4(4): 297- 301. doi: 10.1118/1.594317.
Bues M, Newhauser WD, Titt U, Smith AR. Therapeutic step and shoot proton beam spot-scanning with a
multi-leaf collimator: a Monte Carlo study. Radiation Protection Dosimetry .2005; 115(1–4): 164–9. doi:
1093/rpd/nci259.
Bjerke HH. Application of Novel Accelerator Research for Particle Therapy. 2014.
Sardari D, Hosseini-hamid M, Saeidi P. In-vivo Proton Beam Shaping Using Static Magnetic Field for Cancer
Therapy. World Congress on Medical Physics and Biomedical Engineering. Munich, Germany. 2009; 25(1):
-51. doi: 10.1007/978-3-642-03474-9_266.
Raaymakers BW, Raaijmakers AJ, Lagendijk JJ. Feasibility of MRI guided proton therapy: magnetic field
dose effects. Phys Med Biol. 2008; 53(20): 5615-22. doi: 10.1088/0031-9155/53/20/003.
Schippers JM, Lomax AJ. Emerging technologies in proton therapy. Acta Oncol. 2011; 50(6): 838-50. doi:
3109/0284186X.2011.582513.
Oborn BM, Dowdell S, Metcalfe PE, Crozier S, Mohan R, Keall PJ. Proton beam deflection in MRI fields:
Implications for MRI-guided proton therapy. Med Phys. 2015; 42(5): 2113-24. doi: 10.1118/1.4916661.
Wolf R, Bortfeld T. An analytical solution to proton Bragg peak deflection in a magnetic field. Phys Med.
Biol. 2012; 57(17): 329–37. doi: 10.1088/0031-9155/57/17/N329.
Schellhammer SM, Hoffmann AL. Prediction and compensation of magnetic beam deflection in MRintegrated proton therapy: a method optimized regarding accuracy, versatility and speed. Phys Med Biol.
; 62: 1549-64. doi: 10.1088/1361-6560/62/4/1548. PMID: 28121631.
Schaffner B, Pedroni E, Lomax A. Dose calculation models for proton treatment planning using a dynamic
beam delivery system: An attempt to include density heterogeneity effects in the analytical dose calculation.
Phys Med Biol. 1999; 44: 27–41. doi: 10.1088/0031-9155/44/1/004. PMID: 10071873.
Bortfeld T. An analytical approximation of the Bragg curve for therapeutic proton beams. Med Phys. 1997;
(12): 2024-33. doi: 10.1118/1.598116. PMID: 9434986.
Newhauser WD, Zhang R. The physics of proton therapy. Phys Med Biol. 2015; 60: 155–209. doi:
1088/0031-9155/60/8/R155. PMID: 25803097, PMCID: PMC4407514.
Schulz-Ertner D, Tsujii H. Particle Radiation Therapy Using Proton and Heavier Ion Beams. J Clin Oncol.
; 25(8): 953-64. doi: 10.1200/JCO.2006.09.7816. PMID: 17350944.
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