Dose calculations in proton beams: range straggling corrections and energy scaling

Russell, Kellie R.; Grusell, Erik; Montelius, Anders

doi:10.1088/0031-9155/40/6/005

Cited by 51 publications

(57 citation statements)

References 37 publications

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“…Similarly, the RMS transverse displacements at the end point, r y0 , of 1 H, 4 He and 12 C nuclei incident into water were calculated with varied incident ranges and were compared with the analytical formula (28) and measurements. In addition to Phillips's measurements [11], we included two proton points measured by Preston and Kohler in their unpublished work in 1968, which were ffiffiffi 2 p r y0 ¼ ð0:346 AE 0:009Þ cm for …”

Section: End-point Displacementmentioning

confidence: 99%

“…Fig. 4(a)-(c) show the growths of transverse displacement of 1 H, 4 He and 12 C nuclei in water. In terms of relative agreement with the measurements, the dH and ØS formulations were excellent for 1 H, the FR and dH formulations were good for 4 He and the FR was the excellent for 12 C. Considering their absolute scale and inherent experimental difficulties, the best would be the dH formulation with agreement within 2% or 0.02 cm everywhere.…”

Section: Scattering Anglementioning

confidence: 99%

“…We also give specific symbols to such quantities later in various formulations. For a given model of h 2 ðxÞ, it is possible to numerically obtain effective scattering powerT ¼ ½h 2 ðx þ DxÞ À h 2 ðxÞ=Dx for small step Dx [4,5]. However, it is desirable to have an analytical formula for the scattering power, which is the main objective of this work, not only for theoretical cleanness but also for further analytical derivation of physical quantities.…”

Section: Introductionmentioning

confidence: 99%

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Alternative scattering power for Gaussian beam model of heavy charged particles

Kanematsu

2008

Nuclear Instruments and Methods in Physics Research Section B:

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a b s t r a c tThis study provides an accurate, efficient and simple multiple scattering formulation for heavy charged particles such as protons and heavier ions with a new form of scattering power that is a key quantity for beam transport in matter. The Highland formula for multiple scattering angle was modified to a scattering power formula to be used within the Fermi-Eyges theory in the presence of heterogeneity. An analytical formula for RMS end-point displacement in homogeneous matter was also derived for arbitrary ions. The formulation was examined in terms of RMS angles and displacements in comparison with other formulations and measurements. The results for protons, helium ions and carbon ions in water agreed with them at a level of 2% or the differences were discussed.

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Section: End-point Displacementmentioning

confidence: 99%

Section: Scattering Anglementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Alternative scattering power for Gaussian beam model of heavy charged particles

Kanematsu

2008

Nuclear Instruments and Methods in Physics Research Section B:

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“…pTMS: plans for passive scattering were computed using the pencil-beam algorithm [24,25] of the Nucletron Helax-TMS [26,27]. Beam data were tailored to the Svederberg Laboratory (Sweden) beam line.…”

Section: Treatment-planning Systems and Beammentioning

confidence: 99%

Comparative Planning Study for Proton Radiotherapy of Benign Brain Tumors

et al. 2006

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“…16,17 Accounting for differences in MCS requires the use of proton transport/scattering theories to model the radial width of the pencil beam as a function of depth. Deasy 18 has used Molière scattering theory 19,20 to compute the radial pencil beam width using the Gaussian approximation suggested by Hanson et al 21 Alternatively, various authors 22,23 have used differential approximations to Molière theory with transport equations like those given by Fermi-Eyges theory [23][24][25] to compute the pencil beam width as a function of depth. These differential approximations describe the change in the mean squared MCS angle as a function of depth and are commonly referred to as the scattering power.…”

Section: Introductionmentioning

confidence: 99%

A generalized 2D pencil beam scaling algorithm for proton dose calculation in heterogeneous slab geometries

Westerly¹,

Mo²,

Mackie³

et al. 2013

Medical Physics

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Purpose: Pencil beam algorithms are commonly used for proton therapy dose calculations. Szymanowski and Oelfke ["Two-dimensional pencil beam scaling: An improved proton dose algorithm for heterogeneous media," Phys. Med. Biol. 47, 3313-3330 (2002)] developed a two-dimensional (2D) scaling algorithm which accurately models the radial pencil beam width as a function of depth in heterogeneous slab geometries using a scaled expression for the radial kernel width in water as a function of depth and kinetic energy. However, an assumption made in the derivation of the technique limits its range of validity to cases where the input expression for the radial kernel width in water is derived from a local scattering power model. The goal of this work is to derive a generalized form of 2D pencil beam scaling that is independent of the scattering power model and appropriate for use with any expression for the radial kernel width in water as a function of depth. Methods: Using Fermi-Eyges transport theory, the authors derive an expression for the radial pencil beam width in heterogeneous slab geometries which is independent of the proton scattering power and related quantities. The authors then perform test calculations in homogeneous and heterogeneous slab phantoms using both the original 2D scaling model and the new model with expressions for the radial kernel width in water computed from both local and nonlocal scattering power models, as well as a nonlocal parameterization of Molière scattering theory. In addition to kernel width calculations, dose calculations are also performed for a narrow Gaussian proton beam. Results: Pencil beam width calculations indicate that both 2D scaling formalisms perform well when the radial kernel width in water is derived from a local scattering power model. Computing the radial kernel width from a nonlocal scattering model results in the local 2D scaling formula under-predicting the pencil beam width by as much as 1.4 mm (21%) at the depth of the Bragg peak for a 220 MeV proton beam in homogeneous water. This translates into a 32% dose discrepancy for a 5 mm Gaussian proton beam. Similar trends were observed for calculations made in heterogeneous slab phantoms where it was also noted that errors tend to increase with greater beam penetration. The generalized 2D scaling model performs well in all situations, with a maximum dose error of 0.3% at the Bragg peak in a heterogeneous phantom containing 3 cm of hard bone. Conclusions:The authors have derived a generalized form of 2D pencil beam scaling which is independent of the proton scattering power model and robust to the functional form of the radial kernel width in water used for the calculations. Sample calculations made with this model show excellent agreement with expected values in both homogeneous water and heterogeneous phantoms.

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Dose calculations in proton beams: range straggling corrections and energy scaling

Cited by 51 publications

References 37 publications

Alternative scattering power for Gaussian beam model of heavy charged particles

Alternative scattering power for Gaussian beam model of heavy charged particles

Comparative Planning Study for Proton Radiotherapy of Benign Brain Tumors

A generalized 2D pencil beam scaling algorithm for proton dose calculation in heterogeneous slab geometries

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