On the scattering power of radiotherapy protons

Purpose: In treatment planning of charged-particle radiotherapy, patient heterogeneity is conventionally modeled as variable-density water converted from CT images to best reproduce the stopping power, which may lead to inaccuracies in the handling of multiple scattering and nuclear interactions. Although similar conversions can be defined for these individual interactions, they would be valid only for specific CT systems and would require additional tasks for clinical application. This study aims to improve the practicality of the interaction-specific heterogeneity correction. Methods: We calculated the electron densities and effective densities for stopping power, multiple scattering, and nuclear interactions of protons and ions, using the standard elemental-composition data for body tissues to construct the invariant conversion functions. We also simulated a proton beam in a lung-like geometry and a carbon-ion beam in a prostate-like geometry to demonstrate the procedure and the effects of the interaction-specific heterogeneity correction. Results: Strong correlations were observed between the electron density and the respective effective densities, with which we formulated polyline conversion functions. Their effects amounted to 10% differences in multiple-scattering angle and nuclear-interaction mean free path for bones compared to those in the conventional heterogeneity correction. Although their realistic effect on patient dose distributions would be generally small, it could be at the level of a few percent when a carbon-ion beam traverses a large bone. Conclusions: The present conversion functions are invariant and may be incorporated in treatment planning systems with a common function relating CT number to electron density. This will enable improved beam dose calculation while minimizing initial setup and quality management of the user's specific system.

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“…Gottschalk derived the scattering length for heavy charged particles. 11 For a composite material, it is given by…”

Section: Multiple Scatteringmentioning

confidence: 99%

Relationship between electron density and effective densities of body tissues for stopping, scattering, and nuclear interactions of proton and ion beams

Kanematsu¹,

Inaniwa²,

Koba³

2012

Med. Phys.

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“…In gold, only  MC at depth of 0.97R 0 was validated since the proton range in gold was too short, and the resultant increment of is small. The values were compared with those derived from Highland formula ( ighland ) 28,29 . In water,  ighland is a little bit greater than  MC , which agrees with the behaviors investigated before in ref 30 .…”

Section: Discussionmentioning

confidence: 99%

Biological effect of dose distortion by fiducial markers in spot‐scanning proton therapy with a limited number of fields: A simulation study

et al. 2012

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Purpose: In accurate proton spot-scanning therapy, continuous target tracking by fluoroscopic X-ray during irradiation is beneficial not only for respiratory moving tumors of lung and liver but also for relatively stationary tumors of prostate. Implanted gold markers have been used with great effect for positioning the target volume by a fluoroscopy, especially for the cases of liver and prostate with the targets surrounded by water-equivalent tissues.However, recent studies have revealed that gold markers can cause a significant underdose in proton therapy. This paper focuses on prostate cancer and explores the possibility that multiple-field irradiation improves the underdose effect by markers on Tumor Control Probability (TCP). Methods:A Monte Carlo simulation was performed to evaluate the dose distortion effect. A spherical gold marker was placed at several characteristic points in a water phantom. Markers were with two different diameters of 2 mm and 1.5 mm, both visible on fluoroscopy. Three beam arrangements of SFUD (single-field uniform dose)were examined: one lateral field, two opposite lateral fields, and three fields (two opposite lateral fields + anterior field). The Relative Biological Effectiveness (RBE) was set to 1.1 and a dose of 74 Gy (RBE) was delivered to the target of a typical prostate size in 37 fractions. The ratios of TCP to that without the marker (TCP r ) were compared with the parameters of the marker sizes, number of fields, and marker positions. To take into account the dependence of biological parameters in TCP model,  values of 1.5, 3, and 10 Gy (RBE) were considered.Results: It was found that the marker of 1.5 mm diameter does not affect the TCPs with all  values when two or more fields are used. On the other hand, if the marker size is 2 mm, more than two irradiation fields are required to suppress the decrease in TCP from TCP r by less than 3%. This is especially true when multiple (two or three) markers are used for alignment of a patient. Conclusions:It is recommended that 1.5 mm markers be used to avoid the reduction of TCP as well as to spare the surrounding critical organs, as long as the markers are visible on X-ray fluoroscopy. When 2 mm markers are implanted, more than two fields should be used and the markers should not be placed close to the distal edge of any of the beams.

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“…27) and adapted for radiotherapy protons by Gottschalk. 26 The latter formula (referred to as T IC in Ref. 26) is used in this work and is given by…”

Section: W −Ic (Z E)mentioning

confidence: 99%

“…As discussed by Gottschalk 26 and Kanematsu, 23 scattering power models generally fall into one of two categories: local models which ignore the effects of single scattering and for which Eq. (7) holds true, and nonlocal models, which account for single scattering effects and consider both the type and thickness of overlying material when computing the mean squared MCS angle at depth.…”

Section: Iic Limitations Of the Existing Modelmentioning

confidence: 99%

“…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. 23,26,27 Fermi-Eyges theory provides a Gaussian approximation to proton transport and computes the root-mean-squared (RMS) pencil beam width by integrating the projected change in the mean squared MCS angle as a function of depth. Slab geometry is assumed for the calculation, and any material dependence is taken into account in the scattering power model.…”

Section: Introductionmentioning

confidence: 99%

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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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On the scattering power of radiotherapy protons

Cited by 76 publications

References 19 publications

Relationship between electron density and effective densities of body tissues for stopping, scattering, and nuclear interactions of proton and ion beams

Relationship between electron density and effective densities of body tissues for stopping, scattering, and nuclear interactions of proton and ion beams

Biological effect of dose distortion by fiducial markers in spot‐scanning proton therapy with a limited number of fields: A simulation study

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

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