Implementation of pencil kernel and depth penetration algorithms for treatment planning of proton beams

Russell, Kellie R.; Isacsson, Ulf; Saxner, M.; Ahnesjö, Anders; Montelius, Anders; Grusell, Erik; Dahlgren, Christina Vallhagen; Lorin, Stefan; Glimelius, Bengt

doi:10.1088/0031-9155/45/1/302

Cited by 62 publications

(46 citation statements)

References 40 publications

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“…Since the range of the boron fragment is longer than the primary particle a secondary tail of È is seen. 11 B ions in a 0.6 mm diameter 12 C beam in water (solid curves). The absorbed dose of these heavy fragments is clearly influenced by rapidly increasing energy loss towards the end of their ranges, cf.…”

Section: Resultsmentioning

confidence: 99%

“…Based on the simple Fokker-Plank approximation of the multiple scattering collision term of the Boltzmann equation, the first analytical solution for pencil beam transport was derived by Fermi in 1941 [3] and Eyges in 1948 [4] taking energy losses within the continuous slowing down approximation (CSDA) into account. This pencil beam solution has further been generalized to describe the lateral spread of arbitrary Gaussian beams of known initial mean square radial " r 2 ð0Þ, angular spread, " 2 ð0Þ, and covariance " r ð0Þ [5,6], of clinical electron beams in a patient during radiation therapy of malignant tumors [5][6][7][8], as well as to describe the transport of light ions in different media [9][10][11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

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Solution of the Boltzmann equation for primary light ions and the transport of their fragments

Kempe

Brahme

2010

Phys. Rev. ST Accel. Beams

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The Boltzmann equation for the transport of pencil beams of light ions in semi-infinite uniform media has been calculated. The equation is solved for the practically important generalized 3D case of Gaussian incident primary light ion beams of arbitrary mean square radius, mean square angular spread, and covariance. The transport of the associated fragments in three dimensions is derived based on the known transport of the primary particles, taking the mean square angular spread of their production processes, as well as their energy loss and multiple scattering, into account. The analytical pencil and broad beam depth fluence and absorbed dose distributions are accurately expressed using recently derived analytical energy and range formulas. The contributions from low and high linear energy transfer (LET) dose components were separately identified using analytical expressions. The analytical results are compared with SHIELD-HIT Monte Carlo (MC) calculations and found to be in very good agreement. The pencil beam fluence and absorbed dose distributions of the primary particles are mainly influenced by an exponential loss of the primary ions combined with an increasing lateral spread due to multiple scattering and energy loss with increasing penetration depth. The associated fluence of heavy fragments is concentrated at small radii and so is the LET and absorbed dose distribution. Their transport is also characterized by the buildup of a slowing down spectrum which is quite similar to that of the primaries but with a wider energy and angular spread at increasing penetration depths. The range of the fragments is shorter or longer depending on their nuclear mass to charge ratio relative to that of the primary ions. The absorbed dose of the heavier fragments is fairly similar to that of the primary ions and also influenced by a rapidly increasing energy loss towards the end of their ranges. The present analytical solution of the Boltzmann equation accurately accounts for the loss of primary particles as well as their energy losses and multiple scattering. At the same time these quantities for the fragments are also accurately derived as based on the generalized Gaussian solution of the primaries and compared both with Monte Carlo and experimental data. The results are useful for fast transport calculations and biologically optimized therapy planning with light ion beams.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Solution of the Boltzmann equation for primary light ions and the transport of their fragments

Kempe

Brahme

2010

Phys. Rev. ST Accel. Beams

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“…(3), as well as the nonlocal generalized highland formula computed with Eq. (6). Subsequent rows show the accuracy of both 2D scaling formalisms in reproducing each nominal curve when said curve is used as input for the calculations.…”

Section: Iiid Calculation Detailsmentioning

confidence: 99%

“…[4][5][6][7][8][9][10] Conceptually similar to the convolution algorithms used in modern photon therapy treatment planning, 11,12 pencil beam algorithms model the full proton beam as a two-dimensional (2D) convolution of the proton fluence with a pencil beam dose kernel computed over surfaces normal to the proton beam's initial direction at each depth within the calculation geometry. The pencil beam kernel represents the dose distribution in water created by an elementary pencil beam of unit fluence with kinetic energy corresponding to the beam's full range, and can be calculated using various combinations of physics models and/or measured data.…”

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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“…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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Implementation of pencil kernel and depth penetration algorithms for treatment planning of proton beams

Cited by 62 publications

References 40 publications

Solution of the Boltzmann equation for primary light ions and the transport of their fragments

Solution of the Boltzmann equation for primary light ions and the transport of their fragments

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

Comparative Planning Study for Proton Radiotherapy of Benign Brain Tumors

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