Energy‐range relation and mean energy variation in therapeutic particle beams

Kempe, Johanna; Brahme, Anders

doi:10.1118/1.2815935

Cited by 23 publications

(26 citation statements)

References 38 publications

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“…The bipartition model in here is illustrated with the SHIELD-HIT+ MC simulations. The Monte Carlo SHIELD-HIT+ code has advantageous features in implementing radiation for charged particles, see [29,30]. The results are discussed in the aspect of the primary particles fluence, planar fluence and absorbed dose of primary 1 H ions and their associated 1 H fragments in tissue-like media with ranges of clinical interest.…”

Section: Monte Carlo Simulationsmentioning

confidence: 98%

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Ion transport in inhomogeneous media based on the bipartition model for primary ions

Asadzadeh

Brahme

Kempe

2010

Computers & Mathematics with Applications

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a b s t r a c tThe present paper is focused on the mathematical modeling of the charged particle transport in nonuniform media. We study the energy deposition of high energy protons and electrons in an energy range of ≈50-500 MeV. This work is an extension of the bipartition model; for high energy electrons studied by Luo and Brahme in [Z. Luo, A. Brahme, High energy electron transport, Phys. Rev. B 46 (1992) 739-752] [42]; and for light ions studied by Luo and Wang in [Z. Luo, S. Wang, Bipartition model of ion transport: an outline of new range theory for light ions, Phys. Rev. B 36 (1987) 1885-1893]; to the field of high energy ions in inhomogeneous media with the retained energy-loss straggling term. In the bipartition model, the transport equation is split into a coupled system of convection-diffusion equations controlled by a partition condition. A similar split is obtained in an asymptotic expansion approach applied to the linear transport equation yielding pencil beam and broad beam models, which are again convection-diffusion type equations. We shall focus on the bipartition model applied for solving three types of problems: (i) normally incident ion transport in a slab; (ii) obliquely incident ion transport in a semi-infinite medium; (iii) energy deposition of ions in a multilayer medium. The broad beam model of the proton absorbed dose was illustrated with the results of a modified Monte Carlo code: SHIELD -HIT +.

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Section: Monte Carlo Simulationsmentioning

confidence: 98%

“…X -ray) and charged (electron and ion) particle beams are extensively used in radiation therapy both for early cancer detection and dose computations/algorithms see, e.g. [24][25][26][27][28][29][30][31][32][33][34][35].…”

Section: Introductionmentioning

confidence: 99%

Ion transport in inhomogeneous media based on the bipartition model for primary ions

Asadzadeh

Brahme

Kempe

2010

Computers & Mathematics with Applications

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“…The analytical solutions are combined with recently developed accurate energy loss, range relations, and multiple scattering expressions for the primary ions and their generated fragments [16,17]. The loss of primaries as well as their associated secondaries is shown to be largely based on closely exponential particle fluence attenuation.…”

Section: Introductionmentioning

confidence: 98%

“…The loss of primaries as well as their associated secondaries is shown to be largely based on closely exponential particle fluence attenuation. The Monte Carlo code SHIELD-HIT [18,19] as well as the modified version SHIELD-HIT þ [16,17] were used to calculate the fluence and absorbed dose for broad beams and narrow pencil beams. The code SHIELD-HIT þ was used to calculate the double differential fluence in both energy and angle for plane monodirectional and monoenergetic incident 7 Li, 11 C, and 12 C ion beams.…”

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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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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“…It is the fitted range in water (1), R FIT = A (mm) if ρ = 1g/cm 3 . The range in water as a function of the proton-beam energy is a well-studied dependence [11][12][13][14]. We adopted the model proposed in Ref.…”

Section: Energy -Scalingmentioning

confidence: 99%

Ranges of protons in biological targets

Pavlovič

Hammerle

2017

Journal of Electrical Engineering

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The paper introduces a simple fitting function for quick assessment of proton ranges in biological targets and human tissues. The function has been found by fitting an extensive data set of Monte Carlo proton ranges obtained with the aid of the SRIM-2013 code. The data has been collected for 28 different targets at 8 energies in the interval from 60 MeV to 220 MeV. The paper shows that at a given kinetic proton-beam energy, the Monte Carlo ranges can be satisfactorily fitted by a power function that depends solely on the target density. This is a great advantage for targets, for which the exact chemical composition is not known, or the mean ionizing potential is not reliably known. The satisfactory fit is meant as the fit that stays within the natural range straggling of the Monte Carlo ranges. In the second step, the energy-scaling yielding a universal fitting formula for proton ranges as a function of proton-beam energy and target density is introduced and discussed. This paper is an extended version of the contribution presented at the APCOM2017 conference.K e y w o r d s: biological targets, proton range, proton therapy, range straggling, SRIM

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Energy‐range relation and mean energy variation in therapeutic particle beams

Cited by 23 publications

References 38 publications

Ion transport in inhomogeneous media based on the bipartition model for primary ions

Ion transport in inhomogeneous media based on the bipartition model for primary ions

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

Ranges of protons in biological targets

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