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تسجيل مستخدم جديدSemi-empirical formulation of multiple scattering for Gaussian beam model of heavy charged particles stopping in tissue-like matter
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Nobuyuki Kanematsu
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Dose calculation for radiotherapy with protons and heavier ions deals with a large volume of path integrals involving a scattering power of body tissue. This work provides a simple model for such demanding applications. There is an approximate linearity between RMS end-point displacement and range of incident particles in water, empirically found in measurements and detailed calculations. This fact was translated into a simple linear formula, from which the scattering power that is only inversely proportional to residual range was derived. The simplicity enabled analytical formulation for ions stopping in water, which was designed to be equivalent with the extended Highland model and agreed with measurements within 2% or 0.02 cm in RMS displacement. The simplicity will also improve the efficiency of numerical path integrals in the presence of heterogeneity.
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This 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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A model for beam customization with collimators and a range-compensating filter based on the phase-space theory for beam transport is presented for dose distribution calculation in treatment planning of radiotherapy with protons and heavier ions. Ind
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onal pencil-beam algorithm to deal with these structures due to beam-size growth during transport. This study aims to resolve the problem with a novel computational model. The pencil beams are initially defined at the range compensating filter with angular-acceptance correction for the upstream collimators followed by the range compensation effects. They are individually transported with possible splitting near the downstream collimator edges to deal with its fine structure. The dose distribution for a carbon-ion beam was calculated and compared with existing experimental data. The penumbra sizes of various collimator edges agreed between them to a submillimeter level. This beam-customization model will complete an accurate and efficient dose-calculation algorithm for treatment planning with heavy charged particles.
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