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SU‐FF‐T‐158: Determination of the Energy Spectrum of Bremsstrahlung of Linear Accelerations by Monte‐Carlo Calculations and An Analysis of Depth Dose Curves
Author(s) -
Ulmer W
Publication year - 2006
Publication title -
medical physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.473
H-Index - 180
eISSN - 2473-4209
pISSN - 0094-2405
DOI - 10.1118/1.2241082
Subject(s) - monte carlo method , bremsstrahlung , kernel (algebra) , computational physics , laplace transform , physics , mathematics , photon , mathematical analysis , optics , statistics , combinatorics
Purpose: The knowledge of the bremsstrahlung spectrum of a linear accelerator (6 MV up to 18 MV) represents the physical base of therapy planning systems. It is obtained by Monte‐Carlo calculations by taking account of the complete beam‐line (geometry/materials). It is also obtained by an analysis of depth dose curves of small fields via Laplace transform, if the electron energy E el is known (upper limit of photon energy). Method and Materials: Monte‐Carlo calculations with EGSnrc with respect to the beam‐line of 6/18 MV (Varian 2300 C/D) and 6 MV (Varian 600C) have been performed for the AAA algorithm (Eclipse). The analysis of absorption depth dose curves in water (3×3 cm 2 / 4×4 cm 2 fields) of the mentioned machines has been performed for the central ray and tilted rays with the Laplace transform of a power sequence of Poisson distributions, which provide the reproducing kernel and the energy spectrum. The scatter profiles have been removed by a deconvolution. Results: Monte‐Carlo calculations and the Laplace transform method are in good agreement (standard deviation: ca. 1%) in the above cases. The formal integration of the reproducing kernel provides an analytical spectral distribution function f ( E ) = ( 1 − exp ( − α ⋅ E / E el) ) ⋅ exp ( − β E 2/ E el 2) ⋅ ( 1 − E / E el ) qThe parameter α and q depend on the radial distance of tilted rays from the central ray at surface. It is also used to fit fluctuations of Monte‐Carlo calculations. Conclusion: The Laplace transform method even works, if only E el , the measured depth dose curves and profiles of small field sizes are known. A comparison of 6 MV (2300 C/D) with 6 MV (600C) shows that the spectral distribution of the latter case rather corresponds to the 10 MV mode of a 2300 C/D machine. This results from the Pb‐alloy of the flattening filter, whereas the 6/10 MV modes of the 2300 C/D use a Cu‐filter.