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Title: Orthogonal Dirichlet Polynomials
Abstract. Let fj g1 j=1 be a sequence of distinct positive numbers. Let w be a nonnegative function, integrable on the real line. One can form orthogonal Dirichlet polynomials fng from linear combinations of n  more » « less
Award ID(s):
Author(s) / Creator(s):
Daras, N.; Rassias, T.
Date Published:
Journal Name:
Approximation and Computation in Science and Engineering
Page Range / eLocation ID:
Medium: X
Sponsoring Org:
National Science Foundation
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  5. Abstract Background

    In a recent study, we reported beam quality correction factors,fQ, in carbon ion beams using Monte Carlo (MC) methods for a cylindrical and a parallel‐plate ionization chamber (IC). A non‐negligible perturbation effect was observed; however, the magnitude of the perturbation correction due to the specific IC subcomponents was not included. Furthermore, the stopping power data presented in the International Commission on Radiation Units and Measurements (ICRU) report 73 were used, whereas the latest stopping power data have been reported in the ICRU report 90.


    The aim of this study was to extend our previous work by computingfQcorrection factors using the ICRU 90 stopping power data and by reporting IC‐specific perturbation correction factors. Possible energy or linear energy transfer (LET) dependence of thefQcorrection factor was investigated by simulating both pristine beams and spread‐out Bragg peaks (SOBPs).


    The TOol for PArticle Simulation (TOPAS)/GEANT4 MC code was used in this study. A 30 × 30 × 50 cm3water phantom was simulated with a uniform 10 × 10 cm2parallel beam incident on the surface. A Farmer‐type cylindrical IC (Exradin A12) and two parallel‐plate ICs (Exradin P11 and A11) were simulated in TOPAS using the manufacturer‐provided geometrical drawings. ThefQcorrection factor was calculated in pristine carbon ion beams in the 150–450 MeV/u energy range at 2 cm depth and in the middle of the flat region of four SOBPs. ThekQcorrection factor was calculated by simulating thefQocorrection factor in a60Co beam at 5 cm depth. The perturbation correction factors due to the presence of the individual IC subcomponents, such as the displacement effect in the air cavity, collecting electrode, chamber wall, and chamber stem, were calculated at 2 cm depth for monoenergetic beams only. Additionally, the mean dose‐averaged and track‐averaged LET was calculated at the depths at which thefQwas calculated.


    The ICRU 90fQcorrection factors were reported. Thepdiscorrection factor was found to be significant for the cylindrical IC with magnitudes up to 1.70%. The individual perturbation corrections for the parallel‐plate ICs were <1.0% except for the A11pcelcorrection at the lowest energy. ThefQcorrection for the P11 IC exhibited an energy dependence of >1.00% and displayed differences up to 0.87% between pristine beams and SOBPs. Conversely, thefQfor A11 and A12 displayed a minimal energy dependence of <0.50%. The energy dependence was found to manifest in the LET dependence for the P11 IC. A statistically significant LET dependence was found only for the P11 IC in pristine beams only with a magnitude of <1.10%.


    The perturbation andkQcorrection factor should be calculated for the specific IC to be used in carbon ion beam reference dosimetry as a function of beam quality.

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