A model for the energy and angular distribution of x rays emitted from an x‐ray tube. Part I. Bremsstrahlung production

Omar, Artur; Andreo, Pedro; Poludniowski, Gavin

doi:10.1002/mp.14359

Cited by 24 publications

(32 citation statements)

References 39 publications

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“…The x‐ray emission model presented in this work combines the analytical description of bremsstrahlung emission developed in Part I 16 with a previously developed analytical description of characteristic x‐ray emission 17 . Since the specifics of the methods used have been provided in previous papers, only a summary is given here.…”

Section: Methodsmentioning

confidence: 99%

“…In order to evaluate the performance of the different spectrum models, x‐ray spectra emerging from thick tungsten and molybdenum targets have been calculated using the PENELOPE 2014 MC system 18 . Since the geometry, MC transport settings, and features of PENELOPE essential for the performed simulations have been specified in Part I 16 only a general outline of the MC simulations is provided here.…”

Section: Methodsmentioning

confidence: 99%

“…The uniform approximation has, however, been shown to be a poor approximation of the actual physics involved. 15 Hence, in Part I, 16 an analytical bremsstrahlung model was developed that considers in detail the electron and intrinsic bremsstrahlung angular distributions. In this paper, Part II, the performance of the complete model for x-ray emission (bremsstrahlung and characteristic x-ray emission) is validated by comparison with MC calculations, measurements, and models developed by other authors.…”

Section: Introductionmentioning

confidence: 99%

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A model for the energy and angular distribution of x rays emitted from an x‐ray tube. Part II. Validation of x‐ray spectra from 20 to 300 kV

2020

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To present and validate a complete x-ray emission model (bremsstrahlung and characteristic x-ray emission) for the energy range 20-300 kV. Methods: An analytical x-ray spectrum model that combines the bremsstrahlung emission model developed in Part I with a previously developed characteristic x-ray emission model is validated by comparison with Monte Carlo calculations, published measured spectra, and models developed by other authors. Furthermore, the assumptions and limitations of previous spectrum models are summarized, and their predictions are compared with results obtained by Monte Carlo simulations of x rays emitted from tungsten and molybdenum targets. Results: The model is able to reproduce narrow-beam Monte Carlo calculations to within 0.5% in terms of the first and second aluminum half-value layer thickness (HVL). Compared with measured spectra, the difference in HVL is < 2% for typical diagnostic and therapeutic beam qualities available at primary standard laboratories. Compared with previous spectrum models, the present model performs especially well for low kilovoltage x-ray beams (below 50 kV), and is reliable for a wider range of takeoff angles, that is, the angle between the target surface and the direction of emission. The difference in model and Monte Carlo predictions of the energy-fluence weighted air kerma (i.e., the photon energy absorption in air) is < 0.5% using the present model, while previous spectrum models can differ by more than 10%. Conclusions: The x-ray emission model developed in this work has been validated against Monte Carlo calculations and measured results. The model provides an efficient alternative to comprehensive Monte Carlo simulations and is an improvement over previous models. The model can be used to predict both central-and off-axis spectra, as well as off-axis effects such as the (anode) heel effect.

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Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A model for the energy and angular distribution of x rays emitted from an x‐ray tube. Part II. Validation of x‐ray spectra from 20 to 300 kV

2020

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“…The physics of metal-penetrating electron beams 6 and the resulting x-ray spectra 7 have been studied for approximately 100 yr, and theoretical models have been incrementally proposed and refined [8][9][10][11][12][13][14][15] to estimate x-ray spectra. Poludniowski's book chapter 16 provides a comprehensive review of the development of such models, and recent publications 17,18 describe the latest advances. Many of these models have been implemented as analytical tools 19,20 to provide researchers the ability to quickly obtain estimated spectra for conditions of interest; target material, kVp, takeoff angle, and filtration can often be varied.…”

Section: A Physics-based Modelsmentioning

confidence: 99%

Semiempirical, parameterized spectrum estimation for x‐ray computed tomography

Fitzgerald

Araujo

et al. 2021

Medical Physics

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To develop a tool to produce accurate, well-validated x-ray spectra for standalone use or for use in an open-access x-ray/CT simulation tool. Spectrum models will be developed for tube voltages in the range of 80 kVp through 140 kVp and for anode takeoff angles in the range of 5°to 9°. Methods: Spectra were initialized based on physics models, then refined using empirical measurements, as follows. A new spectrum-parameterization method was developed, including 13 spline knots to represent the bremsstrahlung component and 4 values to represent characteristic lines. Initial spectra at 80, 100, 120, and 140 kVp and at takeoff angles from 5°to 9°were produced using physics-based spectrum estimation tools XSPECT and SpekPy. Empirical experiments were systematically designed with careful selection of attenuator materials and thicknesses, and by reducing measurement contamination from scatter to <1%. Measurements were made on a 64-row CT scanner using the scanner's detector and using multiple layers of polymethylmethacrylate (PMMA), aluminum, titanium, tin, and neodymium. Measurements were made at 80, 100, 120, and 140 kVp and covering the entire 64-row detector (takeoff angles from 5°to 9°); a total of 6,144 unique measurements were made. After accounting for the detector's energy response, parameterized representations of the initial spectra were refined for best agreement with measurements using two proposed optimization schemes: based on modulation and based on gradient descent. X-ray transmission errors were computed for measurements vs calculations using the nonoptimized and optimized spectra. Half-value, tenth-value, and hundredth-value layers for PMMA, Al, and Ti were calculated. Results: Spectra before and after parameterization were in excellent agreement (e.g., R 2 values of 0.995 and 0.997). Empirical measurements produced smoothly varying curves with x-ray transmission covering a range of up to 3.5 orders of magnitude. Spectra from the two optimization schemes, compared with the unoptimized physic-based spectra, each improved agreement with measurements by twofold through tenfold, for both postlog transmission data and for fractional value layers. Conclusion:The resulting well-validated spectra are appropriate for use in the open-access x-ray/CT simulator under development, the x-ray-based Cancer Imaging Toolkit (XCIST), or for standalone use. These spectra can be readily interpolated to produce spectra at arbitrary kVps over the range of 80 to 140 kVp and arbitrary takeoff angles over the range of 5°to 9°. Furthermore, interpolated spectra over these ranges can be obtained by applying the standalone Matlab function available at https:// github.com/xcist/documentation/blob/master/XCISTspectrum.m.

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“…Various authors have successfully modeled the spectra of planar anode surfaces which can be used to calculate the expected reduced total x-ray output O' total resulting from d' x-ray (y). [13][14][15][16][17][18][19][20][21] In contrast to earlier publications, in which the surface roughening was also successfully linked with measurements or simulations, this work uses high-resolution surface data that accurately depicts the surface morphology of modern high-performance x-ray anodes. 1,3,5,7 In addition to the changes in the internal filtration due to surface roughening investigated in the past, the extensive shading effects of large surface features can be made visible.…”

Section: Introductionmentioning

confidence: 99%

Geometrical model for calculating the effect of surface morphology on total x‐ray output of medical x‐ray tubes

Siller¹,

Minkkinen

Bogust

et al. 2021

Medical Physics

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Correlation of characteristic surface appearance and surface roughness with measured air kerma (kinetic energy released in air) reduction of tungsten-rhenium (WRe) stationary anode surfaces. Methods: A stationary anode test system was developed and used to alter nine initially ground sample surfaces through thermal cycling at high temperatures. A geometrical model based on high resolution surface data was implemented to correlate the measured reduction of the air kerma rate with the changing surface appearance of the samples. In addition to the nine thermally cycled samples, three samples received synthetic surface structuring to prove the applicability of the model to nonconventional surface alterations. Representative surface data and surface roughness values were acquired by laser scanning confocal microscopy. Results: After thermal cycling in the stationary anode test system, the samples showed surface features comparable to rotating anodes after long-time operation. The established model enables the appearance of characteristic surface features like crack networks, pitting, and local melting to be linked to the local x-ray output at 100 kV tube voltage ,10°anode take off angle and 2 mm of added Al filtration. The results from the conducted air kerma measurements were compared to the predicted total x-ray output reduction from the geometrical model and show, on average, less than 10 % error within the 12 tested samples. In certain boundaries, the calculated surface roughness R a showed a linear correlation with the measured air kerma reduction when samples were having comparable damaging characteristics and similar operation parameters. The orientation of the surface features had a strong impact on the measured air kerma rate which was shown by testing synthetically structured surfaces.Conclusions: The geometrical model used herein considers and describes the effect of individual surface features on the x-ray output. In close boundaries arithmetic surface roughness R a was found to be a useful characteristic value on estimating the effect of surface damage on total x-ray output.

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A model for the energy and angular distribution of x rays emitted from an x‐ray tube. Part I. Bremsstrahlung production

Cited by 24 publications

References 39 publications

A model for the energy and angular distribution of x rays emitted from an x‐ray tube. Part II. Validation of x‐ray spectra from 20 to 300 kV

A model for the energy and angular distribution of x rays emitted from an x‐ray tube. Part II. Validation of x‐ray spectra from 20 to 300 kV

Semiempirical, parameterized spectrum estimation for x‐ray computed tomography

Geometrical model for calculating the effect of surface morphology on total x‐ray output of medical x‐ray tubes

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