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

Omar, Artur; Andreo, Pedro; Poludniowski, Gavin

doi:10.1002/mp.14360

Cited by 22 publications

(32 citation statements)

References 41 publications

(92 reference statements)

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…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

View full text Add to dashboard Cite

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.

show abstract

Section: A Physics-based Modelsmentioning

confidence: 99%

Semiempirical, parameterized spectrum estimation for x‐ray computed tomography

Fitzgerald

Araujo

et al. 2021

Medical Physics

View full text Add to dashboard Cite

show abstract

“…1 and Table 1. The characteristic x‐ray emission has been treated in previous work 16 and is included in Part II, 17 where the complete model (bremsstrahlung and characteristic x rays) is evaluated.…”

Section: Theorymentioning

confidence: 99%

“…In this paper, Part I, the theory for bremsstrahlung production in an x‐ray target is described and analyzed. The performance of the complete model (including an analytical model for characteristic x rays 16 ) is evaluated in the second paper, Part II, 17 where the model predictions are compared with MC calculations, measurements, and models developed by other authors.…”

Section: Introductionmentioning

confidence: 99%

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

2020

Self Cite

View full text Add to dashboard Cite

Purpose: To develop an analytical model for bremsstrahlung production in a thick x-ray target (i.e., the x-ray tube anode) that takes into account the intrinsic bremsstrahlung angular distribution. Methods: X-ray spectrum models developed from theoretical principles have traditionally treated the angular distribution of the bremsstrahlung production as spherically uniform. This assumption stems from the rationale that electrons promptly attain a diffuse directional distribution in an x-ray target due to multiple scattering, thereby effectively masking the intrinsic bremsstrahlung angular distribution. In this work, a model that explicitly accounts for the angular distribution of the bremsstrahlung production is presented. The model combines Monte Carlo-calculated depth, energy, and angular distributions of electrons penetrating the x-ray target, and incorporates theoretical results for the differential bremsstrahlung cross section. The effects of using different simplified model assumptions for the electron penetration and the intrinsic bremsstrahlung angular distribution are analyzed for tungsten and molybdenum targets in the energy range 20-300 keV. Results: Typical assumptions of previous models are shown to introduce errors in calculated spectra. Particularly, it is shown that predictions of fluence and air kerma free-in-air can be overestimated by 15-30% (2-3% in aluminum half-value layer thickness) for clinically relevant beam qualities. The present model is able to reproduce comprehensive Monte Carlo calculations of the bremsstrahlung production generally to within 1%. Conclusions: The bremsstrahlung model developed in this work is an improvement over previous models in that the main features of the electron penetration and the resulting bremsstrahlung are considered in detail. The model can be used for more accurate predictions of the energy and angular distribution of x rays emitted from an x-ray tube.

show abstract

“…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%

“…In this case d’ x‐ray (y) is increased locally due to surface alterations like cracks, pitting, or local melting which decrease the total x‐ray output (O total ). 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) 13–21 …”

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

View full text Add to dashboard Cite

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.

show abstract

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

Cited by 22 publications

References 41 publications

Semiempirical, parameterized spectrum estimation for x‐ray computed tomography

Semiempirical, parameterized spectrum estimation for x‐ray computed tomography

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

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

Contact Info

Product

Resources

About