An empirical model of diagnostic x‐ray attenuation under narrow‐beam geometry

Mathieu, Kelsey Boitnott; Kappadath, S. Cheenu; White, R. Allen; Atkinson, E. Neely; Cody, Dianna D.

doi:10.1118/1.3592933

Cited by 15 publications

(15 citation statements)

References 16 publications

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“…Figure 2 shows the experimental setup for the nonrotating method. In the service engineering mode, the X‐ray tube was positioned at 6 o'clock direction, the ionization chamber was placed free‐in‐air at the isocenter of the gantry, (1,4) and the aluminum filters were placed on a 25 mm wide lead collimator 75 mm above the bottom surface of the gantry.…”

Section: Methodsmentioning

confidence: 99%

Accuracy of measuring half‐ and quarter‐value layers and appropriate aperture width of a convenient method using a lead‐covered case in X‐ray computed tomography

Matsubara

Ichikawa

Murasaki

et al. 2014

J Applied Clin Med Phys

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Determination of the half‐value layer (HVL) and quarter‐value layer (QVL) values is not an easy task in X‐ray computed tomography (CT), because a nonrotating X‐ray tube must be used, which requires the assistance of service engineers. Therefore, in this study, we determined the accuracy of the lead‐covered case method, which uses X‐rays from a rotating X‐ray tube, for measuring the HVL and QVL in CT. The lead‐covered case was manufactured from polystyrene foam and a 4 mm thick lead plate. The ionizing chamber was placed in the center of the case and aluminum filters were placed 15 cm above the aperture surface. Aperture widths of 1.0, 2.0, and 3.0 cm for a tube voltage of 110 kV and an aperture width of 2.0 cm for the tube voltages of 80 and 130 kV were used to measure exposure doses. The results of the HVL and QVL were compared with those of the conventional nonrotating method. A 2.0 cm aperture was believed to be adequate, because of its small differences in the HVL and QVL in the nonrotating method and its reasonable exposure dose level. When the 2.0 cm aperture was used, the lead‐covered case method demonstrated slightly larger HVLs and QVLs (0.03‐0.06 mm for the HVL and 0.2‐0.4 mm for the QVL) at all the tube voltage settings. However, the differences in the effective energy were 0.1‐0.3 keV; therefore, it could be negligible in an organ‐absorbed dose evaluation and a quality assurance test for CT.PACS numbers: 87.57.‐s; 87.57.Q‐; 87.57.uq

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Section: Methodsmentioning

confidence: 99%

Accuracy of measuring half‐ and quarter‐value layers and appropriate aperture width of a convenient method using a lead‐covered case in X‐ray computed tomography

Matsubara

Ichikawa

Murasaki

et al. 2014

J Applied Clin Med Phys

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“…The Lambert-W function has applications in various scientific disciplines, and recently it has been utilized in modeling of kilovoltage x-ray beam attenuation. 16 It will be shown that the proposed model has a computational complexity far less compared with the existing methods and provides a close match to the gold standard modeling techniques, such as MC simulation.…”

Section: Introductionmentioning

confidence: 92%

“…whose solution involves the Lamber-W function (readers are advised to refer to Appendix A of 16 ) given by E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 2 0 ; 6 3 ; 5 6 6 I ¼…”

Section: Generalized Beer-lambert Law (Proposed Model)mentioning

confidence: 99%

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Generalized Beer–Lambert model for near-infrared light propagation in thick biological tissues

2016

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The attenuation of near-infrared (NIR) light intensity as it propagates in a turbid medium like biological tissue is described by modified the Beer–Lambert law (MBLL). The MBLL is generally used to quantify the changes in tissue chromophore concentrations for NIR spectroscopic data analysis. Even though MBLL is effective in terms of providing qualitative comparison, it suffers from its applicability across tissue types and tissue dimensions. In this work, we introduce Lambert-W function-based modeling for light propagation in biological tissues, which is a generalized version of the Beer–Lambert model. The proposed modeling provides parametrization of tissue properties, which includes two attenuation coefficients μ0 and η. We validated our model against the Monte Carlo simulation, which is the gold standard for modeling NIR light propagation in biological tissue. We included numerous human and animal tissues to validate the proposed empirical model, including an inhomogeneous adult human head model. The proposed model, which has a closed form (analytical), is first of its kind in providing accurate modeling of NIR light propagation in biological tissues.

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“…Appendix: Excluding the model by Mathieu et al 31 proposed an attenuation model based on the Lambert W function. According to this model the measured intensities should be described by the following equation: However, our data clearly deviate from eq.…”

Section: Acknowledgmentsmentioning

confidence: 99%

Correction of beam hardening in X-ray radiograms

Baur

Uhlmann

Pöschel

et al. 2019

Review of Scientific Instruments

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The intensity of a monochromatic X-ray beam decreases exponentially with the distance it has traveled inside a material; this behavior is commonly referred to as Beer-Lambert's law. Knowledge of the materialspecific attenuation coefficient µ allows to determine the thickness of a sample from the intensity decrease the beam has experienced. However, classical X-ray tubes emit a polychromatic bremsstrahlung-spectrum. And the attenuation coefficients of all materials depend on the photon energy: photons with high energy are attenuated less than photons with low energy. In consequence, the X-ray spectrum changes while traveling through the medium; due to the relative increase of high energy photons this effect is called beam hardening. For this varying spectrum, the Beer-Lambert law only remains valid if µ is replaced by an effective attenuation coefficient µ eff which depends not only on the material, but also its thickness x and the details of the X-ray setup used. We present here a way to deduce µ eff (x) from a small number of auxiliary measurements using a phenomenological model. This model can then be used to determine an unknown material thickness or in the case of a granular media its volume fraction.

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An empirical model of diagnostic x‐ray attenuation under narrow‐beam geometry

Abstract: The proposed Lambert W model accurately describes attenuation of both monoenergetic radiation and (kilovoltage) polyenergetic beams (under narrow-beam geometry).

Cited by 15 publications

References 16 publications

Accuracy of measuring half‐ and quarter‐value layers and appropriate aperture width of a convenient method using a lead‐covered case in X‐ray computed tomography

Accuracy of measuring half‐ and quarter‐value layers and appropriate aperture width of a convenient method using a lead‐covered case in X‐ray computed tomography

Generalized Beer–Lambert model for near-infrared light propagation in thick biological tissues

Correction of beam hardening in X-ray radiograms

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