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

被引:11
|
作者
Mathieu, Kelsey B. [1 ]
Kappadath, S. Cheenu [2 ]
White, R. Allen [3 ]
Atkinson, E. Neely [4 ]
Cody, Dianna D. [2 ]
机构
[1] Rice Univ, Dept Bioengn, Houston, TX 77005 USA
[2] Univ Texas MD Anderson Canc Ctr, Div Diagnost Imaging, Houston, TX 77030 USA
[3] Univ Texas MD Anderson Canc Ctr, Div Bioinformat & Computat Biol, Houston, TX 77030 USA
[4] Rice Univ, Dept Stat, Houston, TX 77005 USA
关键词
CT; mammography; radiography; polyenergetic; half-value layer; HALF-VALUE LAYER; SPECTRA; CT;
D O I
10.1118/1.3592933
中图分类号
R8 [特种医学]; R445 [影像诊断学];
学科分类号
1002 ; 100207 ; 1009 ;
摘要
Purpose: The purpose of this study was to develop and validate a mathematical model to describe narrow-beam attenuation of kilovoltage x-ray beams for the intended applications of half-value layer (HVL) and quarter-value layer (QVL) estimations, patient organ shielding, and computer modeling. Methods: An empirical model, which uses the Lambert W function and represents a generalized Lambert-Beer law, was developed. To validate this model, transmission of diagnostic energy x-ray beams was measured over a wide range of attenuator thicknesses [0.49-33.03 mm Al on a computed tomography (CT) scanner, 0.09-01.93 mm Al on two mammography systems, and 0.1-0.45 mm Cu and 0.49-14.87 mm Al using general radiography]. Exposure measurements were acquired under narrow-beam geometry using standard methods, including the appropriate ionization chamber, for each radiographic system. Nonlinear regression was used to find the best-fit curve of the proposed Lambert W model to each measured transmission versus attenuator thickness data set. In addition to validating the Lambert W model, we also assessed the performance of two-point Lambert W interpolation compared to traditional methods for estimating the HVL and QVL [i.e., semi-logarithmic (exponential) and linear interpolation]. Results: The Lambert W model was validated for modeling attenuation versus attenuator thickness with respect to the data collected in this study (R-2 > 0.99). Furthermore, Lambert W interpolation was more accurate and less sensitive to the choice of interpolation points used to estimate the HVL and/or QVL than the traditional methods of semilogarithmic and linear interpolation. Conclusions: The proposed Lambert W model accurately describes attenuation of both monoenergetic radiation and (kilovoltage) polyenergetic beams (under narrow-beam geometry). (C) 2011 American Association of Physicists in Medicine. [DOI: 10.1118/1.3592933]
引用
收藏
页码:4546 / 4555
页数:10
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