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

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

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

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, 0.09-1.93 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., semilogarithmic (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 (R2 > 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).

Original languageEnglish (US)
Pages (from-to)4546-4555
Number of pages10
JournalMedical physics
Volume38
Issue number8
DOIs
StatePublished - Aug 2011

Fingerprint

X-Rays
X-Ray Computed Tomography Scanners
Mammography
Radiography
Theoretical Models
Radiation

Keywords

  • CT
  • half-value layer
  • mammography
  • polyenergetic
  • radiography

ASJC Scopus subject areas

  • Biophysics
  • Radiology Nuclear Medicine and imaging

Cite this

An empirical model of diagnostic x-ray attenuation under narrow-beam geometry. / Mathieu, Kelsey B.; Kappadath, S. Cheenu; White, R. Allen; Atkinson, E. Neely; Cody, Dianna D.

In: Medical physics, Vol. 38, No. 8, 08.2011, p. 4546-4555.

Research output: Contribution to journalArticle

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