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

• Published in: Medical physics (Lancaster) 2011-08, Vol.38 (8), p.4546-4555
• Main Authors: Mathieu, Kelsey B., Kappadath, S. Cheenu, White, R. Allen, Atkinson, E. Neely, Cody, Dianna D.
• Format: Article
• Language: English
• Subjects: ABSORPTION; Aluminium; BEAMS; biological organs; BIOMEDICAL RADIOGRAPHY; Biophysical Phenomena; Computed tomography; Computer modeling; Computer Simulation; computerised tomography; COMPUTERIZED TOMOGRAPHY; Data analysis; diagnostic radiography; Female; half-value layer; Humans; INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND TECHNOLOGY; INTERPOLATION; IONIZATION CHAMBERS; LAYERS; MAMMARY GLANDS; Mammography; Mammography - statistics & numerical data; MATHEMATICAL MODELS; Models, Theoretical; PATIENTS; polyenergetic; Radiation Measurement Physics; Radiation monitoring, control, and safety; RADIATION PROTECTION; Radiography; Radiography - statistics & numerical data; RADIOLOGY AND NUCLEAR MEDICINE; Radiometry; REGRESSION ANALYSIS; Scattering, Radiation; SIMULATION; THICKNESS; Tomography, X-Ray Computed - statistics & numerical data; TRANSMISSION; Transmission measurement; X RADIATION; X‐ and γ‐ray instruments; X‐ray absorption; X‐ray apparatus; X‐ray spectra
• ISSN: 0094-2405; 2473-4209; 0094-2405
• DOI: 10.1118/1.3592933

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).