Parameterized algorithms for quantitative differentials in spectrally equivalent medical diagnostic x‐ray beams

Abstract

Qualitative and quantitative equivalence of spectra transmitted by two different elemental filters require a good match in terms of shape and size over the entire energy range of 0-150 keV used in medical diagnostic radiology. However, the photoelectric absorptions and Compton scattering involved in the interaction of x rays with matter at these relatively low photon energies differ in a nonuniform manner with energy and atomic number. By careful choice of thicknesses for filter materials with an atomic number between 12 and 39, when compared with aluminum, it is possible to obtain transmitted beams of the same shape (quality) but not of the same size (quantity). In this paper, calculations have been carried out for the matching of the shapes and sizes of beams transmitted through specified thicknesses of aluminium filter and spectrally equivalent thicknesses of other filter materials (different from aluminium) using FORTRAN source codes traceable to the American Association of Physics in Medicine (AAPM), College Park, MD, USA. Parametrized algorithms for the evaluation of quantitative differentials (deficit or surplus) in radiation output (namely, photon fluence, exposure, kerma, energy imparted, absorbed dose, and effective dose) from these transmitted spectrally equivalent beams were developed. These differentials range between 1%, and 4% at 1 mm Al filtration and between 8%, and 25% for filtration of 6 mm Al for different filter materials in comparison with aluminum. Also developed were models for factors for converting measures of photon fluence, exposure-area product, (EAP), and kerma-area product (KAP) to risk related quantities such as energy imparted, absorbed dose, and effective dose from the spectrally equivalent beams. The thicknesses of other filter materials that are spectrally equivalent to given thicknesses of aluminum filter were characterized using polynomial functions. The fact that the use of equivalent spectra in radiological practice can provide means of ranking the differentials in radiographic image quality and stochastic risk is discussed.

Alternative X-ray filters for an intra-oral digital radiographic system

“…6 The increase in thickness of the filter generates more secondary radiation which will be scattered, requiring higher tube currents or exposure times and causing a decline in the lifespan of the X-ray tube. 15 This can be considered a problem for the DenOptix system as this system creates more noise than others and therefore needs a higher radiation dose. 2,16,17 In the present study the noise was not evaluated; we evaluated the reproducibility of the contrast which showed high values, even with the addition of a tissue-equivalent that produces scattering similar to that caused by the soft tissue of a patient.…”

Computer simulations and models for the performance characteristics of spectrally equivalent X-ray beams in medical diagnostic radiology

“…From the earlier work reported,[6] for a given filter material m in comparison with aluminum filter at spectrally equivalent thickness,…”

“…(9) are reported in Table 1 of Okunade[6] for filter materials m with atomic numbers ranging from 12 to 39 and kVp ranging between 50 and 140 when reference filter is assumed to be aluminum.…”

“…By careful choice of thickness, two different elemental filters can be made to transmit beams that are simultaneously of the same/close shape (quantity) and size (quality). [3–6] When used under the same irradiation condition, beams that are strictly equivalent or relatively equivalent in terms of shape and size will produce identical or relatively identical image quality and patient dose. The results of theoretical and experimental approaches to the comparative ranking of the transmissions of filter materials on the basis of closeness of hardening (size) and attenuation (quantity) properties have been reported earlier in literature.…”

“…Analytical models similar to those earlier reported[6] for quantitative parameters were derived for the evaluation of differences in parameters for image quality, such as contrast-to-noise ratio (CNR) and figure-of-merit (FOM) for filter materials that transmit spectrally equivalent beams. For the purpose of clinical assessment of the performance characteristics of spectrally equivalent beams, iterative computer software EQSPECT.FOR was developed for the evaluation of these models.…”