WAXS fat subtraction model to estimate differential linear scattering coefficients of fatless breast tissue: Phantom materials evaluation

Purpose: Develop a method to subtract fat tissue contributions to wide-angle x-ray scatter (WAXS) signals of breast biopsies in order to estimate the differential linear scattering coefficients μs of fatless tissue. Cancerous and fibroglandular tissue can then be compared independent of fat content. In this work phantom materials with known compositions were used to test the efficacy of the WAXS subtraction model. Methods: Each sample 5 mm in diameter and 5 mm thick was interrogated by a 50 kV 2.7 mm diameter beam for 3 min. A 25 mm2 by 1 mm thick CdTe detector allowed measurements of a portion of the θ = 6° scattered field. A scatter technique provided means to estimate the incident spectrum N 0(E) needed in the calculations of μs[x(E, θ)] where x is the momentum transfer argument. Values of \documentclass[12pt]{minimal}\begin{document}$\overline{\mu }_{\mathrm{s}}$\end{document} μ ¯ s for composite phantoms consisting of three plastic layers were estimated and compared to the values obtained via the sum \documentclass[12pt]{minimal}\begin{document}$\overline{\mu }_{\mathrm{s}}^{\sum }(x) = \nu _{1} \mu _{\mathrm{s}1}(x) + \nu _{2} \mu _{\mathrm{s}2}(x) + \nu _3 \mu _{\mathrm{s}3}(x)$\end{document} μ ¯ s ∑ ( x ) = ν 1 μ s 1 ( x ) + ν 2 μ s 2 ( x ) + ν 3 μ s 3 ( x ) , where νi is the fractional volume of the ith plastic component. Water, polystyrene, and a volume mixture of 0.6 water + 0.4 polystyrene labelled as fibphan were chosen to mimic cancer, fat, and fibroglandular tissue, respectively. A WAXS subtraction model was used to remove the polystyrene signal from tissue composite phantoms so that the μs of water and fibphan could be estimated. Although the composite samples were layered, simulations were performed to test the models under nonlayered conditions. Results: The well known μs signal of water was reproduced effectively between 0.5 < x < 1.6 nm−1. The \documentclass[12pt]{minimal}\begin{document}$\overline{\mu }_{\mathrm{s}}$\end{document} μ ¯ s obtained for the heterogeneous samples agreed with \documentclass[12pt]{minimal}\begin{document}$\overline{\mu }_{\mathrm{s}}^{\sum }$\end{document} μ ¯ s ∑ . Polystyrene signals were subtracted successfully from composite phantoms. The simulations validated the usefulness of the WAXS models for nonlayered biopsies. Conclusions: The methodology to measure μs of homogeneous samples was quantitatively accurate. Simple WAXS models predicted the probabilities for specific x-ray scattering to occur from hete