Characterization of breast samples via basis function methods using differential linear x-ray scattering coefficients

Despite advances in imaging and histology, discrepancies and sampling errors persist, prompting research into complementary methods like Wide Angle X-ray Scatter (WAXS) for improved cancer diagnosis. This study was focused on extracting an estimation of the differential linear x-ray scattering coefficient (μs) of stroma tissue and then using it in a three basis function method to estimate the make up of composite breast tissue samples. This work made use of μs of malignant, benign, and fibroglandular tissues measured by Kidane et al. Phys. Med. Biol. 44 (1999) for extraction of μs stroma. Using histological data from Kidane et al., μs values for stroma were extracted from (i) malignant samples composed of malignant epithelium and stroma (ii) benign samples: benign epithelium and stroma, and (iii) fibroglandular samples: fat and stroma. The cell model by LeClair et al. J. of Med. Imag. 2 (2015) was employed to estimate μs of cells which was used to approximate μs of malignant and benign epithelium. An average value of μs stroma was calculated. Using this μs stroma, the μs cell and a μs fat from Kidane et al., a three-basis function method was applied. The fractional volumes for stroma, cells, and fat denoted by νstr, νcell, νfat, respectively, were calculated using the singular value decomposition (SVD) method. In fact, the three-basis function was reduced to a two-basis function method by the constraint that νstr + νcell + νfat = 1. A momentum transfer range of 0.8nm−1 to 3.2nm−1 was used when fitting Kidane et al. data whereas a range of 0.8nm−1 to 2.5nm−1 was used when fitting of LeClair et al. Med. Phys. 33 (2006) data. For a cancer specimen from LeClair et al. νstr = 0.58, νcell = 0.43, νfat = −0.01, whereas for a benign specimen from Kidane et al. νstr = 0.94, νcell = 0.11, νfat = −0.05. The negative volume coefficients for fat indicate its absence from the samples. Cancerous samples exhibit higher cell content, confirming uncontrolled cell-proliferation as a cancer hallmark, while benign samples primarily reflect increased “fibrous” tissue. The fitting algorithm was effective for characterizing composite breast specimens, with results aligning well with known cancer biology.

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