Optimal X-Ray Spectra Selection in Digital Mammography: A Semi-Analytical Study

In this work, a semi-analytical model was developed to determine the contrast-to-noise ratio (CNR) and the normalized average glandular dose (D̅_gN) in digital mammography, taking into account interactions up to second order. The optimal x-ray spectra were investigated using a Figure of Merit (FOM), for different breast thicknesses (3 cm ≤ L ≤ 7 cm) and glandularities (20% and 50%), anti-scatter grids types, considering a-Se and CsI image receptors. The anode/filter combinations evaluated were: Mo/Mo, Mo/Rh, Rh/Rh, and a W anode combined with k-edge filters (Mo, Ru, Rh, Pd, Ag, Cd, In and Sn), for tube potential between 23 and 35 kVp. Results demonstrate that the W-anode spectra combined with k-edge filters show a superior performance compared to the Mo/Mo combination traditionally employed in mammography, for all conditions analyzed. The optimum general x-ray spectra for 3 cm, 5 cm and 7 cm breasts are, respectively, W/Mo at 23 kVp, W/Pd at 28 kVp and W/Ag at 30 kVp. For the a-Se receptor, the optimum filter atomic number is one unit higher than that obtained for the CsI, while the optimal tube potentials are the same. The optimal tube potential was up to 1-2 kVp greater for a linear grid than that obtained without grid or with a cellular grid. For breast thicker than 7 cm, the optimum filter atomic number also increases by one unit for a linear grid. Compared to standard technique, the performance improvement of a W anode with proper k-edge filters is more noticeable for thicker and denser breasts, for a a-Se receptor and a linear grid. Finally, it was verified that the semi-analytical model implemented provided results of optimum x-ray spectra in a fast and simple way, with a good agreement with those obtained experimentally or by Monte Carlo simulation.