PSI - Issue 33

Niki Martini et al. / Procedia Structural Integrity 33 (2021) 295–303 Martini/ Structural Integrity Procedia 00 (2021) 000–000

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2. Materials and Methods 2.1. Simulation

2.1.1. Monoenergetic study Considering that along the X-ray beam path a torso of 20.8 cm thick (Cirs Inc., Martini et al. 2021), consisting of surrounding tissue and kidney/uteric stones or atherosclerotic plaques’ calcifications, the attenuated intensities for the low-and high-energy beams were calculated by the analytical model of the present study (Equations 1 & 2). The attenuation coefficients of water were used to simulate the surrounding tissue. The kidney/uteric stones and atherosclerotic plaques’ calcifications were simulated as a mixture of epoxy resin and mineral as of such mixture were composed the constructed phantoms for the experimental evaluation of the method. ���� � ���� �� ���� � � � �� �. (1) ���� � ���� �� ���� � � �� ���������� � � � � �� �. (2) where ���� and ���� are the attenuated intensities for the low-and high-energy, respectively. ���� and ���� are the attenuated intensities for the low-and high-energy, respectively, when only the surrounding tissue is along the X-ray beam path. ���� and ���� are the attenuated intensities for the low-and high-energy, respectively, when both the surrounding tissue and the kidney/uteric stone or atherosclerotic plaque’s calcification are along the X-ray beam path. ���� , ���� , ���������� and ���������� re the energy-dependent linear attenuation coefficients (cm -1 ) of the surrounding tissue and the minerals for the low-and high-energy, respectively. � and � are the thicknesses of the surrounding tissue and the minerals for the low-and high-energy, respectively. The mineral types examined, regardless stones or calcifications were investigated, were hydroxyapatite (Ca 10 (PO 4 ) 6 (OH) 2 ), with a density of 3.18 g cm -3 (Gong et al. 1964), calcium carbonate (CaCO 3 ) with a density of 2.93 g cm –3 (Lemacks et al. 2002), and calcium oxalate (CaC 2 O 4 ) with a density of 2.20 g cm -3 (Brandan and Ramirez 2006). The epoxy resin (C 19 H 23 CIO 4 ) used in the simulation study had a density of 1.06 g cm -3 (Resoltech, Rousset, France). The minerals are referred to as HAp, CaCO 3 and CaC 2 O 4 . For all energies in the range of 40 to 140 keV, at 1 keV increments, were calculated the unattenuated intensities for the low-and high-energy using the entrance surface dose ( � ), calculated as follows. � � � � 8.�� ∙ 10 �� 1.83 ∙ 10 �� ���� � � � �� � �� � ��� � � �� �. (3) where ���� and ���� are the attenuated intensities for the low-and high-energy, respectively. � �� ⁄ � ��� is the X-ray mass energy absorption coefficient of air for the low-and high-energy, respectively, obtained from literature (Hubbell and Seltzer et al. 1995). The entrance surface dose was 8 mGy and was split evenly between the low-and high-energy. The hydroxyapatite thicknesses investigated ranged from 0.5 to 3 mm, at 100 μm increments. The calcium oxalate and calcium carbonate thicknesses investigated were those resulting in equal number of photons to each hydroxyapatite thickness, after the X-ray beam passed through the torso. Table 1 has indicative hydroxyapatite thicknesses and the equivalent thicknesses of calcium oxalate and calcium carbonate.

Table 1. Indicative hydroxyapatite thicknesses and the equivalent of calcium oxalate and carbonate. Hydroxyapatite Calcium carbonate Calcium oxalate 0.50 0.61 0.99 1.00 1.24 2.08 1.50 1.86 3.13 2.00 2.47 4.17 2.50 3.10 5.21 3.00 3.71 6.25