PSI - Issue 33

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Martini/ Structural Integrity Procedia 00 (2021) 000–000

298 Niki Martini et al. / Procedia Structural Integrity 33 (2021) 295–303 The effective �� � ⁄ was calculated for all mineral types examined with the following formula (Fountos et al. 1997, Martini et al. 2017, Martini et al. 2021). � �� � � � �� �� ∗� ��� � ��� ���� �� ∗� ��� � ��� � �� �� ∗� ������ ���� �� ∗� ������ � ∙ 3.0679 (4) where �� � Δ � ����� � �� � Δ � ������ � ��� �� � �� �� for the low- and high-energy, respectively. Δ � ����� � � ����� � � ���� and Δ � ������� � � ������ � � ���� �� � �� �� for the low- and high-energy, respectively. μ Ca , μ PO4 and μs are the energy depended linear attenuation coefficients (1 cm -1 ) for calcium, phosphate and soft tissue, respectively. The modified analytical model calculates the effective �� � ⁄ for all the examined minerals. However, phosphorus is present only in the molecule of hydroxyapatite. As the present study investigates the potential of mineral characterization based on the attenuation intensity, the linear attenuation coefficients of PO 4 were used in the calculations of the �� � ⁄ for all minerals. The term “effective” for the �� � ⁄ is used as the CO 3 and C 2 O 4 amounts correspond to smaller amount of PO 4 , when equal photon number in the attenuated intensities is required, since CO 3 and C 2 O 4 have lower linear attenuation coefficients than PO 4 (Büsing1981, Martini et al. 2017, Martini et al. 2021). Considering Poisson distribution for the photons and using the error theory, the coefficient of variation of the �� � ⁄ for all minerals was calculated as follows (Equation 5). The energy pair that would minimize the � � �� � � ⁄ would be selected as the optimum energy pair. � � �� � � ⁄ � � 1 ���� � 1 ���� � ∙ � � ��� � ��� � � �� �� ∗ ��� � ��� � � � �� ∗ ��� � ��� �� � � � ������ � � �� �� ∗ ������ � � � �� ∗ ������ �� � � ∙ 100 � � � � � ���� � � � ���� � ∙ � �� ��� � ��� � � ��� �� ∗� ��� � ��� ���� �� ∗� ��� � ��� �� � � �� ������ � � ��� �� ∗� ������ ���� �� ∗� ������ �� � � ∙ 100 � (5) 2.1.2. Polyenergetic study Several filters were applied to unfiltered spectra, obtained from TASMIP spectral models generated from Tungsten anode, at 50 kVp 200mAs and 90 kVp 400 mAs for the low-and high-energy, respectively, in order to obtain mean energies similar to those demonstrated by the monoenergetic study (Boone and Seibert 1997). Cerium, Praseodymium, Neodymium, Promethium, Samarium and Europium, due to their K-edges, were applied to low energy spectrum. Aluminum was also applied to the low energy spectrum as it is a commonly used filter in X-ray systems for low energy attenuation. Gallium, Vanadium, Antimony, Chromium, Tin, Copper and Bismuth, due to their high densities, were applied to the high energy spectrum. The thickness range examined for all filters was 0.01 to 3 cm, at 0.01 increments. The Radcal 2026C (Radcal Corporation, Monrovia, USA) ionization chamber (Koukou et al. 2015) was placed at 66 cm from the tube output to measure the entrance surface doses for the low-and high-energy. The measured dose of low energy was 2.31 mGy and for the high energy was 30.50 mGy. A nonparametric statistical analysis considering Poisson distribution for the attenuated intensities was conducted and for each one 5000 random values were calculated. Thus, 5000 effective �� � ⁄ values were calculated for each mineral examined. Previous studies of our team concluded that normal Kernel distribution describes the random value effective �� � ⁄ (Büsing1981, Martini et al. 2017, Martini et al. 2021). For all examined mineral types and thicknesses were obtained the Kernel probability functions and the false positive and false negative values were calculated.