PSI - Issue 43

Apolena Šustková et al. / Procedia Structural Integrity 43 (2023) 276–281 Author name / Structural Integrity Procedia 00 (2022) 000 – 000

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In Eq. (2), CT is a unitless gray value (pixel intensity) obtained from the image datasets with calibration phantom, see Fig. 1 b). For the models with nonhomogeneous distribution, Young's modulus was calculated for each pixel of all considered datasets and mapped onto the corresponding finite element mesh. Using the software CTPixelMapper (Borák and Marcián 201 , a script was generated, which was used to assign the material properties to the geometry of the trabecular bone (see Fig. 3).

Figure 3: Nonhomogeneous distribution of Young’s modulus in the trabecular structure for variants 0.25 N and 0.65 N .

2.4. Load and boundary conditions To determine the apparent material properties in three considered directions, the loads were applied on the model based on the literature (Ševeček et al. 201 a, 201 b . Loads were applied on a layer of nodes of 0.05 mm thickness. Regarding the boundary conditions, fixed support was applied to one surface preventing movement in all directions. On the opposite surface, the remote displacement was applied (set as rigid). Remote displacement was set as 1% of the length of the segment. 2.5. Model variants From one dataset, nine geometry models were created, differing with the choice of a threshold value according to the density marked as 0.25; 0.3; 0.35; 0.4; 0.45; 0.5; 0.55; 0.6; 0.65. In addition, two material models were used for each of these models – homogeneous and nonhomogeneous (further referred to as H and N). Each of these models was loaded in three directions. Thus, a total of 54 model variants (0.25 H , 0.3 H , …, 0. 5 H , 0.25 N , … , 0.65 N ) were investigated. 3. Results The analysis of apparent Young's modulus (E app ) in each direction was performed. The value of E app was calculated in three directions (x, y, z) according to (Ševeček et al. 201 a, 201 b . In Figure 4, all determined values of E app are shown. Furthermore, the distribution of strain intensity (defined as maximum shearing strain) in one particular trabeculae was analyzed. Figure 5 presents the results for the variant with loading in the Y axis direction for all solved variants of the models of geometry. Strain isolines are plotted with the same color range. In addition, the results are plotted in the graph using a path on the same trabeculae (variants of models of geometry with minimum and maximum threshold values are selected for this comparison).