Since the bone destruction occurs locally (it starts in single layer), we assumed that instead of fractal analysis for the whole U0126 Sigma sample it is better to calculate the fractal dimension for the single layers of the sample. To calculate fractal dimensions we applied box-counting method [21] using Sarkar and Chauduri’s algorithm [22]. We used its extended version, that is, shifting differential box counting (SDBC) presented by Wen-Shiung et al. [23]. In this SDBC algorithm fractal dimension for box sizes (in voxels for the whole sample and in pixels��for single layers) was calculated, varying from 2 �� 2 �� 2 (2 �� 2 for layers) up to 45% of the maximal size of microCT stack image (image size).At each calculation stage box shifting was assumed for two voxels for the whole sample (two pixels for single layer).

Finally, the mean fractal dimension was calculated as the slope of the regression line for logarithms of box counts and sizes. The determination coefficient R2 for the relation between the logarithms of box counts and box size was always over 0.97 for each image.For each sample fractal dimension single layer (Df) was calculated and respectively mean fractal dimension (Dfm) for the whole sample. Then, standard deviation for Dfm (SDDfm) and relative standard deviation for Dfm (RSDDfm) were calculated.2.5. Compression ForceBased on the literature descriptive characteristics of bone material [20] and the structure of our samples (microCT of our study) we applied the finite element method (FEM). Thus we may virtually assess the force producing certain deformation of bone structure.

In our study compression force numerical analyses were performed with FEM software (Ansys 11.0 software, ANSYS Corp., Canonsburg, PA, USA). Analyses were carried out for a bone model consisting of layers, reconstructed according to the ��voxel to element�� method. The mesh characteristic for this method was prepared so a piece of a geometric structure��voxel��was directly transformed to finite element SOLID45.To maintain stability of the calculation iteration process the elements not affecting the stiffness of the analyzed structure were removed from the mesh at the stage of solving the numerical problem. Also the elements that could freely turn round their axis, perpendicular to the sample cylinder axis, were removed. An example of the mesh used for numerical analysis of bone structure is presented in Figure 2(a).

Figure 2Numerical analysis of bone structure: (a) mesh; (b) schema of boundary condition.For analyses of the structural character, isotropic material properties described by the tissue Young modulus E = 10GPa and Poisson coefficient �� = 0.3 [20] were accepted. For the above assumptions the results of force calculations depend solely on the structure of the modeled Drug_discovery tissue.