Fig 1.
Scheme of the adopted procedures for porcine bone specimens (a. to e.) and for human vertebrae (f. to j.).
Porcine bone specimens: a) Cylindrical sample of trabecular bone obtained from porcine vertebrae and embedded into aluminium endcaps. b) Greyscale 2D-image of density distribution obtained from DXA scanning. c) Experimental compressive testing on bone samples. d) FE-analyses on simplified sample geometry and DXA-based stiffness distribution. e) Definition of the Strain Index of Bone (SIB) based on the outcome of the numerical analyses. Human vertebrae: f) DXA scan of the spine, evidenced with a white border, 1 pixel thick. g) Greyscale 2D-image of the density distribution of a single vertebra, obtained from DXA scanning. h) Selection of literature formulas to estimate stiffness and loads from the density. i) FE-analyses on simplified sample geometry and DXA-based stiffness distribution. e) estimation of SIB based on the outcome of the numerical analyses.
Fig 2.
a) Greyscale image obtained from a DXA on a porcine bone sample. b) Schematic of the FE-model of the cylindrical sample, including the mesh, the loading and boundary conditions. Each colour corresponds to a specific stiffness value, as shown in the colour bar. c) Greyscale image obtained from a DXA of a spine from a patient fractured not in the lumbar area (corresponding to P3 in Table 2). b) Example of minimum principal strain (εpmin) field in vertebra L1.
Fig 3.
Validation of the numerical procedure: a) Linear correlation between the numerical global stiffness, EFEM, and the experimental global stiffness, E0. b) Linear correlation between the numerical Yield Strain Index of Bone SIBY, the and experimental yield strain, εY. The linear correlation is shown for both the maximum SIBY value, SIBYmax, and the mean SIBY value, SIBYmean. SIBY is calculated, for each model, by using the load causing yield in each sample.
Fig 4.
Results of the numerical simulations referred to the specimen in Fig 2: a) Minimum principal strain field (εpmin). The grey-coloured regions at the upper and lower grips are excluded from the SIB post-processing. b) Trend of the average local stiffness E per rows through the specimen height. The red dot evidences the section with minimum stiffness. The distance along y-axis is the measure from the bottom grip (0 mm) to the upper grip (24 mm). c) Trend of SIBmax and SIBmean per rows along the specimen height. The red dot evidences the section with maximum SIB.
Table 1.
Adjusted linear determination coefficients () between the numerical SIBmax and SIBmean, and the experimental clinical and mechanical parameters.
Grey-coloured cells represent a significant linear correlation, with p-value < 0.05.
Fig 5.
Variation of: a) SIBmax and b) TBS—before and after damage—for different mechanical damage levels (G1%, G2%, G3.5%, and G5%). The filled bars represent the results before damage and the unfilled ones after damage. Panel (b) reproduced with permission from (Mirzaali et al., 2018) PLOS ONE 2018. c) Trend of SIBmax vs TBS for pre- and post-damaged specimens considering the mean value and with the standard deviation. Each colour corresponds to a different damage level.
Table 2.
Summary of BMD (g/cm2), T-score, TBS and SIBmax (104 mm/mm) for each vertebra of three case-studies on patients.