*Histograms*

There are so many points involved in the correlations that the plots of density against the different variables are very difficult to distinguish. Instead, histograms are used to show the percentage of volume occupied by those elements whose values of AMP*σ* or AMP*ε* are within a given range. The elements of cortical (*ρ* > 1.2 g/cm3) and trabecular bone (*ρ* ≤ 1.2 g/cm3) have been separated into two different histograms and the results for the three constitutive models were plotted jointly (see Figure 6). Thus, for example, in the model *AnisoH*, the elements of trabecular bone whose AMP*ε* is in the range [200,600] μ*ε* occupy 30% of the total volume of trabecular bone (*ρ* ≤ 1.2 g/cm3).

It can be seen that while the strain range is similar for cortical and trabecular bone, the stresses are completely different, with trabecular bone having stresses several orders of magnitude lower than cortical bone. In general, strains are found in a very narrow range, especially in the cortical bone, for which 87% of the volume has AMP*ε* in the range of 200–600 μ*ε*. This is not so evident in trabecular bone, though 51% is still within the range of 200–1000 μ*ε* and 65% is in the range of 200–1400 μ*ε*. This is still a narrow range, as overload strains are up to 4000 μ*ε* [36,37].

**Figure 6.** Distribution of the absolute maximum principal stress (AMP*σ*) and strain (AMP*ε*) for the elements of trabecular (*ρ* ≤ 1.2 g/cm3) and cortical bone (*ρ* < 1.2 g/cm3). The Y axis shows the percentage of the total volume occupied by the elements, whose AMP*σ* or AMP*ε* are in a given range.
