**5. Conclusions**

The 3D full-field residual strain distribution of compact and trabecular bone subjected to high-energy SR irradiation was computed using DVC applied to SR-microCT images acquired at different temperatures. Lowering the temperature during irradiation to only 0 ◦C had a positive effect on trabecular bone tissue, which—unlike such bone imaged at room temperature—did not present visible microcracks, and residual strain values were not increased with further radiation. However, a minimal effect was observed in compact bone. A shrinkage behaviour induced by both the beam-induced temperature and high-energy irradiation may well be the source of the irradiation-induced damage and microcracks in bone tissue. DVC applied to high-resolution SR-microCT images has proven to be a useful tool for understanding crack formation and propagation in bone tissue. Further work is needed to clearly establish protocols for the application of SR-microCT to the in situ mechanics of bone and potentially extend the knowledge to other biological tissues in order to minimise SR irradiation-induced damage.

**Supplementary Materials:** The following are available online at http://www.mdpi.com/1996-1944/11/11/2155/ s1, Figure S1: Relationship between (**a**) MAER and (**b**) SDER with the sub-volume size for the four bone specimens, Figure S2: Histograms of the residual strain distribution in compact bone tissue imaged at room temperature (top) and 0 ◦C (bottom). (**a**) Third principal strains (<sup>ε</sup>p3) and (**b**) maximum shear strains (γmax) after each acquired tomogram are shown, Table S1: Random errors for the three displacement components for compact and trabecular bone specimens. Median values of the two specimens per group are shown.

**Author Contributions:** Conceptualization, M.P.F., E.D., G.T.; Methodology, M.P.F., E.D., G.T.; Validation, M.P.F., G.T.; Formal Analysis, M.P.F., A.J.B.; Investigation, M.P.F., A.P.K., A.J.B., A.K.; Resources, G.W.B., G.T.; Data Curation, M.P.F.; Writing-Original Draft Preparation, M.P.F.; Writing-Review & Editing, M.P.F., E.D., A.P.K., A.J.B., G.T.; Visualization, M.P.F.; Supervision, G.T.; Project Administration, G.T.; Funding Acquisition, A.H.B., G.W.B., G.T.

**Funding:** The project was partially funded by the Engineering and Physical Sciences Research Council (EPSRC, Frontier Grant Multisim, EP/K03877X/1).

**Acknowledgments:** The authors would like to thank Diamond Light Source (UK) for time at the Diamond-Manchester Imaging Branchline I13-2 and its associated Data Beamline [68] under proposal MT16497, and the Zeiss Global Centre (University of Portsmouth) for post-processing. We further acknowledge Dave Hollis (LaVision Ltd.) for assistance with DaVis software, Kazimir Wanelik for help during the experiment and image reconstruction at Diamond Light Source, and Kamel Madi for fruitful discussions during the experiment.

**Conflicts of Interest:** The authors declare no conflict of interest.
