Three-Dimensional Local Measurements of Bone Strain and Displacement: Comparison of Three Digital Volume Correlation Approaches

Different digital volume correlation (DVC) approaches are currently available or under development for bone tissue micromechanics. The aim of this study was to compare accuracy and precision errors of three DVC approaches for a particular three-dimensional (3D) zero-strain condition. Trabecular and cortical bone specimens were repeatedly scanned with a micro-computed tomography (CT). The errors affecting computed displacements and strains were extracted for a known virtual translation, as well as for repeated scans. Three DVC strategies were tested: two local approaches, based on fast-Fourier-transform (DaVis-FFT) or direct-correlation (DaVis-DC), and a global approach based on elastic registration and a finite element (FE) solver (ShIRT-FE). Different computation subvolume sizes were tested. Much larger errors were found for the repeated scans than for the virtual translation test. For each algorithm, errors decreased asymptotically for larger subvolume sizes in the range explored. Considering this particular set of images, ShIRT-FE showed an overall better accuracy and precision (a few hundreds microstrain for a subvolume of 50 voxels). When the largest subvolume (50-52 voxels) was applied to cortical bone, the accuracy error obtained for repeated scans with ShIRT-FE was approximately half of that for the best local approach (DaVis-DC). The difference was lower (250 microstrain) in the case of trabecular bone. In terms of precision, the errors shown by DaVis-DC were closer to the ones computed by ShIRT-FE (differences of 131 microstrain and 157 microstrain for cortical and trabecular bone, respectively). The multipass computation available for DaVis software improved the accuracy and precision only for the DaVis-FFT in the virtual translation, particularly for trabecular bone. The better accuracy and precision of ShIRT-FE, followed by DaVis-DC, were obtained with a higher computational cost when compared to DaVis-FFT. The results underline the importance of performing a quantitative comparison of DVC methods on the same set of samples by using also repeated scans, other than virtual translation tests only. ShIRT-FE provides the most accurate and precise results for this set of images. However, both DaVis approaches show reasonable results for large nodal spacing, particularly for trabecular bone. Finally, this study highlights the importance of using sufficiently large subvolumes, in order to achieve better accuracy and precision.