ARUP; ISBN: 978-0-9562121-5-3 - CMBBE 2012 - Cardiff University

RMS error was 0.054 and the strains were overestimated by 0.018.
From the registration of the images that were homogenously displaced by 0.5 voxel, we
found that the accuracy of the displacement map was 0.0006 voxel (0.4 nm) and the
precision was 0.176 voxel (130 nm) as determined from the RMS error of the
displacements. The strain maps computed for imposed strains between 0.00 and 0.05
did show a systematic error. The mean error of the strain was not significantly different
from zero (p < 0.05, using a one-sample t-test), while the precision was between 0.011
and 0.013.
The spatial resolution of the strain maps was defined as the frequency at which the MTF
indicates a modulation of 10%. For the strain maps this was found at 49.5 line pairs per
mm, corresponding to a resolution of 13.5 voxels (10.0 µm). For the DVC stage at the
smallest sub-image size (25 voxels) 10% modulation was at 29.9 line pairs per mm
equivalent to a resolution of 22.6 voxels (16.7 µm). For the displacements, a modulation
of 10% was found at 49.3 line pairs per mm, corresponding to a resolution of 13.7
voxels (10.1 µm).
5. DISCUSSION
In the present study, deformable image registration was used to compute 3D strain maps
for cortical bone microstructure. A novel procedure to calculate the 3D deformation and
strain maps with a high spatial resolution was established to analyze time-lapsed
tomographic images of the cortical bone microstructure. The method was optimized
using realistic deformations for the propagation of microcracks. Furthermore, the
displacement and strain maps were validated. We found that at a nominal image
resolution of 740 nm the spatial resolution of the strain maps was 10 µm (MTF), while
the error of the displacements and strains were 130 nm and 0.013, respectively.
Therefore, the spatial resolution of both the displacement and strain maps are in the
order of 10 µm and can hence be used to measure the impact of microstructural features
such as canals or osteocyte lacunae on the local strain and displacement field.
The validation based on homogenous displacements and homogenous strains showed
that strain maps computed by previous procedures using DVC alone (6, 7) were more
precise than what we measured, while the precision of the displacements was similar,
which serves as the base to compute strains. We found that the precision of the
displacements was 0.175 voxel (130 nm), while the precision of the strain was 0.012.
Comparing several correlation metrics, Liu and Morgan (7) reported a precision of
0.046 to 0.167 voxel (1.66 to 6.01 µm) for the displacements by the same test used in
the current study, whereas the precision of the strain maps was measured from a
repeated measurement of the unloaded sample, where errors of 0.0004 to 0.0013 were
reported. The difference in the precision of the strain maps is mostly due to the higher
spatial resolution of the method introduced in this study, and the fact that the effect of
errors in the displacement on the error in strains is dependent on this spatial resolution,
so that strain maps with a higher resolution inherently have a larger error. To confirm
this, we computed the strain maps again after applying a mean filter with a width of 41
voxel, corresponding to the size of the sub-images used in (7) and found a RMSE of
0.0018 for the strain, which is very similar to values reported previously (6, 7).