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

transfer function (MTF). The images were deformed according to an artificially created
displacement field with an edge function in one displacement component so that shear
motion was imposed on the image at the position of the edge. Subsequently, the
displacement and the strain maps were calculated and the profile of the corresponding
shear strain component was extracted by averaging over the cross section of the image.
The resulting profile of the shear strain corresponded to the line spread function (LSF)
of the strain mapping procedure. Therefore, the MTF could be directly calculated as the
Fourier transform of the shear strain profile. The spatial resolution of the displacement
field was computed similarly; with the exception that the LSF was calculated as the first
derivative of the edge spread function.
4. RESULTS
The evaluation of the displacement field resulting from DVC alone showed that the
RMS error was reduced by using increasingly smaller sub-images (Fig. 1). However,
the correlation decreased from 50 voxel to 25 voxel sub-images. For the smallest subimage
size, the optimal threshold in mutual information was 0.15. At the same time, this
yielded the smallest RMS error (0.73 µm, 1 voxel) and the best correlation (R = 0.76).
Subsequently, three steps of DVC were used with the sub-image reduced from 100
voxel to 50, and to 25 voxels, respectively.
Fig. 1 Optimization of the DVC. Root mean square error (left) and linear correlation (right) for the three
steps of decreasing sub-image sizes and different thresholds for the optimization metric.
The error of the displacement field computed by the demons deformable registration
was smallest with a stiffness parameter of 10 (RMS error = 0.21 µm, 0.28 voxel), and
the correlation was also optimal in this case (R = 0.96). However, the error and the
correlation did not improve considerably from a stiffness parameter of 6 onwards. In
favor of displacement maps with a high spatial resolution, a stiffness parameter of 6 was
used (RMS error = 0.23 µm and R = 0.96, respectively).
The correlation of the strain map was best with the widest Gaussian filter investigated
( =4). Nonetheless, we hereafter used a Gaussian filter with ( =2) in order to
obtain a strain map with the same localization as the displacement map. In this case, the