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

allows the calculation of strain maps from the displacement field. The individual
components of the displacements were smoothed by Gaussian filtration before the local
gradients in the displacement field, equivalent to the deformation gradient , were
calculated by central difference. From the deformation gradient, the Green-Lagrange
strain tensor was derived.
3.2 Materials
The left femurs from three mature female mice of the inbred strain C3H/He (C3H) were
used in this study. At an age of 19 weeks the animals were sacrificed. All animal
procedures were reviewed and approved by the local authorities. The femurs were
prepared and imaged as previously described (2). The specimens were imaged within
the mid-diaphysis using SR-CT at a nominal resolution of 740 nm.
3.3 Validation
The following models were created by warping directly from the tomographic images of
the samples before loading:
Model I. In order to study the accuracy of the strain mapping, a horizontal crack across
half the cross section was artificially introduced in image. Linear elastic FE simulations
of a tensile deformation by 1% in vertical direction were used to compute realistic
displacements and strains. The resulting displacements were then used to deform the
original image by warping. This model was used to determine an optimal set of
parameters. For the DVC phase we investigated the effect of the different sizes of subimages
(100, 50 and 25 voxel) and the threshold in mutual information (between 0 and
0.25) deciding on whether the sub-image should be considered for the interpolation of
the displacement field. For the demons deformable registration, the stiffness parameter
was analyzed between 2 and 10. And for the actual strain mapping, we determined the
effect of the width () of the Gaussian filter between 2 and 4 voxels. For each parameter
of the DVC and demons deformable registration, the root mean square (RMS) error and
the coefficient of correlation (R) between the resulting displacement field and the
originally applied displacement was calculated within the region of strain concentration
(regions with apparent strain larger than 1 %). For strain mapping, the resulting map
was compared to the map resulting from the originally applied displacements. The
resulting set of parameters was then used for the remainder of the study.
Model II. To determine the accuracy and precision of the displacement maps in a more
controlled and comparable way, the images were displaced by 0.5 voxel in each
coordinate direction (resulting in a total displacement of 0.87 voxel) using b-spline
interpolation. In contrast to Model I, the gray-scale images instead of the segmented
images were used for the warping and were segmented after the deformation.
Model III. The accuracy and precision of the strain maps was measured from images
with artificially imposed strains between 0.00 and 0.05 using homogenous strains over
the entire image. The case of zero applied strain was computed with strain maps derived
from model II. As in model II, the gray-scale images were deformed using b-spline
interpolation and segmented afterwards.
Model IV. The spatial resolution of the strain map was measured by the modulation