Wavelet based characterization of ex vivo vertebral trabecular bone structure with 3T MRI compared to microCT Page: 4 of 6
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Eight cylindrical cores were obtained from human vertebral
bone with an 8 mm inner diameter diamond tipped coring drill
bit mounted on a drill press. The resulting cores ranged from
10 mm to 18 mm in length. A diameter of 8 mm allowed the
cores to be mounted in the pCT machine and imaged at the
desired spatial resolution. Additionally, this diameter allowed
for adequate preparation for MR imaging. In preparation for
MR scanning, each core was defatted in a 10% solution of an
enzyme-active powdered detergent and then mounted in a
The cores were then immersed in 0.5 volume-%
gadolinium-DTPA-doped water to simulate the contrast found
between yellow marrow and trabecular bone. After that, the
container with the specimen was placed in a vacuum pump
and degassed prior to imaging to reduce artifacts arising from
differences in susceptibility between air, solvent, and bone.
B. Image Acquisition
MR images were obtained using a four-element phased
array coil at 3 T (Nova Medical, Wilmington, MA) on a Signa
MRI system (General Electric, Milwaukee, WI). High
resolution coronal images were acquired using a 3D fast
gradient echo (FGRE) sequence. The imaging parameters used
are shown in Table 1. The MR image containing the specimen
as subimages was divided into eight smaller volumes (99 x 99
X z pixels), where the number of slices (z) varied between 48
and 128 depending on the length of the core.
After MRI acquisition, pCT images were acquired
(Scanco Medical AG, Bassersdorf, Switzerland) with isotropic
resolution of 16 gm. The pCT images had a matrix size of
1024 x 1024 pixels and up to 1200 slices depending on the
length of the specimen.
MRL Scanning Parameters at 3T
Parameter 3 Tesla
TE/TR 23.5 / 11.1 ms
Flip angle 20
Bandwidth 15.63 Hz/pix
In plane resolution 0.117 mm
Slice thickness 0.3 mm
Imaging time 30 min
C. Standard Measurement of Structural Parameters
From the MRI dataset 2D structural parameters analogous to
bone histomorphometry were derived using the MIL method
based on the plate model for MRI analysis . This method
involves the extension of a set of parallel rays across the
binarized image at a series of angles (0). Structural parameters
derived included app.BV/TV (bone volume/total volume) and
app.Tb.Th (trabecular thickness).
Determination of app. Tb.Th. begins with counting the
number of black (bone) and white (marrow) pixel interfaces
that are encountered by a set of parallel rays at a given angle
0. This value is used to determine the mean intercept length
(MIL) by taking the ratio of the total area of the black pixels in
the ROI versus half the number of edges counted. The overall
mean width of the black pixels (app. Tb.Th.) is obtained by
taking the average MIL for all angles. App. BV/TV is
calculated as the total number of black pixels representing
bone over the total number of pixels in the ROI.
For pCT images, only trabecular thickness was determined
by the wavelet method, since in this case the BV/TV is
obtained by a simple binarization of the image. Determination
of Tb.Th. by the direct 3D distance transformation method is
accomplished by filling the bone phase of the binarized image
with maximal spheres as described in  and . The mean
diameter of all of the spheres used to fill the bone phase
corresponds to the mean thickness of the trabecular network.
D. New Wavelet Approach
Trabecular thickness was also measured using a new 3D
wavelet-based filter that was developed to visualize structural
features in noisy biological data . The filter's only
adjustable parameter is the wavelet "size", which represents a
characteristic linear size of the feature of interest, i.e., the
trabeculae. The wavelet "size" is measured in pixels, the
natural unit to use in image processing. The filter transforms
the original spatial distribution of intensities into a spatial
distribution of correlations that has the visual appearance of
the original image, but with strong highlighting of the regions
whose size is similar to the wavelet "size". Wavelet sizes from
1 to 15 pixels were used, thus, each data set generated 15 new
data sets, one for each wavelet size.
The wavelet filter is normalized so that the maximum
response (correlation) is obtained when the characteristic size
of the feature of interest (trabelcular thickness) equals the
wavelet size. In order to neglect very weak responses, a global
threshold was set automatically equal to the mean of the 15
wavelet responses at each spatial point. Values below this
threshold were set equal to zero.
The residual responses were weighted according to their
magnitudes and summed in order to get the trabecular
thickness at each pixel. The result of this procedure can be
interpreted as a map of the trabecular size. The app. BV/TV
was determined using this thickness map by placing a ROI for
each slice. These values were then compared with results from
image binarization by means of dual reference intensity
threshold described in . The same ROIs were used for both
A. MRI measurements
A typical MR image is shown in Figure 1 along with its
thickness map resulting from the wavelet transformation
described above. The pixel values are indicated on the color
bar for each image. The figure shows that the trabeculae are
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Krug, R.; Carballido-Gamio, J.; Burghardt, A.; Haase, S.; Sedat, J. W.; Moss, W. C. et al. Wavelet based characterization of ex vivo vertebral trabecular bone structure with 3T MRI compared to microCT, article, April 11, 2005; Livermore, California. (https://digital.library.unt.edu/ark:/67531/metadc890836/m1/4/: accessed April 25, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.