Download Comparison of structure extraction methods for in vivo trabecular

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Computerized Medical Imaging and Graphics 23 (1999) 69–74
Comparison of structure extraction methods for in vivo trabecular
bone measurements
A. Laib*, P. Rüegsegger
Institute for Biomedical Engineering, University of Zürich and Swiss Federal institute of Technology (ETH), Moussonstrasse 18, CH-8044 Zürich, Switzerland
Received 26 August 1998
Abstract
In vivo trabecular bone structure measurements have become available recently using high resolution quantitative computed tomography
(3D-QCT) or magnetic resonance imaging. In this work different structure extraction and morphometric evaluation techniques are compared,
which are of potential use for in vivo assessment of human cancellous bone structure. Given the spatial resolution of actual in vivo
examination procedures, best results are obtained by extracting first the skeleton of the structure and applying model independent 3D
techniques to calculate trabecular number, then deriving mean trabecular thickness and separation from densitometric bone volume fraction
and Tb.N*. Traditional histomorphometric methods based on bone surface and volume ratios and assuming a plate model performed less
well. 䉷 1999 Elsevier Science Ltd. All rights reserved.
Keywords: Computed tomography; Bone microarchitecture; Trabecular bone structure; Quantitative bone morphology
1. Introduction
Osteoporosis is characterized by low bone mass and
structural deterioration. It is expected that a quantification
of microarchitectural features in addition to bone density [1]
might improve predictions of bone strength and fracture
risk, e.g. Kleerekoper et al. [2] have shown in a study on
biopsies of the iliac crest of an age, sex, race, menopausal
status, and densitometric bone mass matched group that the
number of plates in individuals with vertebral fractures is
more than one standard deviation below the number of
plates found in persons without previous fractures. They
conclude that ‘‘mean trabecular plate density evidently
discriminates more efficiently between patients with and
without vertebral fractures than does trabecular bone
volume alone’’. Techniques have become available recently
[3–5] that allow patient examinations of the trabecular bone
structure at peripheral sites, although (in contrast to ex vivo
techniques such as serial sectioning, micromagnetic resonance imaging, microcomputed tomography or synchrotron
CT [6–10]) with spatial resolutions which are not sufficient
to depict the true individual thicknesses of the trabeculae.
The much higher level of noise has to be taken into consideration as well, when in vivo examinations are performed.
In a previous publication [5], a new method to assess a
* Corresponding author. Tel.: ⫹41 1 632 4592; fax: ⫹41 1 632 1214.
E-mail address: [email protected] (A. Laib)
measure for the number of trabeculae – called Ridge
number density (RND) – was introduced for an irregularly
shaped volume of interest in the distal radius. In a further
study [11] the technique was calibrated with comparative
measurements of fifteen bone biopsies. They were measured
both in a 3D peripheral quantitative computed tomography
scanner (3D-QCT) for patient examinations with 165 3 mm 3
voxel size and in a MicroCT scanner with a resolution of
28 3 mm 3. The resulting structural indices were compared,
taking the MicroCT data as the gold standard for the
lower resolution images. The calibration was obtained
with a quality of fit between r 2 ˆ 0.81 and 0.96 for trabecular number (Tb.N), trabecular thickness (Tb.Th) and
trabecular separation (Tb.Sp). The mean bone volume to
tissue volume (BV/TV) was derived from the densitometric
values with r 2 ˆ 0.98.
The motivation for using the RND technique is the fact
that at the given voxel size of 165 3 mm 3, the trabeculae
cannot be represented with their correct individual thickness. Hence, the information of the number of trabeculae
is extracted directly from the gray-scale image with the
ridge detection and then a mean trabecular thickness and
separation are derived from Tb.N and BV/TV. Another
approach is to perform a full segmentation of the original
data, being aware that the structure is represented with inaccurate individual trabecular shape, but assuming that even if
the values are biased, the average structural indices still
correlate with the correct values.
0895-6111/99/$ - see front matter 䉷 1999 Elsevier Science Ltd. All rights reserved.
PII: S0895-611 1(98)00071-8
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A. Laib, P. Rüegsegger / Computerized Medical Imaging and Graphics 23 (1999) 69–74
Fig. 1. Low pass filtered 3D-QCT slice on the left and the same slice through the Laplace–Hamming full structure extraction on the right.
In this work, the same set of fifteen bone biopsies as in the
calibration study is taken and either the full structure or only
the ridges are extracted. Then structural indices are assessed
with different morphometric evaluation procedures, either
traditional histomorphometric methods working with
derivations of the bone surface and bone volume and
a plate-model assumption to derive Tb.N, Tb.Th and
Tb.Sp; or methods measuring directly the metric
distances in 3D without a model assumption to give
Tb.Th*, Tb.Sp*, and Tb.N*, where the asterisk denotes
the directly assessed indices. The traditional indices
Tb.N, Tb.Th and Tb.Sp are calculated for the full structure
segmentation only, as the ridge image does not contain the
information about bone surface and bone volume anymore.
The aim of this article is to compare the approach of a
full segmentation to the ridge extraction technique and to
find the adequate morphometric evaluation for the given
resolution.
2. Materials and methods
2.1. Specimens
Trabecular bone samples were taken from the BIOMED I
project of the European Union ‘‘Assessment of Quality of
Bone in Osteoporosis’’ [12]. Fifteen specimens from the
femoral head were selected in such a way that their bone
volume to tissue volume (BV/TV) covered a large range
from 12% to 34%, as measured previously by the MicroCT
system. The biopsies had a cylindrical shape with a diameter
of 8 mm and a length of 10–12 mm.
2.2. Computed tomography measurements
All samples were first scanned with a high resolution
MicroCT system [9], which is commercially available
under the name m CT 20 (Scanco Medical, Bassersdorf,
Fig. 2. Ridge extraction slice on the left and mid axis transformed Laplace–Hamming slice on the right, same slice location as in Fig. 1.
A. Laib, P. Rüegsegger / Computerized Medical Imaging and Graphics 23 (1999) 69–74
Fig. 3. Schematic drawing of largest sphere, which fits inside the background of the 3D ridge image (a 2D cut is shown for clarity). The ridge
extraction and the Tb.N* assessment are both independent on the thickness
of trabeculae.
Switzerland) with cubic voxels with side-lengths of 28 mm.
Subsequently, 3D-QCT measurements were performed with
a voxel size of 165 3 mm 3 [5]. The matching of the volume of
interest for the two measurements of each sample was done
in the following way: The sampleholder of the specimens
was aligned along the z-axis for the MicroCT and the 3DQCT scans to have identical axial directions. The axial position, i.e., the corresponding slice range, was found by visual
comparison of the images. The matching uncertainty is 1
slice (equals 165 mm).
2.3. Structure extraction
For the ridge detection of the 3D-QCT images (slice of
one specimen shown in Fig. 1, left side), a 3D modification
of Haralick’s original method [13] was used. The result is a
skeleton-like binary ridge image (Fig. 2, left side, same
specimen and slice as in Fig. 1). The same parameters of
71
the Gaussian filter (s ˆ 0.7 [voxel]) and the ridge threshold
(t ˆ 55/1000 [arb. units]) were used as for patient
examinations [5].
The segmentation of the full structure for the 3D-QCT
data was carried out with a 3D Laplace-Hamming filter. The
zero crossings of the second derivative (Laplace operator D)
of the gray-scale picture are defined as the structure boundaries, as they correspond to the steepest gradient. The calculation of the second derivative is done in the spatial
frequency domain by multiplying the three-dimensionally
fourier-transformed image with a v 2 function (deriving in
the spatial real domain corresponds to multiplication with
⫺iv in the frequency domain). The original, fourier-transformed image is added with a low weighting factor to this
second derivative curvature image. This ensures that regions
with compact bone are not disrupted, even if there are
density changes within them. For noise smoothing a
Hamming window is simultaneously applied in the
frequency space. The combined image is then fourier-backtransformed into the spatial domain and thresholded with a
fixed threshold for all samples. The values of the Hamming
cut-off frequency, the weighting factor and the fixed threshold were chosen so that they can be directly applied to in
vivo patient examinations. The Hamming cut-off frequency
was chosen visually as a trade-off of noise level and blurring, taking into account the high noise level in the original
images (signal-to-noise ratio is only ⬃ 2; for different
applications with different signal-to-noise levels the
Hamming cut-off frequency can easily be adjusted). The
weighting factor was chosen so that the compact shell in
patient measurements did not get disrupted. The fixed
threshold was determined in this study such that the correlation of the structural indices with the MicroCT indices was
best. The Hamming cut-off frequency is 0.35 of the Nyquist
frequency, the weighting factor 0.1 (i.e., 90% curvature
image and 10% original image) and the threshold 400/
1000 [arb. units]. A stepwise variation of the threshold
from 300/1000 to 550/1000 [arb. units] produced gradually
thinner structures, but the correlation of the structural
indices with the MicroCT indices varied little. In addition,
a variation of the Hamming cut-off frequency to 0.40 did not
change the correlations of the indices much. Fig. 1 (right
side) shows a slice of the segmented structure and Fig. 5 a
3D view of it.
The MicroCT dataset was segmented using a low-pass
filter to remove noise and a fixed threshold to extract the
mineralized bone phase. An example of a slice is shown in
Fig. 4 (the same specimen as in Figs. 1 and 2, the slice
matched to be at the same location) and a 3D representation
is seen in Fig. 6.
2.4. Morphometric evaluation
Fig. 4. Segmented MicroCT slice, matched to be at the same location as the
slices in Figs. 1 and 2.
For the original densitometric 3D-QCT images the mean
trabecular bone density (TBD) was calculated, which is
calibrated with the European Forearm Phantom in
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Table 1
Basic statistics of the 3D-QCT data with different structure extraction and
evaluation methods versus the MicroCT data. (Tb.N*, Tb.Th* and Tb.Sp*
were assessed with direct metric methods. Tb.N, Tb.Th and Tb.Sp were
calculated from volume and surface ratios assuming a plate model.
Tb.Th*derived and Tb.Sp*derived were calculated from BV/TVderived and Tb.N*)
3D-QCT data
Densitometry
Ridge extraction
Laplace–Hamming
full structure
extraction
MicroCT data
Fig. 5. Three dimensional visualisation of the Laplace–Hamming full
structure 3D-QCT image.
Hydroxyapatite (HA) densities [14]. With TBD a mean BV/
TVderived was calculated, assuming a density of fully mineralized bone of 1.2 g HA per cm 3.
For the ridge images, Tb.N* was taken as the inverse of
the mean spacing of the ridges. The local spacings were
assessed with the help of the distance transformation
method [15]: for each voxel of the background (i.e. voxels
not containing ridges) the largest sphere was determined
(Fig. 3), which was completely inside the background and
contained the said voxel (not necessarily as the sphere’s
center). The diameter of this sphere was then taken as the
Fig. 6. Three dimensional visualisation of the MicroCT image.
BV/TVderived[%]
Tb.N* [1/mm]
Tb.Th*derived [mm]
Tb.Sp*derived [mm]
Tb.N* [1/mm]
Tb.Th*derived [mm]
Tb.Sp*derived [mm]
BV/TV [%]
Tb.Th* [mm]
Tb.Sp* [mm]
Tb.N [1/mm]
Tb.Th [mm]
Tb.Sp [mm]
BV/TV [%]
Tb.N* [1/mm]
Tb.Th* [mm]
Tb.Sp* [mm]
Tb.N [1/mm]
Tb.Th [mm]
Tb.Sp [mm]
Mean
SD
24
1.24
0.19
0.62
1.24
0.19
0.63
36
0.43
0.72
0.83
0.31
1.00
24
1.31
0.19
0.72
1.50
0.15
0.53
9.8
0.173
0.057
0.174
0.147
0.062
0.155
9.9
0.045
0.136
0.215
0.059
0.476
8.2
0.176
0.034
0.121
0.266
0.033
0.163
local ridge spacing for this background voxel, and the
inverse of the average over all background voxels yielded
Tb.N*. This procedure is truly three-dimensional. To denote
the direct, model independent nature of this newly defined
index an asterisk was added to the well known abbreviation
of trabecular number. Combining Tb.N* and BV/TVderived
lead to Tb.Thderived ˆ BV/TVderived/Tb.N* and Tb.Spderived ˆ
(1⫺BV/TVderived)/Tb.N* in analogy to standard histomorphometry [16].
For the Laplace–Hamming segmented structures, bone
volume and bone surface were calculated using tetrahedrons
generated with the Marching Cubes method [17]. Mean
Tb.N, Tb.Th, and Tb.Sp were then calculated assuming
the plate model [16]: Tb.N ˆ 0.5 BS/TV; Tb.Th ˆ 2 BV/
BS; Tb.Sp ˆ 2 (TV⫺BV)/BS. The structural indices were
calculated as well with the distance transformation and
denoted Tb.N*, Tb.Th* and Tb.Sp*. They are not based
on an assumed model type and are assessed directly as
metric distances in 3D space by filling the structure or the
background with largest spheres. Tb.Th* was the mean
thickness of the trabecular, Tb.Sp* the mean thickness of
the marrow cavities and Tb.N* was the mean inverse
distance between the mid axes of the structure. These mid
axes were found as the centers of non-redundant spheres that
fill the structure completely. As an example the mid axes of
the Laplace–Hamming segmented 3D-QCT data is shown
in Fig. 2 (right side). In addition for the Laplace–Hamming
structures, Tb.N* was combined with BV/TVderived (determined with TBD from the original densitometric images) to
calculate Tb.Th*derived and Tb.Sp*derived.
A. Laib, P. Rüegsegger / Computerized Medical Imaging and Graphics 23 (1999) 69–74
Table 2
Correlation (r 2) of structural parameters from 3D-QCT and from MicroCT
images (all values p ⬍ 0.0001). Abbreviations as in Table 1
3D-QCT
MicroCT:
BV/TV Tb.N*
Densitometry
Ridge extraction
Laplace–Hamming
full structure
extraction
BV/TVderived 0.98
Tb.N*
Tb.Th*derived
Tb.Sp*derived
Tb.N*
Tb.Th*derived
Tb.Sp*derived
BV/TV
0.98
Tb.Th*
Tb.Sp*
Tb.N
Tb.Th
Tb.Sp
0.69
0.81
Tb.Th*
Tb.Sp*
0.89
0.71
0.92
0.81
0.92
0.84
0.85
0.69
0.91
0.63
The basic descriptive statistics of the data is given in
Table 1. The Laplace–Hamming method results in structures that are generally too thick. This is seen in the mean
BV/TV, which is overestimated by 33% and the mean thickness Tb.Th*, too large by 126%. Tb.N*, however, is only
6% underestimated. The traditional histomorphometric
indices derived from BS and BV ratios, in contrast, show
a Tb.N that is too low by a factor of two and in consequence
also Tb.Th and Tb.Sp are off by a factor of two.
Tb.N* from both structure extractions of the 3D-QCT
images show the same mean value. The ridge extraction
can thus be seen as a short cut to building a complete (albeit
too thick) structure first and then performing a mid axis
transformation. The indices Tb.Th*derived and Tb.Sp*derived
Table 3
Regression lines of the 3D-QCT and the MicroCT data
BV/TV ˆ
Tb.N* ˆ
Tb.Th* ˆ
Tb.Sp* ˆ
4.0 ⫹ 0.83 BV/TVderived
0.17 a ⫹ 0.91 Tb.N*
0.08 ⫹ 0.57 Tb.Th*derived
0.33 ⫹ 0.62 Tb.Sp*derived
Laplace–Hamming 3D-QCT
⫺4.0 ⫹ 0.81 BV/TV
⫺0.05 a ⫹ 1.10 Tb.N*
0.09 ⫹ 0.54 Tb.Th*derived
0.26 ⫹ 0.72 Tb.Sp*derived
Denotes non-significant values (p ⬎ 0.01), all other values have p ⬍
0.0001.
a
4. Discussion
0.84
3. Results
Ridge 3D-QCT
calculated from BV/TVderived and Tb.N* correspond best
with the MicroCT indices Tb.Th* and Tb.Sp* for both the
ridge extraction and the Laplace–Hamming segmentation.
This is also seen in Table 2, which shows the correlations
between structural indices from the MicroCT with the 3DQCT data. Again, differences between the two methods are
small if Tb.N*, Tb.Th*derived and Tb.Sp*derived are used. The
values of the least-square fit regression lines between 3DQCT and MicroCT indices are shown in Table 3.
0.84
For the MicroCT data the direct metric indices Tb.N*,
Tb.Th* and Tb.Sp* were calculated with the distance transformation method, and the model-assuming indices Tb.N,
Tb.Th and Tb.Sp were derived from BV, BS, and TV from
Marching-Cube generated tetrahedrons.
All calculated parameters were cross-correlated within
each measurement method and between MicroCT and 3DQCT data sets with SAS/INSIGHT (Statistical Analysis
Software, SAS Institute, Cary NC, USA).
MicroCT
73
The purpose of this article was to compare different structural extraction and different morphometric evaluation
methods for data obtained with a high resolution 3D-QCT
scanner at the given voxel size used for in vivo examinations. It is shown that taking the densitometric TBD and
deriving bone volume to tissue volume leads to almost the
same results as MicroCT measurements of BV/TV with a
quality of fit of 0.98. BV/TV assessed with the full structure
extraction method yields the same r 2, but the absolute values
show a large bias because of the inaccurate representation of
Tb.Th.
Tb.N is best obtained with the distance transformation
method as the mean inverse distance between skeletal
elements. The skeleton can either be extracted directly
from the gray-scale image with the ridge detection method;
or it can be determined by mid axis transformation of the
Laplace–Hamming full structure image. The coefficient of
correlation of Tb.N* from 3D-QCT and MicroCT then is
r 2 ˆ 0.81. Tb.Th* from the full structure 3D-QCT images
shows that trabeculae are broadend because of partial
volume effects. Better results are obtained by combining
BV/TVderived and Tb.N* to calculate Tb.Th*derived.
When employing traditional histomorphometric methods
– using bone surface and volume ratios and assuming a
plate-model – on the full Laplace–Hamming structure,
the resulting structural indices correlate not as well (r 2 ⬎
0.63) with the MicroCT data, and the absolute values are
biased. This shows that the morphometric method with
which structure is evaluated has a large influence on the
results when images with a voxel size of 165 mm are
used. This result is in accordance with previous findings
[11] in which the MicroCT data was compared to scaled
up MicroCT data, which were calculated by combining
the 28 mm voxels in such a way that unblurred and almost
noise-free images with a voxel size of 165 mm were
produced. It was found that the indices assessed by directly
measuring metric distances were very accurate (Tb.N*,
Tb.Th*, Tb.Sp* with r 2 ⬎ 0.93), but that the surface determination, also of this low-noise, unblurred ‘artificial’ data
set, was not correct enough for a reliable assessment of the
traditional indices Tb.N, Tb.Th and Tb.Sp (r 2 ˆ 0.69 to
0.83).
Performing a full structure extraction of the 3D-QCT data
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A. Laib, P. Rüegsegger / Computerized Medical Imaging and Graphics 23 (1999) 69–74
has the advantage that a direct determination of the degree
of anisotropy is possible with methods such as mean intercept length [18]. The comparison with the MicroCT,
however, shows a r 2 of 0.43 only. Further work is in
progress to study the connectivity of the trabecular structure
in the full structure segmented data and to determine the
accuracy of it.
The ridge detection method is a more direct approach to
get the information of the skeleton, but the data presented
here does not allow a qualified decision in favor of one
extraction method. Both methods are affected by the
signal-to-noise ratio and by the limited resolution, which
in turn are further coupled to each other by the low-pass
filtering step in the structure extraction by the choice of s
for the ridge detection or by the Hamming cut-off frequency
for the full structure extraction.
In summary, the very high correlations of the indices
obtained from the high resolution 3D-QCT and the
MicroCT data illustrate the trustworthiness of the structure
extraction procedure for patient measurements. It is
expected that the additional information of the trabecular
structure will be useful to improve the assessment of bone
strength and fracture risk.
Acknowledgements
This work was supported in part by grant 31-45811.95
from the Swiss National Science Foundation.
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Andres Laib received his MSc degree in Experimental Physics in 1994
and his Ph.D. degree in Physics in 1999 from the ETH Zürich, Switzerland. He is currently working as a post-doc at the Institute for Biomedical Engineering of the ETH and University of Zürich, Switzerland.
His main research interests are in bone structure analysis and computed
tomography.
Peter Rüegsegger graduated from the University of Zürich, Switzerland and got his Ph.D. in Physics in 1972. After a few postdoctoral years
at the newly founded Institute for Biomedical Engineering of the ETH
and University of Zürich, Switzerland, he switched to the Biodynamics
Research unit at the Mayo Clinic, Rochester, MN, where he helped to
design the so called dynamic spatial reconstructor (DSR), a 3D-CT
system for the investigation of the beating heart. In 1977 he went
back to the Institute for Biomedical Engineering where he focused on
bone densitometry and bone structure analysis based on high precision
quantitative computed tomography. In 1990 he became Professor for
Biomedical Engineering and Medical Physics.