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Original Research |
1 Department of Radiology, Hospital Quirón, Avda. Blasco
Ibáñez, 14, 46010 Valencia, Spain.
2 Electronics Engineering Department, Universidad Politècnica de
València, Valencia, Spain.
Received December 10, 2007;
accepted after revision April 13, 2008.
Address correspondence to A. Alberich-Bayarri
(aalberich.val{at}quiron.es).
Abstract
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SUBJECTS AND METHODS. A series of wrist MR images were acquired with high-spatial-resolution (180 µm) isotropic voxels from 40 subjects without reported bone disease. After image postprocessing, the bone volume-to-total volume ratio, trabecular thickness, trabecular separation, and trabecular number were calculated in the morphologic analysis. Trabecular bone was mechanically simulated using the finite-element method to calculate the apparent elastic modulus parameter. The relationship between morphologic and mechanical parameters was studied. The influence of the analyzed bone volume was also investigated.
RESULTS. Statistically significant sex influences were found on the bone volume-to-total volume ratio (p = 0.003), trabecular thickness (p = 0.02), and apparent elastic modulus (p = 0.01); these parameters were lower in women. However, trends were found only on trabecular separation (p = 0.06) and trabecular number (p = 0.07). Age had no statistically significant influence in any morphologic (bone volume-to-total volume ratio, r = –0.24, p = 0.13; trabecular thickness, r = –0.03, p = 0.88; trabecular separation, r = 0.12, p = 0.47; and trabecular number, r = –0.23, p = 0.16) or elastic (apparent elastic modulus, r = –0.18, p = 0.26) parameter. A statistically significant relationship between apparent elastic modulus and the square of bone volume-to-total volume ratio was found (r = 0.968, p < 0.001). This association was not seen (r = 0.185, p = 0.25) and apparent elastic modulus results were considerably different (p < 0.001) if the volume of analyzed bone was reduced.
CONCLUSION. We found that bone volume-to-total volume ratio, trabecular thickness, and apparent elastic modulus are parameters significantly influenced by sex. Apparent elastic modulus results show a relationship with bone volume-to-total volume ratio. Trabecular bone volume should be maximized for an appropriate mechanical analysis.
Keywords: elastic modulus • finite element • MRI • osteoporosis • trabecular bone
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The diagnosis of osteoporosis is based on the quantification of bone mineral density (BMD) by dual energy x-ray absorptiometry (DEXA) techniques. Because osteoporosis affects not only the BMD but also the trabecular bone microarchitecture [1], BMD is not sufficiently comprehensive for complete characterization of trabecular bone de te ri oration [2]. The architectural abnormalities associated with osteoporosis produce an alteration of specific structural organization and mechanical parameters of cancellous bone.
With the aim of quantifying trabecular bone characteristics, advanced image post-processing techniques with morphologic and mechanical elastic analysis can be applied to series of axial 3D MR images of the wrist to evaluate both morphology and mechanical bone properties in healthy subjects. Because trabecular thinning and pore size increment are clear biomarkers of osteoporosis [3], it seems quite relevant to develop a structural characterization of trabecular bone on the basis of morphologic parameters. The most relevant morphologic values in the characterization of trabecular bone are the bone volume-to-total volume ratio, trabecular thickness, trabecular separation, and trabecular number.
On the other hand, microarchitecture deterioration induced by osteoporosis supposes an increase in the fracture risk due to trabeculae disorganization. Any approach to the quantification of trabecular bone microstructure elasticity degree should be considered to evaluate the fracture risk. Different material properties related to the stress–strain relationship, such as elasticity, can be evalu ated by the quantification of the apparent elastic modulus (also called ap parent Young's modulus) parameter.
Structural simulations are currently being developed in biomedical engineering by application of the finite element (FE) method, which consists of the division of a continuum into discrete elements that define a linear system of equations with displacements and forces to be solved. A study of the mechanical properties of the trabecular bone can be obtained by the application of the FE method to the trabecular bone voxel-meshed structures [4]. Trabecular bone recon structions can be simulated under com pression to obtain stresses, strains, and displacements of each element in the cancellous bone discrete model. Processing of these mechanical solutions can be implemented by the direct application of the homogenization theory to estimate the ap parent elastic modulus of the whole trabe cular bone model.
Our objective was to characterize the architectural structure of cancellous bone in healthy subjects to obtain reference morphologic and elastic parameters to define their values and the relationships between them. This knowledge may be useful if these properties are finally determined to be bone disease biomarkers.
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Three-Dimensional Reconstruction of the Trabeculae
Processing algorithms were implemented in Matlab R2007a software (The
MathWorks). An initial segmentation of the trabecular region in each slice was
developed with an automated location of the radial cortex. The key of the
method lies in the observation of two adjacent slices: Cortical bone conserves
its shape, whereas intensities corresponding to the bone marrow are different
from each other. Using this property, automated segmentation was performed by
contour-fitting techniques on the basis of snakes (adaptive contour fitting
technique) [5,
6]. The initial contour needed
to start the segmentation algorithm was obtained by the application of image
filters followed by pixel binarization. Each calcu lated contour was used as
the initial condition for the adjacent slice.
Once the trabecular bone region was isolated, the bone volume fraction (BVF) map was calculated after discriminating voxels of pure marrow from those partially occupied by bone. Small signal intensity heterogeneities associated with the use of surface coils were statistically corrected by determining the local threshold intensities. Afterward, this local threshold was used to classify pixels into bone or marrow, performing the image equalization [7].
Because the true trabecula dimension (approximately 80–150 µm) is smaller than the acquired pixel size (180 µm), images were processed to virtually increase the spatial resolution, remove the trabecular blur, and minimize partial volume effects. Subvoxel processing was applied [8], finally obtaining voxels of 90 x 90 x 180 µm. Complete discrimination between bone and marrow voxels was achieved after thresholding binarization in each image set with the Otsu's method [9]. Finally, a logical 3D reconstruction of the whole cancellous structure was obtained (Fig. 2).
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The trabecular thickness represents the mean thickness value of all the beams of trabecular bone of the 3D structure, measured in each slice and then averaged for all the slices of the 3D structure. First, a 2D skeletonization algorithm was applied and pixels labeled as trabeculae axis selected. Pixels corresponding to the boundary of the trabeculae were also detected by the application of a contour-detection algorithm. Then, the distance-transform method [10] was applied to the contour image to obtain the minimum distance from each pixel to the contour. The skeletonized image was multiplied by the result of the transform distance to obtain the minimum distance from each pixel of the skeleton or center line of the trabecular bone rod to the boundary—that is, the half value of the trabecular thickness.
The mean size of the intertrabecular spaces or pores defined the trabecular separation and was determined by calculating the mean number of contiguous voxels occupied by marrow in each one of the three space directions. The trabecular number, which gives an idea of the percentage of trabecular bone present in the volume against the mean trabecular thickness, was calculated by dividing the bone volume-to-total volume ratio by the trabecular thickness [11].
Mechanical Analysis
Trabecular bone was mechanically tested under simulation using the obtained
3D trabecular reconstructions. The FE method was applied on cubic samples of
trabecular bone reconstruction of large dimensions (1.5 x 2 x 1
cm; total, 3 cm3) to simulate a static uniaxial compression
stress–strain test, with a total computation time of approximately 4
hours (PC with an Intel Core 2 Duo processor at 1.86 GHz and 1 GB of RAM).
The FE meshes were built by direct conversion from the 3D reconstruction
voxels to eight-noded isotropic hexahedron (brick) elements
(Fig. 3) (Saxena R, et al.,
presented at the 1999 annual Northeast Bioengineering Conference of the IEEE)
using a self-developed fast-mesher algorithm. Each element was set to have
compact bone material properties (Young's modulus, E = 10 GPa;
Poisson's ratio, 
= 0.3)
[12,
13]. In the simulation, null
displacement was imposed on nodes from one side whereas a deformation (
)
of 10% of the edge length was specified on nodes from the opposite side to
simulate compression.
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The solution of the FE linear system of equations was calculated using Ansys, version 10.0 software (Ansys). Results of nodal displacements of the structure, nodal stresses and strains, and reaction forces were obtained in the solution of the FE method [14]. Moreover, an elastic characterization of the whole structure was performed by application of the homogenization theory [15, 16]. Results of the FE solution were processed to obtain the apparent elastic modulus parameter of the trabecular bone sample.
Reaction forces on nodes (Fn) from the fixed side were
processed to obtain the apparent elastic modulus value
(Eapp) of the specimen by
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and,
finally, Eapp was calculated for the whole 3D
structure.
Relationship Between Morphologic and Mechanical Parameters
The morphology–elasticity relationships for estimation of elastic
properties of human trabecular bone were also assessed. The relation ship
between apparent elastic modulus and bone volume-to-total volume ratio
[17,
18] was calculated to validate
our apparent elastic modulus measurements and further characterize cancellous
bone properties.
Influence of Analyzed Volume
With the aim of reducing the computational burden and to save time, an
evaluation of the influence of the 3D sample size in the reliability of the
measurements and the relationship between morphologic and mechanical
parameters was also calculated. Therefore, simulations were also appli ed to a
volume with reduced dimensions (0.5 x 0.5 x 1 cm; total, 0.25
cm3), with a total computation time of approximately 20 minutes
(91.6% decrease).
Statistical Analysis
Normal data distribution was checked by the application of the
Kolmogorov-Smirnov test. Mean values were compared between men and women using
the Student's t test distribution for independent samples with
Levene's test for the equality of variances. The limit of significance was set
at p < 0.05. The relationship between all the morphologic and
mechanical parameters and age was analyzed by a linear regression and the
Pearson's product–moment correlation coefficient in case of normal
distribution. For nonnormal data distribution, a Spearman's rank test was used
to analyze the association of morphologic and mechanical results. Agreement
between the methods described for the elastic modulus measurement was assessed
by the analysis of variance and its F test. The Bland-Altman method was used
for graphically assessing the agreement.
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Significant differences were found between male and female subjects for the results of apparent elastic modulus (p = 0.01), with lower values in women, as can be observed in Table 1. There was no significant age influence (r = –0.18, p = 0.26).
A statistically significant relationship was found between the elastic modulus and the square of the bone volume-to-total volume ratio calculation (r = 0.968, p < 0.001), reflecting the high linear function between mechanical and structural parameters.
The volume of analyzed bone had an influence on the elastic results. Although the statistically significant difference between male and female results for apparent elastic modulus calculated in the small volume of interest (VOI) (p = 0.002) was maintained, reliability of results was reduced, and a statistically significant difference (p < 0.001) between apparent elastic modulus results obtained for the large VOI and those obtained for the small VOI (189.84 ± 20.02 MPa vs 81.56 ± 16.86 MPa) was obtained. Furthermore, the use of small volumes for elasticity calculation provided a nonnormal distribution and gave no statistical correlation (r = 0.185, p = 0.25) with the square of the bone volume-to-total volume ratio para meter. The behavior of the relationship between elastic modules calculated from the two different volumes and square of the bone volume-to-total volume ratio is seen in Figure 4, in which a linear performance is shown for the large volume, whereas no goodness of fit is found in the small volume estimation. Differences between apparent elastic modulus results for the two different analyzed volumes become greater when the values of the elastic parameter grow, as can be seen in the Bland-Altman plot (Fig. 5).
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In recent years, a morphologic analysis has been developed to test several trabecular bone physical properties such as the trabeculae dimensions and bone volume percentage [10, 11]. It has been also recognized that an evaluation of the mechanical behavior of the complete trabecular structure helps in the characterization of some bone properties [12, 15]. Therefore, any study designed to evaluate osteoporosis should include a detailed characterization of the trabecular bone structure as well as the bone mechanical properties. Also, to our knowledge, the evaluation of the influence of reducing the volume of analyzed bone, and therefore the computational burden, in the calculation of bone elastic properties has not been performed previously.
Image processing algorithms applied to high-resolution images are an important advance in the detection of new parameters acting as disease biomarkers. In our series, MR images were acquired from the distal metaphysis of the radius with a high spatial resolution, achieved in vivo with isotropic voxels of 180 µm. This small voxel size enables the development of a 3D model, allowing the characterization of the trabecular bone properties as new biomarkers of disease. Advanced image processing techniques, with segmentation, filtering, interpolation, and binarization of the trabecular bone region, were applied slice by slice to prepare the data for the 3D analysis.
Sex, but not age, has a clear influence on the morphologic bone parameters calculated from the trabecular 3D structure. Therefore, normal values of these parameters have to be stratified by sex. Variability of the obtained morphologic parameters also may be influenced by the acquisition and image processing techniques. In our study, the obtained morphologic parameters were in accordance with those previously published in other studies [12, 19]. However, some differences have to be mentioned. Our mean bone volume-to-total volume ratio was lower compared with Newitt et al. [12] (0.22 ± 0.04 vs 0.36 ± 0.05, respectively). Because those authors studied morphologic parameter results in a population of postmenopausal women and used a higher 3D slice partition thickness, these differences in spatial resolution and age distribution may be responsible for the disparity. Our mean trabecular thickness is in accordance with that obtained by Newitt et al. (0.19 ± 0.01 mm vs. 0.21 ± 0.02 mm) because the method of distance transform is characterized by its robustness in those cases having a higher spatial resolution than the typical dimensions of the tissue under study [10]. Our mean trabecular separation is also similar to that obtained in another study [19] for trabecular bone samples of the radius (0.85 ± 0.12 mm vs 0.75 ± 0.35 mm). Results obtained for trabecular number are also close to those published in that study (1.16 ± 0.19 mm–1 vs 0.96 ± 0.20 mm–1).
Mechanical 3D analysis of complex structures by FE modeling has become a well-established method in engineering. The use of this tool has grown widely in recent years in bioengineering medical science, mainly because of the improvement of clinical imaging CT and MR scanners. The higher spatial resolution achieved with high-field 3-T MR scanners allows the development of 3D reconstructions of tissues with the possibility of simulation in defined conditions. Several studies [4, 12, 15] have shown the potential for application of the FE method in combination with image processing techniques and voxel-based FE meshes to test the elasticity and quality of the trabecular bone.
In our study, simulated mechanical tests were applied to the in vivo trabecular bone reconstructions using the FE method with voxel-meshed structures. More accurate mechanical simulations are achieved by using a direct conversion from the voxels of the 3D reconstruction to the brick hexahedron elements of the FE model. Sex showed a significant influence on apparent elastic modulus results; Young's modulus results were greater in men, in accordance with our expectations [20].
We found that the mean elastic modulus obtained in our series was lower than the value obtained by Newitt et al. [12] for uniaxial compression (189.84 ± 126.62 MPa vs. 2,050 ± 590 MPa, respectively). Although the mechanical analysis presented by Newitt et al. is very similar to the one in this study, the methodology in our study presented some differences in acquisition technique regard ing main magnetic field intensity (3 T vs 1.5 T), contrast sequence parameters (56/5 and flip angle, 25° vs 29/5.6 and flip angle, 30°), slice thickness (180 µm vs 500 µm), and image postprocessing (a subvoxel processing algorithm was developed in our study). Müller and Rüegsegger [21] obtained a compressive elastic modulus of the cancellous bone of the radius of 564 MPa using high-resolution CT with a slice thickness of 480 µm and the application of the FE method by tetrahedrons. Therefore, use of different acquisition tech niques, image spatial resolution, and pro cessing methods clearly influences the stan dardization of the apparent elastic modulus values.
When comparing in vivo relationships between elastic and morphology
results, a high correlation for both sexes between elastic modulus (mechanical
parameter) and the square of bone volume-to-total volume ratio (structural
parameter) was found, agreeing with ex vivo tests in the relationship between
apparent elastic modulus and bone volume-to-total volume ratio
[17,
18]. This behavior agrees with
the theory [22,
23] of the existence of a
strong relationship between the elastic modulus and the square of porosity of
a material in the elastic regime. This observed exponential dependence for the
compressive modulus takes the form
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The main problems in the application of the FE method to trabecular bone meshes come from the high computational cost that composes the calculus of the solution of the linear system of equations (24 equations per voxel). To minimize the computational burden, a representative VOI may be chosen as small as possible if it provides reliable results. However, we have shown that the value of the results diminishes as the restricted volume dimensions decrease.
In our study, we have tested two different cancellous bone segmented volumes to evaluate the variation and reliability of the results. We have found that the mechanical analysis results applied to the large sample volumes of trabecular bone better characterize its properties, with significant differences between male and female subjects for the apparent elastic modulus parameter. As expected, results for this parameter were greater in men [23].
Some bias should be mentioned. In comparing age distribution in both sex populations, the female group presented three subjects over 60 years old, possibly distorting the tendency to provide significance. To test if these outliers could influence our results for the female group, the mean values for all the structural and mechanical parameters were compared between this small (three subjects) subpopulation and the remaining 18 female subjects using a Student's t test. Means were not significantly different between these two groups (p = 0.68, apparent elastic mod ulus; p = 0.60, bone volume-to-total volume ratio; p = 0.89, trabecular thickness; p = 0.18, trabecular separation; p = 0.59, trabecular number). Thus, it was decided not to exclude them from the study.
No relationship was found between age and any of the parameters studied. These unlinked results probably may be enhanced by the relative youth of the subjects in our study (38 ± 15 years) in comparison with older patients, who tend to have an increase of osteoclast resorption, especially in women after menopause because of estrogen reduction [17]. This needs further study with larger and more age-representative series.
In conclusion, using advanced analysis of high-resolution 3-T MR images, it is possible to achieve 3D models of trabecular bone. Computer-generated 3D models of the cancellous bone can be used to further characterize bone, simulating different mech anical and structural scenarios for studying values and relationships of the obtained characteristic trabecular bone para meters. We found that bone volume-to-total volume ratio, trabecular thickness, and the elastic modulus are parameters influenced by the MR acquisition technique, computer processing, and sex. On the contrary, trabecular separation and trabecular number are independent values. Age did not seem to significantly influence any parameter in the healthy subjects analyzed. A high relationship has been found between elastic modulus and bone volume-to-total volume ratio. This association is lost when reducing the volume under analysis, also diminishing the reliability of the results. The usefulness of these morphologic and mechanical parameters in osteoporosis needs further evaluation. Results of the parameters comparing large series of osteoporotic and healthy subjects of different ages should provide knowledge for the establishment of new biomarkers of disease; offer more information to the patient; and, in so doing, both improve patient care and place radiology as an advanced technology in the implementation of new methods of diagnosis.
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= large VOI, 
= small VOI.