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Keywords:

  • bone microstructure;
  • bone stiffness;
  • finite element model;
  • micro magnetic resonance imaging;
  • micro computed tomography

Abstract

  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and Methods
  5. Results
  6. Discussion
  7. Disclosures
  8. Acknowledgements
  9. References

Micro magnetic resonance imaging (µMRI) is an in vivo imaging method that permits 3D quantification of cortical and trabecular bone microstructure. µMR images can also be used for building microstructural finite element (µFE) models to assess bone stiffness, which highly correlates with bone's resistance to fractures. In order for µMRI-based microstructural and µFE analyses to become standard clinical tools for assessing bone quality, validation with a current gold standard, namely, high-resolution micro computed tomography (µCT), is required. Microstructural measurements of 25 human cadaveric distal tibias were performed for the registered µMR and µCT images, respectively. Next, whole bone stiffness, trabecular bone stiffness, and elastic moduli of cubic subvolumes of trabecular bone in both µMR and µCT images were determined by voxel-based µFE analysis. The bone volume fraction (BV/TV), trabecular number (Tb.N*), trabecular spacing (Tb.Sp*), cortical thickness (Ct.Th), and structure model index (SMI) based on µMRI showed strong correlations with µCT measurements (r2 = 0.67 to 0.97), and bone surface-to-volume ratio (BS/BV), connectivity density (Conn.D), and degree of anisotropy (DA) had significant but moderate correlations (r2 = 0.33 to 0.51). Each of these measurements also contributed to one or many of the µFE-predicted mechanical properties. However, model-independent trabecular thickness (Tb.Th*) based on µMRI had no correlation with the µCT measurement and did not contribute to any mechanical measurement. Furthermore, the whole bone and trabecular bone stiffness based on µMRI were highly correlated with those of µCT images (r2 = 0.86 and 0.96), suggesting that µMRI-based µFE analyses can directly and accurately quantify whole bone mechanical competence. In contrast, the elastic moduli of the µMRI trabecular bone subvolume had significant but only moderate correlations with their gold standards (r2 = 0.40 to 0.58). We conclude that most microstructural and mechanical properties of the distal tibia can be derived efficiently from µMR images and can provide additional information regarding bone quality. © 2010 American Society for Bone and Mineral Research.


Introduction

  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and Methods
  5. Results
  6. Discussion
  7. Disclosures
  8. Acknowledgements
  9. References

Osteoporosis, a metabolic bone disease of major proportions, is classically diagnosed by dual-energy X-ray absorptiometry (DXA) via areal bone mineral density (aBMD). It is becoming increasingly apparent, however, that other factors, independent of aBMD, contribute significantly to fracture risk.1 Evidence for an independent role of bone microarchitecture as a determinant of the bone's mechanical competence and fracture risk has been documented in many studies.2–8 Thus there has been great interest in developing new in vivo imaging methods capable of measuring bone microstructure that then could be used to derive new quantitative microstructural and mechanical measures for the clinical detection of osteoporosis. One such technology is micro magnetic resonance imaging (µMRI). MRI is an important focus for in vivo trabecular bone morphometry because of its absence of ionizing radiation, high innate contrast between bone and marrow, and widely distributed population of general-purpose clinical MRI instruments.3, 7–18 µMRI permits the visualization and quantification of trabecular network architecture at voxel sizes comparable with trabecular thickness, which makes the method sufficient for resolving individual microstructural elements and quantifying network topology. µMRI images can also be used for building microstructural finite element (µFE) models to assess bone stiffness,6, 18, 19 a measurement which highly correlates with bone's resistance to fractures. Currently, the signal-to-noise ratio (SNR) of µMRI confines the scan to locations that permit the use of either a closely coupled volume transmit-receive coil or surface coil arrays, for example, the distal radius,7, 9, 20 the distal tibia,11, 12 and the calcaneus,3, 8, 15, 21 in order to achieve a resolution close to the low end of trabecular thickness. Measurements of microstructure at the proximal femur also have been reported, albeit at a considerably lower resolution.22 In several clinical studies, high-resolution in vivo µMRI has been performed at the distal radius, distal tibia, and calcaneus to assess trabecular bone microstructure. The morphological and mechanical properties of trabecular bone derived from in vivo µMRI have associations with fracture risk and are sensitive to drug interventions.6, 7, 11, 12, 17, 18, 23, 24

A few in vitro validation studies have compared the microstructural measurements of high-resolution µMR images of trabecular bone samples from the distal radius and calcaneus with either micro computed tomography (µCT) or contact radiography and showed significant correlations.14, 20, 25–27 µMRI image-based µFE predictions of trabecular bone samples have also been validated with µCT-based µFE predictions as standard reference.28 However, these existing studies focused on the measurements of small bone samples or volumes of interest. Currently, there is no data validating µMRI of whole bone segments. Microstructural analyses of µMRI images of whole bone segments can provide more accurate estimates of trabecular bone microstructure as the inhomogeneity of the trabecular network can be taken into consideration, and additional measurement of cortical thickness can be provided. Moreover, whole bone stiffness can provide an estimate of the overall mechanical competence with the contributions from both the trabecular and cortical bone compartments. In order for µMRI-based microstructural and µFE analyses to become standard clinical tools for assessing bone quality, the data from µMRI must be thoroughly validated and compared with those from a current gold standard, namely, high-resolution µCT.

In this study, one of the primary purposes was to validate the 3D model-independent microstructural measurements of 1.5 T high-resolution µMRI against gold standard µCT measurements of the distal tibia. The second purpose was to validate the axial stiffness of the distal tibial bone segment, with and without the cortex, as assessed by µMRI-based µFE models against its gold standard, µCT-based µFE measurement. In addition, the anisotropic elastic moduli of trabecular bone based on µFE analyses of cubic subvolumes of µMR images were also compared with those of µCT images. Lastly, the ability of µMRI microstructural measurements to predict mechanical properties calculated by µCT-based µFE analyses was investigated. This represents the first validation study for µMRI-based microstructural and mechanical measurements of whole bone segments of human distal tibia.

Materials and Methods

  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and Methods
  5. Results
  6. Discussion
  7. Disclosures
  8. Acknowledgements
  9. References

Specimen preparation and µCT imaging

Twenty-five freshly frozen human cadaveric tibias from 15 donors (10 pairs and 5 singles, 11 males and 4 females) were obtained from the International Institute for the Advancement of Medicine (Scranton, PA, USA). The age of donors ranged from 55 to 84 years, with an average of 70.6 years. The donors' medical histories were screened to exclude metabolic bone diseases and chronic conditions that could affect bone metabolism, such as osteomalacia, Paget disease, primary hyperparathyroidism, chronic kidney disease, chronic obstructive pulmonary disease, HIV positivity, or bone cancer. However, donors could still have osteoporosis. Using a band saw, starting at approximately 15 mm proximal to the tibia endplate, each distal tibia was cut into a 25-mm section along the axial direction. The central 10-mm section along the axial direction was then scanned with a µCT system (vivaCT 40 or µCT 80, Scanco Medical AG, Bassersdorf, Switzerland). An ex vivo scanning setting (70 kVp, 114 µA, 700-ms integration time) was used for the µCT scanning, resulting in an isotropic 25-µm voxel size.

µMRI

After µCT scanning, the bone marrow was removed from the distal tibial bone segments using a gentle water jet. Then each demarrowed bone segment was placed in a 250-mL cylindrical glass jar, immersed in 1 mM aqueous gadolinium–diethylenetriammine-pentaacetate (Gd-DTPA) to shorten the longitudinal relaxation time to that approximating fatty bone marrow (T1 ≈ 300 ms at 64 MHz). Each bone segment's anatomic orientation was aligned carefully with two distilled-water-filled capillary tubes attached to the inner surface of each jar, the large (small) capillary tube marking the anterior (medial) side of the specimen. Air bubbles trapped in the marrow spaces (which would cause artifactual signal voids and susceptibility artifacts) were removed through centrifugation at 1500 rpm (approximately 6g).29 The specimens were imaged distal end first (analogous to feet first in patient scans) and anterior side up (analogous to supine position in patient scans) on a 1.5-T whole-body clinical MRI scanner (Siemens MAGNETOM Sonata, Siemens Medical Solutions, Erlangen, Germany) equipped with 40 mT/m gradients using an in-house-built receive-only two-element phased-array surface coil for imaging the ankle. Axial and sagittal localizer spin-echo images were acquired to prescribe the high-resolution 20-mm (inferosuperior) imaging slabs. The pulse sequence used was a more advanced and robust version of the 3D fast large-angle spin-echo (FLASE) pulse sequence30 detailed in Magland and colleagues.31 The center of this slab was selected as the center of the 25-mm bone segments. The FLASE pulse sequence used the following parameters: flip angle = 140 degrees; TR/TE = 80/10.5 ms; readout bandwidth = 7.81 kHz; field of view = 7 × 6.4 cm; 32 slices within the inferior-superior slab; 512 data points along the frequency-encoding direction (anterior-posterior); and 460 phase-encoding points for the distal tibia. The typical acquisition time was 16 minutes and 23 seconds for the distal tibia, yielding a final raw data voxel size of 160 × 160 × 160 µm3.

Next, the 3D grayscale images were input into the virtual bone biopsy (VBB) data-processing chain to yield thresholded binary images. Briefly, a local threshold algorithm was applied to correct marrow-intensity variations resulting from the sensitivity profile of the surface coil.32 The images were then sinc-interpolated by a factor of 3 × 3 × 3 by zero filling in the k-space domain resulting in, after Fourier transformation, a final image voxel size of 53 × 53 × 53 µm3.33 These images were then contrast inverted to yield a bone volume fraction (BVF) map in which voxel intensities ranged from 0 to 100 such that 0 was pure marrow and 100 represented pure bone. Here the images were thresholded at an empirically optimized value of 50% BVF to yield 3D binary images.33 This thresholding procedure and setting are being used in the current µMRI clinical studies of human subjects.

Mutual information–based registration of µMRI and µCT Images

To register the µCT images to µMR images, a pyramid three-step registration approach was employed using the landmark-initialized mutual information–based registration toolkit34, 35 of an open-source software (National Library of Medicine Insight Segmentation and Registration Toolkit, USA).36 The subvoxel processed grayscale µMR images were held in fixed position while the grayscale µCT images were rotated and translated to match the µMR images. The registration accuracy was tested on simulated images and showed an alignment error smaller than 10% of the µCT voxel size (2.5 µm). All µCT images were registered successfully to the corresponding µMR images to encompass the same volume of interest (Fig. 1) and were confirmed by visual inspection using an open-source medical image display application (FusionViewer).37

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Figure 1. The registered 2D grayscale images (A, B), 3D thresholded images (C, D), and 3D cubic subvolumes (E, F) of µCT and µMRI images of human distal tibia. The first row shows the high-resolution µCT images, and the second row shows the corresponding µMR images.

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Standard 3D model-independent morphological analyses of µCT images

The standard µCT evaluation protocol was performed for the registered µCT images. First, the endosteal cortical surface was contoured semiautomatically to segment the trabecular and cortical regions, followed by Gaussian filtering and specimen-specific global thresholding to extract the mineralized phase using the standard protocol of Scanco software (Scanco Medical AG, Bassersdorf, Switzerland) for µCT analysis. Based on the thresholded trabecular bone images, the bone volume fraction (BV/TV) and 3D model-independent parameters trabecular thickness (Tb.Th*), trabecular spacing (Tb.Sp*), and trabecular number (Tb.N*) were determined based on a distance transformation.38 In addition, the bone surface-to-volume ratio (BS/BV), structure model index (SMI), connectivity density (Conn.D), and degree of anisotropy (DA) were also evaluated for each trabecular bone image. BS/BV was computed by dividing the trabecular bone surface (BS) by the trabecular bone volume (BV), with BS and BV determined by a triangulation approach.39 The SMI estimates, on average, the plate versus rod characteristics of trabecular bone.40–43 For an ideal plate to an ideal rod structure, SMI ranges from 0 to 3, respectively. Conn.D quantifies trabecular connectivity by calculating the number of handles or closed loops in the trabecular network.44, 45 DA reflects the orientation of the trabecular bone network.46, 47 To evaluate the cortical thickness (Ct.Th), both periosteal and endosteal surfaces of the tibial cortex were contoured manually using the semiautomatic Scanco software to isolate the cortex as the volume of interest. The Ct.Th was determined as the cortical volume divided by the mean of the periosteal and endosteal bone surface areas according to a standard Scanco protocol for µCT images. All morphological analyses of the µCT images were performed using the standard morphologic analysis software on an HP AlphaStation of a VivaCT 40 system (Scanco Medical).

Morphological analyses for µMR Images

All µMR images were analyzed by two evaluation protocols. First, the standard 3D model-independent morphological analyses were applied to the thresholded µMR images at a 53-µm voxel size. The BV/TV, Tb.N*, Tb.Th*, Tb.Sp*, Ct.Th, SMI, BS/BV, DA, and Conn.D values of each µMR image were calculated. The methods of these analyses are the same as the standard morphological analysis for µCT images, as described in the preceding section.

Due to the limited resolution of µMR images, a 2D analysis using the mean intercept length method based on the plate model has been used widely to achieve evaluation of trabecular bone microstructure.14, 26, 48, 49 This 2D analysis was applied to each µMR images to derive Tb.N, Tb.Th, and Tb.Sp. The same set of parameters derived by the 3D model-independent method was denoted by an asterisk (ie, Tb.N*, Tb.Th*, and Tb.Sp*) to distinguish them from the 2D parameters.

Finite element analyses for µMR and µCT images

Three µFE analyses were performed for each µMR and µCT image. The first analysis was performed for the whole tibial bone segment to determine its axial stiffness. The second analysis was conducted for the tibial trabecular bone segment without the cortex to determine the trabecular bone axial stiffness. The third analysis was applied to a cubic subvolume of trabecular bone selected from the center of the sample to calculate the full anisotropic elastic moduli by using strict uniaxial strain boundary conditions.50 These three µFE analyses provide distinct mechanical parameters of the distal tibia that are important in clinical assessments of mechanical competence. The axial stiffness is the overall mechanical competence, whereas trabecular bone axial stiffness provides an estimation of the overall structural contributions of the trabecular bone compartment. The subvolume trabecular bone µFE analysis reveals important anisotropic material properties of the trabecular bone component. Each bone voxel of a thresholded µMR image was converted directly to an 8-node elastic brick element with an element size of 53 × 53 × 53 µm3. Each µCT image was resampled from 25 to 40 µm and then converted to µFE models with an element size of 40 × 40 × 40 µm3. A convergence study was conducted in three randomly selected µCT images to determine the axial stiffness with different element sizes (25, 30, 40, 60, and 80 µm). Results showed that the maximum difference in axial stiffness between the models constructed at 40 and 25 µm was 1.67%. For each µFE analysis, bone tissue was modeled as an isotropic, linearly elastic material with a Young's modulus (Es) of 15 GPa and a Poisson's ratio of 0.3 for all the models.51 This assumption focuses the current study to imaging-related issues rather than variations in bone tissue properties, which currently cannot be assessed in patients. To evaluate axial stiffness for a whole bone segment with and without the cortical shell, a uniaxial displacement equaling 1% of the bone segment height was applied perpendicularly to the distal surface of the tibia while the proximal surface was imposed with zero displacement along the same direction. Both ends of the tibia were allowed to translate freely in the transverse plane. The total reaction force was calculated from the linear FE analysis, and the axial stiffness was calculated as the reaction force divided by the imposed displacement. The parallel FE program Olympus was used to solve these FE models.52 Olympus is built on a serial finite-element analysis program (FEAP),37 a parallel multigrid equation solver called Prometheus,53 and the parallel numerical framework PETSc.54 All the parallel computations were conducted on an IBM Power4 supercomputer (IBM Corporation, Armonk, NY, USA) at the San Diego Supercomputer Center using a maximum of 256 CPUs in parallel. Whole bone segment stiffness and trabecular bone stiffness were calculated for each µMR and µCT image, respectively.

A 143 × 143 × 143 voxel cubic subvolume of trabecular bone was extracted from each registered and resampled µCT image (40-µm voxel size) corresponding to a 108 × 108 × 108 voxel cubic subvolume (53-µm voxel size) from the µMR image (Fig. 1), which was equivalent to a physical size of 5.74 × 5.74 × 5.74 mm3. The subvolumes from the two modalities were converted to µFE models. Using a customized element-by-element preconditioned conjugate gradient solver,55 six µFE analyses were performed for each model, representing three strict uniaxial compressions along the three imaging axes (x, y, and z) and three strict uniaxial shears.50 The general anisotropic stiffness matrix was first determined based on the results from the preceding analyses. A new coordinate system of orthotropic axes (X1, X2, and X3) representing the best orthotropic symmetry was then calculated by using a numerical optimization algorithm, Powell's method,56 to minimize an orthotropy objective function.50 Transformation of the anisotropic matrix to a new coordinate system yielded the full orthotropic stiffness tensor.50 The elastic constants and stiffness matrix were sorted such that E11 was in the direction of the lowest axial modulus and E33 was in the direction of the highest axial modulus. The elastic moduli (three Young's moduli, E11 < E22 < E33 and three shear moduli, G23, G31, and G12) were then derived from the orthotropic stiffness tensor. All the µFE analyses for subvolumes were implemented on a Dell XPS PC workstation (Dell, Inc., Round Rock, TX, USA).

Statistical analysis

Linear correlations between the µMRI microstructural measurements and the corresponding measurements from gold standard µCT images were performed. Linear correlations were also conducted to compare the mechanical measurements of µMR and µCT images including whole bone segment stiffness, trabecular bone stiffness, and six elastic moduli of trabecular bone subvolumes. Paired Student's t tests were performed to test for significant differences between corresponding µCT and µMRI measurements.

Furthermore, each of the microstructural measurements based on µMRI and µCT were correlated individually with the mechanical properties derived from the corresponding µCT-based µFE models by linear regression. Next, a forward stepwise multiple linear regression was performed to predict the mechanical properties from the microstructural measurements of µMRI (BV/TV, Tb.N*, Tb.Th*, Tb.Sp*, Tb.N, Tb.Th, Tb.Sp, BS/BV, SMI, Conn.D, and DA) and µCT (BV/TV, Tb.N*, Tb.Th*, Tb.Sp*, BS/BV, SMI, Conn.D, and DA), respectively. At each step of the forward stepwise regression method, the eligible independent variable with the highest statistical strength (p < .05) entered in the model. At any subsequent step where two or more independent variables were selected into the model, the variable with the least statistical strength was removed from the model. The process was terminated when no eligible independent variable exceeded the critical value (p < .05) for model entry or when no independent variable in the model reached the standard (p > .1) for variable removal. The significant and independent predictors of microstructure parameters were selected to yield the best prediction of each calculated mechanical parameter.

The stepwise multiple linear regressions were performed by SPSS 10.0 software (SPSS, Inc., Chicago, IL, USA). All other statistical analyses were performed using KaleidaGraph 3.6 software (Synergy Software, Reading, PA, USA) with p ≤ .05 considered statistically significant.

Results

  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and Methods
  5. Results
  6. Discussion
  7. Disclosures
  8. Acknowledgements
  9. References

On qualitative inspection of the µMR and registered µCT images, similar trabecular bone patterns and cortical geometry were found; however, subtle local differences existed in both the trabecular and cortical microstructure between µMR and µCT images (Fig. 1). The local difference was more noticeable when comparing the cubic subvolumes.

The mean and SD of the microstructural and mechanical measurements of the µMR and µCT images are presented in Table 1 and 2. Except for the Tb.N*, all the microstructural µMRI measurements were significantly different from the corresponding µCT measurements (p < .05; Table 1). The µMRI-derived microstructural measurements BV/TV, Tb.N*, Tb.N, Tb.Sp*, Tb.Sp, SMI, and Ct.Th correlated significantly and highly (r2 = 0.67 to 0.97) with those derived from the µCT images (Fig. 2). Significant but moderate correlations were also found for the Tb.Th, BS/BV, Conn.D, and DA of µMR and µCT images (r2 = 0.23 to 0.51). However, no correlation existed between the Tb.Th* of µMRI and µCT. Comparing the 3D and 2D measurements from µMRI, we found that Tb.N* and Tb.Sp* from 3D analysis had higher correlation coefficients (r2 = 0.92 and 0.97) and regression slopes closer to 1 than Tb.N and Tb.Sp from 2D analysis (r2 = 0.81 and 0.86) with the µCT measurements. However, the Tb.Th* from 3D analysis had no correlation, whereas the Tb.Th from 2D analysis showed a significant correlation with µCT measurement.

Table 1. Microstructural and Mechanical Measurements of µMR and µCT Images of Distal Tibiae
µMRIµCTDifference between µMRI and µCT
ParametersMeanSDParametersMeanSDMeanSD
BV/TV0.210.04BV/TV0.140.050.060.02
Tb.N* (1/mm)1.190.16Tb.N* (1/mm)1.180.180.010.05
Tb.N (1/mm)1.090.17−0.090.07
Tb.Th* (mm)0.250.02Tb.Th* (mm)0.150.020.090.02
Tb.Th (mm)0.190.020.040.02
Tb.Sp* (mm)0.770.13Tb.Sp* (mm)0.830.13−0.060.02
Tb.Sp (mm)0.750.16−0.080.06
Ct.Th (mm)0.660.15Ct.Th (mm)0.510.200.170.12
BS/BV (1/mm)10.740.94BS/BV (1/mm)17.32.7−6.552.34
SMI1.770.36SMI1.240.450.540.25
DA1.720.13DA2.170.15−0.460.12
Conn.D (1/mm3)1.870.58Conn.D (1/mm3)4.141.40−2.271.06
Table 2. Mechanical Measurements of µMR and µCT Images of Distal Tibias
ParameterµMRIµCTDifference between µMRI and µCT
MeanSDMeanSDMeanSD
Whole bone stiffness (N/mm)318,544164,894356,742200,318−38,19849,871
Trabecular bone stiffness (N/mm)106,19580,784103,10783,7523,08832,166
E11 (MPa)424157186129238103
E22 (MPa)766251347170419193
E33 (MPa)15294391091500438353
G23 (MPa)421127228112192104
G31 (MPa)263861339013062
G12 (MPa)21160915312048
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Figure 2. Correlations between microstructural measurements based on µMRI and their respective µCT gold standards.

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The whole-bone stiffness and trabecular bone stiffness based on µMRI and estimated by µFE analyses correlated significantly and strongly with their gold standards (r2 = 0.86 and 0.96; Fig. 3). In contrast, the elastic moduli of the µMRI trabecular bone subvolume had significant but only moderate correlations with their gold standards (r2 = 0.40 to 0.58; Fig. 3). There was no statistical difference between the trabecular bone stiffness values derived from µMR and µCT images. However, the estimated whole bone stiffness derived from the µMR images was significantly lower than that obtained from the µCT images. In contrast, the estimated elastic moduli of the trabecular bone subvolumes of the µMR images were significantly higher than those obtained from the µCT images.

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Figure 3. Correlations between (A) whole bone stiffness, (B) trabecular bone stiffness, (C) elastic moduli, and (D) shear moduli of registered subvolumes of µMR and µCT images.

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The trabecular microstructural measurements BV/TV, Tb.Sp*, and SMI of the µCT images and the BV/TV, Tb.N, Tb.Sp*, Tb.Sp, and SMI of the µMRI images were significantly correlated with the whole bone stiffness, trabecular bone stiffness, and elastic moduli of distal tibias estimated by µCT-based µFE analyses (Table 3). Results for Ct.Th from both µMRI and µCT show that it only contributes to whole bone stiffness measurements (Table 3). The Tb.N* values of both the µMR and the µCT images were significantly correlated with most mechanical measurements except that there was no correlation between the Tb.N* of the µCT images and whole bone stiffness. Plate model–based Tb.Th of µMRI was significantly correlated with the whole bone and trabecular bone stiffness but not trabecular bone elastic moduli. Model-independent Tb.Th* estimated from µMRI had no correlation with any of the mechanical measurements, whereas the Tb.Th* estimated from the µCT images was significantly correlated with all the mechanical measurements. The BS/BV of µMRI was negatively and significantly correlated with the whole bone stiffness and trabecular bone stiffness, whereas the BS/BV of the µCT images was negatively and significantly correlated with all the mechanical measurements. Except for a weak correlation between the DA of the µMR images and whole bone stiffness, neither µMRI- nor µCT-based DA was correlated with any of the mechanical measurements. The Conn.D of the µMRI images was significantly correlated with trabecular bone stiffness and elastic moduli, whereas the Conn.D measurement of µCT had no correlation with any mechanical measurements except for the trabecular elastic modulus E33 (Table 3).

Table 3. Correlation (r2) Between the Microstructural Measurements of µMR and µCT Images and the Mechanical Measurements of µCT Images
  µCT-based mechanical properties
Whole bone stiffnessTrabecular bone stiffnessE11E22E33G23G31G12
  • Note: (–) indicates negative correlation.

  • p < .001.

  • p < .01.

  • §

    p < .05.

  • NS: p > .05.

µMRI microstructural measurementsBV/TV0.440.540.370.450.460.410.340.35
Tb.N* (1/mm)0.19§0.340.330.360.450.350.330.36
Tb.Th* (mm)NSNSNSNSNSNSNSNS
Tb.Sp* (mm)(−) 0.24§(−) 0.37(−)0.35(−) 0.35(−) 0.45(−) 0.34(−) 0.33(−) 0.34
Tb.N (1/mm)0.270.480.450.510.560.500.440.48
Tb.Th (mm)0.340.49NSNSNSNSNSNS
Tb.Sp (mm)(−) 0.32(−) 0.49(−) 0.41(−) 0.47(−) 0.50(−) 0.45(−) 0.39(−) 0.41
Ct.Th (mm)0.32NSNSNSNSNSNSNS
BS/BV (1/mm)(−) 0.37(−) 0.21§NSNSNSNSNSNS
SMI(−) 0.41(−) 0.49(−) 0.39(−) 0.50(−) 0.45(−) 0.47(−) 0.36(−) 0.39
DA0.16§NSNSNSNSNSNSNS
Conn.D (1/mm3)NS0.390.400.480.510.480.400.47
µCT microstructural measurementsBV/TV0.350.590.530.690.670.650.530.61
Tb.N* (1/mm)NS0.23§0.310.360.480.360.320.36
Tb.Th* (mm)0.270.340.260.480.320.430.250.33
Tb.Sp* (mm)(−) 0.23§(−) 0.38(−) 0.38(−) 0.40(−) 0.50(−) 0.38(−) 0.37(−) 0.39
Ct.Th (mm)0.34NSNSNSNSNSNSNS
BS/BV (1/mm)(−) 0.29(−) 0.43(−) 0.33(−) 0.55(−) 0.43(−) 0.51(−) 0.33(−) 0.42
SMI(−) 0.32(−) 0.56(−) 0.47(−) 0.64(−) 0.57(−) 0.63(−) 0.47(−) 0.54
DANSNSNSNSNSNSNSNS
Conn.D (1/mm3)NSNSNSNS0.21§NSNSNS

The results from the multiple linear regression analyses suggested that the BV/TV based on µMRI and the BV/TV, Conn.D, and BS/BV based on µCT were the most important predictors of trabecular bone stiffness (Table 4). By adding Ct.Th, the combination of these predictors also provided the strongest prediction for whole bone stiffness. For predictions of E11, E22, E33, G23, G31, and G12 of the trabecular bone subvolumes, BV/TV based on µCT was the only independent and significant predictor. In contrast, the Conn.D based on µMRI was the only independent and significant predictor for E11, G31, and G12, whereas the combination of Conn.D and SMI or DA significantly predicted E22, E33, and G23 of the bone subvolumes (Table 4).

Table 4. Correlation (Adjusted r2) and Independent Predictors of Multilinear Regression for Prediction of the Gold Standard Mechanical Measurements by the Microstructural Measurements of µMRI and µCT
µCT-based mechanical propertiesµMRIµCT
Independent predictorsConstantCoefficientAdjusted r2Independent predictorsConstantCoefficientAdjusted r2
  1. Note: The order of predictors is the order in which predictors enter the stepwise regression model. All the predictions are statistically significant with p < .001.

Whole-bone stiffnessBV/TV−626,7312,774,4700.60BV/TV−1,501,0866,615,5130.76
     Ct.Th 601,797 
 Ct.Th 616,230 Conn.D −87,140 
     BS/BV 55,260 
Trabecular stiffnessBV/TV−204,3991,480,2460.52BV/TV−588,7343,225,7010.79
     Conn.D −40,511 
     BS/BV 22,579 
E11Conn.D−781410.38BV/TV−1092,0650.52
E22SMI494−2070.55BV/TV−963,0850.68
 Conn.D 118     
E33Conn.D−20886590.56BV/TV−1929,0070.69
 DA 1,136     
G23Conn.D297820.53BV/TV−561,9810.65
 SMI −125     
G31Conn.D−51990.38BV/TV−731,4440.52
G12Conn.D−26620.45BV/TV−399040.60

Discussion

  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and Methods
  5. Results
  6. Discussion
  7. Disclosures
  8. Acknowledgements
  9. References

In this study, ex vivo microstructural and mechanical measurements of the human distal tibia from µMR images at a 160-µm isotropic voxel size (subvoxel processed to 53 µm), which are now achievable in vivo, were validated against the gold standard, high-resolution µCT images at a 25-µm isotropic voxel size. Given the large dataset and expensive computational time for whole bone analysis, most published studies have been using smaller subvolumes of trabecular bone for validating µMR with reference to µCT images.14, 26, 48, 49 To our knowledge, this is the first study that directly compares µMR images of whole bone segments of human distal tibia with µCT images. Moreover, the accuracy of the estimated stiffness of whole bone segments with or without cortex by the µMRI-based FE analyses was addressed for the first time in this study.

Of the microstructural measurements from µMRI, most were correlated significantly with their respective gold standards (r2 = 0.33 to 0.97), with the exception of Tb.Th* (p > .05). Particularly high correlations with µCT measurements were found for BV/TV, Tb.N*, Tb.Sp*, Ct.Th, and SMI (r2 = 0.67 to 0.97). These parameters quantify the important microstructural features of both trabecular and cortical bone, and the measurement results based on µMR images could be good indicators of bone quality given their high correlations with the gold standard measurements. On the other hand, greater dispersions were observed in BS/BV, DA, and Conn.D of µMR images compared with gold standard µCT images. BS/BV, DA, and Conn.D are standard measurements for high-resolution µCT images. Correlation results of these measurements suggest that they are more sensitive to the limited image resolution and relatively low SNR of µMR images and thus may not accurately reflect bone quality when applied to µMRI. It should be noted that there is a systematic overestimation of the bone phase: Except for the Tb.N*, the absolute values of the µMRI measurements differed significantly from the gold standard (Table 1). The values of the trabecular BV/TV and Ct.Th of the µMR images were significantly higher and the Tb.Sp was significantly lower than those of the corresponding µCT images. In addition, trabecular bone microstructure represented by µMR images had lower BS/BV, DA, and Conn.D values as well as a higher SMI compared with µCT images, indicating a more rodlike and isotropic trabecular network with less structural connections. These results were comparable with those reported in trabecular bone subvolumes from the radius, calcaneus, and femoral head extracted from µMRI images acquired at 1.5 or 3.0 T.14, 49, 57 In general, the correlations of BV/TV, Tb.N*, Tb.Sp*, Tb.N, and Tb.Sp with µCT measurements were similar or slightly higher in this study than those reported previously.14, 49, 57 However, the correlation for the 2D measurement of Tb.Th in this study (r2 = 0.23) was lower than that found in previous studies.14, 49, 57 Moreover, the model-independent Tb.Th* showed no correlation with the corresponding µCT measurement, whereas moderate correlations were reported for the radius and calcaneus.49, 57 In this study, the trabecular thickness of the 25 distal tibia specimens ranged from 0.12 to 0.19 mm, as measured by high-resolution µCT images. In contrast, the trabecular thickness derived from µMRI measurement by a distance transformation method was significantly overestimated and fell in a much narrower range (from 0.22 to 0.27 mm). Therefore, the voxel-based distance transformation method used in this study is inadequate for quantifying trabecular thickness in the in vivo µMRI resolution range.

There are several factors that could cause the differences between the measurements of µCT and µMRI. The high resolution and SNR of in vitro µCT result in two distinct phases in the intensity histogram. The bone phase then can be thresholded accurately by using a global thresholding technique.58 However, at in vivo resolution and SNR, the intensity histogram of µMRI is monomodal. Therefore, there is no unique criterion for the choice of threshold for binarization. Too high a threshold causes artifactual erosion, whereas too low a value leads to inclusion of noise. Here the images were thresholded at an empirically optimized value of 50% BVF to maintain 3D bone microarchitecture with minimal noise.33 However, the differences in thresholding techniques could cause discrepancies between the measurements of the two modalities. Second, the overestimation of the bone phase could be caused by the partial-volume effect associated with the limited image resolution. This has been shown to be the case in high-resolution peripheral quantitative computed tomography (HR-pQCT), an in vivo CT scanner for bone microstructure at 80-µm voxel size.59 Third, the larger BV/TV and lower DA values of the µMRI data could be a consequence of artifactual thickening of trabeculae owing to shortened transverse relaxation times (T2*) of marrow protons in close proximity to bone.60

In this study, for both µMR and µCT image-based µFE models, cortical and trabecular bone tissue properties were assumed to be constant and homogeneous for all specimens, and the resulting mechanical measurements of the µFE analysis reflected only the influence of the bone microstructure and not the intrinsic mineral quality. This modeling strategy has been used widely in both µCT- and µMRI-based FE analyses,2, 6, 18, 61, 62 and the µCT-based model has been validated by comparison with mechanical testing results.63 The significant and high correlations of the estimated whole bone and trabecular bone stiffness of the µMR images with those of the µCT images demonstrate that µMRI-based µFE analyses can directly and accurately quantify whole bone mechanical competence. The linear correlation of trabecular bone stiffness between µMR and µCT images had a 0.96 slope, which was not significantly different from 1. Furthermore, the trabecular stiffness derived from µMRI images was statistically the same as that derived from µCT images. After inclusion of the contribution from the cortex, the correlation of the whole-bone stiffness measurement (r2) between the µMRI and µCT increased from 0.85 to 0.96, although the whole bone stiffness of the µMRI images was slightly underestimated. The partial-volume effect to the mechanical measurements of µMR images was manifest when the analyses were applied to trabecular bone subvolumes. The elastic moduli derived from µMRI images were significantly overestimated and yielded only moderate correlations with the corresponding µCT measurements (r2 = 0.40 to 0.58). The more constrained boundary conditions in these subvolume computations may amplify the overestimation of BV/TV in the µMRI images. At the limited spatial resolution of the µMRI, bone voxels can contain a range of grayscale values resulting from the partial-volume effect. Therefore, a second strategy to generate µFE models is to incorporate the grayscale information of bone voxels by linearly scaling the tissue moduli of the element according to the voxel bone volume fraction.64 Rajapakse and colleagues previously demonstrated significant and high correlations between the grayscale µFE predictions of µMRI and µCT images at a 160-µm isotropic resolution achievable in vivo based on trabecular bone subvolumes.64 This modeling strategy should be considered to improve the accuracy of the mechanical measurements from µMR images, especially for analyses of subvolumes of the trabecular bone compartment.

The ability of µMRI-based microstructural measurements to reflect mechanical measurements of the distal tibia is comparable to that of µCT (Table 3). Most of the µMRI-based microstructural measurements were significantly correlated with one or more of the mechanical properties of the distal tibia derived from high-resolution µCT images. However, µMRI-derived Tb.Th* did not correlate with any mechanical measurement. In contrast, Tb.Th* obtained from µCT was significantly correlated with each of the mechanical measurements. Once again, the current spatial resolution of µMRI may not be sufficient for the voxel-based distance transformation method to quantify Tb.Th*.

When all microstructural measurements were combined to predict mechanical competence, the independent predictors appeared to be different for µMR and µCT images. For the µMR images, BV/TV and Ct.Th were the only significant predictors of whole bone stiffness, as well as BV/TV of trabecular bone stiffness. Although many other microstructural measurements were highly correlated with the gold standard measurements or individually contributed to the estimated mechanical properties, they did not make additional contributions to bone stiffness prediction. Furthermore, BV/TV of the µCT images was the only significant predictor of each elastic modulus. In contrast, for µMR images, Conn.D appeared to be an independent and significant predictor of all elastic moduli. The SMI also added independent contributions to E22 and G23, as well as DA to E33. It is interesting that the Conn.D of the µCT images had no contribution to any of the mechanical properties. However, the Conn.D of the µMRI images was shown to be an independent and important indicator of the elastic moduli of trabecular bone.

This study has several limitations. First, µMRI of cadaveric bone is not affected by patient motion artifacts commonly encountered in vivo. Second, all the microstructural analyses in this study were 3D model–independent morphological analyses based on thresholded bone images. These analysis techniques have become the standard for analyzing bone structure of high-resolution µCT images. There was a concern that the spatial resolution of µMRI images achievable in vivo was lower than that required for the 3D model–independent morphological analyses.14 However, the data from this study show that most µMRI-derived analyses had significant correlations with µCT reference measurements, except for trabecular thickness (Tb.Th*). An alternative approach is the fuzzy distance transform,65, 66 a technique for measuring structural thickness in the limited-resolution regime. Instead of using the thresholded images, this analysis technique works on the grayscale images, which contain more information about each voxel; therefore, it could provide more accurate estimations of the bone microstructure. The application of this technique to µMR images of the whole trabecular bone segment will be of interest in future studies. Finally, most of the bones used in this study were from male donors. However, in this study, the values of BV/TV by µCT did cover a broad range from 0.06 to 0.22, and µMRI has been shown to be an important imaging modality in clinical studies of both men and women.7, 11, 12, 16–18

Currently, high-resolution µMRI is capable of imaging the 3D microstructure of bone but is limited to peripheral skeletal sites. Recent studies have provided in vivo evidence that structural indices derived from µMR images of the radius discriminate between subjects with and without vertebral compression deformities.7, 67 In addition, we recently found significant correlations of the elastic stiffness of the radius and tibia estimated by HR-pQCT images-based µFE models with that of the proximal femur and lumbar spine (r2 = 0.4 to 0.5, p < .001) estimated by central quantitative computed tomography (cQCT)–based µFE models in the same subjects.68 This finding suggests that the mechanical competence of the distal radius and tibia can indicate vertebral and femoral mechanical properties.68

In conclusion, the accuracy of microstructural and mechanical measurements of µMR images of the human distal tibia at resolutions achievable in vivo has been tested with reference to the current gold standard, high-resolution µCT. Differences between µMRI and gold standard µCT measurements should be considered when intermodality comparisons are made. However, the high correlations we observed between the microstructural measurements and the mechanical measurements of human distal tibia suggest that µMRI has the potential of becoming a clinical standard for microstructural aspects of bone quality. Microstructural measurements and mechanical parameters of the distal tibia can be derived efficiently from 3D µMRI images and can provide additional information regarding bone fragility.

Disclosures

  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and Methods
  5. Results
  6. Discussion
  7. Disclosures
  8. Acknowledgements
  9. References

FWW is chairman of the Scientific Advisory Board and owns stock in MicroMRI, Inc. All the other authors state that they have no conflicts of interest.

Acknowledgements

  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and Methods
  5. Results
  6. Discussion
  7. Disclosures
  8. Acknowledgements
  9. References

This work was supported in part by grants from the NIH (R01 AR051376, R01 AR055647, T32 EB000814, and F31 EB007448).

References

  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and Methods
  5. Results
  6. Discussion
  7. Disclosures
  8. Acknowledgements
  9. References