Classification of trabeculae into three-dimensional rodlike and platelike structures via local inertial anisotropy.

Trabecular bone microarchitecture is a significant determinant of the bone's mechanical properties and is thus of major clinical relevance in predicting fracture risk. The three-dimensional nature of trabecular bone is characterized by parameters describing scale, topology, and orientation of structural elements. However, none of the current methods calculates all three types of parameters simultaneously and in three dimensions. Here the authors present a method that produces a continuous classification of voxels as belonging to platelike or rodlike structures that determines their orientation and estimates their thickness. The method, dubbed local inertial anisotropy (LIA), treats the image as a distribution of mass density and the orientation of trabeculae is determined from a locally calculated tensor of inertia at each voxel. The orientation entropies of rods and plates are introduced, which can provide new information about microarchitecture not captured by existing parameters. The robustness of the method to noise corruption, resolution reduction, and image rotation is demonstrated. Further, the method is compared with established three-dimensional parameters including the structure-model index and topological surface-to-curve ratio. Finally, the method is applied to data acquired in a previous translational pilot study showing that the trabecular bone of untreated hypogonadal men is less platelike than that of their eugonadal peers.

Trabecular structure quantified with the MRI-based virtual bone biopsy in postmenopausal women contributes to vertebral deformity burden independent of areal vertebral BMD.

UNLABELLED: In postmenopausal women with a wide range of vertebral deformities, MRI-based structural measures of topology and scale at the distal radius are shown to account for as much as 30% of vertebral deformity, independent of integral vertebral BMD. INTRODUCTION: Trabecular bone architecture has been postulated to contribute to overall bone strength independent of vertebral BMD measured by DXA. However, there has thus far been only sparse in vivo evidence to support this hypothesis. MATERIALS AND METHODS: Postmenopausal women, 60-80 yr of age, were screened by DXA, and those with T-scores at either the hip or spine falling within the range of -2.5 +/- 1.0 were studied with the MRI-based virtual bone biopsy, along with heel broadband ultrasound absorption and pQCT of the tibia. The data from 98 subjects meeting the enrollment criteria were subjected to microMRI at the distal tibia and radius, and measures of topology and scale of the trabecular bone network were computed. A spinal deformity index (SDI) was obtained from morphometric measurements in midline sagittal MR images of the thoracic and lumbar spine to evaluate associations between structure and deformity burden. RESULTS: A number of structural indices obtained at the distal radius were correlated with the SDI. Among these were the topological surface density (a measure of trabecular plates) and trabecular bone volume fraction, which were inversely correlated with SDI (p < 0.0001). Combinations of two structural parameters accounted for up to 30% of the variation in SDI (p < 0.0001) independent of spinal BMD, which was not significantly correlated. pQCT trabecular BMD was also weakly associated, whereas broadband ultrasound absorption was not. No significant association between SDI and structural indices were found at the tibia. CONCLUSIONS: Structural measures at the distal radius obtained in vivo by microMRI explained a significant portion of the variation in total spinal deformity burden in postmenopausal women independent of areal BMD.

Implications of resolution and noise for in vivo micro-MRI of trabecular bone.

Osteoporotic bone loss is accompanied by impaired structural integrity of the trabecular network, leading to a decrease in the overall mechanical properties of the bone. The development of the "virtual bone biopsy" (VBB), a method combining magnetic resonance microimaging (microMRI) and digital image processing techniques, has previously been shown to quantify topology and scale of human trabecular bone noninvasively. The aim of this work was to determine the extent to which structural parameters derived from images acquired in the limited spatial resolution regime of in vivo imaging are sensitive to resolution and noise and further, whether under these conditions, a small amount of bone loss and its associated structural manifestations can be detected. Toward these goals 3D models of trabecular bone representing multiple anatomic locations were generated on the basis of microCT images of human cadaveric bone cores. These images were binarized and the resulting data arrays representing pure bone (proton density=0) and pure marrow (proton density=255) subjected to simulated MR imaging by Cartesian sampling of k space, yielding, after 3D Fourier reconstruction, voxel sizes currently achievable in vivo. Subsequently, realistic levels of Gaussian noise were superimposed on the complex data and magnitude images were computed. The resulting images were subsequently VBB processed for a range of signal-to-noise ratio (SNR) values and image voxel sizes. For comparison of the predicted behavior to in vivo data, images from a recent patient study were evaluated as well. Systematic changes of the derived structural parameters changing progressively with decreasing SNR were noted, and it is shown that the errors are correctable using simple linear transformations, thereby allowing the data to be normalized. The predicted dependence of the structural parameters on SNR also closely parallel those observed in vivo. Finally, in order to assess the sensitivity of the VBB processing algorithms to detect bone loss during disease progression or regression in response to treatment, the high-resolution specimen data were subjected to 5% bone loss either by homogeneous or heterogeneous erosion and microMR images simulated at in vivo resolution and SNR. At typical in vivo SNR (SNR=12) and effective image resolution (160 microm isotropic and 137 x 137 X 410 microm3), VBB algorithms were able to detect the structural implications of a 5% loss in bone volume fraction with high statistical significance.

Spatial autocorrelation and mean intercept length analysis of trabecular bone anisotropy applied to in vivo magnetic resonance imaging.

Osteoporosis is characterized by bone loss and deterioration of the trabecular bone (TB) architecture that leads to impaired overall mechanical strength of the bone. Bone mineral density (BMD) measured by dual-energy x-ray absorptiometry is currently the standard clinical metric assessing bone integrity but it fails to capture the structural changes in the TB. Recent research suggests that structure contributes to bone strength in a manner complementary to BMD. Besides parameters of scale such as the mean TB thickness and mean bone volume fraction, parameters describing the anisotropy of the trabecular architecture play an important role in the characterization of TB since trabeculae are preferentially oriented along the direction of local loading. Therefore, the degree of structural anisotropy is of pivotal importance to the bone's mechanical competence. The most common method for measuring structural anisotropy of TB is the mean-intercept length (MIL). In this work we present a method, based on the three-dimensional spatial autocorrelation function (ACF), for mapping of the full structural anisotropy ellipsoid of both TB thickness and spacing and we examine its performance as compared to that of MIL. Not only is the ACF method faster by several orders of magnitude, it is also considerably more robust to noise. Further, it is applicable at lower spatial resolution and is relatively insensitive to image shading. The chief reason for ACF's superior performance is that it does not require binarization, which is difficult to achieve in the limited spatial regime of in vivo magnetic resonance imaging. MIL and ACF have been applied to high-resolution magnetic resonances images of the tibia in a group of ten healthy postmenopausal women by comparing the structural anisotropy and principal direction of the computed fabric tensor for each method. While there is fair agreement between the two methods, ACF analysis yielded greater anisotropy than MIL for both TB thickness and spacing. There was good agreement between the two techniques as far as the eigenvectors of the fabric ellipsoids were concerned, which parallel the bone's macroscopic axis.

Experimental and computational analyses of the effects of slice distortion from a metallic sphere in an MRI phantom.

Susceptibility artifacts due to metallic prostheses are a major problem in clinical magnetic resonance imaging. We theoretically and experimentally analyze slice distortion arising from susceptibility differences in a phantom consisting of a stainless steel ball bearing embedded in agarose gel. To relate the observed image artifacts to slice distortion, we simulate images produced by 2D and 3D spin-echo (SE) and a view angle tilting (VAT) sequence. Two-dimensional SE sequences suffer from extreme slice distortion when a metal prosthesis is present, unlike 3D SE sequences for which--since slices are phase-encoded--distortion of the slice profile is minimized, provided the selected slab is larger than the region of interest. In a VAT sequence, artifacts are reduced by the application of a gradient along the slice direction during readout. However, VAT does not correct for the excitation slice profile, which results in the excitation of spins outside the desired slice location and can lead to incorrect anatomical information in MR images. We propose that the best sequences for imaging in the presence of a metal prosthesis utilize 3D acquisition, with phase encoding replacing slice selection to minimize slice distortion, combined with excitation and readout gradient strengths at their maximum values.

Effect of testosterone replacement on trabecular architecture in hypogonadal men.

UNLABELLED: We evaluated the effect of testosterone treatment on trabecular architecture by microMRI in 10 untreated severely hypogonadal men. After 2 years, microMRI parameters of trabecular connectivity improved significantly, suggesting the possibility that testosterone improves trabecular architecture. INTRODUCTION: Osteoporosis, characterized by low BMD and diminished bone quality, is a significant public health problem in men. Hypogonadal men have decreased BMD and deteriorated trabecular architecture compared with eugonadal men, and testosterone treatment improves their BMD. We tested the hypothesis that testosterone replacement in hypogonadal men would also improve their trabecular architecture. MATERIALS AND METHODS: We selected 10 untreated severely hypogonadal men and treated them with a testosterone gel for 24 months to maintain their serum testosterone concentrations within the normal range. Each subject was assessed before and after 6, 12, and 24 months of testosterone treatment by magnetic resonance microimaging (microMRI) of the distal tibia and by DXA of the spine and hip. The microMRI parameters reflect the integrity of the trabecular network and include the ratio of all surface voxels (representing plates) to curve voxels (representing rods) and the topological erosion index, a ratio of topological parameters expected to increase on trabecular deterioration to those expected to decrease. The higher the surface-to-curve ratio and the lower the topological erosion index, the more intact the trabecular network. RESULTS: Serum testosterone concentrations increased to midnormal after 3 months of treatment and remained normal thereafter. After 24 months of testosterone treatment, BMD of the spine increased 7.4% (p<0.001), and of the total hip increased 3.8% (p=0.008). Architectural parameters assessed by microMRI also changed: the surface-to-curve ratio increased 11% (p=0.004) and the topological erosion index decreased 7.5% (p=0.004). CONCLUSIONS: These results suggest the possibility that testosterone replacement of hypogonadal men improves trabecular architecture.

A novel local thresholding algorithm for trabecular bone volume fraction mapping in the limited spatial resolution regime of in vivo MRI.

Recent advances in micro-magnetic resonance imaging have shown the possibility of in vivo assessment of trabecular bone architecture. However, the small feature size and relatively low signal-to-noise ratio (SNR) achievable in vivo cause the intensity histogram to be unimodal. The critical first step in the processing of these images is the extraction of bone volume fraction for each voxel. Here, we propose a local threshold algorithm (LTA) that determines the marrow intensity value in the neighborhood of each voxel based on nearest-neighbor statistics. Using the local marrow intensities we threshold the image and scale the intensities of voxels partially occupied by bone to produce a marrow volume fraction map of the trabecular bone region. We show that structural parameters derived with the LTA are highly correlated with those obtained with the previously published histogram deconvolution algorithm (HDA) and that the LTA is robust to image noise corruption. The LTA is found to correctly identify trabeculae with a significantly higher reliability than HDA. Finally, we demonstrate that the LTA is superior in preserving connectivity by showing for 75 in vivo images that the genus of the trabecular bone surface is always higher than when processed with the HDA.

In vivo microMRI-based finite element and morphological analyses of tibial trabecular bone in eugonadal and hypogonadal men before and after testosterone treatment.

Osteoporosis is a major public health problem in men. Hypogonadal men have decreased BMD and deteriorated trabecular bone architecture compared with eugonadal men. Testosterone treatment improves their BMD and trabecular structure. We tested the hypothesis that testosterone replacement in hypogonadal men would also improve their bone's mechanical properties. Ten untreated severely hypogonadal and 10 eugonadal men were selected. The hypogonadal men were treated with a testosterone gel for 24 mo to maintain their serum testosterone concentrations within the normal range. Each subject was assessed before and after 6, 12, and 24 mo of testosterone treatment by microMRI of the distal tibia. A subvolume of each microMR image was converted to a microfinite element (microFE) model, and six analyses were performed, representing three compression and three shear tests. The anisotropic stiffness tensor was calculated, from which the orthotropic elastic material constants were derived. Changes in microarchitecture were also quantified using newly developed individual trabeculae segmentation (ITS)-based and standard morphological analyses. The accuracy of these techniques was examined with simulated microMR images. Significant differences in four estimated anisotropic elastic material constants and most morphological parameters were detected between the eugonadal and hypogonadal men. No significant change in estimated elastic moduli and morphological parameters was detected in the eugonadal group over 24 mo. After 24 mo of treatment, significant increases in estimated elastic moduli E(22) (9.0%), E(33) (5.1%), G(23) (7.2%), and G(12) (9.4%) of hypogonadal men were detected. These increases were accompanied by significant increases in trabecular plate thickness. These results suggest that 24 mo of testosterone treatment of hypogonadal men improves estimated elastic moduli of tibial trabecular bone by increased trabecular plate thickness.

In vivo magnetic resonance detects rapid remodeling changes in the topology of the trabecular bone network after menopause and the protective effect of estradiol.

INTRODUCTION: Estrogen depletion after menopause is accompanied by bone loss and architectural deterioration of trabecular bone. The hypothesis underlying this work is that the microMRI-based virtual bone biopsy can capture the temporal changes of scale and topology of the trabecular network and that estrogen supplementation preserves the integrity of the trabecular network. MATERIALS AND METHODS: Subjects studied were early postmenopausal women, 45-55 yr of age (N = 65), of whom 32 were on estrogen (estradiol group), and the remainder were not (control group). Early menopause was defined by amenorrhea for 6-24 mo and elevated serum follicle-stimulating hormone (FSH) concentration. The subjects were evaluated with three imaging modalities at baseline and 12 and 24 mo to determine the temporal changes in trabecular and cortical architecture and density. microMRI of the distal radius and tibia was performed at 137 x 137 x 410-microm(3) voxel size. The resulting bone volume fraction maps were Fourier interpolated to a final voxel size of 45.7 x 45.7 x 136.7 microm(3), binarized, skeletonized, and subjected to 3D digital topological analysis (DTA). Skeletonization converts trabecular rods to curves and plates to surfaces. Parameters quantifying scale included BV/TV, whereas DTA parameters included the volume densities of curves (C) and surface (S)-type voxels, as well as composite parameters: the surface/curve ratio (S/C), and erosion index (EI, ratio of the sum of parameters expected to increase with osteoclastic resorption divided by the sum of those expected to decrease). For comparison, pQCT of the same peripheral locations was conducted, and trabecular density and cortical structural parameters were measured. Areal BMD of the lumbar vertebrae and hip was also measured. RESULTS: Substantial changes in trabecular architecture of the distal tibia, in particular as they relate to topology of the network, were detected after 12 mo in the control group. S/C decreased 5.6% (p < 0.0005), and EI increased 7.1% (p < 0.0005). Most curve- and profile-type voxels (representative of trabecular struts), increased significantly (p < 0.001). Curve and profile edges resulting from disconnection of rod-like trabeculae increased by 9.8% and 5.1% (p = 0.0001 and <0.001, respectively). Similarly, DXA BMD in the spine and hip decreased 2.6% and 1.3% (p < 0.0001 and <0.005, respectively), and pQCT cortical area decreased 3.6% (p = 0.0001). However, neither trabecular density nor BV/TV changed. Furthermore, none of the parameters measured in the estradiol group were significantly different after 12 mo. Substantial differences in the mean changes from baseline between the estradiol treatment and control groups, in particular after 24 mo, were observed, with relative group differences as large as 13% (S/C, p = 0.005), and the relative changes in the two groups had the opposite sign for most parameters. The observed temporal alterations in architecture are consistent with remodeling changes that involve gradual conversion of plate-like to rod-like trabecular bone along with disconnection of trabecular elements, even in the absence of a net loss of trabecular bone. The high-resolution 3D rendered images provide direct evidence of the above remodeling changes in individual subjects. The radius structural data indicated similar trends but offered no definitive conclusions. CONCLUSIONS: The short-term temporal changes in trabecular architecture after menopause, and the protective effects of estradiol ensuring maintenance of a more plate-like TB architecture, reported here, have not previously been observed in vivo. This work suggests that MRI-based in vivo micromorphometry of trabecular bone has promise as a tool for monitoring osteoporosis treatment.

Coherence-induced artifacts in large-flip-angle steady-state spin-echo imaging.

High-resolution imaging of trabecular bone aimed at analyzing the bone's microarchitecture is preferably performed with spin-echo-type pulse sequences. Unlike gradient echoes, spin-echoes are immune to artifactual broadening of trabeculae caused by local static field gradients near the bone-bone marrow interface and signal loss from chemical shift dephasing at k-space center. However, the previously practiced 3D fast large-angle spin-echo (FLASE) pulse sequence was found to be prone to a low-frequency modulation artifact in both the readout and slice direction. The artifact is caused by deviations in the effective flip angle of the nonselective 180 degrees pulse, which converts a fraction of the phase-encoded transverse magnetization to longitudinal magnetization. The latter recurs as transverse magnetization in the subsequent pulse sequence cycle forming a spurious stimulated echo. The objective of this work was to perform a k-space analysis of this steady-state artifact and propose two modifications of the original 3D FLASE that effectively remove it. The results of the simulations were in exact agreement with the experiments and the proposed remedy was found to eliminate the artifact.