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Trabecular Bone Structure Analysis in the Limited Spatial Resolution Regime of In Vivo MRI

Posted Nov 30, 2008 Updated Apr 7, 2023
By Jeremy F. Magl PhD , Felix W. Wehrli PhD
12 min read

Rationale and Objectives

To develop a method for processing and visualization of trabecular bone networks on the basis of magnetic resonance (MR) images acquired in the limited spatial resolution regime of in vivo imaging at which trabecular thickness is comparable to voxel size.

Materials and Methods

A sequence of processing steps for analyzing the topologic structure of trabecular bone networks is presented and evaluated using three types of datasets: images of synthetic structures with various levels of superimposed Gaussian noise, micro-computed tomographic images of human trabecular bone downsampled to in vivo resolution, and in vivo micro-MR images from a prior longitudinal study investigating the structural implications of testosterone treatment of hypogonadal men. The simulated images were analyzed at a voxel size of 150 μm 3 , the clinical MR image data had been acquired with 137 × 137 × 410 μm 3 voxel size. The technique is a modification to the virtual bone biopsy processing chain that involves a sinc convolution step immediately preceding binarization, and employs the Manzanera-Bernard thinning algorithm for obtaining the three-dimensional skeleton before topologic classification. The detectability of plate and rod bone elements was also analyzed theoretically.

Results

As compared with previously published techniques, the approach produced a more accurate bone skeleton in the micro-computed tomographic and simulation experiments, with clear improvement in preservation of rod and plate elements. Simulations suggest that rods are detectable down to a diameter of approximately 50% of the MR image voxel length, whereas plates can be detected at thicknesses of 20% or more of voxel length. For in vivo studies, it was shown that the method could recover the treatment response in terms of the ensuing topologic changes in patients undergoing antiresorptive treatment.

Conclusions

The algorithm for processing of in vivo micro-MR images of trabecular bone is superior to prior approaches in preserving the topology of the network in the presence of noise.

The recognition of the role of architecture as a determinant of bone strength, second in importance to density ( ), has given substantial impetus toward the development of image-based methods for quantification of the three-dimensional (3D) structure of trabecular bone. Because trabecular bone remodels several times faster than cortical bone, it also responds faster to hormonal changes, such as loss of estrogen after menopause ( ), or intervention with pharmacologic agents ( ) or cyclical loading ( ). Trabecular bone architecture is also altered in a characteristic manner in osteoarthritis ( ). A number of programs, including the proclamation of the National Bone and Joint Decade by the US government, have fostered the development of capabilities for in vivo assessment of trabecular bone architecture in recent years.

Both micro–computed tomography (μ-CT) and micro–magnetic resonance imaging (μ-MRI) have demonstrated their potential as modalities to provide quantitative information on the bone’s microarchitecture in specimen studies at a resolution of tens of micrometers or better ( ). In recent years, both modalities have evolved to the stage allowing in vivo imaging of the trabecular microarchitecture at peripheral skeletal locations such as the distal radius, tibia, or calcaneus at voxel sizes on the order of 80–200 μm ( ).

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Materials and methods

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Partial Volume Effects and Sinc Interpolation

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Figure 1, (a) Synthetic structure mimicking trabecular bone. Two parallel plates (spacing of 880 μm) interconnected by three rods with thicknesses 150 μm (top and bottom) and 85 μm (middle). (b) Simulated (noiseless) image of a section parallel to the plates bisecting the object at a resolution 150 × 150 × 150 μm 3 . The slice is parallel to (and in between) the two plates. (c) Three-dimensional (3D) volume obtained by thresholding the simulated 3D magnetic resonance imaging (MRI) dataset at 80% of the marrow level, demonstrating that simple thresholding is not adequate for analyzing topologic structure; (d, f, h) are subvoxel (subvox) processed image sections (parallel to and in between the two plates), and (e, h, i) are the corresponding volumes obtained by thresholding at 80%. (j) Section of the dataset sinc interpolated by 6 × 6 × 6 and apodized using a 3D Fermi filter with 20% transition width. (k) Three-dimensional volume obtained from (j) using a threshold at 80%.

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Virtual Bone Biopsy Processing Chain

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Synthetic Plate and Rod Simulations

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MRI Simulations Based on High-Resolution μ-CT Data

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In Vivo Analysis

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Results

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Figure 2, (a) In vivo micro-magnetic resonance imaging of the distal tibia; (b) region of interest isolated using an automatic segmentation algorithm ( 23 ); (c) intensity normalized to remove coil shading using local threshold algorithm ( 26 ); (d) sinc interpolated by factor of 3 × 3 × 3; (e) thresholded at 80% of marrow intensity; (f) skeleton map obtained with Manzanera-Bernard algorithm ( 31 ); (g) three-dimensional core of skeleton; (h) digital topologic analysis classification showing surfaces (resulting from skeletonization of plates) in red and curves (resulting from skeletonization of rods) in blue .

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Figure 3, Simulated signal profiles for rods and plates of varying thicknesses using sinc interpolation. Dotted lines show the apparent thickness after thresholding at 80% of the marrow level; (a–d) show profiles for rods (cylinders of infinite length), and (e–h) show profiles for plates (two-dimensional infinite sheets).

Figure 4, Simulated apparent thickness versus actual thickness for (a) rods, (b) plates, and (c) perforations in plates when thresholded at 80% of the marrow intensity. Note that rods become undetectable when the diameter falls below around half of the voxel size, whereas plates can be detected down to a thickness of 20% of voxel size, and perforations can be detected for diameters exceeding 120% of the voxel size. As noted in the text, these numbers depend on the chosen threshold.

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Figure 5, Virtual bone biopsy processing steps, with the starting point being a three-dimensional micro-computed tomographic (μCT) image dataset of trabecular bone in a tibia specimen (left), downsampled to micro-magnetic resonance imaging (μMRI) resolution (150 μm isotropic), sinc interpolated, binarized, and skeletonized as described in the text (upper double row of images). Subsequently, Gaussian noise was added to the simulated MRI data, to achieve signal-to-noise ratio of approximately 13:1 (lower double row of images). Color coding of DTA classified images: surfaces (resulting from skeletonization of plates) are red ; curves (resulting from skeletonization of rods) are blue . It is visually apparent that the topology of the structure is largely preserved after downsampling to in vivo MRI resolution and addition of noise.

Figure 6, Skeletonized data set using (left) subvoxel processing and digital topologic analysis (DTA) classification and (right) sinc interpolation and Manzanera-Bernard followed by DTA skeletonization.

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Figure 7, In vivo baseline (a) and 6-month follow-up (b) scans of the distal tibia of a 42-year-old woman. The three-dimensional skeletons obtained at two different locations using the new virtual bone biopsy processing procedure. The trabecular bone at site #1 is considerably sparser. Note the visually apparent agreement between baseline and follow-up images.

Table 1

Topologic Classification Parameters for Cores Shown in Fig 7 Demonstrating Reproducibility from Baseline to Follow-up

Site #1 Site #2 Baseline Follow-up Baseline Follow-up Skeleton density 1.71% 1.74% 2.99% 3.14% Plate density 1.48% 1.52% 2.62% 2.79% Rod density 0.19% 0.18% 0.28% 0.26% Junction density 0.04% 0.04% 0.09% 0.09%

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Figure 8, Percent change in two composite virtual bone biopsy parameters for a group of 10 hypogonadal men treated with testosterone over a period of 2 years. Both indicate an increase in surface/curve ratio as well as decrease in erosion index commensurate with an improvement in the trabecular network over time. The statistical significance for the new processing results is generally greater than that found for the previously published data ( 30 ) using the original processing algorithms.

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Discussion

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Conclusions

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Acknowledgment

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Academic Radiology, Volume 15, Issue 12
Journals General Radiology
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