An orientation distribution function for trabecular bone

Histological evaluation of titanium fiber mesh-coated implants in a rabbit femoral condyle model

OBJECTIVES

This study was aimed to comparatively evaluate new bone formation into the pores of a flexible titanium fiber mesh (TFM) applied on the surface of implant.

METHODS

Twenty-eight custom made cylindrical titanium implants (4 ×10 mm) with and without a layer of two different types of TFM (fiber diameter of 22 µm and 50 µm, volumetric porosity ~70%) were manufactured and installed bilaterally in the femoral condyles of 14 rabbits. The elastic modulus for these two TFM types was ~20 GPa and ~5 GPa respectively, whereas the solid titanium was ~110 GPa. The implants (Control, TFM-22, TFM-50) were retrieved after 14 weeks of healing and prepared for histological assessment. The percentage of the bone area (BA%), the bone-to-implant contact (BIC%) and amount were determined.

RESULTS

Newly formed bone into mesh porosity was observed for all three types of implants. Histomorphometric analyses revealed significantly higher (~2.5 fold) BA% values for TFM-22 implants (30.9 ± 9.5%) compared to Control implants (12.7 ± 6.0%), whereas BA% for TMF-50 did not significantly differ compared with Control implants. Furthermore, both TFM-22 and TFM-50 implants showed significantly higher BIC% values (64.9 ± 14.0%, ~2.5 fold; 47.1 ± 14.1%, ~2 fold) compared to Control (23.6 ± 17.4%). Finally, TFM-22 implants showed more and thicker trabeculae in the peri-implant region.

SIGNIFICANCE

This in vivo study demonstrated that implants with a flexible coating of TFM improve bone formation within the inter-fiber space and the peri-implant region.

Trabecular health of vertebrae based on anisotropy in trabecular architecture and collagen/apatite micro-arrangement after implantation of intervertebral fusion cages in the sheep spine

Healthy trabecular bone shows highly anisotropic trabecular architecture and the preferential orientation of collagen and apatite inside a trabecula, both of which are predominantly directed along the cephalocaudal axis. This makes trabecular bone stiff in the principally loaded direction (cephalocaudal axis). However, changes in these anisotropic trabecular characteristics after the insertion of implant devices remain unclear. We defined the trabecular architectural anisotropy and the preferential orientation of collagen and apatite as parameters of trabecular bone health. In the present study, we analyzed these parameters after the implantation of two types of intervertebral fusion cages, open and closed box-type cages, into sheep spines for 2 and 4months. Alteration and evolution of trabecular health around and inside the cages depended on the cage type and implantation duration. At the boundary region, the values of trabecular architectural anisotropy and apatite orientation for the closed-type cages were similar to those for isotropic conditions. In contrast, significantly larger anisotropy was found for open-type cages, indicating that the open-type cage tended to maintain trabecular anisotropy. Inside the open-type cage, trabecular architectural anisotropy and apatite orientation significantly increased with time after implantation. Assessing trabecular anisotropy might be useful for the evaluation of trabecular health and the validation and refinement of implant designs.

Long range node-strut analysis of trabecular bone microarchitecture

PURPOSE

We present a new morphometric measure of trabecular bone microarchitecture, called mean node strength (NdStr), which is part of a newly developed approach called long range node-strut analysis. Our general aim is to describe and quantify the apparent "latticelike" microarchitecture of the trabecular bone network.

METHODS

Similar in some ways to the topological node-strut analysis introduced by Garrahan et al. [J. Microsc. 142, 341-349 (1986)], our method is distinguished by an emphasis on long-range trabecular connectivity. Thus, while the topological classification of a pixel (after skeletonization) as a node, strut, or terminus, can be determined from the 3 × 3 neighborhood of that pixel, our method, which does not involve skeletonization, takes into account a much larger neighborhood. In addition, rather than giving a discrete classification of each pixel as a node, strut, or terminus, our method produces a continuous variable, node strength. The node strength is averaged over a region of interest to produce the mean node strength of the region.

RESULTS

We have applied our long range node-strut analysis to a set of 26 high-resolution peripheral quantitative computed tomography (pQCT) axial images of human proximal tibiae acquired 17 mm below the tibial plateau. We found that NdStr has a strong positive correlation with trabecular volumetric bone mineral density (BMD). After an exponential transformation, we obtain a Pearson's correlation coefficient of r = 0.97. Qualitative comparison of images with similar BMD but with very different NdStr values suggests that the latter measure has successfully quantified the prevalence of the "latticelike" microarchitecture apparent in the image. Moreover, we found a strong correlation (r = 0.62) between NdStr and the conventional node-terminus ratio (Nd∕Tm) of Garrahan et al. The Nd∕Tm ratios were computed using traditional histomorphometry performed on bone biopsies obtained at the same location as the pQCT scans.

CONCLUSIONS

The newly introduced morphometric measure allows a quantitative assessment of the long-range connectivity of trabecular bone. One advantage of this method is that it is based on pQCT images that can be obtained noninvasively from patients, i.e., without having to obtain a bone biopsy from the patient.

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.

Skeletal deformations in medaka (Oryzias latipes) visualized by synchrotron radiation micro-computer tomography (SRmicroCT)

Synchrotron radiation micro-computer tomography (SRmicroCT) offers the possibility to investigate biomineralized structures in high detail. Two animals of adult medaka fish (Oryzias latipes) were analyzed by SRmicroCT with a resolution of 6.55 microm: the wild-type animal was normally developed whereas the second animal showed an idiopathic deformation of the cranial and axial skeleton. These deformations could be followed on the macro- and on the microscale (i.e., on the level of the individual ribs and fin bones). Our study clearly demonstrates that SRmicroCT is an excellent technique to study alterations in the skeletal structure of fish in detail.

Comparative assessment of bone mass and structure using texture-based and histomorphometric analyses

The purpose of this study was to develop a methodology for quantitatively assessing bone quantity and anisotropy based on texture analysis using Gabor wavelets. The wavelet approach has the capability to simultaneously examine the images at low and high resolutions to gain information on both global and detailed local features of the bone image. The program that implemented the texture analysis gave measures of density (M(Density)) and anisotropy (M(Anisotropy)). It also allowed us to examine the texture energy at four orientations (0 degrees , 45 degrees , 90 degrees , 135 degrees) to gain insight about the details of the anisotropy. Analysis of templates of four simulated patterns, which had same number of dots but with differing orientations, demonstrated how the texture-based analysis differentiated between these templates. The measures of M(Anisotropy) discriminated between the four simulated patterns. The M(Density) measures were similar across all patterns. These outcomes matched the design intent of the simulated patterns. We also compared the trabecular bone images obtained from a previous study, in which the right forelimbs of normal female retired breeder beagle dogs (5-7 years old) were cast for 12 months to induce bone loss, using both histomorphometry and texture analysis. Both histomorphometry and the texture analysis detected significant differences in the trabecular bone of the distal metatarsal between the control and disuse groups. Percent trabecular bone (Tb.Ar/T.Ar) and the textural density parameter (M(Density)) were highly correlated (r=0.962). M(Anisotropy) was decreased (3.9%) after the 12-month disuse protocol, but was not significantly different from normal. However, the texture energy values at all orientations (0 degrees , 45 degrees , 90 degrees and 135 degrees) were significantly decreased in the disuse group. Therefore, texture analysis was able to assess anisotropy, which could not be extracted from histomorphometric parameters. We conclude that texture analysis is an effective tool for assessing 2D bone images that yields information regarding the quantity of bone as well as the orientation of the trabecular structure that can augment our ability to discriminate between normal and pathological bone tissue.

A biomechanical analysis of the effects of resorption cavities on cancellous bone strength

We evaluated the effects of resorption cavities on cancellous bone strength using computational methods. Adding cavities to cancellous bone caused reductions in strength and stiffness that were greater than expected from the associated changes in bone volume and more pronounced when cavities were targeted to regions of high tissue strain.

INTRODUCTION

The amount of bone turnover in the skeleton has recently been implicated as a factor influencing bone strength. One mechanism proposed to explain this effect is that resorption cavities reduce the effective thickness of trabeculae and modify local stress distributions leading to reduced mechanical performance of the entire structure. In this study, we tested the plausibility of this mechanism.

MATERIALS AND METHODS

High-resolution finite element models were created from muCT images of 16 vertebral cancellous bone samples, as well as from images of the samples in which cavities had been added digitally-either at regions of high strain (targeted) or placed at random on the bone surface (nontargeted). The effect of resorption cavities on predicted bone strength and stiffness was evaluated by comparing the relationships between mechanical properties and bone volume fraction among the three groups (the original images, those with nontargeted cavities, and those with targeted cavities).

RESULTS

Addition of resorption cavities modified the relationship between mechanical properties and bone volume fraction in the finite element models such that, for a given bone volume fraction, stiffness and yield strength were reduced compared with the original images (p < 0.05). The differences in yield strength-volume fraction relationships between the original models and those with targeted cavities were significantly greater than those between the original models and those with nontargeted cavities (p < 0.05). None of the differences in predicted mechanical properties per unit bone volume fraction could be accounted for by 3D measures of microarchitecture.

CONCLUSIONS

Resorption cavities may influence cancellous bone strength and stiffness independent of their effect on bone volume. The effects of cavities on bone mechanical performance relative to bone volume are greater when cavities are targeted to regions of high strain and cannot be predicted using standard microarchitecture measures.