Anisotropy Of Trabecular Bone Research Articles

Diffusion MRI for Assessment of Bone Quality; A Review of Findings in Healthy Aging and Osteoporosis.

Diffusion MRI (dMRI) is a growing imaging technique with the potential to provide biomarkers of tissue variation, such as cellular density, tissue anisotropy, and microvascular perfusion. However, the role of dMRI in characterizing different aspects of bone quality, especially in aging and osteoporosis, has not yet been fully established, particularly in clinical applications. The reason lies in the complications accompanied with implementation of dMRI in assessment of human bone structure, in terms of acquisition and quantification. Bone is a composite tissue comprising different elements, each contributing to the overall quality and functional competence of bone. As diffusion is a critical biophysical process in biological tissues, early changes of tissue microstructure and function can affect diffusive properties of the tissue. While there are multiple MRI methods to detect variations of individual properties of bone quality due to aging and osteoporosis, dMRI has potential to serve as a superior method for characterizing different aspects of bone quality within the same framework but with higher sensitivity to early alterations. This is mainly because several properties of the tissue including directionality and anisotropy of trabecular bone and cell density can be collected using only dMRI. In this review article, we first describe components of human bone that can be potentially detected by their diffusivity properties and contribute to variations in bone quality during aging and osteoporosis. Then we discuss considerations and challenges of dMRI in bone imaging, current status, and suggestions for development of dMRI in research studies and clinics to segregate different contributing components of bone quality in an integrated acquisition. Level of Evidence: 5 Technical Efficacy Stage: 2J. Magn. Reson. Imaging 2020;51:975–992.

Trabecular architecture in the humeral metaphyses of non-avian reptiles (Crocodylia, Squamata and Testudines): Lifestyle, allometry and phylogeny.

The lifestyle of extinct tetrapods is often difficult to assess when clear morphological adaptations such as swimming paddles are absent. According to the hypothesis of bone functional adaptation, the architecture of trabecular bone adapts sensitively to physiological loadings. Previous studies have already shown a clear relation between trabecular architecture and locomotor behavior, mainly in mammals and birds. However, a link between trabecular architecture and lifestyle has rarely been examined. Here, we analyzed trabecular architecture of different clades of reptiles characterized by a wide range of lifestyles (aquatic, amphibious, generalist terrestrial, fossorial, and climbing). Humeri of squamates, turtles, and crocodylians have been scanned with microcomputed tomography. We selected spherical volumes of interest centered in the proximal metaphyses and measured trabecular spacing, thickness and number, degree of anisotropy, average branch length, bone volume fraction, bone surface density, and connectivity density. Only bone volume fraction showed a significant phylogenetic signal and its significant difference between squamates and other reptiles could be linked to their physiologies. We found negative allometric relationships for trabecular thickness and spacing, positive allometries for connectivity density and trabecular number and no dependence with size for degree of anisotropy and bone volume fraction. The different lifestyles are well separated in the morphological space using linear discriminant analyses, but a cross-validation procedure indicated a limited predictive ability of the model. The trabecular bone anisotropy has shown a gradient in turtles and in squamates: higher values in amphibious than terrestrial taxa. These allometric scalings, previously emphasized in mammals and birds, seem to be valid for all amniotes. Discriminant analysis has offered, to some extent, a distinction of lifestyles, which however remains difficult to strictly discriminate. Trabecular architecture seems to be a promising tool to infer lifestyle of extinct tetrapods, especially those involved in the terrestrialization.

Modeling of anisotropic remodeling of trabecular bone coupled to fracture

As a living tissue, bone is subjected to internal evolutions of its trabecular architecture under normal everyday mechanical loadings leading to damage. The repeating bone remodeling cycle aims at repairing the damaged zones in order to maintain bone structural integrity; this activity of sensing the peak stress at locations where damage or microcracks have occurred, removing old bone and apposing new bone is achieved thanks to a complicated machinery at the cellular level involving specialized cells (osteocytes, osteoclasts, and osteoblasts). This work aims at developing an integrated remodeling-to-fracture model to simulate the bone remodeling process, considering trabecular bone anisotropy. The effective anisotropic continuum mechanical properties of the trabecular bone are derived from an initially discrete planar hexagonal structure representative of femur bone microstructure, relying on the asymptotic homogenization technique. This leads to scaling laws of the effective elastic properties of bone versus effective density at an intermediate mesoscopic scale. An evolution law for the local bone apparent density is formulated in the framework of the thermodynamics of irreversible processes, whereby the driving force for density evolutions is identified as the local strain energy density weighted by the locally accumulated microdamage. We adopt a classical nonlinear damage model for high cycle fatigue under purely elastic strains, where the assumed homogeneous damage is related to the number of cycles bone experiences. Based on this model, we simulate bone remodeling for the chosen initial microstructure, showing the influence of the external mechanical stimuli on the evolution of the density of bone and the incidence of this evolution on trabecular bone effective mechanical properties.

Accounting for spatial variation of trabecular anisotropy with subject-specific finite element modeling moderately improves predictions of local subchondral bone stiffness at the proximal tibia

IntroductionPreviously, a finite element (FE) model of the proximal tibia was developed and validated against experimentally measured local subchondral stiffness. This model indicated modest predictions of stiffness (R2=0.77, normalized root mean squared error (RMSE%)=16.6%). Trabecular bone though was modeled with isotropic material properties despite its orthotropic anisotropy. The objective of this study was to identify the anisotropic FE modeling approach which best predicted (with largest explained variance and least amount of error) local subchondral bone stiffness at the proximal tibia. MethodsLocal stiffness was measured at the subchondral surface of 13 medial/lateral tibial compartments using in situ macro indentation testing. An FE model of each specimen was generated assuming uniform anisotropy with 14 different combinations of cortical- and tibial-specific density-modulus relationships taken from the literature. Two FE models of each specimen were also generated which accounted for the spatial variation of trabecular bone anisotropy directly from clinical CT images using grey-level structure tensor and Cowin’s fabric-elasticity equations. Stiffness was calculated using FE and compared to measured stiffness in terms of R2 and RMSE%. ResultsThe uniform anisotropic FE model explained 53–74% of the measured stiffness variance, with RMSE% ranging from 12.4 to 245.3%. The models which accounted for spatial variation of trabecular bone anisotropy predicted 76–79% of the variance in stiffness with RMSE% being 11.2–11.5%. ConclusionsOf the 16 evaluated finite element models in this study, the combination of Synder and Schneider (for cortical bone) and Cowin’s fabric-elasticity equations (for trabecular bone) best predicted local subchondral bone stiffness.

Association between regional heterogeneity in the mid-facial bone micro-architecture and increased fragility along Le Fort lines.

Le Fort lines have traditionally been considered as zones of weakness in the mid-facial skeleton although the structural basis of increased bone fragility at these sites has not yet been investigated. Considering recent findings of occlusal loading-related regional heterogeneity in the mid-facial bone micro-architecture, the aim of this study was to explore whether such heterogeneity in cortical and cancellous bone micro-architecture may contribute to increased fragility at Le Fort fracture sites. Twenty-five cortical and thirteen cancellous bone specimens were harvested from a dry skull and analyzed by micro-CT. Specimens were classified into Le Fort or Non-Le Fort groups based on their location in the mid-facial skeleton. Cortical bone along Le Fort lines showed tendencies toward lower thickness (1.5±0.63 vs 1.75±0.79; P=.39) and greater porosity (11.48±5.67 vs 10.28±5.28; P=.59). A significant difference was detected in the trabecular degree of anisotropy which was higher in cancellous bone from Le Fort fracture sites (2.14±0.69 vs 1.58±0.34; P=.02). Regional heterogeneity in cortical bone micro-architecture could not fully explain increased fragility of the mid-facial skeleton at the Le Fort lines. However, regional differences in trabecular bone anisotropy may contribute to increased bone fragility.

Quantification of trabecular spatial orientation from low-resolution images

No accepted methodology exists to assess trabecular bone orientation from clinical CT scans. The aim of this study was to test the hypothesis that the distribution of grey values in clinical CT images is related to the underlying trabecular architecture and that this distribution can be used to identify the principal directions and local anisotropy of trabecular bone. Fourteen trabecular bone samples were extracted from high-resolution (30 μm) micro-CT scans of seven human femoral heads. Trabecular orientations and local anisotropy were calculated using grey-level deviation (GLD), a novel method providing a measure of the three-dimensional distribution of image grey values. This was repeated for different image resolutions down to 300 μm and for volumes of interest (VOIs) ranging from 1 to 7 mm. Outcomes were compared with the principal mechanical directions and with mean intercept length (MIL) as calculated for the segmented 30-μm images. For the 30-μm images, GLD predicted the mechanical principal directions equally well as MIL. For the 300-μm images, which are resolutions that can be obtained in vivo using clinical CT, only a small increase (3°–6°) in the deviation from the mechanical orientations was found. VOIs of 5 mm resulted in a robust quantification of the orientation. We conclude that GLD can quantify structural bone parameters from low-resolution CT images.

A novel approach to estimate trabecular bone anisotropy from stress tensors.

Continuum finite element (FE) models of bones and bone-implant configurations are usually based on clinical CT scans. In virtually all of these models, material properties assigned to the bone elements are chosen as isotropic. It has been shown, however, that cancellous bone can be highly anisotropic and that its elastic behavior is best described as orthotropic. Material models have been proposed to derive the orthotropic elastic constants from measurements of density and a fabric tensor. The use of such relationships in FE models derived from CT scans, however, is hampered by the fact that the measurement of such a fabric tensor is not possible from clinical CT images since the resolution of such images is not good enough to resolve the trabecular micro-architecture. In this study, we explore an alternative approach that is based on the paradigm that bone adapts its micro-architecture to the loading conditions, hence that fabric and stress tensors should be aligned and correlated. With this approach, the eigenvectors and eigenvalues of the element continuum-level stress tensor are used as an estimate of the element fabric tensor, from which the orthotropic material properties then are derived. Using an iterative procedure, element orthotropic material properties and fabric tensors are updated until a converged situation is reached. The goals of this study were to investigate the feasibility and accuracy of such an iterative approach to derive orthotropic material properties for a human proximal femur and to investigate whether models derived in this way can provide more accurate results than isotropic models. Results were compared to those obtained from models of the same femurs for which the fabric was measured from micro-CT scans. It was found that the iterative approach could well estimate the orientation of the fabric principal directions. When comparing the stress/damage values in the models with material properties based on estimated and measured fabric tensors, the differences were not significant, suggesting that the material properties based on the estimated fabric tensor well reflected those based on the measured fabric tensor. Errors were less than those obtained when using isotropic models. It is concluded that this novel approach can provide a reasonable estimate of anisotropic material properties of cancellous bone. We expect that this approach can lead to more accurate results in particular for models used to study implants, which are usually anchored in highly anisotropic cancellous bone regions.

Prediction of bone anisotropic mechanical properties in osteoporotic human vertebral body from microstructural parameters

Microstructural (Keller et al. 1992) and mechanical (Keaveny and Hayes 1993) properties and anisotropy of trabecular bone have been widely documented in the literature. Both structural and mechanic...

Is there any information on micro-structure in microwave tomography of bone tissue?

In this work, two-dimensional simulations of the microwave dielectric properties of models with ellipses and realistic models of trabecular bone tissue are performed. In these simulations, finite difference time domain methodology has been applied to simulate two-phase structures containing inclusions. The results presented here show that the micro-structure is an important factor in the effective dielectric properties of trabecular bone. We consider the feasibility of using the dielectric behaviour of bone tissue to be an indicator of bone health. The frequency used was 950MHz. It was found that the dielectric properties can be used as an estimate of the degree of anisotropy of the micro-structure of the trabecular tissue. Conductivity appears to be the most sensitive parameter in this respect. Models with ellipse shaped-inclusions are also tested to study their application to modelling bone tissue. Models with ellipses that had an aspect ratio of a/b=1.5 showed relatively good agreement when compared with realistic models of bone tissue. According to the results presented here, the anisotropy of trabecular bone must be accounted for when measuring its dielectric properties using microwave imaging.

Generalizing the mean intercept length tensor for gray-level images

The mean intercept length tensor is the most used technique to estimate microstructure orientation and anisotropy of trabecular bone. This paper proposes an efficient extension of this technique to gray-scale images based on a closed formulation of the mean intercept length tensor and a generalization using different angular convolution kernels. First, the extended Gaussian image is computed for the binary or gray-scale image. Second, the intercepts are computed for all possible orientations through an angular convolution with the half-cosine function. Finally, the tensor is computed by means of the covariance matrix. The complexity of the method is O(n + m) in contrast with O(nm) of traditional implementations, where n is the number of voxels in the image and m is the number of orientations used in the computations. The method is generalized by applying other angular convolution kernels instead of the half-cosine function. As a result, the anisotropy of the tensor can be controlled while keeping the eigenvectors intact. The proposed extension to gray-scale yields accurate results for reliable computations of the extended Gaussian image and, unlike the traditional methodology, is not affected by artifacts generated by discretizations during the sampling of different orientations. Experiments show that the computations on both binary and gray-scale images are correlated, and that computations in gray-scale are more robust, enabling the use of the mean intercept length tensor to clinical examinations of trabecular bone. The use of kernels based on the von Mises-Fisher distribution is promising as the anisotropy can be adjusted with a parameter in order to improve its power to predict mechanical properties of trabecular bone.

The potential of multi-slice computed tomography based quantification of the structural anisotropy of vertebral trabecular bone

In the present paper we addressed the problem of whether the information about the structural anisotropy of trabecular bone can be retrieved from low-quality data, captured with clinical multi-raw spiral CT scanners. Two measures of quantifying structural anisotropy were tested – the current standard mean intercept length (MIL) and the gray-level structure tensor (GST). Thirty two vertebral bodies were μCT and CT scanned. The reference values of structural anisotropy were measured in μCT images and compared with the measures of structural anisotropy determined from low-quality CT data. MIL-based measures of structural anisotropy cannot be reliably determined from CT data. The assessment of the GST is significantly better than that of MIL, but the accuracy is not, in general, satisfactory. Based on the results of experiments with artificial data and the analysis of the real images, it can be concluded that a possible reason of the poor performance is anisotropic resolution of clinical CT scanners.

Vertebral trabecular main direction can be determined from clinical CT datasets using the gradient structure tensor and not the inertia tensor—A case study

Osteoporosis is a wide spread disease with one-third of all women beyond their menopause and a fifth of men above the age of 50 years suffering from it. Patient specific finite element models would be a great improvement for the diagnosis of vertebral fracture risk. Different material models have been proposed, which incorporate information about the anisotropy of trabecular bone in addition to bone mineral density (BMD) using a second rank structure tensor.Two alternative structure measurement methods, gradient structure tensor (GST) and inertia tensor (IT), were investigated. Structure was determined from in situ scans. This was compared to structure computed with the mean intercept length (MIL) tensor from μCT scans at the same locations.GST delivered information comparable to MIL regarding the structural main direction even at normal dose standard clinical settings (median of the scalar products of up to ≈0.98). IT was not comparable to MIL (median ≈0.4). Neither of the alternatives could determine eigenvalues comparable to these determined from MIL (p>0.5).In conclusion, this study could show that the measurement of the structural main direction is possible for in situ scans in a clinical setting. It was shown that the method of choice to determine trabecular main direction in situ is GST. Knowing the main direction a transverse isotropic fabric tensor can be constructed.

Sampling sphere orientation distribution: An efficient method to quantify trabecular bone fabric on grayscale images

A novel Sampling Sphere Orientation Distribution (SSOD) method based on mobile sampling spheres is developed for describing microstructural anisotropy of trabecular bone using grayscale images. Efficient implementation of SSOD on segmented and unsegmented 3D microCT images of human trabecular bone samples from different anatomical locations is demonstrated. The second order fabric tensor of SSOD corresponds well with the one derived from the mean intercept length (MIL) method applied on segmented images. The results of SSOD are extended to higher order fabric approximations and the effect of sampling sphere radius is examined. Finally, performance of the method on artificial microstructures is presented.

Micromechanical Modeling of the Anisotropy of Elastic Biological Composites

In this paper, a Mori–Tanaka micromechanical modeling of effective elastic properties of trabecular bone is coupled with experimental measurements of morphology obtained from X-ray microtomography. The principle of modeling is based on the Eshelby and Hill polarization tensors of isolated ellipsoidal inclusions embedded in an infinite matrix. The problem is entirely geometrized and is treated in terms of averages of Walpole's components of the fourth-order tensors describing the problem. The structural anisotropy of trabecular bone was determined in three-dimensional space by means of the mean intercept length method and expressed by a fabric tensor, which is a second rank tensor describing the orientation distribution of inclusions volume fractions and degree of anisotropy of trabecular bone. Modeling results showed the high effects of the aspect ratio and orientation distribution of pores on the effective elastic properties of trabecular bone.

Direct measurement of trabecular bone anisotropy using directional fractal dimension and principal axes of inertia

Precise in vivo measurement of the trabecular bone's mechanical properties is very important for endosseous dental implant treatment and design in clinical practice. The fractal structure of trabecular bone shows directional anisotropy of the architecture, as is shown in most biological fractals. To analyze the anisotropy of the trabecular bone, the fractal geometry technique was applied to 2-dimensional plain radiographs. The power spectrum was used to calculate the fractal dimensions (FD) of the trabecular bone. The FDs calculated as a function of orientation yielded the fractal information reflecting the spatial characteristics of the trabecular bone in each direction. A polar plot of directional FDs was defined as an ellipse of inertia. The principal loading direction in a local region of the trabecular bone was determined from the minimum moment of inertia for the ellipse of FDs. The anisotropy was calculated directly as the ratio of the 2 principal moments of inertia from the ellipse. The anisotropies were measured for radiographs from the angle and incisor region of 21 human mandibles based on the principal axes of inertia and the best-fitting ellipse. The anisotropy of the angle region was significantly greater than that of the incisor region of the mandibles. The method using directional FDs as determined by the principal axis of inertia measures the anisotropy directly, using 2-dimensional plain radiographs. It can quantify the anisotropy of trabecular bone in vivo. The investigation can be applied to the analysis of the relationships between in vivo 2-dimensional parameters and 3-dimensional mechanical properties, which enables us to predict the bone mechanical properties such as strength in vivo in various regions of the mandible.

Nonhuman anthropoid primate femoral neck trabecular architecture and its relationship to locomotor mode

Functional analyses of human and nonhuman anthropoid primate femoral neck structure have largely ignored the trabecular bone. We tested hypotheses regarding differences in the relative distribution and structural anisotropy of trabecular bone in the femoral neck of quadrupedal and climbing/suspensory anthropoids. We used high-resolution X-ray computed tomography to analyze quantitatively the femoral neck trabecular structure of Ateles geoffroyi, Symphalangus syndactylus, Alouatta seniculus, Colobus guereza, Macaca fascicularis, and Papio cynocephalus (n = 46). We analyzed a size-scaled superior and inferior volume of interest (VOI) in the femoral neck. The ratio of the superior to inferior VOI bone volume fraction indicated that the distribution of trabecular bone was inferiorly skewed in most (but not all) quadrupeds and evenly distributed the climbing/suspensory species, but interspecific comparisons indicated that all taxa overlapped in these measurements. Degree of anisotropy values were generally higher in the inferior VOI of all species and the results for the two climbing/suspensory taxa, A. geoffroyi (1.71 +/- 0.30) and S. syndactylus (1.55 +/- 0.04), were similar to the results for the quadrupedal anthropoids, C. guereza (male = 1.64 +/- 0.13; female = 1.68 +/- 0.07) and P. cynocephalus (1.47 +/- 0.13). These results suggest strong trabecular architecture similarity across body sizes, anthropoid phylogenetic backgrounds, and locomotor mode. This structural similarity might be explained by greater similarity in anthropoid hip joint loading mechanics than previously considered. It is likely that our current models of anthropoid hip joint mechanics are overly simplistic.

A robust method for measuring trabecular bone orientation anisotropy at in vivo resolution using tensor scale

Trabecular bone (TB) is a network of interconnected struts and plates that constantly remodels to adapt dynamically to the stresses to which it is subjected in such a manner that the trabeculae are oriented along the major stress lines (Wolff's Law). Next to bone density, TB anisotropy has been found to be one of the most significant determinants of the bone's biomechanical behavior. Typically, orientational anisotropy of TB networks is expressed in terms of the fabric tensor, obtained by measuring the mean intercept length between structure elements along test lines. This method, however, can provide only a global statistical average of TB orientation anisotropy and, in general, requires a large sampling volume. Here, we present a new method, based on the recently conceived notion of “tensor scale”, which provides regional information of TB orientation anisotropy. Regional structure is represented by local best fit ellipsoid (ellipse in 2D) and the structural orientation is determined from the eigenvectors along the semi-axes. The method is found to be remarkably robust over a wide range of resolution regimes and image rotation as shown with micro-CT images from specimens of the human distal radius, the latter showing the characteristic differences in structural anisotropy for transverse and longitudinal sections. Finally, the method's applicability to in vivo MR imaging is demonstrated with data from the distal tibia.

Assessment of trabecular bone structure in postmenopausal and senile osteoporosis in women by image analysis

Objective: The aim of the study was to assess bone trabecular structure in postmenopausal and senile osteoporosis.Methods: The study was performed on transiliac specimens obtained from women with postmenopausal (n=10) and senile osteoporosis (n=10) and on normal autopsy bone (n=7). Digitalized microradiographs were analysed using dedicated software allowing for selection of longitudinal and transversal elements.Results: Significant differences between transversal and control, as well as between longitudinal and control trabecular areas were observed in senile osteoporosis (p<0.005). In postmenopausal osteoporosis, such differences were found for longitudinal trabeculae only (p<0.005). Mean longitudinal trabecular area loss in senile and postmenopausal osteoporosis as compared to control group was 57.2% and 25.7%, respectively. Respective values for transversal trabecular area were 35.0% and 59.4%.Conclusion: Structural anisotropy of trabecular bone is greater in postmenopausal than in senile osteoporosis and control group. The method developed allows the evaluation of bone structures in radiographs with uneven exposure.

The three-dimensional structure of trabecular bone in the femoral head of strepsirrhine primates

It has been hypothesized for over a hundred years that trabecular bone plays an important structural role in the musculoskeletal system of animals and that it responds dynamically to applied loads through growth. The objectives of this study are to quantify the three-dimensional structure of femoral head trabecular bone in a sample of extant strepsirrhines and to relate patterns of interspecific variation to locomotor behavioral differences. The bone volume fraction (BV/TV) and fabric anisotropy of trabecular bone in the femoral heads of Cheirogaleus major, Avahi laniger, Galago senegalensis, Galago alleni, Loris tardigradus, Otolemur crassicaudatus, and Perodicticus potto were quantified in three dimensions using serial high-resolution X-ray computed tomography scan data. A volume based method was used to quantify the structural anisotropy in three cubic samples located inside the central portion of the femoral head. Significant structural differences were found between the predominantly leaping galagines and indriids and the nonleaping lorisines and cheirogaleids. The leapers in general have relatively anisotropic trabecular bone. The galagines display a unique pattern of decreasing bone volume and increasing anisotropy moving from the superior to the inferior half of the femoral head. By contrast, the nonleaping taxa possess relatively uniform and isotropic bone throughout the femoral head. The differences in femoral head trabecular structure among these taxa seem to be related to locomotor behavioral differences, reflecting variation in the use and loading of the hip joint during normal locomotion.

Fractal-based image texture analysis of trabecular bone architecture.

Fractal-based image analysis methods are investigated to extract textural features related to the anisotropic structure of trabecular bone from the X-ray images of cubic bone specimens. Three methods are used to quantify image textural features: power spectrum, Minkowski dimension and mean intercept length. The global fractal dimension is used to describe the overall roughness of the image texture. The anisotropic features formed by the trabeculae are characterised by a fabric ellipse, whose orientation and eccentricity reflect the textural anisotropy of the image. Tests of these methods with synthetic images of known fractal dimension show that the Minkowski dimension provides a more accurate and consistent estimation of global fractal dimension. Tests on bone x-ray (eccentricity range 0.25-0.80) images indicate that the Minkowski dimension is more sensitive to the changes in textural orientation. The results suggest that the Minkowski dimension is a better measure for characterising trabecular bone anisotropy in the x-ray images of thick specimens.