Bone mineral density and trabecular structure together determine the mechanical strength of trabecular bone. The main objective of imaging trabecular bone structure is to determine morphological parameters of the trabecular architecture. These morphologic parameters may help to determine the efficacy of therapeutic treatments for osteoporosis and predict individuals at risk for bone fracture. Standard histomorphometric measures of bone structure include: bone volume fraction (BV/TV), trabecular thickness (Tb.Th), mean intercept lenght, trabecular number (Tb.N), and trabecular spacing (Tb.S). These parameters have been adapted to analyze MR images of trabecular structure.
Because the resolution of in vivo MR images is on the same scale as trabecular dimensions, these histomorphometric parameters are the measures of the trabeculae projected across the slice thickness. Majumdar et al. introduced “apparent” measures, indicating that the morphometric measures obtained from in vivo MR images may not be exactly equivalent, however are related to those obtained from higher resolution modalities. It was found that trabecular spacing and trabecular number are relatively independent of resolution. Trabecu- lar thickness, however, was strongly dependent on resolution with lower resolutions resulting in thicker trabeculae. A 3 dimensional distance technique was introduced by Hilde- brand and Ruegsegger to determine mean thickness by fitting spheres within the structure. This measure was able to distinguish between trabecular bone composed of a greater percentage of plates or rods. It has also been used calculate histomorphometric parameters such as app.Tb.Th and app.Tb.Sp from MR images. The morphological parameters calculated using the distance technique correlated well with those calculated using the mean intercept length. Because osteoporosis is thought to result in a thinning of tra- beculae and loss of trabecular connectivity, measures of connectivity are important in determining osteoporotic bone quality. Connectivity measures have been established to measure the degree of connectivity of the trabecular network in trabecular bone. Connectivity indicates the maximum number of branches that can be broken before the structure is separated into two parts. It is a topological invariant, which means it does not change if the structure is stretched, bent, twisted or other rubber-like deformation. Connectivity can be calculated in terms of the Euler characteristic. Previous studies have used the Euler number to analyze MR images of trabecular bone and found that connectivity can vary between regions within a bone and is significantly correlated with bone density and bone volume fraction.
Fractal dimensions are a measure of the self-similarity of a structure over different scales and have also been used to characterize trabecular architecture. Fractal dimension (D) can be determined using a box-counting technique in which a grid of boxes is superimposed on the trabecular structure. The number of boxes (N) that contain trabeculae is determined for various sizes (e) of grids. Others have used analysis based on Brownian motion to estimate the Hurst exponent (H), which indicates if the structure is random or contains patterns, and derived the fractal dimension from H. Studies found that fractal dimension decreased with age, was significantly lower in patients with vertebral compression fracture and hip fracture, and was not correlated with bone mineral density. Interestingly it was found that fractal dimension was not different between those with osteopenia and osteoporosis, but was nonetheless an independent predictor of bone failure strength. It has been proposed that a decrease in fractal dimension is related to a disorganization of trabecular architecture and loss of connectivity.
Pothuaud et al. proposed further classification of the trabecular architecture using a skeleton graph of the trabecular network. The skeleton graph preserved topographical equivalence with the original network, meaning the connectivity did not change as the trabeculae were thinned to 1 pixel width. This method provides further insight into the influence of connectivity on overall trabecular structure. Others went on to classify the connectivity in terms of curves, surfaces, and junctions of the two. They found that parameters from this digital topological analysis correlated well with bone volume fraction and measures of mechanical integrity, such as Young’s modulus. You can afford your pills. Buy on
Trabecular bone structure is anisotropic, and architectural measures may, therefore, differ depending on the orientation. Spatial autocorrelation analysis is a method to quantify not only the distance between trabeculae, but also how this varies with respect to orientation (i.e. the amount of anisotropy). The autocorrelation function (ACF) is a measure of the probability of finding bone n pixels away from a certain pixel and is equal to the product of the bone volume fractions for
the two pixels. Parameters derived from the ACF provide measures of the structure’s alignment perpendicular to the slice plane (tubularity) and distribution within the slice plane (transverse contiguity). One advantage of autocorrelation analysis is that it does not depend on thresholding or binarizing the images into bone and marrow. It was found that ACF measures of anisotropy correlate well with Young’s modulus and are different for normal and osteoporotic trabecular bone. The scaling index method (SIM) has also been used to measure non-linear structural information from non-binarized tra- becular bone images. The scaling index (a) is a measure of the isotropy of the structure with larger values of a indicating a more random structure. The scaling index correlated better with mechanical strength and BMD than traditional histomor- phometric measures.