Autocorrelation analysis of bone structure

Abstract

We propose a method called spatial autocorrelation analysis (SACA) to determine the spatial anisotropy of the trabecular bone in order to investigate osteoporosis. For demonstrating the potential of SACA we first evaluate the method on rectangular, simulated test patterns as a simple model for the anisotropic pore structure of the bone. As a next step towards biomedical application, photographic reference images of human vertebral bone were investigated by SACA. Osteoporotic bone structure could be clearly differentiated from non-osteoporotic sample images. Moreover, for demonstration of the applicability and potential of the method for in vivo characterization of osteoporosis, the microstructure of the human calcaneus was investigated by MR-microimaging on a young healthy male subject and an osteoporotic female. The measurements were performed using a high-field (3T) whole-body MR tomograph equipped with a special, strong head gradient system. The signal was acquired with a surface coil mounted on an in-house-built device for convenient immobilization of the subject's foot. Using a 3D gradient echo sequence a resolution of 0.254 ؋ 0.254 ؋ 2.188 mm 3 was achieved in vivo. Selected images were inverted, gradient corrected for the inhomogeneous but sensitive detection by the surface coil, and subsequently analyzed by SACA. The anisotropy of bone structure detected by SACA is a possible candidate for noninvasive determination of the osteoporotic status, potentially complementing standard bone mineral density measurements. J. Magn. Reson. Imaging 2001;14:87-93.

Quantitative MRI for the assessment of bone structure and function

“…SMI proved to be useful for characterizing structures derived from TB m-CT images of human specimens from multiple anatomic locations and providing insight into age-related changes in TB architecture (13). Other 3D approaches make use of the quasi-regularity of trabecular networks (125,126). Hwang et al (125) showed on the basis of micro-MRI data obtained in specimens of human trabecular bone that spatial autocorrelation analysis, discussed later in more detail, can provide information on intertrabecular spacing and orientation without the need to resort to binary images.…”

“…For such a lattice, the first peak of the autocorrelation function (ACF) occurs at the lattice spacing whereas the full width at half maximum of the parent peak is a measure of structural thickness. Rotter et al (126) proposed AC analysis as a means of characterizing TB. More recently, Wald et al worked out an algorithm for mapping the full anisotropy ellipsoid for TB thickness and spacing from in vivo MR images (153).…”

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

“…Recent studies determined the anisotropy from high resolution magnetic resonance datasets using autocorrelation analysis on clinically gained datasets. These experiments were restricted to peripheral sites (Rotter et al, 2001;Wald et al, 2007). Rao and Schunk (1991) proposed the gradient structure tensor (Y GST ) to determine texture orientation.…”

High-Resolution Imaging Techniques for Bone Quality Assessment

“…The importance of connecting rods perpendicular to the major loading axis in the context of femoral bone strength has been previously emphasized [242]. More recent approaches include topology-based orientation analysis of trabecular bone networks [233] and 3D spatial autocorrelation function (ACF) [243,244]. ACF is defined as the convolution of the image with its complex conjugated mirrored image.…”