Tensor Scale: A New Method for Quantifying Structural Anisotropy in Trabecular Bone Images

P. K. Saha, F. W. Wehrli University of Pennsylvania, Philadelphia, PA 19104, United States SYNOPSIS: Trabecular bone (TB) is a network of interconnected struts and plates. During remodeling the bone responds to the forces to which it is subjected and the trabeculae thus follow major stress lines (Wolff’s law). Trabecular anisotropy can be expressed in terms of the fabric tensor. Next to volume fraction, structural orientation (fabric) is the largest contributor to bone strength. Here, we present a new method, based on the recently conceived notion of tensor scale, to quantify regional TB orientation and anisotropy in high-resolution in vivo images of TB bone. INTRODUCTION: Trabecular bone (TB) is a network of interconnected struts and plates. During remodeling the bone responds to the forces to which it is subjected forcing the trabeculae to align with major stress lines (Wolff’s law). TB anisotropy can be expressed in terms of the fabric tensor which is obtained from a directional measurement of mean intercept length (MIL). Fabric is an important determinant of bone strength. However, MIL provides only a global statistical average and thus requires a large analysis volume. Here, we present a new method, based on the notion of tensor scale, which provides regional information of TB orientation and anisotropy. METHOD: Tensor scale parametric images were obtained from μ-MR or μ-CT TB bone images (Fig. 1) which were first preprocessed to yield bone volume fraction (bvf). Although tensor scale is a 3D property, we confine ourselves to the measurement of TB structural anisotropy in 2D.