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Quantification of trabecular bone anisotropy by means of 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 (Wolf's Law). Structural anisotropy can be expressed in terms of the fabric tensor. Next to bone density, TB has been found to be the largest determinant of bone biomechanical behavior. Existing methods, including mean intercept length (MIL), provide only a global statistical average of TB anisotrophy and, generally, require a large sample volume. In this paper, we present a new method, based on the recently conceived notion of tensor scale, which provides regional information of TB orientation and anisotropy. Preliminary evaluation of the method in terms of its sensitivity to resolution and image rotation is reported. The characteristic differences between TB anisotropy computed from transverse and longitudinal sections have been studied and potential applications of the method to in vivo MR imaging are demonstrated. Finally, the ongoing extension of three-dimensional tensor scale in quantitative analysis of tissue morphology is discussed.