Computational methods for analyzing the structure of cancellous bone in planar sections

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Abstract
Conventional stereologic methods for expressing the orientation of anisotropic materials are limited to materials assumed to possess orthogonal directions of orientation. In many substances, including cancellous bone, this assumption is unsubstantiated. Presented here are two simple methods for characterizing the orientation of any anisotropic material within a plane. By modeling the substance as a series of lines oriented in particular directions, it is possible to arrive at either a “phase distribution” that expresses the degree of orientation distributed over a range of angles or a series of “primary orientations” that express the degree of orientation at a select number of angles, with an additional measure of the degree of isotropy. This characterization of anisotropy is highly dependent on such parameters as feature size, sample size, test line spacing, and test line width. Given the careful selection of these parameters, the new methods provide simple measures of orientation, which may prove useful in testing Wolff's trajectorial theory of the relationship between mechanical stresses and the orientation of cancellous bone.