Anisotropy

Trabecular bone aligned to its fabric tensor showing preferential orientation of plates and rodsDegree of anisotropy (DA) is a measure of how highly oriented substructures are within a volume. Trabecular bone varies its orientation depending on mechanical load and can become anisotropic. This plugin uses the mean intercept length (MIL) method for determining anisotropy. Briefly, a large number of vectors of the same length originating from a random point within the sample are drawn through the sample. When each vector hits a boundary between foreground and background, an intercept is counted for that vector. The mean intercept length on that vector is then the vector length divided by the number of boundary hits. A cloud of points is built up, where each point represents the vector times its mean intercept length. Fitting an ellipsoid to the point cloud, construction of a material anisotropy tensor and subsequent eigendecomposition results in eigenvalues giving the lengths of the ellipsoid's axes and eigenvectors giving the orientation of the axes. DA is calculated as 1 - length of the shortest axis / length of the longest axis. New random points with the same vectors are sampled and DA updated with the new MIL counts until either the minimum number of sampling points is reached or the coefficient of variation of DA falls below a threshold.

Odgaard A (1997) Three-dimensional methods for quantification of cancellous bone architecture. Bone 20: 315-28. doi:10.1016/S8756-3282(97)00007-0.

Harrigan TP, Mann RW (1984) Characterization of microstructural anisotropy in orthotropic materials using a second rank tensor. J Mater Sci 19: 761-767. doi:10.1007/BF00540446.

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