Fourier Transform-Based Algorithm for the Quantification of the Spatial Orientation Distribution of 3D Fiber Networks
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Several materials and tissues are characterized by a microstructure composed of fibrous units embedded in a ground matrix. Determining the spatial orientation distribution of such fibers is of paramount importance for an accurate mechanical modeling using anisotropic models that account for non-symmetrical fiber dispersion. To date, the distribution is measured from two-dimensional images of the microstructure using image processing algorithms, among which those based on the 2D discrete Fourier transform are the most widespread. However, this approach limits the description of a three-dimensional fiber network to a two-dimensional fiber orientation distribution, with a consequent negative impact on the quality of the mechanical prediction. In this work, a novel three-dimensional (3D) Fourier transform-based algorithm for quantifying the distribution of fiber orientations in the 3D space domain is presented. The method allows for an accurate identification of individual fiber families, their in-plane and out-of-plane dispersion, showing fast computation times. We validated the algorithm using artificially generated 3D images, in terms of fiber dispersion by considering the error between the standard deviation of the reconstructed and the prescribed distributions of the artificial fibers. In addition, we considered the measured mean orientation angles of the fibers and validated the robustness using a measure of fiber density. Finally, the method is employed to reconstruct a full 3D view of the distribution of collagen fiber orientations based on in vitro second harmonic generation microscopy of collagen fibers in human and mouse skin.
