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Human Brain Imaging by Optical Coherence Tomography
Published in Francesco S. Pavone, Shy Shoham, Handbook of Neurophotonics, 2020
Caroline Magnain, Jean C. Augustinack, David Boas, Bruce Fischl, Taner Akkin, Ender Konukoglu, Hui Wang
Computational algorithms have been widely used to quantify the orientation information on histological slices with myelin stains or neural tracers, and volumetric brains of small animals with clearing and labeling orientation (Budde and Frank, 2012; Choe et al., 2012; Schmitt et al., 2004; Budde et al., 2011; Leergaard et al., 2010). Those algorithms are exclusively based on digital signal processing of 2D or 3D images with features highlighting the fiber tracts, including gradient-based edge detection, Fourier transform, and structure tensor (Bigun, 1987). Structure tensor is a second-moment matrix that is derived from the gradient in an immediate neighborhood of a point and is capable of extracting the dominant directions of local features in the image. It has been used in histology and cleared brains to quantify fiber orientations in the brain (Ye et al., 2016; Budde and Frank, 2012). Wang et al. incorporated the structure tensor method in serial sectioning PS OCT and applied it to volumetric retardance images to obtain the 3D fiber orientation in the mouse brain (2015). Based on the orientation metric, tractography is conducted using a conventional dMRI tool to create fiber tracts at microscopic resolution. Here we briefly review the workflow for structure tensor analysis on volumetric PS OCT images.
Finite element modelling
Published in C M Langton, C F Njeh, The Physical Measurement of Bone, 2016
At this level the cancellous bone structural properties are first characterized by the bone volume fraction (often represented by the parameter BV/TV: bone volume over total volume), which is the volume of bone per tissue unit of volume and is dimensionless. A similar scalar quality is the total mass per unit volume of bone, called the structural density or apparent density, which measures the degree of mineralization as well (dimensions: kg m−3). Since the bone volume fraction does not provide any information about the actual structure of the bone (other than its density), other parameters have been developed. Among these are scalar parameters that quantify the average geometry of the trabeculae (e.g. mean trabecular thickness and spacing), the connectivity and the fractal dimension of the trabecular network. In order to quantify the directionality and the anisotropy of the structure, tensor parameters have been introduced. The one most commonly used is the mean intercept length (MIL) [144, 145]. In MIL measurements, a grid of parallel lines is projected over a cross-sectional image of the bone structure. The number of bone-marrow interfaces is then counted for a large number of grid angles. When representing the total line length over the number of bone-marrow interfaces in a polar plot, an ellipse-shaped figure results (an ellipsoid in three dimensions), with its largest principal axis indicating the principal or axial direction of the material. The ratio between the lengths of the principal axes is an indication of the anisotropy of the structure. It should be emphasized, however, that no unique definition exists for the structural anisotropy of bone; other tensor measures have been developed as well [27].
Oriented electrospun nanofibers on stand-alone multi-segmented cylindrical collectors
Published in The Journal of The Textile Institute, 2021
Sairish Malik, Tanveer Hussain, Ahsan Nazir, Nabyl Khenoussi, Saeed Ashraf Cheema
To study the effect of each process parameter on the fibers orientation, the orientation value was determined from the SEM images, using Orientation J image analysis software based on structure tensor (Rezakhaniha et al., 2012). Structure tensor is defined as matrix member of half-done derivative. Structure tensor plays a very important role in image processing. It is used to find out the native Orientation as well as isotropic properties (i.e. energy and coherency) of every single pixel of the image by using the Orientation J. These values result from the structure tensor that is well justified for every pixel as the 2 × 2 symmetric matrix K. where fa and fb are the half-done three-dimensional derivatives of the spitting image f (a, b), alongside the major directions a and b, respectively. Moreover, the weighted inward products among two arbitrary images m and n is defined in Equation (2). w(x, y) is the Gaussian weighting function that postulates the part of attention. If the structure tensor is defined, confined orientation, energy and coherency for every single pixel can be measured easily. The local leading orientation θ in the considered region, links to the route of the largest eigenvector of the tensor and it is therefore given in Equation (3).