Three independent analysis methods were developed to investigate the distribution of solid mass in foams analyzed by X-ray tomography with effective pixel sizes larger than the thickness of the solid network (sub-pixel conditions). Validation of the methods was achieved by a comparison with the results obtained employing high-resolution tomography for the same set of foams. The foams showed different solid mass distribution, which varied from being preferentially located on the edges, with a fraction of mass in the struts nearing 0.6, to materials in which the fraction of mass in the struts was low, under 0.15. In all cases, the accuracy of the proposed approaches was greater for materials with a higher fraction of mass in the struts. The method based on deconvolution of the attenuation probability density function yielded the closest results to the high-resolution characterizations. In contrast, analysis of the solid matrix thickness distribution after watershed segmentation, and binarization of high thickness regions (struts segmentation) required normalization through macroscopic measurements and revealed higher deviations with respect to the high-resolution results. However, segmentation-based methods allowed investigation of the heterogeneity of the fraction of mass in the struts along the sample.

This work presents a series of three-dimensional computational methods with the objective of analyzing and quantifying some important structural characteristics in a collection of low-density polyolefin-based foams. First, the solid phase tortuosity, local thickness, and surface curvature, have been determined over the solid phase of the foam. These parameters were used to quantify the presence of wrinkles located at the cell walls of the foams under study. In addition, a novel segmentation technique has been applied to the continuous solid phase. This novel method allows performing a separate analysis of the constituting elements of this phase, that is, cell struts and cell walls. The methodology is based on a solid classification algorithm and evaluates the local topological dissimilarities existing between these elements. Thanks to this method it was possible to perform a separate analysis of curvature, local thickness, and corrugation ratio in the solid constituents that reveals additional differences that were not detected in the first analysis of the continuous structure. The methods developed in this work are applicable to other types of porous materials in fields such as geoscience or biomedicine.

Stereological techniques using the optical disectors require estimation of final section thickness, but frozen tissue irregularities may interfere with this estimation. Cryostat slices from rodent nerve tissues (dorsal root ganglia, spinal cord, and brain), cut at 16, 40, and 50 μm, were digitized with a confocal microscope and visualized through 3D software. Geometric section thickness of tissue (Tgeom) was defined as tissue volume/area. Maximal section thicknesses (Tmax), from the top to the bottom of the section, were measured in a random sample of vertical ZX planes. Irregularities were mostly related to blood vessels traversing the tissue and neuronal somas protruding over the cut surfaces, with other neuron profiles showing a fragmented appearance. Irregularities contributed to increasing the distance between the tops and bottoms of slices sectioned in different laboratories. Significant differences were found between Tmax and Tgeom for all thickness studies and counting frames (p<0.01). The Tgeom/Tmax average rate was 68.4–85.7% in volumes around cell profiles (∼600–1,200 μm2) and 83.3–91.8% in subcellular samples (∼25–160 μm2). Confocal microscopy may help to assess tissue irregularities, which might lead to an overestimation of tissue volume if section thickness is estimated by focusing on the top and bottom of the sections.

To analyze nanocrystalline structures quantitatively in 3D, a novel method is presented based on electron diffraction. It allows determination of the average size and morphology of the coherently scattering domains (CSD) in a straightforward way without the need to prepare multiple sections. The method is applicable to all kinds of bulk nanocrystalline materials. As an example, the average size of the CSD in nanocrystalline FeAl made by severe plastic deformation is determined in 3D. Assuming ellipsoidal CSD, it is deduced that the CSD have a width of 19 ± 2 nm, a length of 18 ± 1 nm, and a height of 10 ± 1 nm.

Three-dimensional (3D) analysis is an essential tool to obtain quantitative results from 3D datasets. Considerable progress has been made in 3D imaging techniques, resulting in a growing need for more flexible, complete analysis packages containing advanced algorithms. At the Centre for X-ray Tomography of the Ghent University (UGCT), research is being done on the improvement of both hardware and software for high-resolution X-ray computed tomography (CT). UGCT collaborates with research groups from different disciplines, each having specific needs. To meet these requirements the analysis software package, Morpho+, was developed in-house. Morpho+ contains an extensive set of high-performance 3D operations to obtain object segmentation, separation, and parameterization (orientation, maximum opening, equivalent diameter, sphericity, connectivity, etc.), or to extract a 3D geometrical representation (surface mesh or skeleton) for further modeling. These algorithms have a relatively short processing time when analyzing large datasets. Additionally, Morpho+ is equipped with an interactive and intuitive user interface in which the results are visualized. The package allows scientists from various fields to obtain the necessary quantitative results when applying high-resolution X-ray CT as a research tool to the nondestructive investigation of the microstructure of materials.

The horizontal cells are known to form a mono-layered mosaic in the adult retina, but are scattered at different retinal depths in early development. To help clarifying when and which spatial constraints appear in the relative positioning of these cells, we have performed a quantitative analysis of the three-dimensional (3D) organization of the horizontal cell mosaic at different developmental stages in the postnatal rat retina. We first analyzed the two-dimensional (2D) distribution of the horizontal cell projections onto a plane parallel to the upper retinal surface in retinal flat-mounts, and thus to the future mature horizontal cell mosaic. We found that this 2D distribution was non random since postnatal day 1 (P1), and had a subsequent stepwise improvement in regularity. This preceded the alignment of cells in a single monolayer, which was observed on P6. We then computed true horizontal cell spacing in 3D, finding non-random 3D positioning already on P1. Simulation studies showed that this order might simply derive from the 2D order observed in the projections of the cells in flat-mount, combined with their limited spread in retinal depth. Throughout the period analyzed, the relative positions of horizontal cells are in good agreement with a minimal spacing rule in which the exclusion zone corresponds to the average size of the inner core of the cell dendritic tree estimated from P1 samples. These data indicate the existence of different phases in the process of horizontal cell 3D spatial ordering, supporting the view that multiple mechanisms are involved in the development of the horizontal cell mosaic.