Linear iterative near-field phase retrieval (LIPR) for dual-energy x-ray imaging and material discrimination.

Near-field x-ray refraction (phase) contrast is unavoidable in many lab-based micro-CT imaging systems. Quantitative analysis of x-ray refraction (a.k.a. phase retrieval) is in general an under-constrained problem. Regularizing assumptions may not hold true for interesting samples; popular single-material methods are inappropriate for heterogeneous samples, leading to undesired blurring and/or over-sharpening. In this paper, we constrain and solve the phase-retrieval problem for heterogeneous objects, using the Alvarez-Macovski model for x-ray attenuation. Under this assumption we neglect Rayleigh scattering and pair production, considering only Compton scattering and the photoelectric effect. We formulate and test the resulting method to extract the material properties of density and atomic number from single-distance, dual-energy imaging of both strongly and weakly attenuating multi-material objects with polychromatic x-ray spectra. Simulation and experimental data are used to compare our proposed method with the Paganin single-material phase-retrieval algorithm, and an innovative interpretation of the data-constrained modeling phase-retrieval technique.

Bayesian approach to time-resolved tomography.

Conventional X-ray micro-computed tomography (µCT) is unable to meet the need for real-time, high-resolution, time-resolved imaging of multi-phase fluid flow. High signal-to-noise-ratio (SNR) data acquisition is too slow and results in motion artefacts in the images, while fast acquisition is too noisy and results in poor image contrast. We present a Bayesian framework for time-resolved tomography that uses priors to drastically reduce the required amount of experiment data. This enables high-quality time-resolved imaging through a data acquisition protocol that is both rapid and high SNR. Here we show that the framework: (i) encompasses our previous, algorithms for imaging two-phase flow as limiting cases; (ii) produces more accurate results from imperfect (i.e. real) data, where it can be compared to our previous work; and (iii) is generalisable to previously intractable systems, such as three-phase flow.

Extending reference scan drift correction to high-magnification high-cone-angle tomography.

The reference scan method is a simple yet powerful method for measuring spatial drift of the x-ray spot during a low-cone-angle µ-CT experiment. As long as the drift is smooth, and occurring on a time scale that is long compared to the acquisition time of each projection, this method provides a way to compensate for the drift by applying 2D in-plane translations to the radiographs. Here we show that this compensation may be extended to the regime of high-magnification, high-cone-angle CT experiments where source drift perpendicular to the detector plane can cause significant magnification changes throughout the acquisition.

Remobilization of residual non-aqueous phase liquid in porous media by freeze-thaw cycles.

The pore-scale behavior of a nonaqueous phase liquid (NAPL) trapped as residual contamination in a porous medium, subject to freeze-thaw cycles, was investigated by X-ray microcomputed tomography. It is shown that freeze-thaw cycles cause significant NAPL remobilization in the direction of the freezing front, due to the rupture and transport of a significant proportion of (supposedly entrapped) larger multipore NAPL ganglia. Significant NAPL remains in place, however, due to substantial ganglion fragmentation into single- and subpore ganglia. The contraction of branched ganglia into more rounded forms, especially near the top surface, is also observed. Three freezing-induced mechanisms are proposed to explain the results. The findings have important implications for NAPL contamination in cold regions, and for the behavior of water-hydrocarbon systems on the Earth and other planets.

Dynamic tomography with a priori information.

We present "dynamic tomography" algorithms that allow for the high-resolution, time-resolved imaging of dynamic (i.e., continuously time evolving) complex systems at existing x-ray micro-CT facilities. The behavior of complex systems is constrained by the underlying physics. By exploiting a priori knowledge of the geometry of the physical process being studied to allow the use of sophisticated iterative reconstruction techniques that incorporate constraints, we improve on current frame rates by at least an order of magnitude. This allows time-resolved imaging of previously intractable processes, such as two-phase fluid flow. We present reconstructions from experimental data collected at the Australian National University x-ray micro-CT facility.

Robust pore size analysis of filamentous networks from three-dimensional confocal microscopy.

We describe a robust method for determining morphological properties of filamentous biopolymer networks, such as collagen or other connective tissue matrices, from confocal microscopy image stacks. Morphological properties including pore size distributions and percolation thresholds are important for transport processes, e.g., particle diffusion or cell migration through the extracellular matrix. The method is applied to fluorescently labeled fiber networks prepared from rat-tail tendon and calf-skin collagen, at concentrations of 1.2, 1.6, and 2.4 mg/ml. The collagen fibers form an entangled and branched network. The medial axes, or skeletons, representing the collagen fibers are extracted from the image stack by threshold intensity segmentation and distance-ordered homotopic thinning. The size of the fluid pores as defined by the radii of largest spheres that fit into the cavities between the collagen fibers is derived from Euclidean distance maps and maximal covering radius transforms of the fluid phase. The size of the largest sphere that can traverse the fluid phase between the collagen fibers across the entire probe, called the percolation threshold, was computed for both horizontal and vertical directions. We demonstrate that by representing the fibers as the medial axis the derived morphological network properties are both robust against changes of the value of the segmentation threshold intensity and robust to problems associated with the point-spread function of the imaging system. We also provide empirical support for a recent claim that the percolation threshold of a fiber network is close to the fiber diameter for which the Euler index of the networks becomes zero.

Assessment of bone ingrowth into porous biomaterials using MICRO-CT.

The three-dimensional (3D) structure and architecture of biomaterial scaffolds play a critical role in bone formation as they affect the functionality of the tissue-engineered constructs. Assessment techniques for scaffold design and their efficacy in bone ingrowth studies require an ability to accurately quantify the 3D structure of the scaffold and an ability to visualize the bone regenerative processes within the scaffold structure. In this paper, a 3D micro-CT imaging and analysis study of bone ingrowth into tissue-engineered scaffold materials is described. Seven specimens are studied in this paper; a set of three specimens with a cellular structure, varying pore size and implant material, and a set of four scaffolds with two different scaffold designs investigated at early (4 weeks) and late (12 weeks) explantation times. The difficulty in accurately phase separating the multiple phases within a scaffold undergoing bone regeneration is first highlighted. A sophisticated three-phase segmentation approach is implemented to develop high-quality phase separation with minimal artifacts. A number of structural characteristics and bone ingrowth characteristics of the scaffolds are quantitatively measured on the phase separated images. Porosity, pore size distributions, pore constriction sizes, and pore topology are measured on the original pore phase of the scaffold volumes. The distribution of bone ingrowth into the scaffold pore volume is also measured. For early explanted specimens we observe that bone ingrowth occurs primarily at the periphery of the scaffold with a constant decrease in bone mineralization into the scaffold volume. Pore size distributions defined by both the local pore geometry and by the largest accessible pore show distinctly different behavior. The accessible pore size is strongly correlated to bone ingrowth. In the specimens studied a strong enhancement of bone ingrowth is observed for pore diameters>100 microm. Little difference in bone ingrowth is measured with different scaffold design. This result illustrates the benefits of microtomography for analyzing the 3D structure of scaffolds and the resultant bone ingrowth.

Analysis of 3D bone ingrowth into polymer scaffolds via micro-computed tomography imaging.

This paper illustrates the utility of micro-computed tomography (micro-CT) to study the process of tissue engineered bone growth. A micro-CT facility for imaging and visualising biomaterials in three dimensions (3D) is described. The facility is capable of acquiring 3D images made up of 2000(3) voxels on specimens up to 60mm in extent with resolutions down to 2 microm. This allows the 3D structure of tissue engineered materials to be imaged across three orders of magnitude of detail. The capabilities of micro-CT are demonstrated by imaging the Haversian network within human femoral cortical bone (distal diaphysis) and bone ingrowth into a porous scaffold at varying resolutions. Phase identification combined with 3D visualisation enables one to observe the complex topology of the canalicular system of the cortical bone. Imaging of the tissue engineered bone at a scale of 1cm and resolutions of 10 microm allows visualisation of the complex ingrowth of bone into the polymer scaffold. Further imaging at 2 microm resolution allows observation of bone ultra-structure. These observations illustrate the benefits of tomography over traditional techniques for the characterisation of bone morphology and interconnectivity and performs a complimentary role to current histomorphometric techniques.

Trapping thresholds in invasion percolation.

We give numerical estimates for the site percolation trapping thresholds for invasion percolation on various three dimensional lattices. We find that in most cases the thresholds for invasion and ordinary percolation coincide. However, for coordination numbers less than five the thresholds diverge. Since most rock networks exhibit coordination numbers less than five the rules for simulating residual saturation in porous rocks must be chosen carefully.

Nonuniversality of invasion percolation in two-dimensional systems.

Employing highly efficient algorithms for simulating invasion percolation (IP) with trapping, we obtain precise estimates for the fractal dimensions of the sample-spanning cluster, the backbone, and the minimal path in a variety of two-dimensional lattices. The results indicate that these quantities are nonuniversal and vary with the coordination number Z of the lattices. In particular, while the fractal dimension D(f) of the sample-spanning cluster in lattices with low Z has the generally accepted value of about 1.82, it crosses over to the value of random percolation, D(f) approximately equal to 1.896, if Z is large enough. Since optimal paths in strongly disordered media and minimum spanning trees on random graphs are related to IP, the implication is that these problems do not also possess universal scaling properties.

Theory and Algorithms for Constructing Discrete Morse Complexes from Grayscale Digital Images.

We present an algorithm for determining the Morse complex of a two or three-dimensional grayscale digital image. Each cell in the Morse complex corresponds to a topological change in the level sets (i.e., a critical point) of the grayscale image. Since more than one critical point may be associated with a single image voxel, we model digital images by cubical complexes. A new homotopic algorithm is used to construct a discrete Morse function on the cubical complex that agrees with the digital image and has exactly the number and type of critical cells necessary to characterize the topological changes in the level sets. We make use of discrete Morse theory and simple homotopy theory to prove correctness of this algorithm. The resulting Morse complex is considerably simpler than the cubical complex originally used to represent the image and may be used to compute persistent homology.

The correlation of pore morphology, interconnectivity and physical properties of 3D ceramic scaffolds with bone ingrowth.

In the design of tissue engineering scaffolds, design parameters including pore size, shape and interconnectivity, mechanical properties and transport properties should be optimized to maximize successful inducement of bone ingrowth. In this paper we describe a 3D micro-CT and pore partitioning study to derive pore scale parameters including pore radius distribution, accessible radius, throat radius, and connectivity over the pore space of the tissue engineered constructs. These pore scale descriptors are correlated to bone ingrowth into the scaffolds. Quantitative and visual comparisons show a strong correlation between the local accessible pore radius and bone ingrowth; for well connected samples a cutoff accessible pore radius of approximately 100 microM is observed for ingrowth. The elastic properties of different types of scaffolds are simulated and can be described by standard cellular solids theory: (E/E(0))=(rho/rho(s))(n). Hydraulic conductance and diffusive properties are calculated; results are consistent with the concept of a threshold conductance for bone ingrowth. Simple simulations of local flow velocity and local shear stress show no correlation to in vivo bone ingrowth patterns. These results demonstrate a potential for 3D imaging and analysis to define relevant pore scale morphological and physical properties within scaffolds and to provide evidence for correlations between pore scale descriptors, physical properties and bone ingrowth.