Multiscale reconstruction of porous media based on multiple dictionaries learning

Digital modeling of the microstructure is important for studying the physical and transport properties of porous media. Multiscale modeling for porous media can accurately characterize macro-pores and micro-pores in a large-FoV (field of view) high-resolution three-dimensional pore structure model. This paper proposes a multiscale reconstruction algorithm based on multiple dictionaries learning, in which edge patterns and micro-pore patterns from homology high-resolution pore structure are introduced into low-resolution pore structure to build a fine multiscale pore structure model. The qualitative and quantitative comparisons of the experimental results show that the results of multiscale reconstruction are similar to the real high-resolution pore structure in terms of complex pore geometry and pore surface morphology. The geometric, topological and permeability properties of multiscale reconstruction results are almost identical to those of the real high-resolution pore structures. The experiments also demonstrate the proposal algorithm is capable of multiscale reconstruction without regard to the size of the input. This work provides an effective method for fine multiscale modeling of porous media

Radial Basis Functions: Biomedical Applications and Parallelization

Radial basis function (RBF) is a real-valued function whose values depend only on the distances between an interpolation point and a set of user-specified points called centers. RBF interpolation is one of the primary methods to reconstruct functions from multi-dimensional scattered data. Its abilities to generalize arbitrary space dimensions and to provide spectral accuracy have made it particularly popular in different application areas, including but not limited to: finding numerical solutions of partial differential equations (PDEs), image processing, computer vision and graphics, deep learning and neural networks, etc. The present thesis discusses three applications of RBF interpolation in biomedical engineering areas: (1) Calcium dynamics modeling, in which we numerically solve a set of PDEs by using meshless numerical methods and RBF-based interpolation techniques; (2) Image restoration and transformation, where an image is restored from its triangular mesh representation or transformed under translation, rotation, and scaling, etc. from its original form; (3) Porous structure design, in which the RBF interpolation used to reconstruct a 3D volume containing porous structures from a set of regularly or randomly placed points inside a user-provided surface shape. All these three applications have been investigated and their effectiveness has been supported with numerous experimental results. In particular, we innovatively utilize anisotropic distance metrics to define the distance in RBF interpolation and apply them to the aforementioned second and third applications, which show significant improvement in preserving image features or capturing connected porous structures over the isotropic distance-based RBF method. Beside the algorithm designs and their applications in biomedical areas, we also explore several common parallelization techniques (including OpenMP and CUDA-based GPU programming) to accelerate the performance of the present algorithms. In particular, we analyze how parallel programming can help RBF interpolation to speed up the meshless PDE solver as well as image processing. While RBF has been widely used in various science and engineering fields, the current thesis is expected to trigger some more interest from computational scientists or students into this fast-growing area and specifically apply these techniques to biomedical problems such as the ones investigated in the present work

Training Images-Based Stochastic Simulation on Many-Core Architectures

In the past decades, multiple-point geostatistical methods (MPS) are increasing in popularity in various fields. Compared with the traditional techniques, MPS techniques have the ability to characterize geological reality that commonly has complex structures such as curvilinear and long-range channels by using high-order statistics for pattern reconstruction. As a result, the computational burden is heavy, and sometimes, the current algorithms are unable to be applied to large-scale simulations. With the continuous development of hardware architectures, the parallelism implementation of MPS methods is an alternative to improve the performance. In this chapter, we overview the basic elements for MPS methods and provide several parallel strategies on many-core architectures. The GPU-based parallel implementation of two efficient MPS methods known as SNESIM and Direct Sampling is detailed as examples

Quantifying solute spreading and mixing in reservoir rocks using 3-D PET imaging

We report results of an experimental investigation into the effects of small-scale (mm-cm) heterogeneities on solute spreading and mixing in a Berea sandstone core. Pulse-tracer tests have been carried out in the Péclet number regime Pe = 6-40 and are supplemented by a unique combination of two imaging techniques. X-ray computed tomography (CT) is used to quantify subcore-scale heterogeneities in terms of permeability contrasts at a spatial resolution of approximately 10 mm3, while [11C] positron emission tomography (PET) is applied to image the spatial and temporal evolution of the full tracer plume non-invasively. To account for both advective spreading and local (Fickian) mixing as driving mechanisms for solute transport, a streamtube model is applied that is based on the one-dimensional advection-dispersion equation. We refer to our modelling approach as semideterministic, because the spatial arrangement of the streamtubes and the corresponding solute travel times are known from the measured rock's permeability map, which required only small adjustments to match the measured tracer breakthrough curve. The model reproduces the three-dimensional PET measurements accurately by capturing the larger-scale tracer plume deformation as well as subcore-scale mixing, while confirming negligible transverse dispersion over the scale of the experiment. We suggest that the obtained longitudinal dispersivity (0.10±0.02 cm) is rock rather than sample specific, because of the ability of the model to decouple subcore-scale permeability heterogeneity effects from those of local dispersion. As such, the approach presented here proves to be very valuable, if not necessary, in the context of reservoir core analyses, because rock samples can rarely be regarded as 'uniformly heterogeneous'

A framework for local terrain deformation based on diffusion theory

Terrains have a key role in making outdoor virtual scenes believable and immersive as they form the support for every other natural element in the scene. Although important, terrains are often given limited interactivity in real-time applications. However, in nature, terrains are dynamic and interact with the rest of the environment changing shape on different levels, from tracks left by a person running on a gravel soil (micro-scale), to avalanches on the side of a mountain (macro-scale). The challenge in representing dynamic terrains correctly is that the soil that forms them is vastly heterogeneous and behaves differently depending on its composition. This heterogeneity introduces difficulties at different levels in dynamic terrains simulations, from modelling the large amount of different elements that compose the oil to simulating their dynamic behaviour. This work presents a novel framework to simulate multi-material dynamic terrains by taking into account the soil composition and its heterogeneity. In the proposed framework soil information is obtained from a material description map applied to the terrain mesh. This information is used to compute deformations in the area of interaction using a novel mathematical model based on diffusion theory. The deformations are applied to the terrain mesh in different ways depending on the distance of the area of interaction from the camera and the soil material. Deformations away from the camera are simulated by dynamically displacing normals. While deformations in a neighbourhood of the camera are represented by displacing the terrain mesh, which is locally tessellated to better fit the displacement. For gravel based soils the terrain details are added near the camera by reconstructing the meshes of the small rocks from the texture image, thus simulating both micro and macro-structure of the terrain. The outcome of the framework is a realistic interactive dynamic terrain animation in real-time

Multimodal Imaging of Anisotropic Hierarchical Materials

The thesis is focused on studying the nanostructure of natural and synthetic hierarchical materials with biological applications, using X-ray scattering imaging and birefringence microscopy. The term "hierarchical materials" is used for structures composed of sub-units organised in different length scales that create the building blocks for the next level. Hierarchical materials are commonly found in nature, with diverse structures and functionalities. In the first part of this thesis, the nanostructure of mineralised tissue, such as tusk and bone, was the focus. Scanning SAXS, SAXS tensor tomography and birefringence microscopy were used to study the helicoidal structure of narwhal tusk. A high degree of anisotropy was found, in which the dentine and cementum have a very highly organised nanostructure with a preferential orientation along the tusk. However, those two main components differ in the deviations from that primary orientation, which revealed a complex helical pattern that could be the source of its anisotropic mechanical properties. A layered structure was also observed using X-ray fluorescence spectroscopy, indicating tusk growth layers that reflect the animal history. Those methods were also applied to study the anisotropic nanostructure of regenerated bone in biodegradable scaffolds and titanium implants in vivo, successfully demonstrating that the scaffold or implant architecture influence the new bone formation. Scaffolds with aligned fibres led to well-structured bone and a faster regeneration process, while scaffolds with randomly oriented fibres only created a callus around the damaged area with poor growth of new tissue.In the second part of this thesis, the anisotropy of self-assembled lyotropic liquid crystals for 3D printing of bone-mimetic composites was studied. This work aimed to understand the fundamental processes and mechanisms that induce the alignment of the self-assembled crystalline units to create composites with more anisotropic mechanical properties. In that study, an in situ characterisation of the nanostructure during flow in the 3D printer was done using scanning SAXS and birefringence microscopy to correlate the manufacturing process with the observed structural alignment of the material. The results demonstrated the role of the shear stress in such liquid crystals, highlighting the effect it has on the anisotropy and morphological transitions in the self-assembled structures. The importance of time and environmental conditions during 3D printing is also shown, which may affect the final structure and orientation