Designing heterogeneous porous tissue scaffolds for additive manufacturing processes

A novel tissue scaffold design technique has been proposed with controllable heterogeneous architecture design suitable for additive manufacturing processes. The proposed layer-based design uses a bi-layer pattern of radial and spiral layers consecutively to generate functionally gradient porosity, which follows the geometry of the scaffold. The proposed approach constructs the medial region from the medial axis of each corresponding layer, which represents the geometric internal feature or the spine. The radial layers of the scaffold are then generated by connecting the boundaries of the medial region and the layer's outer contour. To avoid the twisting of the internal channels, reorientation and relaxation techniques are introduced to establish the point matching of ruling lines. An optimization algorithm is developed to construct sub-regions from these ruling lines. Gradient porosity is changed between the medial region and the layer's outer contour. Iso-porosity regions are determined by dividing the subregions peripherally into pore cells and consecutive iso-porosity curves are generated using the isopoints from those pore cells. The combination of consecutive layers generates the pore cells with desired pore sizes. To ensure the fabrication of the designed scaffolds, the generated contours are optimized for a continuous, interconnected, and smooth deposition path-planning. A continuous zig-zag pattern deposition path crossing through the medial region is used for the initial layer and a biarc fitted isoporosity curve is generated for the consecutive layer with C-1 continuity. The proposed methodologies can generate the structure with gradient (linear or non-linear), variational or constant porosity that can provide localized control of variational porosity along the scaffold architecture. The designed porous structures can be fabricated using additive manufacturing processes

Doctor of Philosophy

dissertationOne of the fundamental building blocks of many computational sciences is the construction and use of a discretized, geometric representation of a problem domain, often referred to as a mesh. Such a discretization enables an otherwise complex domain to be represented simply, and computation to be performed over that domain with a finite number of basis elements. As mesh generation techniques have become more sophisticated over the years, focus has largely shifted to quality mesh generation techniques that guarantee or empirically generate numerically well-behaved elements. In this dissertation, the two complementary meshing subproblems of vertex placement and element creation are analyzed, both separately and together. First, a dynamic particle system achieves adaptivity over domains by inferring feature size through a new information passing algorithm. Second, a new tetrahedral algorithm is constructed that carefully combines lattice-based stenciling and mesh warping to produce guaranteed quality meshes on multimaterial volumetric domains. Finally, the ideas of lattice cleaving and dynamic particle systems are merged into a unified framework for producing guaranteed quality, unstructured and adaptive meshing of multimaterial volumetric domains

Automatic rigging and animation of 3D characters

Animating an articulated 3D character currently requires manual rigging to specify its internal skeletal structure and to define how the input motion deforms its surface. We present a method for animating characters automatically. Given a static character mesh and a generic skeleton, our method adapts the skeleton to the character and attaches it to the surface, allowing skeletal motion data to animate the character. Because a single skeleton can be used with a wide range of characters, our method, in conjunction with a library of motions for a few skeletons, enables a user-friendly animation system for novices and children. Our prototype implementation, called Pinocchio, typically takes under a minute to rig a character on a modern midrange PC.Solidworks CorporationNational Science Foundation (U.S.). Graduate Research Fellowshi

Self Assembly Problems of Anisotropic Particles in Soft Matter.

Anisotropic building blocks assembled from colloidal particles are attractive building blocks for self-assembled materials because their complex interactions can be exploited to drive self-assembly. In this dissertation we address the self-assembly of anisotropic particles from multiple novel computational and mathematical angles. First, we accelerate algorithms for modeling systems of anisotropic particles via massively parallel GPUs. We provide a scheme for generating statistically robust pseudo-random numbers that enables GPU acceleration of Brownian and dissipative particle dynamics. We also show how rigid body integration can be accelerated on a GPU. Integrating these two algorithms into a GPU-accelerated molecular dynamics code (HOOMD-blue), make a single GPU the ideal computing environment for modeling the self-assembly of anisotropic nanoparticles. Second, we introduce a new mathematical optimization problem, filling, a hybrid of the familiar shape packing and covering problem, which can be used to model shaped particles. We study the rich mathematical structures of the solution space and provide computational methods for finding optimal solutions for polygons and convex polyhedra. We present a sequence of isosymmetric optimal filling solutions for the Platonic solids. We then consider the filling of a hyper-cone in dimensions two to eight and show the solution remains scale-invariant but dependent on dimension. Third, we study the impact of size variation, polydispersity, on the self-assembly of an anisotropic particle, the polymer-tethered nanosphere, into ordered phases. We show that the local nanoparticle packing motif, icosahedral or crystalline, determines the impact of polydispersity on energy of the system and phase transitions. We show how extensions of the Voronoi tessellation can be calculated and applied to characterize such micro-segregated phases. By applying a Voronoi tessellation, we show that properties of the individual domains can be studied as a function of system properties such as temperature and concentration. Last, we consider the thermodynamically driven self-assembly of terminal clusters of particles. We predict that clusters related to spherical codes, a mathematical sequence of points, can be synthesized via self-assembly. These anisotropic clusters can be tuned to different anisotropies via the ratio of sphere diameters and temperature. The method suggests a rich new way for assembling anisotropic building blocks.Ph.D.Applied Physics and Scientific ComputingUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/91576/1/phillicl_1.pd

A hierarchical anti-Hebbian network model for the formation of spatial cells in three-dimensional space.

Three-dimensional (3D) spatial cells in the mammalian hippocampal formation are believed to support the existence of 3D cognitive maps. Modeling studies are crucial to comprehend the neural principles governing the formation of these maps, yet to date very few have addressed this topic in 3D space. Here we present a hierarchical network model for the formation of 3D spatial cells using anti-Hebbian network. Built on empirical data, the model accounts for the natural emergence of 3D place, border, and grid cells, as well as a new type of previously undescribed spatial cell type which we call plane cells. It further explains the plausible reason behind the place and grid-cell anisotropic coding that has been observed in rodents and the potential discrepancy with the predicted periodic coding during 3D volumetric navigation. Lastly, it provides evidence for the importance of unsupervised learning rules in guiding the formation of higher-dimensional cognitive maps

Model Simplification for Efficient Collision Detection in Robotics

Motion planning for industrial robots is a computationally intensive task due to the massive number of potential motions between any two configurations. Calculating all possibilities is generally not feasible. Instead, many motion planners sample a sub-set of the available space until a viable solution is found. Simplifying models to improve collision detection performance, a significant component of motion planning, results in faster and more capable motion planners. Several approaches for simplifying models to improve collision detection performance have been presented in the literature. However, many of them are sub-optimal for an industrial robotics application due to input model limitations, accuracy sacrifices, or the probability of increasing false negatives during collision queries. This thesis focuses on the development of model simplification approaches optimised for industrial robotics applications. Firstly, a new simplification approach, the Bounding Sphere Simplification (BSS), is presented that converts triangle-mesh inputs to a collection of spheres for efficient collision and distance queries. Additionally, BSS removes small features and generates an output model less prone to false negatives

Statistical Query Complexity of Manifold Estimation

This paper studies the statistical query (SQ) complexity of estimating $d$-dimensional submanifolds in $\mathbb{R}^n$. We propose a purely geometric algorithm called Manifold Propagation, that reduces the problem to three natural geometric routines: projection, tangent space estimation, and point detection. We then provide constructions of these geometric routines in the SQ framework. Given an adversarial $\mathrm{STAT}(\tau)$ oracle and a target Hausdorff distance precision $\varepsilon = \Omega(\tau^{2 / (d + 1)})$, the resulting SQ manifold reconstruction algorithm has query complexity $O(n \operatorname{polylog}(n) \varepsilon^{-d / 2})$, which is proved to be nearly optimal. In the process, we establish low-rank matrix completion results for SQ's and lower bounds for randomized SQ estimators in general metric spaces.Comment: 81 page

Image-Based Pore-Scale Modeling of Inertial Flow in Porous Media and Propped Fractures

Non-Darcy flow is often observed near wellbores and in hydraulic fractures where relatively high velocities occur. Quantifying additional pressure drop caused by non-Darcy flow and fundamentally understanding the pore-scale inertial flow is important to oil and gas production in hydraulic fractures. Image-based pore-scale modeling is a powerful approach to obtain macroscopic transport properties of porous media, which are traditionally obtained from experiments and understand the relationship between fluid dynamics with complex pore geometries. In image-based modeling, flow simulations are conducted based on pore structures of real porous media from X-ray computed tomographic images. Rigorous pore-scale finite element modeling using unstructured mesh is developed and implemented in proppant fractures. The macroscopic parameters permeability and non-Darcy coefficient are obtained from simulations. The inertial effects on microscopic velocity fields are also discussed. The pore-scale network modeling of non-Darcy flow is also developed based on simulation results from rigorous model (FEM). Network modeling is an appealing approach to study porous media. Because of the approximation introduced in both pore structures and fluid dynamics, network modeling requires much smaller computational cost than rigorous model and can increase the computational domain size by orders of magnitude. The network is validated by comparing pore-scale flowrate distribution calculated from network and FEM. Throat flowrates and hydraulic conductance values in pore structures with a range of geometries are compared to assess whether network modeling can capture the shifts in flow pattern due to inertial effects. This provides insights about predicting hydraulic conductance using the tortuosity of flow paths,which is a significant factor for inertial flow as well as other network pore and throat geometric parameters

Entropically driven self-assembly of pear-shaped nanoparticles

This thesis addresses the entropically driven colloidal self-assembly of pear-shaped particle ensembles, including the formation of nanostructures based on triply periodic minimal surfaces, in particular of the Ia3d gyroid. One of the key results is that the formation of the Ia3d gyroid, re-ported earlier in the so-called pear hard Gaussian overlap (PHGO) approximation and confirmed here, is due to a slight non-additivity of that potential; this phase does not form in pears with true hard-core potential. First, we computationally study the PHGO system and present the phase diagram of pears with an aspect ratio of 3 in terms of global density and particle shape (degree of taper), containing gyroid, isotropic, nematic and smectic phases. We confirm that it is adequate to interpret the gyroid as a warped smectic bilayer phase. The collective behaviour to arrange into interdigitated sheets with negative Gauss curvature, from which the gyroid results, is investigated through correlations of (Set-)Voronoi cells and local curvature. This geometric arrangement within the bilayers suggests a fundamentally different stabilisation mechanism of the pear gyroid phase compared to those found in both lipid-water and di-block copolymer systems forming the Ia3d gyroid. The PHGO model is only an approximation for hard-core interactions, and we additionally investigate, by much slower simulations, pear-assemblies with true hard-core interactions (HPR). We find that HPR phase diagram only contains isotropic and nematic phases, but neither gyroid nor smectic phases. To understand this shape sensitivity more profoundly, the depletion interactions of both models are studied in two pear-shaped colloids dissolved in a hard sphere solvent. The HPR particles act as one would expect from a geometric analysis of the excluded-volume minimisation, whereas the PHGO particles show deviations from this expectation. These differences are attributed to the unusual angle dependency of the (non-additive) contact function and, more so, to small overlaps induced by the approximation. For the PHGO model, we further demonstrate that the addition of a small concentration of hard spheres ("solvent") drives the system towards a Pn3m diamond phase. This result is explained by the greater spatial heterogeneity of the diamond geometry compared to the gyroid where additional material is needed to relieve packing frustration. In contrast to copolymer systems, however, the solvent mostly aggregates near the diamond minimal surface, driven by the non-additivity of the PHGO pears. At high solvent concentrations, the mixture phase separates into “inverse” micelle-like structures with the blunt ends at the micellar centres and thin ends pointing out-wards. The micelles themselves spontaneously cluster, indicative of a hierarchical self-assembly process for bicontinuous structures. Finally, we develop a density functional for hard solids of revolution (including pears) within the framework of fundamental measure theory. It is applied to low-density ensembles of pear-shaped particles, where we analyse their response near a hard substrate. A complex orientational ordering close to the wall is predicted, which is directly linked to the particle shape and gives insight into adsorption processes of asymmetric particles. This predicted behaviour and the differences between the PHGO and HPR model are confirmed by MC simulations