A Left Ventricular Assist Device (LVAD) is a mechanical pump that provides temporary circulatory support when used as bridge-to-transplantation and relieves workload demand placed on a failing heart allowing for myocardia recovery when used as destination therapy. Stroke is the most devastating complication after ventricular assist device (VAD) implantation, with an incidence of 14-47% over 3-6 months. This complication due to thrombus formation and subsequent transport through the vasculature to cerebral vessels continues to limit the widespread implementation of VAD therapy. Patient-specific computational fluid dynamics (CFD) analysis may elucidate ways to reduce this risk. We employed a multi-scale model of the aortic circulation in order to examine the effects on flow conditions resulting from varying the VAD cannula implantation location and angle of incidence of the anastomosis to the ascending aorta based on a patient-specific geometry obtained from CT scans. The multi-scale computation consists of a 0D lumped parameter model (LPM) of the circulation modeled via a 50 degree of freedom (DOF) electrical circuit analogy that includes an LVAD model coupled to a 3D computational fluid dynamics model of the circulation. An in-house adaptive Runge-Kutta method is utilized to solve the 50 DOF LPM, and the Starccm+ CFD code is utilized to solve the flowfield. This 0D-3D coupling for the flow is accomplished iteratively with the 0D LPM providing the pulsatile boundary conditions that drive the 3D CFD time-accurate computations of the flowfield. Investigated angle configurations include cannula implantations at 30°, 60° and 90° to the right lateral wall of the ascending aorta. We also considered placements of the VAD cannula along the ascending aorta in which distances of the VAD anastomosis is varied relative to the take-off of the innominate artery. We implemented a mixed Eulerian-Lagrangian particle-tracking scheme to quantify the number of stroke-inducing particles reaching cerebral vessel outlets and included flow visualization through streamlines to identify regions of strong vorticity and flow stagnation, which can promote thrombus formation. Thrombi were modeled as spheres with perfectly elastic interactions numerically released randomly in time and space at cannula inlet plane. Based on clinical observation of the range of thrombus sizes encountered in such cases, particle diameters of 2.5mm and 3.5mm were investigated in our numerical computations. Pulsatile flow results for aforementioned angles suggest that a 90° cannula implementation causes flow impingement on the left lateral aortic wall and appears to be highly thrombogenic due to large momentum losses and zones of large re-circulation and that shallow and intermediate cannula angles promote more regular flow carrying particles towards the lower body potentially reducing stroke risk. Indications from this pulsatile numerical study suggest that up to a 50% reduction in stroke rate can be achieve with tailoring of cannula implantation. Results are consistent with significant reduction in stroke incidence achieved by tailoring cannula implantation as reported in previous steady flow computations carried out by our group. As such, results of this study suggest that a simple surgical maneuver in the process of VAD implantation may significantly improve patient life.

yes / Biological hydrogels have been increasingly sought after as wound dressings or scaffolds for regenerative medicine, owing to their inherent biofunctionality in biological environments. Especially in moist wound healing, the ideal material should absorb large amounts of wound exudate while remaining mechanically competent in situ. Despite their large hydration, however, current biological hydrogels still leave much to be desired in terms of mechanical properties in physiological conditions. To address this challenge, a multi-scale approach is presented for the synthetic design of cyto-compatible collagen hydrogels with tunable mechanical properties (from the nano- up to the macro-scale), uniquely high swelling ratios and retained (more than 70%) triple helical features. Type I collagen was covalently functionalized with three different monomers, i.e. 4-vinylbenzyl chloride, glycidyl methacrylate and methacrylic anhydride, respectively. Backbone rigidity, hydrogen-bonding capability and degree of functionalization (F: 16 ± 12–91 ± 7 mol%) of introduced moieties governed the structure–property relationships in resulting collagen networks, so that the swelling ratio (SR: 707 ± 51–1996 ± 182 wt%), bulk compressive modulus (Ec: 30 ± 7–168 ± 40 kPa) and atomic force microscopy elastic modulus (EAFM: 16 ± 2–387 ± 66 kPa) were readily adjusted. Because of their remarkably high swelling and mechanical properties, these tunable collagen hydrogels may be further exploited for the design of advanced dressings for chronic wound care.

Previous experimental and numerical studies focused on incompressible flow interactions with multi-scale fractal structures targeting the generation of turbulence at multiple scales. Depending on various flow conditions, it was found that these fractal structures are able to enhance mixing and scalar transport, and in some cases reduce flow generated sound in certain frequency ranges. The interaction of compressible flows with multi-scale fractal structures, however, did not receive attention as the focus was entirely on the incompressible regime. The objective of this study is to conduct large eddy simulations (LES) of flow interactions with a class of fractal plates in the compressible regime, and to extract and analyze different flow statistics in an attempt to determine the effect of compressibility. Immersed boundary methods (IBM) will be employed to overcome the difficulty of modeling the fractal structures via a bodyitted mesh, with adequate mesh resolution around small features of the fractal shapes.

<p> It is possible to interpret multi-resolution analysis from both Fourier-domain and temporal/spatial domain stand-points. While a Fourier-domain interpretation helps in designing a powerful machinery for multi-resolution refinement on regular point-sets and lattices, most of its techniques cannot be directly generalized to the case of irregular sampling. Therefore, in this thesis we provide a new definition and formulation of multi-resolution refinement, based on a temporal/spatial-domain understanding, that is general enough to allow multi-resolution approximation of different spaces of functions by processing samples (or observations) that can be irregularly distributed or even obtained using different sampling methods. We then continue to provide a construction for designing and implementing classes of refinement schemes in these general settings. The framework for multi-resolution refinement that we discuss includes and extends the existing mathematical machinery for multi-resolution analysis; and the suggested construction unifies many of the schemes currently in use, and, more importantly, allows designing schemes for many new settings. </p> / Thesis / Master of Applied Science (MASc)

In recent years, the prevalence and application of composite materials has exploded. Due to the demands of commercial transportation, the aviation industry has taken a leading role in the integration of composite structures. Among the leading concepts to develop lighter, more fuel-efficient commercial transport is the Pultruded Rod Stitched Efficient Unitized Structure (PRSEUS) concept. The highly integrated structure of PRSEUS allows pressurized, non-circular fuselage designs to be implemented, enabling the feasibility of Hybrid Wing Body (HWB) aircraft. In addition to its unique fabrication process, the through-thickness stitching utilized by PRSEUS overcomes the low post-damage strength present in typical composites. Although many proof-of-concept tests have been performed that demonstrate the potential for PRSEUS, efficient computational tools must be developed before the concept can be commercially certified and implemented. In an attempt to address this need, a comprehensive modeling approach is developed that investigates PRSEUS at multiple scales. The majority of available experiments for comparison have been conducted at the coupon level. Therefore, a computational methodology is progressively developed based on physically realistic concepts without the use of tuning parameters. A thorough verification study is performed to identify the most effective approach to model PRSEUS, including the effect of element type, boundary conditions, bonding properties, and model fidelity. Using the results of this baseline study, a high fidelity stringer model is created at the component scale and validated against the existing experiments. Finally, the validated model is extended to larger scales to compare PRSEUS to the current state-of-the-art. Throughout the current work, the developed methodology is demonstrated to make accurate predictions that are well beyond the capability of existing predictive models. While using commercially available predictive tools, the methodology developed herein can accurately predict local behavior up to and beyond failure for stitched structures such as PRSEUS for the first time. Additionally, by extending the methodology to a large scale fuselage section drop scenario, the dynamic behavior of PRSEUS was investigated for the first time. With the predictive capabilities and unique insight provided, the work herein may serve to benefit future iteration of PRSEUS as well as certification by analysis efforts for future airframe development. / PHD

Automated map generalization is a necessary technique for the construction of multi-scale vector map databases that are crucial components in spatial data infrastructure of cities, provinces, and countries. Nevertheless, this is still a dream because many algorithms for map feature generalization are not parameter-free and therefore need human’s interference. One of the major reasons is that map generalization is a process of spatial similarity transformation in multi-scale map spaces; however, no theory can be found to support such kind of transformation. This thesis focuses on the theory of spatial similarity relations in multi-scale map spaces, aiming at proposing the approaches and models that can be used to automate some relevant algorithms in map generalization. After a systematic review of existing achievements including the definitions and features of similarity in various communities, a classification system of spatial similarity relations, and the calculation models of similarity relations in the communities of psychology, computer science, music, and geography, as well as a number of raster-based approaches for calculating similarity degrees between images, the thesis achieves the following innovative contributions. First, the fundamental issues of spatial similarity relations are explored, i.e. (1) a classification system is proposed that classifies the objects processed by map generalization algorithms into ten categories; (2) the Set Theory-based definitions of similarity, spatial similarity, and spatial similarity relation in multi-scale map spaces are given; (3) mathematical language-based descriptions of the features of spatial similarity relations in multi-scale map spaces are addressed; (4) the factors that affect human’s judgments of spatial similarity relations are proposed, and their weights are also obtained by psychological experiments; and (5) a classification system for spatial similarity relations in multi-scale map spaces is proposed. Second, the models that can calculate spatial similarity degrees for the ten types of objects in multi-scale map spaces are proposed, and their validity is tested by psychological experiments. If a map (or an individual object, or an object group) and its generalized counterpart are given, the models can be used to calculate the spatial similarity degrees between them. Third, the proposed models are used to solve problems in map generalization: (1) ten formulae are constructed that can calculate spatial similarity degrees by map scale changes in map generalization; (2) an approach based on spatial similarity degree is proposed that can determine when to terminate a map generalization system or an algorithm when it is executed to generalize objects on maps, which may fully automate some relevant algorithms and therefore improve the efficiency of map generalization; and (3) an approach is proposed to calculate the distance tolerance of the Douglas-Peucker Algorithm so that the Douglas-Peucker Algorithm may become fully automatic. Nevertheless, the theory and the approaches proposed in this study possess two limitations and needs further exploration. • More experiments should be done to improve the accuracy and adaptability of the proposed models and formulae. The new experiments should select more typical maps and map objects as samples, and find more subjects with different cultural backgrounds. • Whether it is feasible to integrate the ten models/formulae for calculating spatial similarity degrees into an identical model/formula needs further investigation. In addition, it is important to find out the other algorithms, like the Douglas-Peucker Algorithm, that are not parameter-free and closely related to spatial similarity relation, and explore the approaches to calculating the parameters used in these algorithms with the help of the models and formulae proposed in this thesis.

Der transformierende Wachstumsfaktor-β (TGFβ) übt verschiedene Wirkungen auf die Regulierung zahlreicher biologischer Prozesse aus. Insbesondere die zytostatische Wirkung von TGFβ ist wichtig, um die Homöostase in Geweben aufrechtzuerhalten und proliferative Störungen, wie in Krebs, zu verhindern. Frühere Studien zur Regulation des Zellzyklus mit TGFβ wurden auf Populationsebene, oft durch physikalische oder chemische Synchronisation durchgeführt. Dabei wird die Heterogenität auf zellulärer Ebene vernachlässigt und die Anfälligkeit gegen potenzielle Artefakte erhöht. Um zu verstehen, wie einzelne Zellen TGFβ-Signale entschlüsseln und diese in die Entscheidung zur Zellproliferation integrieren, wurden sowohl die Dynamik der TGFβ-Signale als auch die Zellzyklusprogression in asynchronen Zellen durch „Live Cell Imaging“ quantifiziert. In Kombination von experimentellen und theoretischen Studien wurde gezeigt, dass TGFβ einen „Alles-oder-Nichts-G1- Stillstand“ auslöst, der sowohl dosisabhängig als auch phasenabhängig ist. Wenn die Zellen während der S / G2 / M-Phase TGFβ ausgesetzt werden, erfahren sie in der darauf folgenden G1-Phase einen ererbten, verzögerten Stillstand. Zusätzlich sind die Zellen nach einem TGFβ-Stimulationsimpuls für weitere TGFβ-Behandlungen unempfindlich. In Anbetracht der Bedeutung von Einzelzellinformationen und den Herausforderungen bei der automatischen Zellverfolgung wurde ein Rahmenkonzept von „Population to Single Cell“ (P2S-Framework) erarbeitet, um von der Populationsdynamik auf die Abstammung einzelner Zellen zu schließen. Zusammengefasst bietet diese Arbeit neue Einblicke in Strategien zur Kontrolle der Zellproliferation durch Manipulation der TGFβ-Signalgebung. / The transforming growth factor-β (TGFβ) exerts diverse effects on regulating numerous biological processes. Especially, the cytostatic effect of TGFβ is important for maintaining tissue homeostasis and preventing proliferative disorders, like cancer. Previous studies on the regulation of cell cycle by TGFβ were conducted at the population level, and often through physical or chemical synchronization, which neglected cellular heterogeneity and might introduce artifacts. To understand how individual cells decode and integrate TGFβ signals into cell proliferation decisions, we quantitatively characterized both TGFβ signaling dynamics and cell cycle progression in asynchronous cells by live cell imaging. Combining experimental and theoretical studies, we demonstrated that TGFβ triggers all-or-none G1 arrest, which is both dose-dependent and phase- dependent. When exposed to TGFβ during S/G2/M phase, cells undergo an inherited, delayed arrest at the next G1 phase. In addition, after one pulse of TGFβ stimulation, cells are refractory to further TGFβ treatments. Considering the importance of single cell information and challenges in automatic cell tracking, we proposed a Population to Single cell framework (P2S framework) to infer single- cell lineages from population dynamics. Taken together, this work provides new insight into strategies to control cell proliferation by manipulating TGFβ signaling.

Three-dimensional woven composites were developed to improve the through-thickness properties which conventional two-dimensional laminate composites currently lack. However, these textile composites generally show lower in-plane mechanical properties due to fibre crimping, and also encounter modelling difficulties due to the complex geometries. In this thesis, the static and fatigue mechanical behaviour of several types of 3D woven composites were experimentally characterised, the influence of the weave architecture on the mechanical performance was revealed, and meso/macro scale numerical models with improved failure criteria were developed to simulate the tensile behaviour of the 3D woven composites. The mechanical characterisation was conducted on six woven structures under tension, compression, and flexural loading, and were also carried out on two weaves under open-hole quasi-static tensile and fatigue loading. Digital image correlation and thermoelastic stress analysis were used to characterise the strain and damage development during static and fatigue loading. The testing results showed that the angle-interlock weave W-3 had higher in-plane quasi-static properties, lower notch sensitivity, higher fatigue damage resistance, but lower delamination resistance. The meso-scale model was developed on the unit cell of the woven structure and the macro-scale model (mosaic model) was created on the testing samples. Both un-notched and notched tensile behaviour were modelled for the angle-interlock weave W-3 and a one-by-one orthogonal weave W-1, and the difference between the predicted and experimental results was within 16% for the unit cell models and within 21% for the mosaic models. A modified failure criterion was developed to better simulate the damage behaviour of the notched macro-scale model and improved the predicted notched strength by 10-20%. Whilst further experimental investigation and improvement in the modelling techniques are still required, the data presented in this thesis provided an essential update for the current 3D woven composites research, and the presented models offered the potential to predict the damage behaviour of large 3D woven structures.

Inflatable Aerodynamic Decelerators (IADs) are a candidate technology NASA began investigating in the late 1960’s. Compared to supersonic parachutes, IADs represent a decelerator option capable of operating at higher Mach numbers and dynamic pressures. IADs have seen a resurgence in interest from the Entry, Descent, and Landing (EDL) community in recent years. The NASA Space Technology Roadmap (STR) highlights EDL systems, as well as, Materials, Structures, Mechanical Systems, and Manufacturing (MSMM) as key Technology Areas for development in the future; recognizing deployable decelerators, flexible material systems, and computational design of materials as essential disciplines for development. This investigation develops a multi-scale flexible material modeling approach that enables efficient high-fidelity IAD design and a critical understanding of the new materials required for robust and cost effective qualification methods. The approach combines understanding of the fabric architecture, analytical modeling, numerical simulations, and experimental data. This work identifies an efficient method that is as simple and as fast as possible for determining IAD material characteristics while not utilizing complicated or expensive research equipment. This investigation also recontextualizes an existing mesomechanical model through validation for structures pertaining to the analysis of IADs. In addition, corroboration and elaboration of this model is carried out by evaluating the effects of varying input parameters. Finally, the present investigation presents a novel method for numerically determining mechanical properties. A sub-scale section that captures the periodic pattern in the material (unit cell) is built. With the unit cell, various numerical tests are performed. The effective nonlinear mechanical stiffness matrix is obtained as a function of elemental strains through correlating the unit cell force-displacement results with a four node membrane element of the same size. Numerically determined properties are validated for relevant structures. Optical microscopy is used to capture the undeformed geometry of the individual yarns.

Novel integral-equation methods for efficiently solving electromagnetic problems that involve more than a single length scale of interest in complex backgrounds are presented. Such multi-scale electromagnetic problems arise because of the interplay of two distinct factors: the structure under study and the background medium. Both can contain material properties (wavelengths/skin depths) and geometrical features at different length scales, which gives rise to four types of multi-scale problems: (1) twoscale, (2) multi-scale structure, (3) multi-scale background, and (4) multi-scale-squared problems, where a single-scale structure resides in a different single-scale background, a multi-scale structure resides in a single-scale background, a single-scale structure resides in a multi-scale background, and a multi-scale structure resides in a multi-scale background, respectively. Electromagnetic problems can be further categorized in terms of the relative values of the length scales that characterize the structure and the background medium as (a) high-frequency, (b) low-frequency, and (c) mixed-frequency problems, where the wavelengths/skin depths in the background medium, the structure’s geometrical features or internal wavelengths/skin depths, and a combination of these three factors dictate the field variations on/in the structure, respectively. This dissertation presents several problems arising from geophysical exploration and microwave chemistry that demonstrate the different types of multi-scale problems encountered in electromagnetic analysis and the computational challenges they pose. It also presents novel frequency-domain integral-equation methods with proper Green function kernels for solving these multi-scale problems. These methods avoid meshing the background medium and finding fields in an extended computational domain outside the structure, thereby resolving important complications encountered in type 3 and 4 multi-scale problems that limit alternative methods. Nevertheless, they have been of limited practical use because of their high computational costs and because most of the existing ‘fast integral-equation algorithms’ are not applicable to complex Green function kernels. This dissertation introduces novel FFT, multigrid, and FFT-truncated multigrid algorithms that reduce the computational costs of frequency-domain integral-equation methods for complex backgrounds and enable the solution of unprecedented type 3 and 4 multi-scale problems. The proposed algorithms are formulated in detail, their computational costs are analyzed theoretically, and their features are demonstrated by solving benchmark and challenging multi-scale problems. / text