The microvasculature has the main function of transport of dissolved gases, nutrients and waste between blood and tissue. Systematically probing transvascular transport rates in these vessels under well defined conditions is challenging. In vivo and in vitro studies are characterized, respectively, by limited optical access and control over perfusion concentrations and failure to resemble the structure and function of an intact organ. In this thesis, I present the development of a microfluidic platform for investigating molecular transport across mouse mesenteric arteries (150-300μm diameter) in a controlled physico-chemical microenvironment. Intact vessels are perfused with 4 kDa FITC-Dextran and the permeation coefficient of this molecule across the vessel wall is quantified using laser scanning confocal microscopy paired with a 2-D numerical model. Functional viability of the examined vessel, through phenylephrine and acetylcholine dose responses, is probed, and shear and phototoxic effects are reported.

The microvasculature has the main function of transport of dissolved gases, nutrients and waste between blood and tissue. Systematically probing transvascular transport rates in these vessels under well defined conditions is challenging. In vivo and in vitro studies are characterized, respectively, by limited optical access and control over perfusion concentrations and failure to resemble the structure and function of an intact organ. In this thesis, I present the development of a microfluidic platform for investigating molecular transport across mouse mesenteric arteries (150-300μm diameter) in a controlled physico-chemical microenvironment. Intact vessels are perfused with 4 kDa FITC-Dextran and the permeation coefficient of this molecule across the vessel wall is quantified using laser scanning confocal microscopy paired with a 2-D numerical model. Functional viability of the examined vessel, through phenylephrine and acetylcholine dose responses, is probed, and shear and phototoxic effects are reported.

Characterization of semi-permeable films promotes the systematic selection of membranes and process design. When acquiring the diffusive and sorption properties of gas transport in non-porous membranes, the time lag method is considered the conventional method of characterization. The time lag method involves monitoring the transient accumulation of species due to permeation on a fixed volume present in a downstream reservoir. In the thesis at hand, an alternative approach to the time lag technique is proposed, termed as the short cut method. The short cut method appoints the use of a two reservoir system, where the species decay in the upstream face of the membrane is monitored, in combination with the accumulation on the downstream end. The early and short time determination of membrane properties is done by monitoring the inflow and outflow flux profiles, including their respective analytical formulas. The newly proposed method was revealed to have estimated the properties at 1/10 the required time it takes for the classical time lag method, which also includes a better abidance to the required boundary conditions. A novel design of the upstream reservoir, consisting of a reference and working volume, is revealed, which includes instructional use, and the mechanics involved with its operation. Transient pressure decay profiles are successfully obtained when the reference and working volumes consisted of only tubing. However when tanks were included in the volumes, large errors in the decay were observed, in particular due to a non-instantaneous equilibration of the pressure during the start up. This hypothesis was further re-enforced by examining different upstream tank-based configurations. iii In the end, a validated numerical model was constructed for the purpose of simulating the two reservoir gas permeation system. A modified form of the finite differences scheme is utilized, in order to account for a concentration-dependent diffusivity of penetrants within the membrane. Permeation behavior in a composite membrane system was disclosed, which provided a new perspective in analyzing the errors associated with the practical aspect of the system.

Under consideration is the finite-size scaling of two thermomechanical responses of random heterogeneous materials. Stochastic mechanics is applied here to the modeling of heterogeneous materials in order to construct the constitutive relations. Such relations (e.g. Hooke's Law in elasticity or Fourier's Law in heat transfer) are well-established under spatial homogeneity assumption of continuum mechanics, where the Representative Volume Element (RVE) is the fundamental concept. The key question is what is the size L of RVE? According to the separation of scales assumption, L must be bounded according to d<L<<LMacro where d is the microscale (or average size of heterogeneity), and LMacro is the macroscale of a continuum mechanics problem. Statistically, for spatially ergodic heterogeneous materials, when the mesoscale is equal to or bigger than the scale of the RVE, the elements of the material can be considered homogenized. In order to attain the said homogenization, two conditions must be satisfied: (a) the microstructure's statistics must be spatially homogeneous and ergodic; and (b) the material's effective constitutive response must be the same under uniform boundary conditions of essential (Dirichlet) and natural (Neumann) types. / In the first part of this work, the finite-size scaling trend to RVE of the Darcy law for Stokesian flow is studied for the case of random porous media, without invoking any periodic structure assumptions, but only assuming the microstructure's statistics to be spatially homogeneous and ergodic. By analogy to the existing methodology in thermomechanics of solid random media, the Hill-Mandel condition for the Darcy flow velocity and pressure gradient fields was first formulated. Under uniform essential and natural boundary conditions, two variational principles are developed based on minimum potential energy and complementary energy. Then, the partitioning method was applied, leading to scale dependent hierarchies on effective (RVE level) permeability. The proof shows that the ensemble average of permeability has an upper bound under essential boundary conditions and a lower bound under uniform natural boundary conditions. / To quantitatively assess the scaling convergence towards the RVE, these hierarchical trends were numerically obtained for various porosities of random disk systems, where the disk centers were generated by a planar Poisson process with inhibition. Overall, the results showed that the higher the density of random disks---or, equivalently, the narrower the micro-channels in the system---the smaller the size of RVE pertaining to the Darcy law. / In the second part of this work, the finite-size scaling of effective thermoelastic properties of random microstructures were considered from Statistical to Representative Volume Element (RVE). Similarly, under the assumption that the microstructure's statistics are spatially homogeneous and ergodic, the SVE is set-up on a mesoscale, i.e. any scale finite relative to the microstructural length scale. The Hill condition generalized to thermoelasticity dictates uniform essential and natural boundary conditions, which, with the help of two variational principles, led to scale dependent hierarchies of mesoscale bounds on effective (RVE level) properties: thermal expansion strain coefficient and stress coefficient, effective stiffness, and specific heats. Due to the presence of a non-quadratic term in the energy formulas, the mesoscale bounds for the thermal expansion are more complicated than those for the stiffness tensor and the heat capacity. To quantitatively assess the scaling trend towards the RVE, the hierarchies are computed for a planar matrix-inclusion composite, with inclusions (of circular disk shape) located at points of a planar, hard-core Poisson point field. Overall, while the RVE is attained exactly on scales infinitely large relative to microscale, depending on the microstructural parameters, the random fluctuations in the SVE response become very weak on scales an order of magnitude larger than the microscale, thus already approximating the RVE. / Based on the above studies, further work on homogenization of heterogeneous materials is outlined at the end of the thesis. / Keywords: Representative Volume Element (RVE), heterogeneous media, permeability, thermal expansion, mesoscale, microstructure.

Characterization of carbonate reservoirs by flow units is a practical way of reservoir zonation. This study represents a petrophysical-based method that uses well loggings and core plug data to delineate flow units within the most productive carbonate reservoir of Derdere Formation in Y field, Southeast Turkey. Derdere Formation is composed of limestones and dolomites. Logs from the 5 wells are the starting point for the reservoir characterization. The general geologic framework obtained from the logs point out for discriminations within the formation. 58 representative core plug data from 4 different wells are utilized to better understand the petrophysical framework of the formation. The plots correlating petrophysical parameters and the frequency histograms suggest the presence of distinctive reservoir trends. These discriminations are also represented in Winland porosity-permeability crossplots resulted in clusters for different port-sizes that are responsible for different flow characteristics. Although the correlation between core plug porosity and air permeability yields a good correlation coefficient, the formation has to be studied within units due to differences in port-sizes and reservoir process speed. Linear regression and multiple regression analyses are used for the study of each unit. The results are performed using STATGRAPH Version Plus 5.1 statistical software. The permeability models are constructed and their reliabilities are compared by the regression coefficients for predictions in un-cored sections. As a result of this study, 4 different units are determined in the Derdere Formation by using well logging data, and core plug analyses with the help of geostatistical methods. The predicted permeabilities for each unit show good correlations with the calculated ones from core plugs. Highly reliable future estimations can be based on the derived methods.

In the history of a reservoir, after the period of primary production, about 30 to 40%, of the original oil in place may be produced using a secondary recovery mechanism. Polymer injection, which is classified as a tertiary method, can be applied to the remaining oil in place. In this thesis, oil/water relative permeabilities, effect of polymer injection on end point relative permeabilities and residual oil saturations in heterogeneous carbonate reservoirs were investigated. Numereous core flood experiments were conducted on different heteroegneous carbonate cores taken from Midyat Formation. Before starting the displacement experiments, porosity, permeability and capillary pressure experiments were performed. The heterogeneity of the cores are depicted from thin sections. Besides the main aim stated above, effect of flow rate and fracture presence on end point relative permeability and on residual oil saturation and were investigated. According to the results of the displacement tests, end point hexane relative permeability increased when polymer solution was used as the displacing phase.Besides, end point hexane relative permeability increased with polymer injection and fracture presence.

Urbanization is viewed as a major threat to global biodiversity because of its role in the loss and fragmentation of low-lying, productive habitats associated with coastal plains and river valleys. My study examines the effects of urbanization on the movements and distribution of songbirds in Calgary, Alberta, Canada. I conducted playback and translocation experiments to assess the permeability of small-scale (e.g. transportation corridors, rivers) and large-scale (e.g. multi-lane expressways, areas of urban development) features of the urban landscape, respectively. I then used these empirical data to parameterize spatially explicit models and determine functional landscape connectivity across the study area. Finally, using point surveys conducted at 183 sites across the urban matrix, I examined the role of land cover type, local vegetation characteristics, landscape-level forest cover, and isolation from natural features on the distribution of songbirds. In 563 playback trials involving the responses of 2241 birds, I found that the size of the gap in vegetation was the most important determinant of movement across linear features; the likelihood of movement sharply decreasing as the gap in vegetation exceeded 30 m. The results of 176 translocation trials provided further evidence of the barrier effect of gaps. Multiple gaps, in particular, constrained the movements of both yellow warblers (Dendroica petechia) and black-capped chickadees (Poecile atricapillus). The bird surveys revealed that natural forest stands played a critical role in sustaining regional avian diversity in the study area. Moreover, functional distance to the nearest forested natural area or water body often explained more variation in the probability of occurrence of focal species than straight-line distance, suggesting that barriers identified from the permeability experiments may have affected not only the movements of songbirds but their settlement patterns as well. Taken together, my results suggest that preserving a functionally connected network of natural areas is vital to conserving avian biodiversity in cities. My research describes novel methodologies for characterizing the composition and configuration of highly heterogeneous and fragmented landscapes. It also provides a unique examination of the link between the movement behaviour of individual birds and population-level distribution patterns within this context. / Ecology

Long-term storage of tissue by cryopreservation is necessary for the efficient mass production of tissue engineered products, and for reducing the urgency and cost of organ transplantation procedures. The goal of this work was to investigate the physical processes thought result in damage during tissue cryopreservation towards development of tissue cryopreservation strategies. Although mathematical models of cell dehydration and intracellular ice formation (IIF) have been successfully used to optimize cryopreservation procedures for cell suspensions, it is not currently possible to use this approach with tissue because of the lack of tissue-specific permeability parameters for predicting cell dehydration during tissue freezing, and because of the increased complexity of the IIF process in tissue. We have measured the membrane permeability properties of tissue comprising a cell monolayer using a fluorescence quenching technique, and compared the results to the corresponding cell suspensions, revealing significant differences in the membrane transport kinetics between monolayers and suspensions. These data enabled the prediction cell dehydration during freezing of cell monolayers. Whereas the mechanisms of IIF are relatively well understood in cell suspensions, tissue is susceptible to new IIF mechanisms. In particular, cell-cell interactions have been shown to increase the IIF probability by enabling the propagation of ice between neighboring cells. We investigated the effect of cell-cell interactions on IIF using genetically modified cells expressing different levels of intercellular junction proteins. A new IIF mechanism was observed in these cells associated with penetration of extracellular ice into the cell-cell interface, and the incidence of this IIF mechanism was reduced in cells expressing the tight junction protein occludin. In addition, we investigated the effect of the cytoplasm supercooling and viscosity on the kinetics of IIF in tissue. We found that increasing the viscosity or decreasing the supercooling significantly decreased the kinetics of IIF, suggesting that IIF protocols for tissue can be optimized by modulating the cytoplasm supercooling and viscosity. Together, these data represent an important step towards developing cryopreservation strategies for tissue.

In this dissertation, we develop multiscale finite element methods and uncertainty quantification technique for Richards' equation, a mathematical model to describe fluid flow in unsaturated porous media. Both coarse-level and fine-level numerical computation techniques are presented. To develop an accurate coarse-scale numerical method, we need to construct an effective multiscale map that is able to capture the multiscale features of the large-scale solution without resolving the small scale details. With a careful choice of the coarse spaces for multiscale finite element methods, we can significantly reduce errors. We introduce several methods to construct coarse spaces for multiscale finite element methods. A coarse space based on local spectral problems is also presented. The construction of coarse spaces begins with an initial choice of multiscale basis functions supported in coarse regions. These basis functions are complemented using weighted local spectral eigenfunctions. These newly constructed basis functions can capture the small scale features of the solution within a coarse-grid block and give us an accurate coarse-scale solution. However, it is expensive to compute the local basis functions for each parameter value for a nonlinear equation. To overcome this difficulty, local reduced basis method is discussed, which provides smaller dimension spaces with which to compute the basis functions. Robust solution techniques for Richards' equation at a fine scale are discussed. We construct iterative solvers for Richards' equation, whose number of iterations is independent of the contrast. We employ two-level domain decomposition pre-conditioners to solve linear systems arising in approximation of problems with high contrast. We show that, by using the local spectral coarse space for the preconditioners, the number of iterations for these solvers is independent of the physical properties of the media. Several numerical experiments are given to support the theoretical results. Last, we present numerical methods for uncertainty quantification applications for Richards' equation. Numerical methods combined with stochastic solution techniques are proposed to sample conductivities of porous media given in integrated data. Our proposed algorithm is based on upscaling techniques and the Markov chain Monte Carlo method. Sampling results are presented to prove the efficiency and accuracy of our algorithm.

Articular cartilage is the translucent, heterogeneous three-component biological load processing gel that overlays the end of the articulating bones of mammalian joints. Normally, healthy intact articular cartilage performs two biomechanical functions very effectively. These are (i) redistribution of stresses due to loads acting on the joint; (ii) act as a near-frictionless interface between contacting bone ends. These principal functions are enabled by its highly elastic properties. Under normal physiological conditions, these essential biomechanical functions are provided over the lifetime of a mammalian joint with little or no degenerative changes. However, certain levels of physiological and traumatic loads and degenerative processes induced by activities such as running, walking, extreme sport, and aging can alter the composition and structure of the tissue, leading to changes in its biomechanical properties. This, inturn, influences its functional characteristics. The most common degenerative change in articular cartilage is osteoarthritis and the management and treatment of this disease is pivotal to all research targeted toward articular cartilage. Several scientific groups around the world have developed models of articular cartilage to predict its fundamental and functional responses to load and altered biochemical conditions through both in vivo and in vitro studies. The most predominant of these models are the biphasic and triphasic models, which are based on the conceptualisation of articular cartilage as a dispersed mixture of its three main components namely collagen fibrils proteoglycan aggregates and water. The triphasic model is an extension of the biphasic model and incorporates swelling as a separate identifiable component of the tissue's biomechanical response. While these models are capable of predicting the elastic and viscoelastic behaviour and certain aspects of the swelling characteristics of articular cartilage, they are incapable of accounting for its short-term responses where the fluid component is the main carrier of the applied pressure. The hydrostatic and swelling components of the fluid content determine the manner of stress-sharing and hence transient load processing within the matrix as stress is transmitted to the underlying structure. Furthermore, the understanding of the nature of this stress-sharing between fluid and solid components of the tissue is fundamental to the comprehension of the nature of degeneration and its biomechanical consequence in the function of the articulating joint. The inability of the biphasic and triphasic theories to predict, in accordance with experimental results, the transient behaviour of the loaded matrix fluid requires a more representative model. This imperative therefore forms the basis for the research work presented in this thesis. In this thesis, a new mathematical model of articular cartilage load carriage is presented which can predict the transient load-induced responses. The model is based on a continuum framework invoking the principle of mechanical consolidation of fluid-saturated, swollen porous elastic materials. The cartilage matrix is conceptualised as a heterogeneous anisotropic fluid-saturated porous material in which its solid component responds to load as a hyperelastic material and whose interaction with the swelling component produces a partially distributed time-varying permeability. In accordance with the principle of consolidation, a phenomenological approach is adopted for developing both analogue/engineering models and mathematical models for the tissue. The models are then used to predict both bulk matrix responses and the properties of the hypothetical layers of the tissue when subjected to physiological loading conditions. Ultimately, the generalized mathematical model is used to analyse the effect of superficial layer laceration on the stress-processing or stress-sharing characteristic of normal healthy articular cartilage. Finally, predicted results are shown to compare with experimental data demonstrating that the new models for swelling deformation, the hyperelastic law for solid skeletal structure and the distributed, time-dependent permeability are representative of the articular cartilage.