Theses and Dissertations at Montana State University (MSU)
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Item Analysis of transport in the brain(Montana State University - Bozeman, College of Engineering, 2021) Ray, Lori Ann; Chairperson, Graduate Committee: Jeffrey Heys; Jeffrey J. Heys was a co-author of the article, 'Fluid flow and mass transport in brain tissue: a literature review' in the journal 'Fluids' which is contained within this dissertation.; Jeffrey J. Iliff and Jeffrey J. Heys were co-authors of the article, 'Analysis of convective and diffusive transport in the brain interstitium' in the journal 'Fluids and barriers of the CNS' which is contained within this dissertation.; Martin Pike, Jeffrey J. Iliff and Jeffrey J. Heys were co-authors of the article, 'Quantification of transport in the whole mouse brain' which is contained within this dissertation.Neurodegeneration is one of the most significant medical challenges facing our time, yet the gap between therapies and understanding of the inner workings of the brain is great. Impairment of waste clearance has been identified as one key underlying factor in the vulnerability of the brain to neurodegeneration, stimulating research towards understanding transport of molecules in the brain. Based on experimental findings, a unique-to-the-brain circulation has been proposed, the glymphatic system, where cerebrospinal fluid surrounding the brain moves into the brain along the periarterial space that surrounds cerebral arteries, flows through the interstitial space between brain cells, where cellular wastes reside, and carries waste out of the brain tissue along perivenous routes. However, current gaps in knowledge about the driving force for fluid flow have generated scientific skepticism, and an independent method for quantifying transport and demonstrating the presence or absence of convection is desirable. In this work, computational transport models are developed and used to analyze published experimental data to determine fundamental transport parameters for different aspects of the glymphatic circulation. Calculated transport parameters are compared to the known diffusivity of tracers through brain tissue to draw conclusions about the presence and significance of bulk flow, or convection. Based on these analyses, transport in the periarterial spaces surrounding major arteries is over 10,000 times faster than diffusion and in brain tissue, containing both periarterial and interstitial space, transport is around 10 times faster than diffusion alone (for characteristic transport lengths around 1 mm). Interstitial velocity is determined to be on the order of 0.01 mm/min, making convection in the interstitial spaces of the brain critical to the transport of large, slow-to-diffuse molecules implicated in neurodegeneration. Convection is demonstrated to be a significant mechanism of transport throughout the brain. Observations and analyses from this work contribute further evidence to a circulatory-like system in the brain with relatively rapid convection along periarterial space, branching throughout the brain tissue and slower convection across that tissue, in the interstitial spaces of the brain. Transport models developed in this work are demonstrated to be useful tools for gleaning further information from experimental data.Item Weighted least-squares finite element methods for PIV data assimilation(Montana State University - Bozeman, College of Engineering, 2011) Wei, Fei; Chairperson, Graduate Committee: Jeffrey HeysThe ability to diagnose irregular flow patterns clinically in the left ventricle (LV) is currently very challenging. One potential approach for non-invasively measuring blood flow dynamics in the LV is particle image velocimetry (PIV) using microbubbles. To obtain local flow velocity vectors and velocity maps, PIV software calculates displacements of microbubbles over a given time interval, which is typically determined by the actual frame rate. In addition to the PIV, ultrasound images of the left ventricle can be used to determine the wall position as a function of time, and the inflow and outflow fluid velocity during the cardiac cycle. Despite the abundance of data, ultrasound and PIV alone are insufficient for calculating the flow properties of interest to clinicians. Specifically, the pressure gradient and total energy loss are of primary importance, but their calculation requires a full three-dimensional velocity field. Echo-PIV only provides 2D velocity data along a single plane within the LV. Further, numerous technical hurdles prevent three-dimensional ultrasound from having a sufficiently high frame rate (currently approximately 10 frames per second) for 3D PIV analysis. Beyond microbubble imaging in the left ventricle, there are a number of other settings where 2D velocity data is available using PIV, but a full 3D velocity field is desired. This thesis develops a novel methodology to assimilate two-dimensional PIV data into a three-dimensional Computational Fluid Dynamics simulation with moving domains. To illustrate and validate our approach, we tested the approach on three different problems: a flap displaced by a fluid jut; an expanding hemisphere; and an expanding half ellipsoid representing the left ventricle of the heart. To account for the changing shape of the domain in each problem, the CFD mesh was deformed using a pseudo-solid domain mapping technique at each time step. The incorporation of experimental PIV data can help to identify when the imposed boundary conditions are incorrect. This approach can also help to capture effects that are not modeled directly like the impacts of heart valves on the flow of blood into the left ventricle.