published_or_final_version / abstract / Surgery / Doctoral / Doctor of Philosophy

published_or_final_version / Dentistry / Master / Master of Orthodontics

published_or_final_version / Dentistry / Master / Master of Orthodontics

published_or_final_version / abstract / Mechanical Engineering / Master / Master of Philosophy

published_or_final_version / Biochemistry / Doctoral / Doctor of Philosophy

Promising strategies for treating diseases and conditions like cancer, tissue necrosis from injury, congenital abnormalities, etc., involve replacing pathologic tissue with healthy tissue. Strategies devoted to the development of tissue to restore, maintain, or improve function is called tissue engineering. Engineering tissue requires three components, cells that can proliferate to form tissue, a microenvironment that nourishes the cells, and a tissue scaffold that provides mechanical stability, controls tissue architecture, and aids in mimicking the cell’s natural extracellular matrix (ECM). Currently, there is much focus on designing scaffolds that recapitulate the topology of cells’ ECM, in vivo, which undoubtedly wields structures with nanoscale dimensions. Although it is widely thought that sub-microscale features in the ECM have the greatest vii impact on cell behavior relative to larger structures, interactions between cells and nanostructures surfaces is not well understood. There have been few comprehensive studies elucidating the effects of both feature dimension and geometry on the initial formation and growth of the axons of individual neurons. Reconnecting the axons of neurons in damaged nerves is vital in restoring function. Understanding how neurons react with nanopatterned surfaces will advance development of optimal biomaterials used for reconnecting neural networks Here, we investigated the effects of micro- and nanostructures of various sizes and shape on neurons at the single cell level. Compulsory to studying interactions between cells and sub-cellular structures is having nanofabrication technologies that enable biomaterials to be patterned at the nanoscale. We also present a novel nanofabrication process, coined Flash Imprint Lithography using a Mask Aligner (FILM), used to pattern nanofeatures in UV-curable biomaterials for tissue engineering applications. Using FILM, we were able to pattern 50 nm lines in polyethylene glycol (PEG). We later used FILM to pattern nanowells in PEG to study the effect of the nanowells on the behavior preadipocytes (PAs). Results of our cell experiments with neurons and PAs suggested that incorporating micro- and nanoscale topography on biomaterial surfaces may enhance biomaterials’ ability to constrain cell development. Moreover, we found the FILM process to be a useful fabrication tool for tissue engineering applications. / text

Signal and image processing is important in a wide range of areas, including medical and astronomical imaging, and speech and acoustic signal processing. There is often a need for the reconstruction of these objects to be very fast, as they have some cost (perhaps a monetary cost, although often it is a time cost) attached to them. This work considers the development of algorithms that allow these signals and images to be reconstructed quickly and without perceptual quality loss. The main problem considered here is that of reducing the amount of time needed for images to be reconstructed, by decreasing the amount of data necessary for a high quality image to be produced. In addressing this problem two basic ideas are considered. The first is a subset selection problem where the aim is to extract a subset of data, of a predetermined size, from a much larger data set. To do this we first need some metric with which to measure how `good' (or how close to `best') a data subset is. Then, using this metric, we seek an algorithm that selects an appropriate data subset from which an accurate image can be reconstructed. Current algorithms use a criterion based upon the trace of a matrix. In this work we derive a simpler criterion based upon the determinant of a matrix. We construct two new algorithms based upon this new criterion and provide numerical results to demonstrate their accuracy and efficiency. A row exchange strategy is also described, which takes a given subset and performs interchanges to improve the quality of the selected subset. The second idea is, given a reduced set of data, how can we quickly reconstruct an accurate signal or image? Compressed sensing provides a mathematical framework that explains that if a signal or image is known to be sparse relative to some basis, then it may be accurately reconstructed from a reduced set of data measurements. The reconstruction process can be posed as a convex optimization problem. We introduce an algorithm that aims to solve the corresponding problem and accurately reconstruct the desired signal or image. The algorithm is based upon the Barzilai-Borwein algorithm and tailored specifically to the compressed sensing framework. Numerical experiments show that the algorithm is competitive with currently used algorithms. Following the success of compressed sensing for sparse signal reconstruction, we consider whether it is possible to reconstruct other signals with certain structures from reduced data sets. Specifically, signals that are a combination of a piecewise constant part and a sparse component are considered. A reconstruction process for signals of this type is detailed and numerical results are presented.

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