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- All Subjects: Applied Mathematics
Description
The retina is the lining in the back of the eye responsible for vision. When light photons hits the retina, the photoreceptors within the retina respond by sending impulses to the optic nerve, which connects to the brain. If there is injury to the eye or heredity retinal problems, this part can become detached. Detachment leads to loss of nutrients, such as oxygen and glucose, to the cells in the eye and causes cell death. Sometimes the retina is able to be surgically reattached. If the photoreceptor cells have not died and the reattachment is successful, then these cells are able to regenerate their outer segments (OS) which are essential for their functionality and vitality. In this work we will explore how the regrowth of the photoreceptor cells in a healthy eye after retinal detachment can lead to a deeper understanding of how eye cells take up nutrients and regenerate. This work uses a mathematical model for a healthy eye in conjunction with data for photoreceptors' regrowth and decay. The parameters for the healthy eye model are estimated from the data and the ranges of these parameter values are centered +/- 10\% away from these values are used for sensitivity analysis. Using parameter estimation and sensitivity analysis we can better understand how certain processes represented by these parameters change within the model as a result of retinal detachment. Having a deeper understanding for any sort of photoreceptor death and growth can be used by the greater scientific community to help with these currently irreversible conditions that lead to blindness, such as retinal detachment. The analysis in this work shows that maximizing the carrying capacity of the trophic pool and the rate of RDCVF, as well as minimizing nutrient withdrawal of the rods and the cones from the trophic pool results in both the most regrowth and least cell death in retinal detachment.
ContributorsGoldman, Miriam Ayla (Author) / Camacho, Erikia (Thesis director) / Wirkus, Stephen (Committee member) / School of Mathematical and Natural Sciences (Contributor, Contributor) / Barrett, The Honors College (Contributor)
Created2017-05
Description
Cancer, a disease which affects many lives, has been the topic of interest for this research. Treatment options are often available to help lessen the effects of the disease and in regards to cutaneous T-cell lymphoma (CTCL), no cure currently exists. An FDA approved drug by the name of Bexarotene has been developed to provide chemotherapeutic effects within CTCL. Bexarotene has also been used in trials of breast cancer, lung cancer, glioblastoma multiforme and various neurodegenerative diseases. Yet the medication often causes serious side effects including hyperthyroidism, raised triglyceride levels and cutaneous toxicity. The focus of this research is to synthesize a hydroxylated analog compound of Bexarotene in efforts to produce a molecule that provides better chemotherapeutic effects while also lessening the various side effects caused. Synthesis of the molecule followed various organic chemistry techniques and reactions to create the final product. Melting point analysis, NMR and other various characterization data helped to confirm the synthesis of the intended molecule. Preliminary bioassay data results of the analog compound showed similar potency to that of Bexarotene. Further testing, however, will be required to determine the full pharmacokinetic profile of the molecule. Future direction of the research focuses on both further testing of the hydroxylated analog as well synthesizing newer analog compounds to find a molecule that can provide the best effects within cutaneous T-cell lymphoma and the various other diseases as well.
ContributorsMinasian, Ani Christina (Author) / Wagner, Carl (Thesis director) / Marshall, Pamela (Committee member) / School of Social and Behavioral Sciences (Contributor) / School of Mathematical and Natural Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05
Description
This project aims to propose a novel approach for visualizing 4D geometry through the utilization of augmented reality (AR). While previous work has explored virtual reality (VR) as a means to bring 4D objects into a 3D environment, as well as 2D projections to display 4D geometry on screens, this project seeks to extend the possibilities by leveraging the immersive nature of AR technology. By overlaying virtual 4D objects onto the real world, users can experience a more tangible representation and gain a deeper understanding of the complex structures present in higher dimensions.
ContributorsHum, Aaron (Author) / Nishimura, Joel (Thesis director) / Wang, Haiyan (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Natural Sciences (Contributor)
Created2023-05
ContributorsHum, Aaron (Author) / Nishimura, Joel (Thesis director) / Wang, Haiyan (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Natural Sciences (Contributor)
Created2023-05
Description
This project aims to propose a novel approach for visualizing 4D geometry through the utilization of augmented reality (AR). While previous work has explored virtual reality (VR) as a means to bring 4D objects into a 3D environment, as well as 2D projections to display 4D geometry on screens, this project seeks to extend the possibilities by leveraging the immersive nature of AR technology. By overlaying virtual 4D objects onto the real world, users can experience a more tangible representation and gain a deeper understanding of the complex structures present in higher dimensions.
ContributorsHum, Aaron (Author) / Nishimura, Joel (Thesis director) / Wang, Haiyan (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Natural Sciences (Contributor)
Created2023-05
Description
The ever-increasing importance of cancer and neurodegenerative diseases continues to grow as populations across the world are affected by death and aging. The vitamin A (RXR) and vitamin D (VDR) receptor pathways offer promising potential to aid in treatment of cancer and Alzheimer’s disease. This thesis discusses the potential application of novel analogs of Bexarotene (RXR agonist), MeTC7 (a new potent VDR antagonist), and vitamin D as possible therapeutics for cancer and Alzheimer’s disease.
ContributorsHong, Jennifer (Author) / Jurutka, Peter (Thesis director) / Wagner, Carl (Committee member) / Marshall, Pamela (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Natural Sciences (Contributor)
Created2023-05
Description
Bexarotene is a synthetic analog of 9-cis-retinoic acid and ligand for the retinoid X receptor which has a history of clinical success in the treatment of T-cell lymphoma. Bexarotene has also shown potential for treating a variety of other cancers, which we seek to explore in this project. The potential of bexarotene lies in its unique mechanisms and wide application, however, it has shown limited effectiveness thus far in the treatment of breast and lung cancer, with moderate levels of efficacy and symptoms such as cutaneous toxicity, hyperlipidemia, and hypothyroidism. For this project several analogs of bexarotene were synthesized with the intentions of making a more potent ligand that can be used to treat these carcinomas while minimizing harmful side effects. We were successful in synthesizing a large variety of analogs over the span of roughly two years, including iso-chroman derivatives of bexarotene and NEt-TMN, in addition to a new series of analogs of the reported NEt-TMN derivative. These analogs were analyzed via melting point determination and nuclear magnetic resonance (NMR) spectroscopy to confirm the molecular structure and determine purity, and it is our intent to continue with further testing of these compounds to determine their effectiveness as well as the side effects they are likely to cause with levels of toxicity. Recent studies suggest that continuing the analysis of these compounds and other rexinoids like the ones described herein is a worthwhile endeavor as similar rexinoids have shown in numerous assays to be more potent and less toxic in the treatment of cancers when compared with bexarotene.
ContributorsMoen, Grant Anthony (Author) / Wagner, Carl (Thesis director) / Deutch, Charles (Committee member) / School of Social and Behavioral Sciences (Contributor) / School of Mathematical and Natural Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2019-05