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Description
Glioblastoma multiforme (GBM) is a malignant, aggressive and infiltrative cancer of the central nervous system with a median survival of 14.6 months with standard care. Diagnosis of GBM is made using medical imaging such as magnetic resonance imaging (MRI) or computed tomography (CT). Treatment is informed by medical images and includes chemotherapy, radiation therapy, and surgical removal if the tumor is surgically accessible. Treatment seldom results in a significant increase in longevity, partly due to the lack of precise information regarding tumor size and location. This lack of information arises from the physical limitations of MR and CT imaging coupled with the diffusive nature of glioblastoma tumors. GBM tumor cells can migrate far beyond the visible boundaries of the tumor and will result in a recurring tumor if not killed or removed. Since medical images are the only readily available information about the tumor, we aim to improve mathematical models of tumor growth to better estimate the missing information. Particularly, we investigate the effect of random variation in tumor cell behavior (anisotropy) using stochastic parameterizations of an established proliferation-diffusion model of tumor growth. To evaluate the performance of our mathematical model, we use MR images from an animal model consisting of Murine GL261 tumors implanted in immunocompetent mice, which provides consistency in tumor initiation and location, immune response, genetic variation, and treatment. Compared to non-stochastic simulations, stochastic simulations showed improved volume accuracy when proliferation variability was high, but diffusion variability was found to only marginally affect tumor volume estimates. Neither proliferation nor diffusion variability significantly affected the spatial distribution accuracy of the simulations. While certain cases of stochastic parameterizations improved volume accuracy, they failed to significantly improve simulation accuracy overall. Both the non-stochastic and stochastic simulations failed to achieve over 75% spatial distribution accuracy, suggesting that the underlying structure of the model fails to capture one or more biological processes that affect tumor growth. Two biological features that are candidates for further investigation are angiogenesis and anisotropy resulting from differences between white and gray matter. Time-dependent proliferation and diffusion terms could be introduced to model angiogenesis, and diffusion weighed imaging (DTI) could be used to differentiate between white and gray matter, which might allow for improved estimates brain anisotropy.
ContributorsAnderies, Barrett James (Author) / Kostelich, Eric (Thesis director) / Kuang, Yang (Committee member) / Stepien, Tracy (Committee member) / Harrington Bioengineering Program (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05
Description
Aberrant glycosylation has been shown to be linked to specific cancers, and using this idea, it was proposed that the levels of glycans in the blood could predict stage I adenocarcinoma. To track this glycosylation, glycan were broken down into glycan nodes via methylation analysis. This analysis utilized information from N-, O-, and lipid linked glycans detected from gas chromatography-mass spectrometry. The resulting glycan node-ratios represent the initial quantitative data that were used in this experiment.
For this experiment, two Sets of 50 µl blood plasma samples were provided by NYU Medical School. These samples were then analyzed by Dr. Borges’s lab so that they contained normalized biomarker levels from patients with stage 1 adenocarcinoma and control patients with matched age, smoking status, and gender were examined. An ROC curve was constructed under individual and paired conditions and AUC calculated in Wolfram Mathematica 10.2. Methods such as increasing size of training set, using hard vs. soft margins, and processing biomarkers together and individually were used in order to increase the AUC. Using a soft margin for this particular data set was proved to be most useful compared to the initial set hard margin, raising the AUC from 0.6013 to 0.6585. In regards to which biomarkers yielded the better value, 6-Glc/6-Man and 3,6-Gal glycan node ratios had the best with 0.7687 AUC and a sensitivity of .7684 and specificity of .6051. While this is not enough accuracy to become a primary diagnostic tool for diagnosing stage I adenocarcinoma, the methods examined in the paper should be evaluated further. . By comparison, the current clinical standard blood test for prostate cancer that has an AUC of only 0.67.
For this experiment, two Sets of 50 µl blood plasma samples were provided by NYU Medical School. These samples were then analyzed by Dr. Borges’s lab so that they contained normalized biomarker levels from patients with stage 1 adenocarcinoma and control patients with matched age, smoking status, and gender were examined. An ROC curve was constructed under individual and paired conditions and AUC calculated in Wolfram Mathematica 10.2. Methods such as increasing size of training set, using hard vs. soft margins, and processing biomarkers together and individually were used in order to increase the AUC. Using a soft margin for this particular data set was proved to be most useful compared to the initial set hard margin, raising the AUC from 0.6013 to 0.6585. In regards to which biomarkers yielded the better value, 6-Glc/6-Man and 3,6-Gal glycan node ratios had the best with 0.7687 AUC and a sensitivity of .7684 and specificity of .6051. While this is not enough accuracy to become a primary diagnostic tool for diagnosing stage I adenocarcinoma, the methods examined in the paper should be evaluated further. . By comparison, the current clinical standard blood test for prostate cancer that has an AUC of only 0.67.
ContributorsDe Jesus, Celine Spicer (Author) / Taylor, Thomas (Thesis director) / Borges, Chad (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / School of Molecular Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05
Description
E-commerce has rapidly become a mainstay in today's economy, and many websites have built themselves around providing a platform for independent sellers. Sites such as Etsy, Storenvy, Redbubble, and Society6 are increasingly popular options for anyone looking to open their own online store. With this project, I attempted to examine the effects of four different marketing techniques on sales in an online store. I opened a shop on Etsy and tracked sales in connection with promotion through social media, selling products in-person at a convention, holding a holiday tie-in sale, and using price anchoring. Social media accounts were opened on Facebook, Tumblr, and Instagram to promote the shop over the course of the project period, and Etsy's web analytics were used to track which sites directed the most traffic to the shop. I attended a convention in mid-January 2016 where I sold my products and distributed business cards with a discount code to track sales resulting from being at the convention. A holiday sale was held in conjunction with Valentine's Day to look at whether holidays influenced purchases. Lastly, a significantly more expensive product was temporarily put in the shop to see whether it produced a price anchoring effect \u2014 that is, encouraged sales of the less expensive products by making them seem affordable in comparison. While the volume of sales data was too small to draw statistically significant conclusions, the project was a highly instructive experience in the process of opening a small online store. The decision-making steps outlined may be helpful to other students looking to open their own online shop.
ContributorsChen, Candice Elizabeth (Author) / Moore, James (Thesis director) / Sanford, Adriana (Committee member) / Harrington Bioengineering Program (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05
Description
The detection and characterization of transients in signals is important in many wide-ranging applications from computer vision to audio processing. Edge detection on images is typically realized using small, local, discrete convolution kernels, but this is not possible when samples are measured directly in the frequency domain. The concentration factor edge detection method was therefore developed to realize an edge detector directly from spectral data. This thesis explores the possibilities of detecting edges from the phase of the spectral data, that is, without the magnitude of the sampled spectral data. Prior work has demonstrated that the spectral phase contains particularly important information about underlying features in a signal. Furthermore, the concentration factor method yields some insight into the detection of edges in spectral phase data. An iterative design approach was taken to realize an edge detector using only the spectral phase data, also allowing for the design of an edge detector when phase data are intermittent or corrupted. Problem formulations showing the power of the design approach are given throughout. A post-processing scheme relying on the difference of multiple edge approximations yields a strong edge detector which is shown to be resilient under noisy, intermittent phase data. Lastly, a thresholding technique is applied to give an explicit enhanced edge detector ready to be used. Examples throughout are demonstrate both on signals and images.
ContributorsReynolds, Alexander Bryce (Author) / Gelb, Anne (Thesis director) / Cochran, Douglas (Committee member) / Viswanathan, Adityavikram (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05
Description
Abstract
The aim of the research performed was to increase research potential in the field of cell stimulation by developing a method to adhere human neural progenitor cells (hNPC’s) to a sterilized stretchable microelectrode array (SMEA). The two primary objectives of our research were to develop methods of sterilizing the polydimethylsiloxane (PDMS) substrate being used for the SMEA, and to derive a functional procedure for adhering hNPC’s to the PDMS. The proven method of sterilization was to plasma treat the sample and then soak it in 70% ethanol for one hour. The most successful method for cell adhesion was plasma treating the PDMS, followed by treating the surface of the PDMS with 0.01 mg/mL poly-l-lysine (PLL) and 3 µg/cm2 laminin. The development of these methods was an iterative process; as the methods were tested, any problems found with the method were corrected for the next round of testing until a final method was confirmed. Moving forward, the findings will allow for cell behavior to be researched in a unique fashion to better understand the response of adherent cells to physical stimulation by measuring changes in their electrical activity.
The aim of the research performed was to increase research potential in the field of cell stimulation by developing a method to adhere human neural progenitor cells (hNPC’s) to a sterilized stretchable microelectrode array (SMEA). The two primary objectives of our research were to develop methods of sterilizing the polydimethylsiloxane (PDMS) substrate being used for the SMEA, and to derive a functional procedure for adhering hNPC’s to the PDMS. The proven method of sterilization was to plasma treat the sample and then soak it in 70% ethanol for one hour. The most successful method for cell adhesion was plasma treating the PDMS, followed by treating the surface of the PDMS with 0.01 mg/mL poly-l-lysine (PLL) and 3 µg/cm2 laminin. The development of these methods was an iterative process; as the methods were tested, any problems found with the method were corrected for the next round of testing until a final method was confirmed. Moving forward, the findings will allow for cell behavior to be researched in a unique fashion to better understand the response of adherent cells to physical stimulation by measuring changes in their electrical activity.
ContributorsBridgers, Carson (Co-author) / Peterson, Mara (Co-author) / Stabenfeldt, Sarah (Thesis director) / Graudejus, Oliver (Committee member) / Harrington Bioengineering Program (Contributor) / School of Human Evolution and Social Change (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05
Description
Chebfun is a collection of algorithms and an open-source software system in object-oriented Matlab that extends familiar powerful methods of numerical computation involving numbers to continuous or piecewise-continuous functions. The success of this strategy is based on the mathematical fact that smooth functions can be represented very efficiently by polynomial interpolation at Chebyshev points or by trigonometric interpolation at equispaced points for periodic functions. More recently, the system has been extended to handle bivariate functions and vector fields. These two new classes of objects are called Chebfun2 and Chebfun2v, respectively. We will show that Chebfun2 and Chebfun2v, and can be used to accurately and efficiently perform various computations on parametric surfaces in two or three dimensions, including path trajectories and mean and Gaussian curvatures. More advanced surface computations such as mean curvature flows are also explored. This is also the first work to use the newly implemented trigonometric representation, namely Trigfun, for computations on surfaces.
ContributorsPage-Bottorff, Courtney Michelle (Author) / Platte, Rodrigo (Thesis director) / Kostelich, Eric (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05
Description
Honey bees (Apis mellifera) are responsible for pollinating nearly 80\% of all pollinated plants, meaning humans depend on honey bees to pollinate many staple crops. The success or failure of a colony is vital to global food production. There are various complex factors that can contribute to a colony's failure, including pesticides. Neonicotoids are a popular pesticide that have been used in recent times. In this study we concern ourselves with pesticides and its impact on honey bee colonies. Previous investigations that we draw significant inspiration from include Khoury et Al's \emph{A Quantitative Model of Honey Bee Colony Population Dynamics}, Henry et Al's \emph{A Common Pesticide Decreases Foraging Success and Survival in Honey Bees}, and Brown's \emph{ Mathematical Models of Honey Bee Populations: Rapid Population Decline}. In this project we extend a mathematical model to investigate the impact of pesticides on a honey bee colony, with birth rates and death rates being dependent on pesticides, and we see how these death rates influence the growth of a colony. Our studies have found an equilibrium point that depends on pesticides. Trace amounts of pesticide are detrimental as they not only affect death rates, but birth rates as well.
ContributorsSalinas, Armando (Author) / Vaz, Paul (Thesis director) / Jones, Donald (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / School of International Letters and Cultures (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05
Description
In the medical industry, there have been promising advances in the increase of new types of healthcare to the public. As of 2015, there was a 98% Premarket Approval rate, a 38% increase since 2010. In addition, there were 41 new novel drugs approved for clinical usage in 2014 where the average in the previous years from 2005-2013 was 25. However, the research process towards creating and delivering new healthcare to the public remains remarkably inefficient. It takes on average 15 years, over $900 million by one estimate, for a less than 12% success rate of discovering a novel drug for clinical usage. Medical devices do not fare much better. Between 2005-2009, there were over 700 recalls per year. In addition, it takes at minimum 3.25 years for a 510(k) exempt premarket approval. Plus, a time lag exists where it takes 17 years for only 14% of medical discoveries to be implemented clinically. Coupled with these inefficiencies, government funding for medical research has been decreasing since 2002 (2.5% of Gross Domestic Product) and is predicted to be 1.5% of Gross Domestic Product by 2019. Translational research, the conversion of bench-side discoveries to clinical usage for a simplistic definition, has been on the rise since the 1990s. This may be driving the increased premarket approvals and new novel drug approvals. At the very least, it is worth considering as translational research is directly related towards healthcare practices. In this paper, I propose to improve the outcomes of translational research in order to better deliver advancing healthcare to the public. I suggest Best Value Performance Information Procurement System (BV PIPS) should be adapted in the selection process of translational research projects to fund. BV PIPS has been shown to increase the efficiency and success rate of delivering projects and services. There has been over 17 years of research with $6.3 billion of projects and services delivered showing that BV PIPS has a 98% customer satisfaction, 90% minimized management effort, and utilizes 50% less manpower and effort. Using University of Michigan \u2014 Coulter Foundation Program's funding process as a baseline and standard in the current selection of translational research projects to fund, I offer changes to this process based on BV PIPS that may ameliorate it. As concepts implemented in this process are congruent with literature on successful translational research, it may suggest that this new model for selecting translational research projects to fund will reduce costs, increase efficiency, and increase success. This may then lead to more Premarket Approvals, more new novel drug approvals, quicker delivery time to the market, and lower recalls.
ContributorsDel Rosario, Joseph Paul (Author) / Kashiwagi, Dean (Thesis director) / Kashiwagi, Jacob (Committee member) / Harrington Bioengineering Program (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05
Description
A Guide to Financial Mathematics is a comprehensive and easy-to-use study guide for students studying for the one of the first actuarial exams, Exam FM. While there are many resources available to students to study for these exams, this study is free to the students and offers an approach to the material similar to that of which is presented in class at ASU. The guide is available to students and professors in the new Actuarial Science degree program offered by ASU. There are twelve chapters, including financial calculator tips, detailed notes, examples, and practice exercises. Included at the end of the guide is a list of referenced material.
ContributorsDougher, Caroline Marie (Author) / Milovanovic, Jelena (Thesis director) / Boggess, May (Committee member) / Barrett, The Honors College (Contributor) / Department of Information Systems (Contributor) / School of Mathematical and Statistical Sciences (Contributor)
Created2015-05
Description
Breast and other solid tumors exhibit high and varying degrees of intra-tumor heterogeneity resulting in targeted therapy resistance and other challenges that make the management and treatment of these diseases rather difficult. Due to the presence of admixtures of non-neoplastic cells with polyclonal cell populations, it is difficult to define cancer genomes in patient samples. By isolating tumor cells from normal cells, and enriching distinct clonal populations, clinically relevant genomic aberrations that drive disease can be identified in patients in vivo. An in-depth analysis of clonal architecture and tumor heterogeneity was performed in a stage II chemoradiation-naïve breast cancer from a sixty-five year old patient. DAPI-based DNA content measurements and DNA content-based flow sorting was used to to isolate nuclei from distinct clonal populations of diploid and aneuploid tumor cells in surgical tumor samples. We combined DNA content-based flow cytometry and ploidy analysis with high-definition array comparative genomic hybridization (aCGH) and next-generation sequencing technologies to interrogate the genomes of multiple biopsies from the breast cancer. The detailed profiles of ploidy, copy number aberrations and mutations were used to recreate and map the lineages present within the tumor. The clonal analysis revealed driver events for tumor progression (a heterozygous germline BRCA2 mutation converted to homozygosity within the tumor by a copy number event and the constitutive activation of Notch and Akt signaling pathways. The highlighted approach has broad implications in the study of tumor heterogeneity by providing a unique ultra-high resolution of polyclonal tumors that can advance effective therapies and clinical management of patients with this disease.
ContributorsLaughlin, Brady Scott (Author) / Ankeny, Casey (Thesis director) / Barrett, Michael (Committee member) / Barrett, The Honors College (Contributor) / Harrington Bioengineering Program (Contributor) / School for the Science of Health Care Delivery (Contributor)
Created2015-05