Matching Items (10)
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- All Subjects: MRI
- Creators: School of Mathematical and Statistical Sciences
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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
Is it possible to treat the mouth as a natural environment, and determine new methods to keep the microbiome in check? The need for biodiversity in health may suggest that every species carries out a specific function that is required to maintain equilibrium and homeostasis within the oral cavity. Furthermore, the relationship between the microbiome and its host is mutually beneficial because the host is providing microbes with an environment in which they can flourish and, in turn, keep their host healthy. Reviewing examples of larger scale environmental shifts could provide a window by which scientists can make hypotheses. Certain medications and healthcare treatments have been proven to cause xerostomia. This disorder is characterized by a dry mouth, and known to be associated with a change in the composition, and reduction, of saliva. Two case studies performed by Bardow et al, and Leal et al, tested and studied the relationships of certain medications and confirmed their side effects on the salivary glands [2,3]. Their results confirmed a relationship between specific medicines, and the correlating complaints of xerostomia. In addition, Vissink et al conducted case studies that helped to further identify how radiotherapy causes hyposalivation of the salivary glands [4]. Specifically patients that have been diagnosed with oral cancer, and are treated by radiotherapy, have been diagnosed with xerostomia. As stated prior, studies have shown that patients having an ecologically balanced and diverse microbiome tend to have healthier mouths. The oral cavity is like any biome, consisting of commensalism within itself and mutualism with its host. Due to the decreased salivary output, caused by xerostomia, increased parasitic bacteria build up within the oral cavity thus causing dental disease. Every human body contains a personalized microbiome that is essential to maintaining health but capable of eliciting disease. The Human Oral Microbiomics Database (HOMD) is a set of reference 16S rRNA gene sequences. These are then used to define individual human oral taxa. By conducting metagenomic experiments at the molecular and cellular level, scientists can identify and label micro species that inhabit the mouth during parasitic outbreaks or a shifting of the microbiome. Because the HOMD is incomplete, so is our ability to cure, or prevent, oral disease. The purpose of the thesis is to research what is known about xerostomia and its effects on the complex microbiome of the oral cavity. It is important that researchers determine whether this particular perspective is worth considering. In addition, the goal is to create novel experiments for treatment and prevention of dental diseases.
ContributorsHalcomb, Michael Jordan (Author) / Chen, Qiang (Thesis director) / Steele, Kelly (Committee member) / Barrett, The Honors College (Contributor) / College of Letters and Sciences (Contributor)
Created2015-05
Description
The reconstruction of piecewise smooth functions from non-uniform Fourier data arises in sensing applications such as magnetic resonance imaging (MRI). This thesis presents a new polynomial based resampling method (PRM) for 1-dimensional problems which uses edge information to recover the Fourier transform at its integer coefficients, thereby enabling the use of the inverse fast Fourier transform algorithm. By minimizing the error of the PRM approximation at the sampled Fourier modes, the PRM can also be used to improve on initial edge location estimates. Numerical examples show that using the PRM to improve on initial edge location estimates and then taking of the PRM approximation of the integer frequency Fourier coefficients is a viable way to reconstruct the underlying function in one dimension. In particular, the PRM is shown to converge more quickly and to be more robust than current resampling techniques used in MRI, and is particularly amenable to highly irregular sampling patterns.
ContributorsGutierrez, Alexander Jay (Author) / Platte, Rodrigo (Thesis director) / Gelb, Anne (Committee member) / Viswanathan, Adityavikram (Committee member) / Barrett, The Honors College (Contributor) / School of International Letters and Cultures (Contributor) / School of Mathematical and Statistical Sciences (Contributor)
Created2013-05
Description
The objective of the research presented here was to validate the use of kinetic models for the analysis of the dynamic behavior of a contrast agent in tumor tissue and evaluate the utility of such models in determining kinetic properties - in particular perfusion and molecular binding uptake associated with tissue hypoxia - of the imaged tissue, from concentration data acquired with dynamic contrast enhanced magnetic resonance imaging (DCE-MRI) procedure. Data from two separate DCE-MRI experiments, performed in the past, using a standard contrast agent and a hypoxia-binding agent respectively, were analyzed. The results of the analysis demonstrated that the models used may provide novel characterization of the tumor tissue properties. Future research will work to further characterize the physical significance of the estimated parameters, particularly to provide quantitative oxygenation data for the imaged tissue.
ContributorsMartin, Jonathan Michael (Author) / Kodibagkar, Vikram (Thesis director) / Rege, Kaushal (Committee member) / Barrett, The Honors College (Contributor) / Chemical Engineering Program (Contributor) / School of Mathematical and Statistical Sciences (Contributor)
Created2013-12
Description
In applications such as Magnetic Resonance Imaging (MRI), data are acquired as Fourier samples. Since the underlying images are only piecewise smooth, standard recon- struction techniques will yield the Gibbs phenomenon, which can lead to misdiagnosis. Although filtering will reduce the oscillations at jump locations, it can often have the adverse effect of blurring at these critical junctures, which can also lead to misdiagno- sis. Incorporating prior information into reconstruction methods can help reconstruct a sharper solution. For example, compressed sensing (CS) algorithms exploit the expected sparsity of some features of the image. In this thesis, we develop a method to exploit the sparsity in the edges of the underlying image. We design a convex optimization problem that exploits this sparsity to provide an approximation of the underlying image. Our method successfully reduces the Gibbs phenomenon with only minimal "blurring" at the discontinuities. In addition, we see a high rate of convergence in smooth regions.
ContributorsWasserman, Gabriel Kanter (Author) / Gelb, Anne (Thesis director) / Cochran, Doug (Committee member) / Archibald, Rick (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor)
Created2014-05
Description
Smart contrast agents allow for noninvasive study of specific events or tissue conditions inside of a patient's body using Magnetic Resonance Imaging (MRI). This research aims to develop and characterize novel smart contrast agents for MRI that respond to temperature changes in tissue microenvironments. Transmission Electron Microscopy, Nuclear Magnetic Resonance, and cell culture growth assays were used to characterize the physical, magnetic, and cytotoxic properties of candidate nanoprobes. The nanoprobes displayed thermosensitve MR properties with decreasing relaxivity with temperature. Future work will be focused on generating and characterizing photo-active analogues of the nanoprobes that could be used for both treatment of tissues and assessment of therapy.
ContributorsHussain, Khateeb Hyder (Author) / Kodibagkar, Vikram (Thesis director) / Stabenfeldt, Sarah (Committee member) / Barrett, The Honors College (Contributor) / Harrington Bioengineering Program (Contributor) / School of Mathematical and Statistical Sciences (Contributor)
Created2014-05
Description
Glioblastoma Multiforme (GBM) is an aggressive and deadly form of brain cancer with a median survival time of about a year with treatment. Due to the aggressive nature of these tumors and the tendency of gliomas to follow white matter tracks in the brain, each tumor mass has a unique growth pattern. Consequently it is difficult for neurosurgeons to anticipate where the tumor will spread in the brain, making treatment planning difficult. Archival patient data including MRI scans depicting the progress of tumors have been helpful in developing a model to predict Glioblastoma proliferation, but limited scans per patient make the tumor growth rate difficult to determine. Furthermore, patient treatment between scan points can significantly compound the challenge of accurately predicting the tumor growth. A partnership with Barrow Neurological Institute has allowed murine studies to be conducted in order to closely observe tumor growth and potentially improve the current model to more closely resemble intermittent stages of GBM growth without treatment effects.
ContributorsSnyder, Lena Haley (Author) / Kostelich, Eric (Thesis director) / Frakes, David (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Harrington Bioengineering Program (Contributor)
Created2014-05
Description
I, Christopher Negrich, am the sole author of this paper, but the tools described were designed in collaboration with Andrew Hoetker. ConstrictR (constrictor) and ConstrictPy are an R package and python tool designed together. ConstrictPy implements the functions and methods defined in ConstrictR and applies data handling, data parsing, input/output (I/O), and a user interface to increase usability. ConstrictR implements a variety of common data analysis methods used for statistical and subnetwork analysis. The majority of these methods are inspired by Lionel Guidi's 2016 paper, Plankton networks driving carbon export in the oligotrophic ocean. Additional methods were added to expand functionality, usability, and applicability to different areas of data science. Both ConstrictR and ConstrictPy are currently publicly available and usable, however, they are both ongoing projects. ConstrictR is available at github.com/cnegrich and ConstrictPy is available at github.com/ahoetker. Currently, ConstrictR has implemented functions for descriptive statistics, correlation, covariance, rank, sparsity, and weighted correlation network analysis with clustering, centrality, profiling, error handling, and data parsing methods to be released soon. ConstrictPy has fully implemented and integrated the features in ConstrictR as well as created functions for I/O and conversion between pandas and R data frames with a full feature user interface to be released soon. Both ConstrictR and ConstrictPy are designed to work with minimal dependencies and maximum available information on the algorithms implemented. As a result, ConstrictR is only dependent on base R (v3.4.4) functions with no libraries imported. ConstrictPy is dependent upon only pandas, Rpy2, and ConstrictR. This was done to increase longevity and independence of these tools. Additionally, all mathematical information is documented alongside the code, increasing the available information on how these tools function. Although neither tool is in its final version, this paper documents the code, mathematics, and instructions for use, in addition to plans for future work, for of the current versions of ConstrictR (v0.0.1) and ConstrictPy (v0.0.1).
ContributorsNegrich, Christopher Alec (Author) / Can, Huansheng (Thesis director) / Hansford, Dianne (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05
Description
The recovery of edge information in the physical domain from non-uniform Fourier data is of importance in a variety of applications, particularly in the practice of magnetic resonance imaging (MRI). Edge detection can be important as a goal in and of itself in the identification of tissue boundaries such as those defining the locations of tumors. It can also be an invaluable tool in the amelioration of the negative effects of the Gibbs phenomenon on reconstructions of functions with discontinuities or images in multi-dimensions with internal edges. In this thesis we develop a novel method for recovering edges from non-uniform Fourier data by adapting the "convolutional gridding" method of function reconstruction. We analyze the behavior of the method in one dimension and then extend it to two dimensions on several examples.
ContributorsMartinez, Adam (Author) / Gelb, Anne (Thesis director) / Cochran, Douglas (Committee member) / Platte, Rodrigo (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor)
Created2013-05
Description
Glioblastoma brain tumors are among the most lethal human cancers. Treatment efforts typically involve both surgical tumor removal, as well as ongoing therapy. In this work, we propose the use of deuterium magnetic resonance imaging (MRI) to delineate tumor boundaries based on spatial distributions of deuterated leucine, as well as resolve the metabolism of leucine within the tumor. Accurate boundary identification contributes to effectiveness of tumor removal efforts, while amino acid metabolism information may help characterize tumor malignancy and guide ongoing treatment. So, we first examine the fundamental mechanisms of deuterium MRI. We then discuss the use of spin-echo and gradient recall echo sequences for mapping spatial distributions of deuterated leucine, and the use of single-voxel spectroscopy for imaging metabolites within a tumor.
ContributorsCostelle, Anna (Author) / Beeman, Scott (Thesis director) / Kodibagkar, Vikram (Committee member) / Barrett, The Honors College (Contributor) / Department of Physics (Contributor) / School of Mathematical and Statistical Sciences (Contributor)
Created2022-05