Matching Items (12)
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- All Subjects: MRI
- Creators: School of Mathematical and Statistical Sciences
- Creators: Kodibagkar, Vikram
- Member of: Barrett, The Honors College Thesis/Creative Project Collection
- Resource Type: Text
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
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
In epilepsy, malformations that cause seizures often require surgery. The purpose of this research is to join forces with the Multi-Center Epilepsy Lesion Detection (MELD) project at University College London (UCL) in order to improve the process of detecting lesions in patients with drug-resistant epilepsy. This, in turn, will improve surgical outcomes via more structured surgical planning. It is a global effort, with more than 20 sites across 5 continents. The targeted populations for this study include patients whose epilepsy stems from Focal Cortical Dysplasia. Focal Cortical Dysplasia is an abnormality of cortical development, and causes most of the drug-resistant epilepsy. Currently, the creators of MELD have developed a set of protocols which wrap various
commands designed to streamline post-processing of MRI images. Using this partnership, the Applied Neuroscience and Technology Lab at PCH has been able to complete production of a post-processing pipeline which integrates locally sourced smoothing techniques to help identify lesions in patients with evidence of Focal Cortical Dysplasia. The end result is a system in which a patient with epilepsy may experience more successful post-surgical results due to the
combination of a lesion detection mechanism and the radiologist using their trained eye in the presurgical stages. As one of the main points of this work is the global aspect of it, Barrett thesis funding was dedicated for a trip to London in order to network with other MELD project collaborators. This was a successful trip for the project as a whole in addition to this particular thesis. The ability to troubleshoot problems with one another in a room full of subject matter
experts allowed for a high level of discussion and learning. Future work includes implementing machine learning approaches which consider all morphometry parameters simultaneously.
commands designed to streamline post-processing of MRI images. Using this partnership, the Applied Neuroscience and Technology Lab at PCH has been able to complete production of a post-processing pipeline which integrates locally sourced smoothing techniques to help identify lesions in patients with evidence of Focal Cortical Dysplasia. The end result is a system in which a patient with epilepsy may experience more successful post-surgical results due to the
combination of a lesion detection mechanism and the radiologist using their trained eye in the presurgical stages. As one of the main points of this work is the global aspect of it, Barrett thesis funding was dedicated for a trip to London in order to network with other MELD project collaborators. This was a successful trip for the project as a whole in addition to this particular thesis. The ability to troubleshoot problems with one another in a room full of subject matter
experts allowed for a high level of discussion and learning. Future work includes implementing machine learning approaches which consider all morphometry parameters simultaneously.
ContributorsHumphreys, Zachary William (Author) / Kodibagkar, Vikram (Thesis director) / Foldes, Stephen (Committee member) / Harrington Bioengineering Program (Contributor) / Barrett, The Honors College (Contributor)
Created2019-05
Description
Magnetic resonance imaging (MRI) of changes in metabolic activity in tumors and metabolic abnormalities can provide a window to understanding the complex behavior of malignant tumors. Both diagnostics and treatment options can be improved through the further comprehension of the processes that contribute to tumor malignancy and growth. By detecting and disturbing this activity through personalized treatments, it is the hope to provide better diagnostics and care to patients. Experimenting with multicellular tumor spheroids (MCTS) allows for a rapid, inexpensive and convenient solution to studying multiple in vitro tumors. High quality magnetic resonance images of small samples, such as spheroid, however, are difficult to achieve with current radio frequency coils. In addition, in order for the information provided by these scans to accurately represent the interactions and metabolic activity in vivo, there is a need for a perfused vascular network. A perfused vascular network has the potential to improve metabolic realism and particle transport within a tumor spheroid. By creating a more life-like cancer model and allowing the progressive imaging of metabolic functions of such small samples, a better, more efficient mode of studying metabolic activity in cancer can be created and research efforts can expand. The progress described in this paper attempts to address both of these current shortcomings of metabolic cancer research and offers potential solutions, while acknowledging the potential of future work to improve cancer research with MCTS.
ContributorsTobey, John Paul (Author) / Kodibagkar, Vikram (Thesis director) / Sadleir, Rosalind (Committee member) / Barrett, The Honors College (Contributor)
Created2016-12
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
This thesis attempts to explain Everettian quantum mechanics from the ground up, such that those with little to no experience in quantum physics can understand it. First, we introduce the history of quantum theory, and some concepts that make up the framework of quantum physics. Through these concepts, we reveal why interpretations are necessary to map the quantum world onto our classical world. We then introduce the Copenhagen interpretation, and how many-worlds differs from it. From there, we dive into the concepts of entanglement and decoherence, explaining how worlds branch in an Everettian universe, and how an Everettian universe can appear as our classical observed world. From there, we attempt to answer common questions about many-worlds and discuss whether there are philosophical ramifications to believing such a theory. Finally, we look at whether the many-worlds interpretation can be proven, and why one might choose to believe it.
ContributorsSecrest, Micah (Author) / Foy, Joseph (Thesis director) / Hines, Taylor (Committee member) / Computer Science and Engineering Program (Contributor) / Barrett, The Honors College (Contributor)
Created2021-05