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Stochastic parameterization of the proliferation-diffusion model of brain cancer in a Murine model

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

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.

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2016-05

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Estimating GL-261 cell growth: A murine model for Glioblastoma Multiforme

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

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.

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2014-05

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Development of a Novel Smart Contrast Agent for Magnetic Resonance Imaging

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

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.

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2014-05

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Incorporating the Sparsity of Edges into the Fourier Reconstruction of Piecewise Smooth Functions

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

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.

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2014-05

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Modeling and Characterization of Mass Transfer Kinetics in Tumor Tissue Using Dynamic Contrast Enhanced Magnetic Resonance Imaging (DCE-MRI)

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

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.

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2013-12

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Edge Detection from Non-Uniform Fourier Data via a Modified Method of Convolutional Gridding

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

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.

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2013-05

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Edge Informed Fourier Reconstruction from Non-Uniform Spectral Data

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

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.

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2013-05

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Branching Worlds: Quantum Mechanics and Hugh Everett's Many-Worlds Interpretation

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 u

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.

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2021-05

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Entanglement, Locality, and Hidden Variables

Description

The purpose of this paper is to provide an analysis of entanglement and the particular problems it poses for some physicists. In addition to looking at the history of entanglement and non-locality, this paper will use the Bell Test as

The purpose of this paper is to provide an analysis of entanglement and the particular problems it poses for some physicists. In addition to looking at the history of entanglement and non-locality, this paper will use the Bell Test as a means for demonstrating how entanglement works, which measures the behavior of electrons whose combined internal angular momentum is zero. This paper will go over Dr. Bell's famous inequality, which shows why the process of entanglement cannot be explained by traditional means of local processes. Entanglement will be viewed initially through the Copenhagen Interpretation, but this paper will also look at two particular models of quantum mechanics, de-Broglie Bohm theory and Everett's Many-Worlds Interpretation, and observe how they explain the behavior of spin and entangled particles compared to the Copenhagen Interpretation.

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2021-05