Matching Items (11)
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- All Subjects: MRI
- Creators: School of Mathematical and Statistical Sciences
- Creators: Fisher, Rebecca
- Creators: Anderies, Barrett James
- Member of: Barrett, The Honors College Thesis/Creative Project Collection
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
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
The purpose of this thesis is to accurately simulate the surface brightness in various spectral emission lines of the HH 901 jets in the Mystic Mountain Formation of the Carina Nebula. To accomplish this goal, we gathered relevant spectral emission line data for [Fe II] 12660 Å, Hα 6563 Å, and [S II] 6720 Å to compare with Hubble Space Telescope observations of the HH 901 jets presented in Reiter et al. (2016). We derived the emissivities for these lines from the spectral synthesis code Cloudy by Ferland et al. (2017). In addition, we used WENO simulations of density, temperature, and radiative cooling to model the jet. We found that the computed surface brightness values agreed with most of the observational surface brightness values. Thus, the 3D cylindrically symmetric simulations of surface brightness using the WENO code and Cloudy spectral emission models are accurate for jets like HH 901. After detailing these agreements, we discuss the next steps for the project, like adding an external ambient wind and performing the simulations in full 3D.
ContributorsMohan, Arun (Author) / Gardner, Carl (Thesis director) / Jones, Jeremiah (Committee member) / Computer Science and Engineering Program (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2020-05
Description
The entirely soft-tissue anatomy of the octopus arm provides the animal with a large amount of freedom of movement, while still allowing the specimen to support itself despite the lack of a skeletal system. This is made possible through the use of various muscle layers within the octopus arm, which act as muscular hydrostats. Magnetic Resonance imaging of the octopus arm was employed to view the muscle layers within the octopus arm and observe trends and differences in these layers at the proximal, middle, and distal portions of the arms. A total of 39 arms from 6 specimens were imaged to give 112 total imaged sections (38 proximal, 37 middle, 37 distal). Significant increases in both the internal longitudinal muscle layer and the nervous core were found between the proximal and middle, proximal and distal, and middle and distal sections of the arms. This could reflect selection for these structures distally in the octopus arm for predator or other noxious stimuli avoidance. A significant decrease in the transverse muscle layer was found in the middle and distal sections of the arms. This could reflect selection for elongation in the proximal portion of the octopus arm or could be the result of selection for the internal longitudinal muscle layer and nervous core distally. Previous studies on Octopus vulgaris showed a preference for using the proximal arms in the pushing movement of crawling and a preference for using the anterior arms in exploring behaviors (Levy et al., 2015 and Byrne et al., 2006). Differences between the anterior and posterior arms for the transverse muscle layer, internal longitudinal muscle layer, and the nervous core were insignificant, reflecting a lack of structure-function relationships. This could also be due to a low sample size. Differences between the left and right arms for the transverse muscle layer, internal longitudinal muscle layer, and the nervous core were insignificant, supporting previous evidence that left versus right eye and arm preferences in octopus are not population-wide, but individual. Some slight trends can be found for individual arms, but the sample size was too small to make definitive statements regarding differences among specific arms.
ContributorsRoy, Cayla C (Author) / Fisher, Rebecca (Thesis director) / Marvi, Hamid (Committee member) / Cherry, Brian (Committee member) / Watts College of Public Service & Community Solut (Contributor) / School of Life Sciences (Contributor) / School of Molecular Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2019-05
Description
Octopus arms employ a complex three dimensional array of musculature, called a
muscular hydrostat, which allows for nearly infinite degrees of freedom of movement without
the structure of a skeletal system. This study employed Magnetic Resonance Imaging with a
Gadoteridol-based contrast agent to image the octopus arm and view the internal tissues. Muscle
layering was mapped and area was measured using AMIRA image processing and the trends in
these layers at the proximal, middle, and distal portions of the arms were analyzed. A total of 39
arms from 6 specimens were scanned to give 112 total imaged sections (38 proximal, 37 middle,
37 distal), from which to ascertain and study the possible differences in musculature. The
images revealed significant increases in the internal longitudinal muscle layer percentages
between the proximal and middle, proximal and distal, and middle and distal sections of the
arms. These structural differences are hypothesized to be used for rapid retraction of the distal
segment when encountering predators or noxious stimuli. In contrast, a significant decrease in
the transverse muscle layer was found when comparing the same sections. These structural
differences are hypothesized to be a result of bending behaviors during retraction. Additionally,
the internal longitudinal layer was separately studied orally, toward the sucker, and aborally,
away from the sucker. The significant differences in oral and aboral internal longitudinal
musculature in proximal, middle, and distal sections is hypothesized to support the pseudo-joint
functionality displayed in octopus fetching behaviors. The results indicate that individual
octopus arm morphology is more unique than previously thought and supports that internal
structural differences exist to support behavioral functionality.
muscular hydrostat, which allows for nearly infinite degrees of freedom of movement without
the structure of a skeletal system. This study employed Magnetic Resonance Imaging with a
Gadoteridol-based contrast agent to image the octopus arm and view the internal tissues. Muscle
layering was mapped and area was measured using AMIRA image processing and the trends in
these layers at the proximal, middle, and distal portions of the arms were analyzed. A total of 39
arms from 6 specimens were scanned to give 112 total imaged sections (38 proximal, 37 middle,
37 distal), from which to ascertain and study the possible differences in musculature. The
images revealed significant increases in the internal longitudinal muscle layer percentages
between the proximal and middle, proximal and distal, and middle and distal sections of the
arms. These structural differences are hypothesized to be used for rapid retraction of the distal
segment when encountering predators or noxious stimuli. In contrast, a significant decrease in
the transverse muscle layer was found when comparing the same sections. These structural
differences are hypothesized to be a result of bending behaviors during retraction. Additionally,
the internal longitudinal layer was separately studied orally, toward the sucker, and aborally,
away from the sucker. The significant differences in oral and aboral internal longitudinal
musculature in proximal, middle, and distal sections is hypothesized to support the pseudo-joint
functionality displayed in octopus fetching behaviors. The results indicate that individual
octopus arm morphology is more unique than previously thought and supports that internal
structural differences exist to support behavioral functionality.
ContributorsCummings, Sheldon Daniel (Author) / Fisher, Rebecca (Thesis director) / Marvi, Hamidreza (Committee member) / Cherry, Brian (Committee member) / Harrington Bioengineering Program (Contributor) / Barrett, The Honors College (Contributor)
Created2019-05