Matching Items (4)
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- All Subjects: MRI
- Creators: Platte, Rodrigo
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
A tumor is a heterogeneous combination of proliferating tumor cells, infiltrating immune cells and stromal components along with a variety of associated host tissue cells, collectively termed the tumor microenvironment (TME). The constituents of the TME and their interaction with the host organ shape and define the properties of tumors and contribute towards the acquisition of hallmark traits such as hypoxia. Hypoxia imparts resistance to cancer from chemotherapy and radiotherapy due to the decreased production of reactive oxygen species and also promotes angiogenesis, malignant progression and metastasis. It also provides a powerful physiological stimulus that can be exploited as a tumor-specific condition, allowing for the rational design of anticancer hypoxia-activated pro-drugs (HAP). Accurate evaluation of tumor oxygenation in response to therapeutics interventions at various stages of growth should provide a better understanding of tumor response to therapy, potentially allowing therapy to be tailored to individual characteristics. The primary goal of this research was to investigate the utility of prospective identification of hypoxic tumors, by two different Magnetic Resonance Imaging (MRI) based oximetry approaches, in successful treatment with hypoxia activated therapy. In the present study, I report the utility of these two techniques 1) PISTOL (Proton Imaging of Siloxanes to map Tissue Oxygenation Levels) and 2) use of a hypoxia binding T1 contrast agent GdDO3NI in reporting the modulations of hypoxia pre and post hypoxia activated therapies in pre-clinical models of cancer. I have performed these studies in non-small cell lung cancer (NSCLC) and epidermoid carcinoma (NCI-H1975 and A431 cell lines, respectively) as well as in patient derived xenograft models of NSCLC. Both the oximetry techniques have the potential to differentiate between normoxic and hypoxic regions of the tumor and reveal both baseline heterogeneity and differential response to therapeutic intervention. The response of the tumor models to therapeutic interventions indicates that, in conjunction with pO2, other factors such as tumor perfusion (essential for delivering HAPs) and relative expression of nitroreductases (essential for activating HAPs) may play an important role. The long term goal of the proposed research is the clinical translation of both the MRI techniques and aiding the design and development of personalized therapy (e.g. patient stratification for novel hypoxia activated pro-drugs) particularly for cancer.
ContributorsAgarwal, Shubhangi (Author) / Kodibagkar, Vikram D (Thesis advisor) / Inge, Landon J (Committee member) / Nikkhah, Mehdi (Committee member) / Pagel, Mark D. (Committee member) / Sadleir, Rosalind J (Committee member) / Arizona State University (Publisher)
Created2017
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 dissertation develops a second order accurate approximation to the magnetic resonance (MR) signal model used in the PARSE (Parameter Assessment by Retrieval from Single Encoding) method to recover information about the reciprocal of the spin-spin relaxation time function (R2*) and frequency offset function (w) in addition to the typical steady-state transverse magnetization (M) from single-shot magnetic resonance imaging (MRI) scans. Sparse regularization on an approximation to the edge map is used to solve the associated inverse problem. Several studies are carried out for both one- and two-dimensional test problems, including comparisons to the first order approximation method, as well as the first order approximation method with joint sparsity across multiple time windows enforced. The second order accurate model provides increased accuracy while reducing the amount of data required to reconstruct an image when compared to piecewise constant in time models. A key component of the proposed technique is the use of fast transforms for the forward evaluation. It is determined that the second order model is capable of providing accurate single-shot MRI reconstructions, but requires an adequate coverage of k-space to do so. Alternative data sampling schemes are investigated in an attempt to improve reconstruction with single-shot data, as current trajectories do not provide ideal k-space coverage for the proposed method.
ContributorsJesse, Aaron Mitchel (Author) / Platte, Rodrigo (Thesis advisor) / Gelb, Anne (Committee member) / Kostelich, Eric (Committee member) / Mittelmann, Hans (Committee member) / Moustaoui, Mohamed (Committee member) / Arizona State University (Publisher)
Created2019