Matching Items (5)
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- All Subjects: Quantum Mechanics
- All Subjects: Diagnostic imaging
- Creators: Kodibagkar, Vikram
- Resource Type: Text
- Status: Published
Description
Magnetic Resonance Imaging using spiral trajectories has many advantages in speed, efficiency in data-acquistion and robustness to motion and flow related artifacts. The increase in sampling speed, however, requires high performance of the gradient system. Hardware inaccuracies from system delays and eddy currents can cause spatial and temporal distortions in the encoding gradient waveforms. This causes sampling discrepancies between the actual and the ideal k-space trajectory. Reconstruction assuming an ideal trajectory can result in shading and blurring artifacts in spiral images. Current methods to estimate such hardware errors require many modifications to the pulse sequence, phantom measurements or specialized hardware. This work presents a new method to estimate time-varying system delays for spiral-based trajectories. It requires a minor modification of a conventional stack-of-spirals sequence and analyzes data collected on three orthogonal cylinders. The method is fast, robust to off-resonance effects, requires no phantom measurements or specialized hardware and estimate variable system delays for the three gradient channels over the data-sampling period. The initial results are presented for acquired phantom and in-vivo data, which show a substantial reduction in the artifacts and improvement in the image quality.
ContributorsBhavsar, Payal (Author) / Pipe, James G (Thesis advisor) / Frakes, David (Committee member) / Kodibagkar, Vikram (Committee member) / Arizona State University (Publisher)
Created2013
Description
Chapter 1 introduces some key elements of important topics such as; quantum mechanics,
representation theory of the Lorentz and Poincare groups, and a review of some basic rela- ´
tivistic wave equations that will play an important role in the work to follow. In Chapter 2,
a complex covariant form of the classical Maxwell’s equations in a moving medium or at
rest is introduced. In addition, a compact, Lorentz invariant, form of the energy-momentum
tensor is derived. In chapter 3, the concept of photon helicity is critically analyzed and its
connection with the Pauli-Lubanski vector from the viewpoint of the complex electromag- ´
netic field, E+ iH. To this end, a complex covariant form of Maxwell’s equations is used.
Chapter 4 analyzes basic relativistic wave equations for the classical fields, such as Dirac’s
equation, Weyl’s two-component equation for massless neutrinos and the Proca, Maxwell
and Fierz-Pauli equations, from the viewpoint of the Pauli-Lubanski vector and the Casimir ´
operators of the Poincare group. A connection between the spin of a particle/field and ´
consistency of the corresponding overdetermined system is emphasized in the massless
case. Chapter 5 focuses on the so-called generalized quantum harmonic oscillator, which
is a Schrodinger equation with a time-varying quadratic Hamiltonian operator. The time ¨
evolution of exact wave functions of the generalized harmonic oscillators is determined
in terms of the solutions of certain Ermakov and Riccati-type systems. In addition, it is
shown that the classical Arnold transform is naturally connected with Ehrenfest’s theorem
for generalized harmonic oscillators. In Chapter 6, as an example of the usefulness of the
methods introduced in Chapter 5 a model for the quantization of an electromagnetic field
in a variable media is analyzed. The concept of quantization of an electromagnetic field
in factorizable media is discussed via the Caldirola-Kanai Hamiltonian. A single mode
of radiation for this model is used to find time-dependent photon amplitudes in relation
to Fock states. A multi-parameter family of the squeezed states, photon statistics, and the
uncertainty relation, are explicitly given in terms of the Ermakov-type system.
representation theory of the Lorentz and Poincare groups, and a review of some basic rela- ´
tivistic wave equations that will play an important role in the work to follow. In Chapter 2,
a complex covariant form of the classical Maxwell’s equations in a moving medium or at
rest is introduced. In addition, a compact, Lorentz invariant, form of the energy-momentum
tensor is derived. In chapter 3, the concept of photon helicity is critically analyzed and its
connection with the Pauli-Lubanski vector from the viewpoint of the complex electromag- ´
netic field, E+ iH. To this end, a complex covariant form of Maxwell’s equations is used.
Chapter 4 analyzes basic relativistic wave equations for the classical fields, such as Dirac’s
equation, Weyl’s two-component equation for massless neutrinos and the Proca, Maxwell
and Fierz-Pauli equations, from the viewpoint of the Pauli-Lubanski vector and the Casimir ´
operators of the Poincare group. A connection between the spin of a particle/field and ´
consistency of the corresponding overdetermined system is emphasized in the massless
case. Chapter 5 focuses on the so-called generalized quantum harmonic oscillator, which
is a Schrodinger equation with a time-varying quadratic Hamiltonian operator. The time ¨
evolution of exact wave functions of the generalized harmonic oscillators is determined
in terms of the solutions of certain Ermakov and Riccati-type systems. In addition, it is
shown that the classical Arnold transform is naturally connected with Ehrenfest’s theorem
for generalized harmonic oscillators. In Chapter 6, as an example of the usefulness of the
methods introduced in Chapter 5 a model for the quantization of an electromagnetic field
in a variable media is analyzed. The concept of quantization of an electromagnetic field
in factorizable media is discussed via the Caldirola-Kanai Hamiltonian. A single mode
of radiation for this model is used to find time-dependent photon amplitudes in relation
to Fock states. A multi-parameter family of the squeezed states, photon statistics, and the
uncertainty relation, are explicitly given in terms of the Ermakov-type system.
ContributorsLanfear, Nathan A (Author) / Suslov, Sergei (Thesis advisor) / Kotschwar, Brett (Thesis advisor) / Platte, Rodrigo (Committee member) / Matyushov, Dmitry (Committee member) / Kuiper, Hendrik (Committee member) / Gardner, Carl (Committee member) / Arizona State University (Publisher)
Created2016
Description
Dynamic susceptibility contrast MRI (DSC-MRI) is a powerful tool used to quantitatively measure parameters related to blood flow and volume in the brain. The technique is known as a “bolus-tracking” method and relies upon very fast scanning to accurately measure the flow of contrast agent into and out of a region of interest. The need for high temporal resolution to measure contrast agent dynamics limits the spatial coverage of perfusion parameter maps which limits the utility of DSC-perfusion studies in pathologies involving the entire brain. Typical clinical DSC-perfusion studies are capable of acquiring 10-15 slices, generally centered on a known lesion or pathology.
The methods developed in this work improve the spatial coverage of whole-brain DSC-MRI by combining a highly efficient 3D spiral k-space trajectory with Generalized Autocalibrating Partial Parallel Acquisition (GRAPPA) parallel imaging without increasing temporal resolution. The proposed method is capable of acquiring 30 slices with a temporal resolution of under 1 second, covering the entire cerebrum with isotropic spatial resolution of 3 mm. Additionally, the acquisition method allows for correction of T1-enhancing leakage effects by virtue of collecting two echoes, which confound DSC perfusion measurements. The proposed DSC-perfusion method results in high quality perfusion parameter maps across a larger volume than is currently available with current clinical standards, improving diagnostic utility of perfusion MRI methods, which ultimately improves patient care.
The methods developed in this work improve the spatial coverage of whole-brain DSC-MRI by combining a highly efficient 3D spiral k-space trajectory with Generalized Autocalibrating Partial Parallel Acquisition (GRAPPA) parallel imaging without increasing temporal resolution. The proposed method is capable of acquiring 30 slices with a temporal resolution of under 1 second, covering the entire cerebrum with isotropic spatial resolution of 3 mm. Additionally, the acquisition method allows for correction of T1-enhancing leakage effects by virtue of collecting two echoes, which confound DSC perfusion measurements. The proposed DSC-perfusion method results in high quality perfusion parameter maps across a larger volume than is currently available with current clinical standards, improving diagnostic utility of perfusion MRI methods, which ultimately improves patient care.
ContributorsTurley, Dallas C (Author) / Pipe, James G (Thesis advisor) / Kodibagkar, Vikram (Thesis advisor) / Frakes, David (Committee member) / Sadleir, Rosalind (Committee member) / Schmainda, Kathleen (Committee member) / Arizona State University (Publisher)
Created2017
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
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