T2 relaxation imaging can be used to measure signal from water trapped between myelin bilayers; the ratio of myelin water signal to total water is termed the myelin water fraction (MWF). First, results from multi-component T2 relaxation and diffusion tensor imaging (DTI) were compared for 19 multiple sclerosis (MS) subjects at 1.5 T to better understand how each measure is affected by pathology. In particular, it was determined that the detection of a long-T2 signal within an MS lesion may be indicative of a different underlying pathology than is present in lesions without long-T2 signal. Next, the single-slice T2 relaxation measurement was implemented, refined, and validated at 3.0 T. Scan parameters were varied for phantoms and in-vivo brain, and changes in multi-exponential fit residuals and T2 distribution-derived parameters such as MWF were monitored to determine which scan parameters minimized artifacts. Measurements were compared between 1.5 T and 3.0 T for 10 healthy volunteers. MWF maps were qualitatively similar between field strengths. MWFs were significantly higher at 3.0 T than at 1.5 T, but with a strong correlation between measurements at the different field strengths. Due to long acquisition times, multi-component T2 relaxation has thus far been clinically infeasible. The next study aimed to validate a new 3D multi-component T2 relaxation imaging technique against the 2D single-slice technique most commonly used. Ten healthy volunteers were scanned with both the 2D single-slice and 3D techniques. MWF maps were qualitatively similar between scans. MWF values were highly correlated between the acquisition methods. Although MWF values were generally lower using the 3D technique, they were only significantly so for peripheral brain structures, likely due to increased sensitivity of slab-selective refocusing pulses used for the 3D approach. The 3D T2 relaxation sequence was then applied to the study of MS to take advantage of the increased brain coverage. Thirteen MS subjects and 11 controls underwent T2 relaxation and DTI examinations to produce histograms of MWF and several DTI-derived metrics. MS MWF histograms differed considerably from those of controls, and differences in MS MWF histograms did not mirror differences in DTI histograms relative to matched controls.

This thesis focuses on spatial resolution enhancement of magnetic resonance imaging (MRI). In particular, it addresses methods of performing such enhancement in the Fourier domain. After a brief review of Fourier theory, the thesis reviews the physics of the MRI acquisition process in order to introduce a mathematical model of the measured data. This model is later used to develop and analyze methods for resolution enhancement, or "super-resolution'', in MRI. We then examine strategies of performing super-resolution MRI (SRMRI). We begin by exploring strategies that use multiple data sets produced by spatial translations of the object being imaged, to add new information to the reconstruction process. This represents a more detailed mathematical examination of the author's Master's work at the University of Calgary. Using our model of the measured data developed earlier in the thesis, we describe how the acquisition strategy determines the efficacy of the SRMRI process that employs multiple data sets. The author then explores the self-similarity properties of MRI data in the Fourier domain as a means of performing spatial resolution enhancement. To this end, a fractal-based method over (complex-valued) Fourier Transforms of functions with compact spatial support, derived from a fractal transform in the spatial domain, is explored. It is shown that this method of "Iterated Fourier Transform Systems" (IFTS) can be tailored to perform frequency extrapolation, hence spatial resolution enhancement. The IFTS method, however, is limited in scope, as it assumes that a spatial function f(x) may be approximated by linear combinations of spatially-contracted and range-modified copies of the entire function. In order to improve the approximation, we borrow from traditional fractal image coding in the spatial domain, where subblocks of an image are approximated by other subblocks, and employ such a block-based strategy in the Fourier domain. An examination of the statistical properties of subblock approximation errors shows that, in general, Fourier data can be locally self-similar. Furthermore, we show that such a block-based self-similarity method is actually equivalent to a special case of the auto-regressive moving average (ARMA) modeling method. The thesis concludes with a chapter on possible future research directions in SRMRI.

This thesis focuses on spatial resolution enhancement of magnetic resonance imaging (MRI). In particular, it addresses methods of performing such enhancement in the Fourier domain. After a brief review of Fourier theory, the thesis reviews the physics of the MRI acquisition process in order to introduce a mathematical model of the measured data. This model is later used to develop and analyze methods for resolution enhancement, or "super-resolution'', in MRI. We then examine strategies of performing super-resolution MRI (SRMRI). We begin by exploring strategies that use multiple data sets produced by spatial translations of the object being imaged, to add new information to the reconstruction process. This represents a more detailed mathematical examination of the author's Master's work at the University of Calgary. Using our model of the measured data developed earlier in the thesis, we describe how the acquisition strategy determines the efficacy of the SRMRI process that employs multiple data sets. The author then explores the self-similarity properties of MRI data in the Fourier domain as a means of performing spatial resolution enhancement. To this end, a fractal-based method over (complex-valued) Fourier Transforms of functions with compact spatial support, derived from a fractal transform in the spatial domain, is explored. It is shown that this method of "Iterated Fourier Transform Systems" (IFTS) can be tailored to perform frequency extrapolation, hence spatial resolution enhancement. The IFTS method, however, is limited in scope, as it assumes that a spatial function f(x) may be approximated by linear combinations of spatially-contracted and range-modified copies of the entire function. In order to improve the approximation, we borrow from traditional fractal image coding in the spatial domain, where subblocks of an image are approximated by other subblocks, and employ such a block-based strategy in the Fourier domain. An examination of the statistical properties of subblock approximation errors shows that, in general, Fourier data can be locally self-similar. Furthermore, we show that such a block-based self-similarity method is actually equivalent to a special case of the auto-regressive moving average (ARMA) modeling method. The thesis concludes with a chapter on possible future research directions in SRMRI.

Blood oxygen level dependent (BOLD) functional magnetic resonance imaging is a non-invasive technique used to trace changes in neural dynamics in reaction to mental activity caused by perceptual, motor or cognitive tasks. The BOLD response is a complex signal, a consequence of a series of physiological events regulated by increased neural activity. A method to infer from the BOLD signal onto underlying neuronal activity (hemodynamic inverse problem) is proposed in Chapter 2 under the assumption of a previously proposed mathematical model on the transduction of neural activity to the BOLD signal. Also, in this chapter we clarify the meaning of the neural activity function used as the input for an intrinsic dynamic system which can be viewed as an advanced substitute for the impulse response function. Chapter 3 describes an approach for recovering neural timing information (mental chronometry) in an object interaction decision task via solving the hemodynamic inverse problem. In contrast to the hemodynamic level, at the neural level, we were able to determine statistically significant latencies in activation between functional units in the model used. In Chapter 4, two approaches for regularization parameter tuning in a regularized-regression analysis are compared in an attempt to find the optimal amount of smoothing to be imposed on fMRI data in determining an empirical hemodynamic response function. We found that the noise autocorrelation structure can be improved by tuning the regularization parameter but the whitening-based criterion provides too much smoothing when compared to cross-validation. Chapter~5 illustrates that the smoothing techniques proposed in Chapter 4 can be useful in the issue of correlating behavioral and hemodynamic characteristics. Specifically, Chapter 5, based on the smoothing techniques from Chapter 4, seeks to correlate several parameters characterizing the hemodynamic response in Broca's area to behavioral measures in a naming task. In particular, a condition for independence between two routes of converting print to speech in a dual route cognitive model was verified in terms of hemodynamic parameters.

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The purpose of this study is to determine features of uterine leiomyoma on Magnetic Resonance Imaging (MRI) that identify predictors of response to Uterine Arterial Embolization (UAE). MRI images were obtained before and after UAE in 35 women. These images were analyzed for uterine and fibroid size changes along with fibroid border characteristics and location for a total of 73 fibroids. Fibroids were classified as either smooth or lobulated based on border appearance on MR imaging to determine any differences in mean fibroid volume reduction post-embolization. The mean decrease in fibroid volume from pre-embolization to post-embolization was 48.1% ± 28.6 % (SD) (P < 0.001). No statistical difference was detected in the mean volume reduction between lobulated and smooth fibroids, 40.6% ± 23.1% (SD) and 50.9% ± 30.2% (SD) respectively, with a confidence interval [-25.1, 4.6, SEM 7.5, Df 71], single factor ANOVA (F[1,71]=1.88, Fcrit=3.98, p=0.17). However, some difference was detected in the failure rate of lobulated versus smooth fibroids to embolization, 5% and 9.4% respectively, ANOVA (F [1, 71]= 0.37, Fcrit= 3.98, p > 0.1), albeit at low statistical power. Also no difference was detected in mean fibroid volume reduction between intramural, submucosal, and subserosal fibroids. Thus, we introduced a novel characteristic by which to classify uterine fibroids based upon border appearance on MR imaging.

Thesis (Ph. D.)--Case Western Reserve University, 2009. / [School of Medicine] Department of Biology. Includes bibliographical references.

Thesis (Ph. D.)--University of Hong Kong, 2001. / Includes bibliographical references.

Thesis (Ph. D.)--University of Texas at Austin, 2000. / Vita. Includes bibliographical references (leaves 165-173). Available also in a digital version from Dissertation Abstracts.

Thesis (M.S.)--Rutgers University, 2008. / "Graduate Program in Biomedical Engineering." Includes bibliographical references (p. 47-49).