Magnetic Resonance Imaging (MRI) is a widely used, non-invasive imaging technique that provides a means to reveal structural and functional information of different body tissues in detail. Susceptibility Weighted Imaging (SWI) is a field in MRI that utilizes the information from the magnetic susceptibility property of different tissues using the gradient echo phase information. Although longer echo times (TEs) have been widely used in applications involving SWI, there are a few problems related with the long TE data, such as the strong blooming effect and phase aliasing even at macroscopic levels. In this thesis, the use of very short TEs is proposed to study susceptibility mapping. The short TEs can be used to study structures with susceptibilities an order of magnitude larger (such as air and bones in and around the brain sinuses, skull and teeth) than those within soft tissue. Using a new iterative susceptibility mapping technique that we recently developed, it becomes possible to map the geometry of such structures, which to date has proven difficult due to the lack of water content (for sinuses) or due to very short T2* (for bones). The method of phase replacement inside the sinuses proposed in this thesis provides more accurate phase information for the inversion than assuming zero or some arbitrary constant inside these structures. The first and second iterations were responsible for most of the changes in mapping out the susceptibility values. The mean susceptibility value in the sphenoid sinus is calculated as +9.3 ± 1.1ppm, close to the expected value of +9.4ppm for air. The reconstruction of the teeth in the in-vivo data provides a mean Δχ(teeth-tissue)=–3.3ppm, thanks to the preserved phase inside the jaw. The mean susceptibility inside a relatively homogeneous region of the skull bone was measured to be Δχ(bone-tissue)=–2.1ppm. Finally, these susceptibilities can be used to help remove the unwanted background fields prior to applying either SHARP or HPF. In addition, the effects of the background field gradient on flow compensation are studied. Due to the presence of these background gradients, an unwanted phase term is induced by the blood flow inside the vessels. Using a 3D numerical model and in vivo data, the background gradients were estimated to be as large as 1.5mT/m close to the air-tissue interfaces and 0.7mT/m inside the brain (leading to a potential signal loss of up to 15%). The quantitative susceptibility mapping (QSM) results were improved in the entire image after removing the confounding arterial phase thanks to the reduced ringing artifacts. Lastly, a novel approach to improve the susceptibility mapping results was introduced and utilized to monitor the changes in venous oxygen saturation levels as well as the changes in oxygen extraction fraction instigated by the vasodynamic agents, caffeine and acetazolamide. The internal streaking artifacts in the susceptibility maps were reduced by giving an initial susceptibility value uniformly to the structure-of-interest, based on the a priori information. For veins, the iterative results, when the initial value of 0.45 ppm was used, were the best in terms of the highest accuracy in the mean susceptibility value (0.453 ppm) and the lowest standard deviation (0.013 ppm). Using this technique, the venous oxygen saturation levels (inside the internal cerebral veins (ICVs)) for normal physiological conditions, post-caffeine and post-Diamox for the first volunteer were calculated as (mean ± standard deviation): Y_Normal = 69.1 ± 3.3 %, Y_Caffeine = 60.5 ± 2.8 % and Y_Diamox = 79.1 ± 4.0%. For the caffeine challenge, the percentage change in oxygen extraction fraction (OEF) for pre and post caffeine results was calculated as +27.0 ± 3.8%; and for the Diamox challenge, the percentage change in OEF was calculated as −32.6 ± 2.1 % for the ICVs. These vascular effects of Diamox and caffeine were large enough to be easily measured with susceptibility mapping and can serve as a sensitive biomarker for measuring reductions in cerebro-vascular reserve through abnormal vascular response, an increase in oxygen consumption during reperfusion hyperoxia or locally varying oxygen saturation levels in regions surrounding damaged tissue. In conclusion, our new approach to QSM offers a means to monitor venous oxygen saturation reasonably accurately and may provide a new means to study neurovascular diseases where there are changes in perfusion that affect the oxygen extraction fraction. / Thesis / Doctor of Philosophy (PhD) / Magnetic Resonance Imaging (MRI) is a widely used, non-invasive imaging technique that provides a means to reveal structural and functional information of different body tissues in detail. Susceptibility Weighted Imaging (SWI) is a field in MRI that utilizes the information from the magnetic susceptibility property of different tissues using the gradient echo phase information. Firstly, we demonstrate that using our phase replacement technique, it becomes possible to map the geometry of structures with almost no MR signal, which to date has proven difficult due to the lack of water content (for sinuses) or due to very short T2* (for bones). Secondly, the effects of the background field gradient on flow compensation were studied. Due to the presence of these background gradients, an unwanted phase term is induced by the blood flow inside the vessels. And, lastly, we present our new approach utilizing SWI data, offering a means to monitor venous oxygen saturation reasonably accurately and, potentially, a new means to study neurovascular diseases where there are changes in perfusion that affect the oxygen extraction fraction.