Physics based iterative reconstruction for MRI: Compensating and estimating field inhomogeneity and T*(2) relaxation

Functional magnetic resonance imaging (fMRI) using the Blood-Oxygenation Level Dependent (BOLD) effect relies on microscopic susceptibility differences between oxygenated and deoxygenated blood to image functional organization in the brain. Higher magnetic field strengths and single-shot acquisitions give fMRI higher BOLD contrast and better temporal resolution, but these same parameters make the scans more sensitive to susceptibility-induced image distortions. Several noniterative image reconstruction methods are currently used to compensate for field inhomogeneities, but these methods assume that the field map that characterizes the off-resonance frequencies is spatially smooth, an assumption that is violated in areas near air/tissue interfaces in the brain. In this thesis, I develop an iterative, inverse problem approach to image reconstruction for MRI that takes into account field inhomogeneity and $T*2$-relaxation during the signal acquisition, receiver coil sensitivities, arbitrary k-space trajectories, and within-voxel gradients in the field map. The iterative reconstruction is not limited by the smoothly-varying field map assumption and does not require the sample density compensation of the non-iterative methods for non-Cartesian trajectories. The iterative reconstruction was extended to simultaneously estimate the image, field map, and $T*2$ map for quantitative fMRI experiments. Also, using under-sampled k-space trajectories and multiple receiver coils, the iterative reconstruction was applied to SENSitivity Encoding (SENSE) experiments. In simulation, phantom, and human experiments, I compare the quality and accuracy of the field-corrected reconstructions using the iterative method versus the standard field-corrected method of conjugate phase. I also examine the stability of the iterative method for reconstructing time-series images from an fMRI study. I conclude that the iterative method results in stable image reconstructions for time series data and results in more accurate reconstructions when non-smooth field inhomogeneities are present. Using the joint estimation algorithm during a fMRI time series, respiration-induced phase variations and main field drift were accurately tracked and compensated. The increased accuracy of the jointly estimated field maps resulted in a larger number of activated voxels detected.