New Fourier-space sampling methods for fast magnetic resonance imaging and flow quantification

Magnetic resonance imaging (MRI) has become a popular and effective diagnostic tool in hospitals since its initial clinical use in the early 1980s. MRI can provide not only in vivo morphological images but also physiological information such as blood flow velocity. The raw signals acquired from an MR scanner are usually interpreted as samples in Fourier space or so-called k-space. This thesis introduces new k-space sampling schemes for significantly reducing the scan times for general imaging and for flow quantification.; The first scheme is a variable-density sampling method which samples the high-spatial-frequency regions with a sampling density lower than that required by the well-known Nyquist sampling theorem. Although aliasing artifacts occur in the image, they can be diffuse and negligible compared to random noise if the sampling positions are adequately arranged. This method is particularly important for fast cardiovascular imaging where the scan time is limited by cardiac and respiratory motion.; The second sampling method slightly offsets the center of spiral trajectories so that the off-centered spiral trajectories are insensitive to the timing mis-registration between gradient and data acquisition systems of the MRI scanner. The timing error can cause shading artifact in spiral images and results in significant errors in quantitative applications such as flow quantification. This off-centered spiral trajectory is a simple but robust method to solve the timing problem.; Lastly a new flow quantification method based on Fourier velocity encoding is presented to overcome the notorious partial volume effects associated with conventional phase contrast methods. A new analysis framework is proposed to estimate the flow rate from low-spatial resolution and low-velocity-resolution velocity images which can be obtained in very short scan times. This method can extend the application of MR flow quantification to smaller vessels.; The concepts introduced in this thesis relieve MRI users from traditional thinking barriers such as Nyquist sampling criteria and partial volume effects. These concepts will stimulate more theoretical research in Fourier-space sampling and facilitate more clinical applications by reducing the scan time.