Advances in Non-Cartesian Parallel Magnetic Resonance Imaging using the GRAPPA Operator (2008)

Magnetic Resonance Imaging (MRI) is an imaging modality which provides anatomical or functional images of the human body with variable contrasts in an arbitrarily positioned slice without the need for ionizing radiation. In MRI, data are not acquired directly, but in the reciprocal image space (otherwise known as k-space) through the application of spatially variable magnetic field gradients. The k-space is made up of a grid of data points which are generally acquired in a line-by-line fashion (Cartesian imaging). After the acquisition, the k-space data are transformed into the image domain using the Fast Fourier Transformation (FFT). However, the acquisition of data is not limited to the rectilinear Cartesian sampling scheme described above. Non-Cartesian acquisitions, where the data are collected along exotic trajectories, such as radial and spiral, have been shown to be beneficial in a number of applications. However, despite their additional properties and potential advantages, working with non-Cartesian data can be complicated. The primary difficulty is that non-Cartesian trajectories are made up of points which do not fall on a Cartesian grid, and a simple and fast FFT algorithm cannot be employed to reconstruct images from non-Cartesian data. In order to create an image, the non-Cartesian data are generally resampled on a Cartesian grid, an operation known as gridding, before the FFT is performed. Another challenge for non-Cartesian imaging is the combination of unusual trajectories with parallel imaging. This thesis has presented several new non-Cartesian parallel imaging methods which simplify both gridding and the reconstruction of images from undersampled data. In Chapter 4, a novel approach which uses the concepts of parallel imaging to grid data sampled along a non-Cartesian trajectory called GRAPPA Operator Gridding (GROG) is described. GROG shifts any acquired k-space data point to its nearest Cartesian location, thereby converting non-Cartesian to Cartesian data. The only requirements for GROG are a multi-channel acquisition and a calibration dataset for the determination of the GROG weights. Chapter 5 discusses an extension of GRAPPA Operator Gridding, namely Self-Calibrating GRAPPA Operator Gridding (SC-GROG). SC-GROG is a method by which non-Cartesian data can be gridded using spatial information from a multi-channel coil array without the need for an additional calibration dataset, as required in standard GROG. Although GROG can be used to grid undersampled datasets, it is important to note that this method uses parallel imaging only for gridding, and not to reconstruct artifact-free images from undersampled data. Chapter 6 introduces a simple, novel method for performing modified Cartesian GRAPPA reconstructions on undersampled non-Cartesian k-space data gridded using GROG to arrive at a non-aliased image. Because the undersampled non-Cartesian data cannot be reconstructed using a single GRAPPA kernel, several Cartesian patterns are selected for the reconstruction. Finally, Chapter 7 discusses a novel method of using GROG to mimic the bunched phase encoding acquisition (BPE) scheme. In MRI, it is generally assumed that an artifact-free image can be reconstructed only from sampled points which fulfill the Nyquist criterion. However, the BPE reconstruction is based on the Generalized Sampling Theorem of Papoulis, which states that a continuous signal can be reconstructed from sampled points as long as the points are on average sampled at the Nyquist frequency. A novel method of generating the “bunched” data using GRAPPA Operator Gridding (GROG), which shifts datapoints by small distances in k-space using the GRAPPA Operator instead of employing zig-zag shaped gradients, is presented in this chapter. With the conjugate gradient reconstruction method, these additional “bunched” points can then be used to reconstruct an artifact-free image from undersampled data. This method is referred to as GROG-facilitated Bunched Phase Encoding, or GROG-BPE.