© RSNA, 2007
MR Myocardial Perfusion Imaging with k-Space and Time Broad-Use Linear Acquisition Speed-up Technique: Feasibility Study
Appendix E1
The k-t BLAST method exploits redundant information contained in time series of dynamic objects. For example, in perfusion imaging only the signals from the heart undergo dynamic changes, while the chest wall remains static. Therefore, the chest wall can be represented with considerably fewer data points than the number of data points required to reconstruct the dynamic changes in the heart. This insight allows considerably increased imaging efficiencies, assuming that the dynamics in the object can be identified. In the k-t BLAST method, imaging acceleration is achieved through regular undersampling of k-space in every dynamic acquisition while shifting the undersampling pattern cyclically over time (Fig E1a, E1c). This results in a sheared grid pattern in the acquired data if the data are viewed in so-called k-t space (Fig E1c). Here k denotes spatial frequency and t represents time. This undersampling of data in k-t space leads to time-varying foldover artifacts in the images if they are reconstructed straightforwardly with the Fourier transform (Fig E1e). To resolve the time-varying foldover from the undersampled data, low-resolution foldover-free images are acquired (Fig E1b, E1d). These low-resolution images are referred to as training data because they allow estimation of image content free of foldover and thereby provide information about the dynamics of the object. In the context of perfusion imaging, the training data are acquired interleaved with the undersampled data to ensure consistent information with respect to contrast agent bolus representation in both. The resulting sampling can be regarded as a variable-density sampling pattern. In image reconstruction, the data acquired are split into the undersampling data set and the training data set, with both data sets being transformed to the reciprocal x-f space, where x denotes spatial position and f temporal frequency. The resulting x-f training images are then used to construct the reconstruction filter (Fig E1f), which resolves the foldover in the undersampled images by distributing the image energy so that the expected reconstruction is minimized in a least-squares sense. This process results in foldover-free high-resolution images (Fig E1g). If one takes into account the acquisition of the training data, the net acceleration factor, Rnet, achievable with the k-t BLAST method can be calculated according to:
Rnet = N/[(N/R) + M],
where N denotes the number of profiles along the phase-encoding direction for a fully sampled (ie, non k-t BLAST) acquisition, R is the nominal reduction or k-t factor, and M contains the number of training profiles.
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| Figure E1: Outline of the k-t BLAST method. Data are acquired according to the sampling pattern (a). In reconstruction, the acquired data are split into the training data (b) and the undersampled data (c). The training data yield low-resolution foldover-free images (d). The undersampled data results in foldover images (e) if processed straightforwardly by using the Fourier transform. If one takes into account the sampling pattern (c) and the training data (b), a filter (f) can be designed (in a least-squares sense) that removes the foldover from the undersampled data (e), resulting in high-resolution foldover-free reconstructed images (g). |
