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Multidimensional MR mapping of multiple components of velocity and acceleration by fourier phase encoding with a small number of encoding steps

Previous studies have shown that the multi‐step approach of velocity or acceleration encoding is highly efficient in terms of the signal‐to‐noise ratio per unit time. This work describes a multidimensional extension of this method for simultaneously measuring multiple components of velocity and acceleration with a few encoding steps. N flow dimensions were encoded with an ND‐matrix, obtained by combining the various flow‐encoding gradients. The small matrix obtained with as few as two encoding steps can be extended by zero‐filling in all N dimensions and using ND‐Fourier transformation to obtain the maximum of the resulting peak in the ND‐matrix, which gives simultaneously all the components of velocity and/or acceleration. The processing time was shortened by using a method of phase computation that gives the same precision as Fourier transformation, but is much faster. A rotating disk was used to show that the velocity‐to‐noise ratio increases with the number of dimensions acquired, demonstrating the efficiency of multidimensional flow measurements. The feasibility of the method is illustrated by 3D maps of the myocardium velocity, and 2D measurement of velocity and acceleration in the ascending aorta—both obtained by multidimensional phase encoding in volunteers. Magn Reson Med 44:723–730, 2000. © 2000 Wiley‐Liss, Inc.