Figure 3:

Phantom results at TE=80ms. A gel phantom was manually and quasi-sinusoidally rotated about the y-axis. (a) The phantom was moved back and forth between two turning points by ±8°, with (b) an angular velocity of about 10°/s. The trajectories shown were acquired with motion correction On, but those with motion correction Off are similar. The dependence of the echo center shift (y-axis) on the rotational velocity (x-axis) is presented in (c) and (d). Without motion correction (c), the echo center was within the sampled k-space window only for velocities ${|\omega }_r|\le 7°/s$. (d) In contrast, when motion correction was On, the shift of the echo signal maximum from the center of the k-space fell within the sampling window for almost all (214/216) acquisitions. However, the graph (d) shows 2 major sub-populations, one when 2 tracking packets were received between the excitation and refocusing pulse (blue circles, positive slope) and one when 3 tracking packets were received (red triangles, negative slope). A few acquisitions saw a single motion update only (green crosses). Also, a few acquisitions were probably misclassified (2 versus 3, and 1 versus 2), causing the regression lines to deviate from the main clusters to some degree. The gray vertical band indicates the range of velocities that the original DWI sequence without intra-sequence updates can tolerate before the echo is shifted outside of k-space.