Figure 4:

Phantom results at TE=68ms. a) and b) the same as in Fig.3 but the maximum angular velocity is about 20°/s. Without motion correction (c), the echo was within the sampled k-space window for velocities ${|\omega }_r|\le 7°/s$. (d) In contrast, when intra-scan 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 (212/216) acquisitions. Also, almost all acquisitions received 2 tracking packets (blue circles), and no split into sub-populations was observed when intra-scan motion updates were applied. The slopes of a linear fit $\Delta k_x^{max}=a{\omega }_r+b$ are c) a=14.35, b=2.86, r²=0.91; and d) a=−0.47, b=3.47, r²=0.07 (subpopulation with two tracking packets received, blue circles). (e) The residual k-space echo shift (after removal of first-order motion term, i.e. velocity) shows a clear linear dependence upon rotational acceleration ∝_r. Parameters from a bivariant linear fit $\Delta k_x^{max}=a_1{\omega }_r+a_2{\propto }_r+b$ are: a₁=−0.47, a₂=0.47, b=3.15, with r²=0.45. 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.