Ideal spiral trajectory and spiral GRAPPA kernels. (a) The trajectory for arm 1 (solid curve) reaches the designed edge of k-space (dotted circle) at ~1.7 ms (white dot) from the start of the readout. Data acquired while rewinding gradient moments (dashed curve) were discarded during reconstruction. (b) The skipped arms of the dynamic data (dotted gray curves) per partition encoding step were reconstructed with through-time spiral GRAPPA. With respect to increasing sampling time (closed arrowhead) and arm index (open arrowhead) in the two insets, the direction of undersampling as well the relative spacing of known (white circles) and target (gray circles) points of the spiral GRAPPA kernel changes as a function of k-space location.