A velocity k-space analysis of flow effects in echo-planar and spiral imaging

A velocity k-space formalism facilitates the analysis of flow effects for imaging sequences involving time-varying gradients such as echo-planar and spiral. For each sequence, the velocity k-space trajectory can be represented by kv(kr); that is, its velocity-frequency (kv) position as a function of spatial-frequency (kr) position. In an echo-planar sequence, kv is discontinuous and asymmetric. However, in a spiral sequence, kv is smoothly varying, circularly symmetric, and small near the kr origin. To compare the effects of these trajectory differences, simulated images were generated by computing the k-space values for an in-plane vessel with parabolic flow. Whereas the resulting echo-planar images demonstrate distortions and ghosting that depend on the vessel orientation, the spiral images exhibit minimal artifacts.