A Velocity k‐Space Analysis of Flow Effects in Echo‐Planar and Spiral Imaging

Abstract

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 k_v (k)_r; that is, its velocity‐frequency (k_r) position as a function of spatial‐frequency (k_r) position. In an echo‐planar sequence, k_r is discontinuous and asymmetric. However, in a spiral sequence, k_r is smoothly varying, circularly symmetric, and small near the k_r 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.