Understanding the zigzags of multi-echo phase signals by numerical simulations.

Understanding the multi-echo phase zigzag signals is instrumental to assuring the quality of MRI phase data acquisition for ensuing phase exploration and exploitation. This paper provides a theoretical and computational mechanism for understanding the zigzag multi-echo phase formation that has been observed in numerical multi-echo gradient-recalled (GRE) simulations of clinical complex-valued brain MRI images. Based on intravoxel dephasing mechanism, we calculated a train of multi-GRE complex-valued voxel signals by simulating field gradient reversals under perturbations in either gradient strength (G±<i>δ</i>G) or gradient duration (Δ±<i>δ</i>Δ), as well as the simultaneous bi-variable gradient perturbations (<i>δ</i>G<i>δ</i>Δ). In this theoretical experiment, we observed a zigzag line of one-shot multi-echo phase signals at a voxel with respect to linear stepwise field gradient variations in<i>δ</i>G ∝ n and<i>δ</i>Δ ∝ n (where n denotes the echo index). However, the multi-echo magnitude signals were invariant to field gradient reversal, i.e. no multi-echo magnitude zigzags. To support our simulations, we analyzed the clinical one-shot multi-echo T2*-weighted MRI phase images and found similar multi-echo phase zigzags. In this way, we provide a theoretical and computational understanding of multi-echo phase zigzag artifacts, specifically for the eddy current effect on one-shot multi-GRE signals in practice.