On the Effective Centre of Excitation and the Point of Gradient Moment Expansion for 2D-Selective Excitation in the Presence of Flow

In this work, we demonstrate the distinction and importance of two virtual time points during excitation for correct flow compensation and quantification: the centre of excitation ($$$t_0^\text{m}$$$) at which spins are excited and thus magnitude is generated, and the isophase time-point ($$$t_0^\text{ph}$$$) at which all excited spins are in phase. A general method to determine $$$t_0^\text{m}$$$ is presented and $$$t_0^\text{ph}$$$ and $$$t_0^\text{m}$$$ are shown to be not necessarily identical. Finally, phantom experiments demonstrate that the knowledge of $$$t_0^\text{m}$$$ is required to remove the displacement artefact in phase-encoding directions to enable correct flow compensation and imaging.