Figure 2
Selective sensing of averages and variances arising from the gradient distributions by (a) symmetric-NOGSE (sNOGSE) and (c) asymmetric-NOGSE (aNOGSE) sequences. The corresponding modulation waveforms f(t) and f 0(t) are shown in panel (b) and (d) for sNOGSE and aNOGSE respectively. (e) Normalized NOGSE signals expected as a function of the delay x, where \((N-\mathrm{2)}x+2y=T{E}_{NOGSE}=TE/2\). By normalizing signals for x ≪ y and then changing x, y while keeping all other parameters – including N and TE– constant, s- and a-NOGSE sequences enable the characterization of the IGDT effects. sNOGSE’ s waveform is symmetric vs the central π refocusing pulse; all cross-terms with the internal gradients are thus zero, freeing the experiment from all internal gradients effects (panel c, black solid line). By contrast, the aNOGSE’ s waveform will be affected by both the 1st and 2nd order effects related to the internal gradient cross-terms. The legends describes the different weightings of these attenuation factors stemming from the background gradient distributions. The quantities \({\rm{\Delta }}{\beta }_{Cross}^{-}\) and \({\rm{\Delta }}{\beta }_{Cross}^{+}\) used to selectively determine the average \(\langle {G}_{0}\rangle \) and variance \(\langle {({\rm{\Delta }}{G}_{0})}^{2}\rangle \) are shown with arrows, where the different signs denote the application of the external gradient G parallel and anti-parallel to the background gradient direction. Other assumptions include \(\langle {G}_{0}\rangle /G=0.1\), \(\sqrt{\langle {\rm{\Delta }}{G}_{0}^{2}\rangle }/\langle {G}_{0}\rangle =1\) and N = 8.
