The development of the algorithm was based on an assumption of small excitation angles, and it was shown that without the described split-and-reflect configuration, the pulses’ selectivity severely degrades when they are scaled to excite large tip-angles. This degradation was attributed to an increasing nonlinear phase variation in the αα profile that

grows with flip angle. Unfortunately, the degradation cannot be mitigated by explicit design of an αα filter with a zero phase response combined with use of the full inverse SLR transform rather than the small-excitation version used in the described algorithm, since check details as noted earlier it is impossible to design an FIR filter with the required αα magnitude response and zero phase response. Nor can the degradation be mitigated by adjusting the areas of the pre- and rewinding A(t)A(t) lobes: this approach could eliminate first-order phase variation Linsitinib in vivo in the αα profile in the slice, but would leave a phase roll across the αα and ββ profiles, and consequently nonzero αIαI and βIβI that would degrade the MxyMxy profile further. While the described split-and-reflect modification

to the pulses enables pulses designed by the algorithm to excite selective large-tip-angle profiles up to 180°, there will still be some loss in selectivity due to the bandwidth narrowing effect [26]. Attaining the most accurate large-tip excitations will require the development of a novel approach to inverting the ββ profile along a bipolar trajectory, subject isometheptene to a zero-phase αα. Recent advances in multidimensional SLR pulse design may lead to the development of such a method in the future [27] and [28]. The design of |B1+|-selective refocusing pulses remains an open problem and will require a different problem formulation than that developed here. Previous reports of |B1+|-selective pulse design approaches [9] and [10] did not address the design of pulses

with tip angles greater than 90°. In addition to the pulse construction described here, Ref. [9] describes a ‘transposed sinc pulse’ configuration (Fig. 6 in Ref. [9]), which is equivalent to playing the first half the waveforms presented here with twice the ΔωRF(t)ΔωRF(t) amplitude. While the shorter duration of these pulses is attractive, compared to the full pulses their excitation profiles are degraded since the |B1+|-frequency trajectory visits only positive frequencies, leading to increased ββ amplitude in the stopband and corresponding undesired excitation. Inversion pulses constructed this way also exhibit substantially degraded and narrowed profiles. It is possible that future work will reveal an approach to design these pulses that can accurately account for or mitigate these effects. There remain multiple questions to be answered regarding the use and performance of |B1+|-selective pulses, which have not been previously addressed and are beyond the scope of the present work.