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Pre-Ramble
Steady-state free precession (SSFP, or more accurately, balanced SSFP1 Purists may object to my use of SSFP throughout this paper to refer to the balanced technique. However, I find "BSSFP" (or "bSSFP") visually and verbally jarring, and "balanced SSFP" wordy. I will take the prerogative of the invited paper and use the term coined by Carr in 1958.) is a magnetic resonance pulse sequence with a long history (Carr, 1958 ), despite being a relative latecomer to functional MRI. With the benefit of hindsight, one occasionally has the feeling that the 1958 NMR paper by Carr contains the "hard work" that underlies all subsequent SSFP-based methods. To those familiar with the technique, Carr's photographs of oscilloscope signal traces seem both quaint and prophetic, having been enthusiastically reproduced as the technique was re- and re-rediscovered in the context of MRI in the 1980s and 2000s (see Fig. 1 ). But to dismiss subsequent work as mere clever tweaks or serendipitous findings would downplay the acumen of those who have taken in the oddities and inconveniences of a notoriously complicated signal and seen novelty and opportunity. To be sure, SSFP has its objectively positive attributes: it can deliver the highest SNR efficiency of all known pulse sequences. But the enduring fascination it holds for many scientists, myself included, has more to do with its peculiar, occasionally troublesome, forever intriguing, properties. Recognizing that this sequence is less well known in the neuroimaging community, I will begin with a description of SSFP and its properties before moving on to its specific use in FMRI. The description of SSFP will necessarily be brief, and readers may wish to refer to: (Miller et al., 2011; Scheffler and Lehnhardt, 2003 ).
A complicated signal
At first encounter, SSFP is a bit bewildering. The sequence itself is fundamentally very simple: a rapid train of identical excitation pulses applied every TR ms in the absence of gradients (or, more accurately, in the presence of "balanced" gradients that induce no net phase to the magnetization by the end of the TR). The key consequence is that the angle between the magnetization and the RF pulse depends on the precession induced by static field off-resonance during the TR, which is kept very...