Improved encoding pulses for Bloch–Siegert mapping
Graphical abstract
Highlights
► A new family of short RF pulses for Bloch–Siegert (BS) mapping is introduced. ► The pulses are shown to produce larger BS phase shifts than pulse currently utilized. ► They produce lower on-resonance excitation than pulses currently utilized. ► They result in improved accuracy in areas with large B0 field inhomogeneities. ► Pulses result in lower SAR in areas with large B0 field inhomogeneities.
Introduction
For magnetic resonance imaging at high field (⩾3 T), and in parallel transmission [1], [2], it is important to consider subject-dependent spatial variations of the magnitude of the transmit RF magnetic field , and many methods have been developed to measure maps. Recently, a field mapping method based on the Bloch–Siegert (BS) shift has been proposed [3], which uses a high-amplitude RF pulse played with a frequency offset far from resonance to impart a phase shift in the MR signal that is approximately proportional to . The method has received significant attention for its ease of implementation and robustness to relaxation effects. It is also accurate and sensitive over a relatively wide range of and inhomogeneities in the main (B0) field. While other phase-based methods exist (such as Ref. [4]), prior to this method most mapping was performed using magnitude-based techniques [5], [6], [7] that suffer from poor dynamic range and are sensitive to errors due to T1 relaxation, necessitating relatively long repetition times (TRs) that limit their speed and applicability. Various T1-insensitive AFI and double angle methods have been introduced [8], [9], but these still generally require longer TRs than phase-based methods due to the large amount of gradient spoiling required [9] or the need to accommodate saturation modules [8].
However, BS mapping is challenging at 7 T and higher due to SAR limitations and signal loss resulting from the high amplitude and long duration of the -encoding pulse used in the sequence (typically 4–6 ms at full RF power [10]). Hence, it is desirable to shorten the pulse while maintaining the sequence’s sensitivity. The pulse also must negligibly tip on-resonant spins towards or away from the z-axis. To achieve this we propose a new method for BS pulse design in which both RF envelope and frequency waveforms are optimized to maximize sensitivity, subject to a constraint requiring negligible on-resonance excitation. Our method produces distinctive and interpretable waveforms. We present the results of simulations and in vivo (human head) and phantom experiments at 7 T to validate the performance of the designed pulses, in terms of BS phase shift and on-resonance excitation. The pulses are compared to Fermi pulses conventionally used in BS mapping [3]. Results show that the designed pulses possess higher sensitivity than much longer Fermi pulses, while producing similar or lower on-resonance excitation. We also show that the shorter duration of the pulses enables BS mapping in anatomical regions with large B0 inhomogeneities, such as the lower brain at 7 T.
Section snippets
Theory
A BS acquisition is typically based on a gradient-recalled echo (GRE) sequence and comprises an excitation pulse, followed by the off-resonance -encoding pulse that is surrounded by bipolar crusher gradients, followed by the signal readout. Denoting the magnetization after the excitation pulse as , the transverse magnetization after the -encoding pulse and its crushers is [11]:where α and β are the net spinor parameters of the
Pulse designs
A 2 ms pulse duration was initially selected with time a step of Δt = 6.4 μs, yielding Nt = 312 amplitude and frequency samples to be optimized, for a total of 624 variables. The optimization was performed on a discretized grid spanning 1–20 μT and ±600 Hz with 1 μT and 15 Hz steps, respectively [10]. βmax was set to 0.01. The maximization problem was solved using the fmincon function in MATLAB (The Mathworks, Natick, USA), which was set to use an interior-point algorithm with a termination
Results
Fig. 2 plots the 6 ms/4 kHz Fermi, 2 ms block, and optimized 2 ms pulses. The optimized 2 ms pulse has a block amplitude waveform, but a frequency waveform that sweeps in a ‘U’ shape from far away from resonance, to near-resonance, and back away from resonance. The frequency spikes at either end are present in all the optimized pulses and differentiate the pulses from a block pulse with a constant frequency offset. The optimized 2 ms waveform has 57% lower SAR than the 6 ms Fermi pulse,
Discussion and conclusions
We have introduced and evaluated a new family of -to-phase encoding pulses for Bloch–Siegert mapping that have improved performance (lower on-resonance excitation over wide frequency bandwidths) and shorter durations than conventional pulses with similar sensitivities. We described the design of these pulses and demonstrated an optimized 2 ms pulse in 7 T human head mapping of central and lower axial brain slices, which comprised wide ranges of and Δf0 values. The optimized pulse
Acknowledgment
This work was supported by NIH (BRP) Grant No. R01EB000461.
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