Elsevier

Journal of Magnetic Resonance

Volume 226, January 2013, Pages 79-87
Journal of Magnetic Resonance

Improved encoding pulses for Bloch–Siegert B1+ mapping

https://doi.org/10.1016/j.jmr.2012.11.004Get rights and content

Abstract

A new family of optimized encoding pulses for Bloch–Siegert (BS) |B1+| mapping is introduced, as well as an algorithm to design them. The pulses are designed by numerical maximization of BS sequence sensitivity, subject to constraints that ensure low on-resonance excitation. The pulses are in all cases characterized by a constant envelope and U-shaped frequency sweep. They are validated in simulations, 7 T in vivo experiments, and an experiment to measure their on-resonance excitation, and are compared to a Fermi pulse conventionally used in the BS method. The pulses are shown to produce larger phase shifts in a shorter time and with lower on-resonance excitation than the Fermi pulse, which results in lower SAR and improved |B1+| accuracy in areas of the body with large main field inhomogeneities.

Highlights

► A new family of short RF pulses for Bloch–Siegert (BS) |B1+| 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 |B1+| 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 (|B1+|), and many methods have been developed to measure |B1+| maps. Recently, a B1+ 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 B1+2. 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 B1+ and inhomogeneities in the main (B0) field. While other phase-based methods exist (such as Ref. [4]), prior to this method most B1+ 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 B1+ 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 B1+-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 B1+ mapping [3]. Results show that the designed pulses possess higher B1+ 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 B1+ 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 B1+-encoding pulse that is surrounded by bipolar crusher gradients, followed by the signal readout. Denoting the magnetization after the excitation pulse as Mxy-,Mz-, the transverse magnetization after the B1+-encoding pulse and its crushers is [11]:Mxy+=(α)2Mxy--β2Mxy-ei2ϕ(x)+2αβMz-eiϕ(x),where α and β are the net spinor parameters of the B1+

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 B1+-Δf0 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 SARk=1Ntak2 than the 6 ms Fermi pulse,

Discussion and conclusions

We have introduced and evaluated a new family of B1+-to-phase encoding pulses for Bloch–Siegert B1+ 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 B1+ mapping of central and lower axial brain slices, which comprised wide ranges of B1+ and Δf0 values. The optimized pulse

Acknowledgment

This work was supported by NIH (BRP) Grant No. R01EB000461.

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