On Variant Strategies To Solve The Magnitude Least Squares Optimization
  Problem In Parallel Transmission Pulse Design And Under Strict SAR And Power
  Constraints

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Abstract

Parallel transmission has been a very promising candidate technology to mitigate the inevitable radio-frequency field inhomogeneity in magnetic resonance imaging (MRI) at ultra-high field (UHF). For the first few years, pulse design utilizing this technique was expressed as a least squares problem with crude power regularizations aimed at controlling the specific absorption rate (SAR), hence the patient safety. This approach being suboptimal for many applications sensitive mostly to the magnitude of the spin excitation, and not its phase, the magnitude least squares (MLS) problem then was first formulated in 2007. Despite its importance and the availability of other powerful numerical optimization methods, this problem yet has been faced exclusively by the pulse designer with the so-called variable exchange method. In this paper, we investigate other strategies and incorporate directly the strict SAR and hardware constraints. Different schemes such as sequential quadratic programming (SQP), interior point (I-P) methods, semi-definite programming (SDP) and magnitude squared least squares (MSLS) relaxations are studied both in the small and large tip angle regimes with real data sets obtained in-vivo on a human brain at 7 Tesla. Convergence and robustness of the different approaches are analyzed, and recommendations to tackle this specific problem are finally given. Small tip angle and inversion pulses are returned in a few seconds and in under a minute respectively while respecting the constraints, allowing the use of the proposed approach in routine.

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Actual flip-angle imaging in the pulsed steady state: a method for rapid three-dimensional mapping of the transmitted radiofrequency field.

Vasily L Yarnykh (2007)

A new method has been developed for fast image-based measurements of the transmitted radiofrequency (RF) field. The method employs an actual flip-angle imaging (AFI) pulse sequence that consists of two identical RF pulses followed by two delays of different duration (TR(1) < TR(2)). After each pulse, a gradient-echo (GRE) signal is acquired. It has been shown theoretically and experimentally that if delays TR(1) and TR(2) are sufficiently short and the transverse magnetization is completely spoiled, the ratio r = S(2)/S(1) of signal intensities S(1) and S(2), acquired at the beginning of the time intervals TR(1) and TR(2), depends on the flip angle (FA) of applied pulses as r = (1 + n * cos(FA))/(n + cos(FA)), where n = TR(2)/TR(1). The method allows fast 3D implementation and provides accurate B(1) measurements that are highly insensitive to T(1). The unique feature of the AFI method is that it uses a pulsed steady-state signal acquisition. This overcomes the limitation of previous methods that required long relaxation delays between sequence repetitions. The method has been shown to be useful for time-efficient whole-body B(1) mapping and correction of T(1) maps obtained using a variable FA technique in the presence of nonuniform RF excitation.

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Transmit SENSE.

Ulrich Katscher, Serge Van Calenbergh, Peter Börnert … (2002)

The idea of using parallel imaging to shorten the acquisition time by the simultaneous use of multiple receive coils can be adapted for the parallel transmission of a spatially-selective multidimensional RF pulse. As in data acquisition, a multidimensional RF pulse follows a certain k-space trajectory. Shortening this trajectory shortens the pulse duration. The use of multiple transmit coils, each with its own time-dependent waveform and spatial sensitivity, can compensate for the missing parts of the excitation k-space. This results in a maintained spatial definition of the pulse profile, while its duration is reduced. This work introduces the concept of parallel transmission with arbitrarily shaped transmit coils (termed "Transmit SENSE"). Results of numerical studies demonstrate the theoretical feasibility of the approach. The experimental proof of principle is provided on a commercial MR scanner. The lack of multiple independent transmit channels was addressed by combining the excitation patterns from two separate subexperiments with different transmit setups. Shortening multidimensional RF pulses could be an interesting means of making 3D RF pulses feasible even for fast T(2)(*) relaxing species or strong main field inhomogeneities. Other applications might benefit from the ability of Transmit SENSE to improve the spatial resolution of the pulse profile while maintaining the transmit duration. Copyright 2003 Wiley-Liss, Inc.

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Parallel excitation with an array of transmit coils.

Y. Zhu (2004)

Theoretical and experimental results are presented that establish the value of parallel excitation with a transmit coil array in accelerating excitation and managing RF power deposition. While a 2D or 3D excitation pulse can be used to induce a multidimensional transverse magnetization pattern for a variety of applications (e.g., a 2D localized pattern for accelerating spatial encoding during signal acquisition), it often involves the use of prolonged RF and gradient pulses. Given a parallel system that is composed of multiple transmit coils with corresponding RF pulse synthesizers and amplifiers, the results suggest that by exploiting the localization characteristics of the coils, an orchestrated play of shorter RF pulses can achieve desired excitation profiles faster without adding strains to gradients. A closed-form design for accelerated multidimensional excitations is described for the small-tip-angle regime, and its suppression of interfering aliasing lobes from coarse excitation k-space sampling is interpreted based on an analogy to sensitivity encoding (SENSE). With or without acceleration, the results also suggest that by taking advantage of the extra degrees of freedom inherent in a parallel system, parallel excitation provides better management of RF power deposition while facilitating the faithful production of desired excitation profiles. Sample accelerated and specific absorption rate (SAR)-reduced excitation pulses were designed in this study, and evaluated in experiments. Copyright 2004 Wiley-Liss, Inc.