First and second order derivatives for optimizing parallel RF excitation waveforms

Majewski, Kurt; Ritter, Daniel

doi:10.1016/j.jmr.2015.06.010

Cited by 11 publications

(10 citation statements)

References 44 publications

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“…Majewski and Ritter (54) have recently made a thorough study on how to calculate first- and second-order derivatives for the MLS problem in the quaternion frame. They give a detailed analysis of the vast number of floating-point operations needed to compute the analytical first- and second-order derivatives.…”

Section: Theorymentioning

confidence: 99%

Local SAR, global SAR, and power‐constrained large‐flip‐angle pulses with optimal control and virtual observation points

Vinding

Guérin

Nielsen

2015

Magnetic Resonance in Med

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Purpose To present a constrained optimal-control (OC) framework for designing large-flip-angle parallel-transmit (pTx) pulses satisfying hardware peak-power as well as regulatory local and global specific-absorption-rate (SAR) limits. The application is 2D and 3D spatial-selective 90° and 180° pulses. Theory and Methods The OC gradient-ascent-pulse-engineering method with exact gradients and the limited-memory Broyden-Fletcher-Goldfarb-Shanno method is proposed. Local SAR is constrained by the virtual-observation-points method. Two numerical models facilitated the optimizations, a torso at 3 T and a head at 7 T, both in eight-channel pTx coils and acceleration-factors up to 4. Results The proposed approach yielded excellent flip-angle distributions. Enforcing the local-SAR constraint, as opposed to peak power alone, reduced the local SAR 7 and 5-fold with the 2D torso excitation and inversion pulse, respectively. The root-mean-square errors of the magnetization profiles increased less than 5% with the acceleration factor of 4. Conclusion A local and global SAR, and peak-power constrained OC large-flip-angle pTx pulse design was presented, and numerically validated for 2D and 3D spatial-selective 90° and 180° pulses at 3 T and 7 T.

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Section: Theorymentioning

confidence: 99%

Local SAR, global SAR, and power‐constrained large‐flip‐angle pulses with optimal control and virtual observation points

Vinding

Guérin

Nielsen

2015

Magnetic Resonance in Med

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“…More background on SAR constraints can be found in [4,5,15]. The RF pulse design problem is to find a SAR-compliant RF waveform, which accurately produces the desired magnetization and also respects the physical capabilities of the scanner hardware; see [12,16] and the example of Section 4.2.…”

Section: Theorymentioning

confidence: 99%

Quick Reduction of Specific Absorption Rate Constraints in Parallel RF Excitation Pulse Design by Maximum Volume Inscribed Ellipsoids

Majewski

2019

Concepts in Magnetic Resonance Part A

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In medical magnetic resonance imaging, parallel radio frequency excitation pulses have to respect a large number of specific absorption rate constraints. Geometrically, each of these constraints can be interpreted as a complex, centered ellipsoid. We propose to replace a collection of such constraints by the single constraint which corresponds to the associated maximum volume inscribed ellipsoid and implies all original constraints. We describe how to compute this ellipsoid via convex programming. Examples show that this reduction has very short computation times but cuts away parts of the feasible power domain.

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“…Using our set-up, this yielded for one single evaluation of the cost-function and its gradient a computation time of 34/50/70 ms respectively for the 5, 7 and 9 k T -points pulses. However, alternative and efficient CPU implementations with more analytical approaches can be attempted as well [18,20]. In our current implementation, no constraint on the k-space trajectory was imposed, which may theoretically lead to non-feasible trajectories.…”

Section: # K Tpointsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…Likewise this design has been studied for various applications including multidimensional pulses [17,18], spokes [19] and k T-points pulses [10,[20][21][22]. For k T -points pulses however, either the blipped k-space trajectory was not optimized [10,20,21] or the constraints were not taken into account [22]. In this work, we build on the previous work of Dupas et al [15] to investigate the simultaneous optimization of non-selective k T -points RF pulses and the blipped k-space trajectories at 7T, under explicit SAR and power constraints, using the Magnitude Least Squares (MLS) cost function [23] and in the large flip angle regime, which can be used for instance for inversion [6] and refocusing [24] purposes.…”

Section: Introductionmentioning

confidence: 99%

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Joint design of k T -points trajectories and RF pulses under explicit SAR and power constraints in the large flip angle regime

Gras

Luong

Amadon

et al. 2015

Journal of Magnetic Resonance

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First and second order derivatives for optimizing parallel RF excitation waveforms

Cited by 11 publications

References 44 publications

Local SAR, global SAR, and power‐constrained large‐flip‐angle pulses with optimal control and virtual observation points

Local SAR, global SAR, and power‐constrained large‐flip‐angle pulses with optimal control and virtual observation points

Quick Reduction of Specific Absorption Rate Constraints in Parallel RF Excitation Pulse Design by Maximum Volume Inscribed Ellipsoids

Joint design of k T -points trajectories and RF pulses under explicit SAR and power constraints in the large flip angle regime

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