A smoothing monotonic convergent optimal control algorithm for nuclear magnetic resonance pulse sequence design

Magnetic Resonance in Med

Skyum

Sangill

et al. 2019

Purpose Some advanced RF pulses, like multidimensional RF pulses, are often long and require substantial computation time because of a number of constraints and requirements, sometimes hampering clinical use. However, the pulses offer opportunities of reduced‐FOV imaging, regional flip‐angle homogenization, and localized spectroscopy, e.g., of hyperpolarized metabolites. Proposed herein is a novel deep learning approach to ultrafast design of multidimensional RF pulses with intention of real‐time pulse updates. Methods The proposed neural network considers input maps of the desired excitation region of interest and outputs a single‐channel, multidimensional RF pulse. The training library is, e.g., retrieved from a large image database, and the target RF pulses trained upon are calculated with a method of choice. Results A relatively simple neural network is enough to produce reliable 2D spatial‐selective RF pulses of comparable performance to the teaching method. For binary regions of interest, the training library does not need to be vast; hence, reestablishment of the training library is not necessarily cumbersome. The predicted pulses were tested numerically and experimentally at 3 T. Conclusion Relatively effortless training of multidimensional RF pulses, based on non‐MRI‐related inputs, but working in an MRI setting still, has been demonstrated. The prediction time of a few milliseconds renders real‐time updates of advanced RF pulses possible.

Section: Discussionmentioning

confidence: 99%

Ultrafast (milliseconds), multidimensional RF pulse design with deep learning

Magnetic Resonance in Med

Skyum

Sangill

et al. 2019

“…As will be seen in the presented comparative study, however, this monotonicity can get compromised for certain ill parameters. This fact has been studied in more detail by Maday et al 51 and Maximov et al 29 The iteration loop should in this case stop and the previous set of controls may be extracted. The δ and η parameters replace the role ε has in GRAPE.…”

Section: The Krotov-based Approachmentioning

confidence: 99%

“…24 Furthermore, for comparison, we adopted a second-order gradient ascent quasi-Newton algorithm known as Broyden 36 40 recently demonstrated that BFGS has a robust and relatively steep convergence in the later iterations, which may complement the Krotov approach being significantly faster in the first iterations. 24,29 Adapting this strategy, Eitan et al 41 found it worthwhile to combine Krotov with BFGS in relation to quantum control problems. In this work, we have adapted the Krotov-BFGS (multiple control variation of Eitan's approach) for the design of MDRF pulses.…”

mentioning

confidence: 99%

“…Without an educated initial guess, the Krotov approach convergences monotonically towards the global optimum. The Krotov approach has lately found applications in NMR spectroscopy, 24,29 quantum chemistry, 33, 34 quantum control, 35 and dynamic nuclear polarization (DNP). 24 Furthermore, for comparison, we adopted a second-order gradient ascent quasi-Newton algorithm known as Broyden 36 40 recently demonstrated that BFGS has a robust and relatively steep convergence in the later iterations, which may complement the Krotov approach being significantly faster in the first iterations.…”

mentioning

confidence: 99%

“…[26][27][28] In these areas, OC has demonstrated a great potential to establish experiments adapting well to technical challenges and constraints included in the cost functional, as for example, rf power limitations, 27 rf inhomogeneity, 22,23 and rf envelope "jaggedness." 29,30 Addressing MRI, OC procedures have so far involved gradient-based methods 20,26,27,31 exploiting conjugated gradient optimization. 32 Such methods are known to be robust and convergent within a finite number of iterations.…”

mentioning

confidence: 99%

See 2 more Smart Citations

Fast numerical design of spatial-selective rf pulses in MRI using Krotov and quasi-Newton based optimal control methods

The Journal of Chemical Physics

Maximov

Tošner

et al. 2012

Self Cite

A variable echo-number method for estimating R 2 in MRI-based polymer gel dosimetry Med. Phys. 38, 975 (2011) The use of increasingly strong magnetic fields in magnetic resonance imaging (MRI) improves sensitivity, susceptibility contrast, and spatial or spectral resolution for functional and localized spectroscopic imaging applications. However, along with these benefits come the challenges of increasing static field (B 0 ) and rf field (B 1 ) inhomogeneities induced by radial field susceptibility differences and poorer dielectric properties of objects in the scanner. Increasing fields also impose the need for rf irradiation at higher frequencies which may lead to elevated patient energy absorption, eventually posing a safety risk. These reasons have motivated the use of multidimensional rf pulses and parallel rf transmission, and their combination with tailoring of rf pulses for fast and low-power rf performance. For the latter application, analytical and approximate solutions are well-established in linear regimes, however, with increasing nonlinearities and constraints on the rf pulses, numerical iterative methods become attractive. Among such procedures, optimal control methods have recently demonstrated great potential. Here, we present a Krotov-based optimal control approach which as compared to earlier approaches provides very fast, monotonic convergence even without educated initial guesses. This is essential for in vivo MRI applications. The method is compared to a second-order gradient ascent method relying on the Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton method, and a hybrid scheme Krotov-BFGS is also introduced in this study. These optimal control approaches are demonstrated by the design of a 2D spatial selective rf pulse exciting the letters "JCP" in a water phantom.

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

Magnetic Resonance in Med

Guérin

Nielsen

2015

Self Cite

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.