On variant strategies to solve the magnitude least squares optimization problem in parallel transmission pulse design and under strict SAR and power constraints

Robust time-shifted spoke pulse design in the presence of large B0 variations with simultaneous reduction of through-plane dephasing, B1+ effects, and the specific absorption rate using parallel transmission

PURPOSE

To design parallel transmission spokes pulses with time-shifted profiles for joint mitigation of intensity variations due to B1+ effects, signal loss due to through-plane dephasing, and the specific absorption rate (SAR) at 7T.

METHODS

We derived a slice-averaged small tip angle (SA-STA) approximation of the magnetization signal at echo time that depends on the B1+ transmit profiles, the through-slice B0 gradient and the amplitude and time-shifts of the spoke waveforms. We minimize a magnitude least-squares objective based on this signal equation using a fast interior-point approach with analytical expressions of the Jacobian and Hessian.

RESULTS

Our algorithm runs in less than three minutes for the design of two-spoke pulses subject to hundreds of local SAR constraints. On a B0/B1+ head phantom, joint optimization of the channel-dependent time-shifts and spoke amplitudes allowed signal recovery in high-B0 regions at no increase of SAR. Although the method creates uniform magnetization profiles (ie, uniform intensity), the flip angle varies across the image, which makes it ill-suited to T1-weighted applications.

CONCLUSIONS

The SA-STA approach presented in this study is best suited to T2*-weighted applications with long echo times that require signal recovery around high B0 regions. Magn Reson Med 76:540-554, 2016. © 2015 Wiley Periodicals, Inc.

Subject- and resource-specific monitoring and proactive management of parallel radiofrequency transmission

PURPOSE

Develop a practical comprehensive package for proactive management of parallel radiofrequency (RF) transmission.

METHODS

With a constrained optimization framework and predictive models from a prescan based multichannel calibration, we presented a method supporting design and optimization of parallel RF excitation pulses that accurately obey the forward/reflected peak and average power limits of the RF power amplifiers in parallel transmit imaging experiments and Bloch simulations. Moreover, local SAR limits were incorporated into the parallel RF excitation pulses using electromagnetic field simulations. Virtual transmit coils concept for minimization of reflected power (effecting subject-specific matching) was additionally demonstrated by leveraging experimentally calibrated power models.

RESULTS

Incorporation of experimentally calibrated power prediction models resulted in accurate compliance with prescribed hardware and global specific absorption rate (SAR) limits. Incorporation of spatial average 10 g SAR models, facilitated by simplifying numerical approximations, provided assurance of patient safety. RF pulses designed with various constraints demonstrated excellent excitation fidelity-the normalized root-mean-square error of the simulated excitation profiles was 2.6% for the fully constrained pulses, comparable to that of the unconstrained pulses. An RF shimming example showed a reduction of the reflected-to-forward power ratio to 1.7% from a conventional approach's 8.1%.

CONCLUSION

Using the presented RF pulse design method, effective proactive management of the multifaceted power and SAR limits was demonstrated in experimental and simulation studies. Magn Reson Med 76:20-31, 2016. © 2015 Wiley Periodicals, Inc.

Distributing coil elements in three dimensions enhances parallel transmission multiband RF performance: A simulation study in the human brain at 7 Tesla

PURPOSE

We explore the advantages of using a double-ring radiofrequency (RF) array and slice orientation to design parallel transmission (pTx) multiband (MB) pulses for simultaneous multislice (SMS) imaging with whole-brain coverage at 7 Tesla (T).

METHODS

A double-ring head array with 16 elements split evenly in two rings stacked in the z-direction was modeled and compared with two single-ring arrays consisting of 8 or 16 elements. The array performance was evaluated by designing band-specific pTx MB pulses with local specific absorption rate (SAR) control. The impact of slice orientations was also investigated.

RESULTS

The double-ring array consistently and significantly outperformed the other two single-ring arrays, with peak local SAR reduced by up to 40% at a fixed excitation error of 0.024. For all three arrays, exciting sagittal or coronal slices yielded better RF performance than exciting axial or oblique slices.

CONCLUSIONS

A double-ring RF array can be used to drastically improve SAR versus excitation fidelity tradeoff for pTx MB pulse design for brain imaging at 7 T; therefore, it is preferable against single-ring RF array designs when pursuing various biomedical applications of pTx SMS imaging. In comparing the stripline arrays, coronal and sagittal slices are more advantageous than axial and oblique slices for pTx MB pulses. Magn Reson Med 75:2464-2472, 2016. © 2016 Wiley Periodicals, Inc.

Parallel transmission pulse design with explicit control for the specific absorption rate in the presence of radiofrequency errors

PURPOSE

A new framework for the design of parallel transmit (pTx) pulses is presented introducing constraints for local and global specific absorption rate (SAR) in the presence of errors in the radiofrequency (RF) transmit chain.

METHODS

The first step is the design of a pTx RF pulse with explicit constraints for global and local SAR. Then, the worst possible SAR associated with that pulse due to RF transmission errors ("worst-case SAR") is calculated. Finally, this information is used to re-calculate the pulse with lower SAR constraints, iterating this procedure until its worst-case SAR is within safety limits.

RESULTS

Analysis of an actual pTx RF transmit chain revealed amplitude errors as high as 8% (20%) and phase errors above 3° (15°) for spokes (spiral) pulses. Simulations show that using the proposed framework, pulses can be designed with controlled "worst-case SAR" in the presence of errors of this magnitude at minor cost of the excitation profile quality.

CONCLUSION

Our worst-case SAR-constrained pTx design strategy yields pulses with local and global SAR within the safety limits even in the presence of RF transmission errors. This strategy is a natural way to incorporate SAR safety factors in the design of pTx pulses. Magn Reson Med 75:2493-2504, 2016. © 2015 Wiley Periodicals, Inc.

Universal pulses: A new concept for calibration-free parallel transmission

PURPOSE

A calibration-free parallel transmission method is investigated to mitigate the radiofrequency (RF) field inhomogeneity problem in brain imaging at 7 Tesla (T).

THEORY AND METHODS

Six volunteers were scanned to build a representative database of RF and static field maps at 7T. Small-tip-angle and inversion pulses were designed with joint k_T -points trajectory optimization to work robustly on all six subjects. The returned "universal" pulses were then inserted in an MPRAGE sequence implemented on six additional volunteers without further field measurements and pulse optimizations. Similar acquisitions were performed in the circularly polarized mode and with subject-based optimizations for comparison. Performance of the different approaches was evaluated by means of image analysis and computation of the flip angle normalized root mean square errors (NRMSE).

RESULTS

For both the excitation and inversion, the universal pulses (NRMSE∼11%) outperformed the circularly polarized (NRMSE∼28%) and RF shim modes (NRMSE∼20%) across all volunteers and returned slightly worse results than for subject-based optimized pulses (NRMSE∼7%).

CONCLUSION

RF pulses can be designed to robustly mitigate the RF field inhomogeneity problem over a population class. This appears as a first step toward another plug and play parallel transmission solution where the pulse design can be done offline and without measuring subject-specific field maps. Magn Reson Med 77:635-643, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

Optimal control design of turbo spin-echo sequences with applications to parallel-transmit systems

Purpose

The design of turbo spin‐echo sequences is modeled as a dynamic optimization problem which includes the case of inhomogeneous transmit radiofrequency fields. This problem is efficiently solved by optimal control techniques making it possible to design patient‐specific sequences online.

Theory and Methods

The extended phase graph formalism is employed to model the signal evolution. The design problem is cast as an optimal control problem and an efficient numerical procedure for its solution is given. The numerical and experimental tests address standard multiecho sequences and pTx configurations.

Results

Standard, analytically derived flip angle trains are recovered by the numerical optimal control approach. New sequences are designed where constraints on radiofrequency total and peak power are included. In the case of parallel transmit application, the method is able to calculate the optimal echo train for two‐dimensional and three‐dimensional turbo spin echo sequences in the order of 10 s with a single central processing unit (CPU) implementation. The image contrast is maintained through the whole field of view despite inhomogeneities of the radiofrequency fields.

Conclusion

The optimal control design sheds new light on the sequence design process and makes it possible to design sequences in an online, patient‐specific fashion. Magn Reson Med 77:361–373, 2017. © 2016 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine

Direct control of the temperature rise in parallel transmission by means of temperature virtual observation points: Simulations at 10.5 Tesla

PURPOSE

A method using parallel transmission to mitigate B1+ inhomogeneity while explicitly constraining the temperature rise is reported and compared with a more traditional SAR-constrained pulse design.

METHODS

Finite difference time domain simulations are performed on a numerical human head model and for a 16-channel coil at 10.5 Tesla. Based on a set of presimulations, a virtual observation point compression model for the temperature rise is derived. This compact representation is then used in a nonlinear programming algorithm for pulse design under explicit temperature rise constraints.

RESULTS

In the example of a time-of-flight sequence, radiofrequency pulse performance in some cases is increased by a factor of two compared with SAR-constrained pulses, while temperature rise is directly and efficiently controlled. Pulse performance can be gained by relaxing the SAR constraints, but at the expense of a loss of direct control on temperature.

CONCLUSION

Given the importance of accurate safety control at ultrahigh field and the lack of direct correspondence between SAR and temperature, this work motivates the need for thorough thermal studies in normal in vivo conditions. The tools presented here will possibly contribute to safer and more efficient MR exams.

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

In Magnetic Resonance Imaging at ultra-high field, kT-points radiofrequency pulses combined with parallel transmission are a promising technique to mitigate the B1 field inhomogeneity in 3D imaging applications. The optimization of the corresponding k-space trajectory for its slice-selective counterpart, i.e. the spokes method, has been shown in various studies to be very valuable but also dependent on the hardware and specific absorption rate constraints. Due to the larger number of degrees of freedom than for spokes excitations, joint design techniques based on the fine discretization (gridding) of the parameter space become hardly tractable for kT-points pulses. In this article, we thus investigate the simultaneous optimization of the 3D blipped k-space trajectory and of the kT-points RF pulses, using a magnitude least squares cost-function, with explicit constraints and in the large flip angle regime. A second-order active-set algorithm is employed due to its demonstrated success and robustness in similar problems. An analysis of global optimality and of the structure of the returned trajectories is proposed. The improvement provided by the k-space trajectory optimization is validated experimentally by measuring the flip angle on a spherical water phantom at 7T and via Quantum Process Tomography.

Signal-domain optimization metrics for MPRAGE RF pulse design in parallel transmission at 7 tesla

PURPOSE

Standard radiofrequency pulse design strategies focus on minimizing the deviation of the flip angle from a target value, which is sufficient but not necessary for signal homogeneity. An alternative approach, based directly on the signal, here is proposed for the MPRAGE sequence, and is developed in the parallel transmission framework with the use of the k_T -points parametrization.

METHODS

The flip angle-homogenizing and the proposed methods were investigated numerically under explicit power and specific absorption rate constraints and tested experimentally in vivo on a 7 T parallel transmission system enabling real time local specific absorption rate monitoring. Radiofrequency pulse performance was assessed by a careful analysis of the signal and contrast between white and gray matter.

RESULTS

Despite a slight reduction of the flip angle uniformity, an improved signal and contrast homogeneity with a significant reduction of the specific absorption rate was achieved with the proposed metric in comparison with standard pulse designs.

CONCLUSION

The proposed joint optimization of the inversion and excitation pulses enables significant reduction of the specific absorption rate in the MPRAGE sequence while preserving image quality. The work reported thus unveils a possible direction to increase the potential of ultra-high field MRI and parallel transmission. Magn Reson Med 76:1431-1442, 2016. © 2015 International Society for Magnetic Resonance in Medicine.

MR-based conductivity imaging using multiple receiver coils

PURPOSE

To propose a signal combination method for MR-based tissue conductivity mapping using a standard clinical scanner with multiple receiver coils.

METHODS

The theory of the proposed method is presented with two practical approaches, a coil-specific approach and a subject-specific approach. Conductivity maps were reconstructed using the transceive phase of the combined signal. The sensitivities of the coefficients used for signal combination were analyzed and the method was compared with other signal combination methods. For validation, multiple receiver brain coils and multiple receiver breast coils were used in phantom, in vivo brain, and in vivo breast studies.

RESULTS

The variation among the conductivity estimates was <15% as determined by the coefficient sensitivity tests. Compared with other signal combination methods, the proposed method yielded fewer artifacts in the conductivity estimates.

CONCLUSION

MR-based tissue conductivity mapping is feasible when using a standard clinical MR scanner with multiple receiver coils. The proposed method reduces systematic errors in phase-based conductivity mapping that can occur due to the inhomogeneous magnitude of the combined receive profile. Magn Reson Med 76:530-539, 2016. © 2015 Wiley Periodicals, Inc.

First and second order derivatives for optimizing parallel RF excitation waveforms

For piecewise constant magnetic fields, the Bloch equations (without relaxation terms) can be solved explicitly. This way the magnetization created by an excitation pulse can be written as a concatenation of rotations applied to the initial magnetization. For fixed gradient trajectories, the problem of finding parallel RF waveforms, which minimize the difference between achieved and desired magnetization on a number of voxels, can thus be represented as a finite-dimensional minimization problem. We use quaternion calculus to formulate this optimization problem in the magnitude least squares variant and specify first and second order derivatives of the objective function. We obtain a small tip angle approximation as first order Taylor development from the first order derivatives and also develop algorithms for first and second order derivatives for this small tip angle approximation. All algorithms are accompanied by precise floating point operation counts to assess and compare the computational efforts. We have implemented these algorithms as callback functions of an interior-point solver. We have applied this numerical optimization method to example problems from the literature and report key observations.

Two-spoke placement optimization under explicit specific absorption rate and power constraints in parallel transmission at ultra-high field

The spokes method combined with parallel transmission is a promising technique to mitigate the B1(+) inhomogeneity at ultra-high field in 2D imaging. To date however, the spokes placement optimization combined with the magnitude least squares pulse design has never been done in direct conjunction with the explicit Specific Absorption Rate (SAR) and hardware constraints. In this work, the joint optimization of 2-spoke trajectories and RF subpulse weights is performed under these constraints explicitly and in the small tip angle regime. The problem is first considerably simplified by making the observation that only the vector between the 2 spokes is relevant in the magnitude least squares cost-function, thereby reducing the size of the parameter space and allowing a more exhaustive search. The algorithm starts from a set of initial k-space candidates and performs in parallel for all of them optimizations of the RF subpulse weights and the k-space locations simultaneously, under explicit SAR and power constraints, using an active-set algorithm. The dimensionality of the spoke placement parameter space being low, the RF pulse performance is computed for every location in k-space to study the robustness of the proposed approach with respect to initialization, by looking at the probability to converge towards a possible global minimum. Moreover, the optimization of the spoke placement is repeated with an increased pulse bandwidth in order to investigate the impact of the constraints on the result. Bloch simulations and in vivo T2(∗)-weighted images acquired at 7 T validate the approach. The algorithm returns simulated normalized root mean square errors systematically smaller than 5% in 10 s.

A generalized slab-wise framework for parallel transmit multiband RF pulse design

PURPOSE

We propose a new slab-wise framework to design parallel transmit multiband pulses for volumetric simultaneous multislice imaging with a large field of view along the slice direction (FOVs).

THEORY AND METHODS

The slab-wise framework divides FOVs into a few contiguous slabs and optimizes pulses for each slab. Effects of relevant design parameters including slab number and transmit B1 (B1+) mapping slice placement were investigated for human brain imaging by designing pulses with global or local SAR control based on electromagnetic simulations of a 7T head RF array. Pulse design using in vivo B1+ maps was demonstrated and evaluated with Bloch simulations.

RESULTS

RF performance with respect to SAR reduction or B1+ homogenization across the entire human brain improved with increasing slabs; however, this improvement was nonlinear and leveled off at ∼12 slabs when the slab thickness reduced to ∼12 mm. The impact of using different slice placements for B1+ mapping was small.

CONCLUSION

Compared with slice-wise approaches where each of the many imaging slices requires both B1+ mapping and pulse optimization, the proposed slab-wise design framework attained comparable RF performance while drastically reducing the number of required pulses; therefore, it can be used to increase time efficiency for B1+ mapping, pulse calculation, and sequence preparation.

Parallel transmit pulse design for patients with deep brain stimulation implants

PURPOSE

Specific absorption rate (SAR) amplification around active implantable medical devices during diagnostic MRI procedures poses a potential risk for patient safety. In this study, we present a parallel transmit (pTx) strategy that can be used to safely scan patients with deep brain stimulation (DBS) implants.

METHODS

We performed electromagnetic simulations at 3T using a uniform phantom and a multitissue realistic head model with a generic DBS implant. Our strategy is based on using implant-friendly modes, which are defined as the modes of an array that reduce the local SAR around the DBS lead tip. These modes are used in a spokes pulse design algorithm in order to produce highly uniform magnitude least-squares flip angle excitations.

RESULTS

Local SAR (1 g) at the lead tip is reduced below 0.1 W/kg compared with 31.2 W/kg, which is obtained by a simple quadrature birdcage excitation without any sort of SAR mitigation. For the multitissue realistic head model, peak 10 g local SAR and global SAR are obtained as 4.52 W/kg and 0.48 W/kg, respectively. A uniform axial flip angle is also obtained (NRMSE <3%).

CONCLUSION

Parallel transmit arrays can be used to generate implant-friendly modes and to reduce SAR around DBS implants while constraining peak local SAR and global SAR and maximizing flip angle homogeneity.