Fast design of local N-gram-specific absorption rate-optimized radiofrequency pulses for parallel transmit systems

Comparison of tight-fitting 7T parallel-transmit head array designs using excitation uniformity and local specific absorption rate metrics

PURPOSE

We model the performance of parallel transmission (pTx) arrays with 8, 16, 24, and 32 channels and varying loop sizes built on a close-fitting helmet for brain imaging at 7 T and compare their local specific absorption rate (SAR) and flip-angle performances to that of birdcage coil (used as a baseline) and cylindrical 8-channel and 16-channel pTx coils (single-row and dual-row).

METHODS

We use the co-simulation approach along with MATLAB scripting for batch-mode simulation of the coils. For each coil, we extracted B1 + maps and SAR matrices, which we compressed using the virtual observation points algorithm, and designed slice-selective RF shimming pTx pulses with multiple local SAR and peak power constraints to generate L-curves in the transverse, coronal, and sagittal orientations.

RESULTS

Helmet designs outperformed cylindrical pTx arrays at a constant number of channels in the flip-angle uniformity at a constant local SAR metric: up to 29% for 8-channel arrays, and up to 34% for 16-channel arrays, depending on the slice orientation. For all helmet arrays, increasing the loop diameter led to better local SAR versus flip-angle uniformity tradeoffs, although this effect was more pronounced for the 8-channel and 16-channel systems than the 24-channel and 32-channel systems, as the former have more limited degrees of freedom and therefore benefit more from loop-size optimization.

CONCLUSION

Helmet pTx arrays significantly outperformed cylindrical arrays with the same number of channels in local SAR and flip-angle uniformity metrics. This improvement was especially pronounced for non-transverse slice excitations. Loop diameter optimization for helmets appears to favor large loops, compatible with nearest-neighbor decoupling by overlap.

Magnetic resonance imaging at 9.4 T: the Maastricht journey

The 9.4 T scanner in Maastricht is a whole-body magnet with head gradients and parallel RF transmit capability. At the time of the design, it was conceptualized to be one of the best fMRI scanners in the world, but it has also been used for anatomical and diffusion imaging. 9.4 T offers increases in sensitivity and contrast, but the technical ultra-high field (UHF) challenges, such as field inhomogeneities and constraints set by RF power deposition, are exacerbated compared to 7 T. This article reviews some of the 9.4 T work done in Maastricht. Functional imaging experiments included blood oxygenation level-dependent (BOLD) and blood-volume weighted (VASO) fMRI using different readouts. BOLD benefits from shorter T₂* at 9.4 T while VASO from longer T₁. We show examples of both ex vivo and in vivo anatomical imaging. For many applications, pTx and optimized coils are essential to harness the full potential of 9.4 T. Our experience shows that, while considerable effort was required compared to our 7 T scanner, we could obtain high-quality anatomical and functional data, which illustrates the potential of MR acquisitions at even higher field strengths. The practical challenges of working with a relatively unique system are also discussed.

No need to detune transmitters in 32-channel receiver arrays at 7 T

Ultrahigh field magnetic resonance imaging facilitates high spatiotemporal resolution that benefits from increasing the number of receiver elements. Because high-density receiver arrays have a relatively small element size compared with the transmitter, a side effect is that such setups cause low flux coupling between the transmitter and receiver. Moreover, when transmitters are designed in a multitransmit configuration, their relative size is much smaller than the sample, reducing coupling to the sample and thereby potentially also the coupling to the receivers. Transmitters are traditionally detuned during reception. In this study, we investigate, for a 32-channel receiver head array at 7 T, if transmitter detuning of a quadrature birdcage or of an eight-channel transmit coil can be omitted without substantially sacrificing signal-to-noise ratio (SNR). The transmit elements are operated once with and once without detuning and, in the latter, the received signals are either merged with the array or excluded for image reconstruction. For each of the three measurements, SNR and 1/g-factor maps are investigated. The tuning of the quadrature and eight-channel transmit coils during signal reception introduced a 10.1% and 6.5% penalty in SNR, respectively, relative to the SNR received with detuned transmitters. When also incorporating the signal of the transmit coils, the SNR was regained to 98.5% or 101.4% for the quadrature and eight-channel coil, respectively, relative to the detuned transmitters, while the 1/g-factor maps improved slightly. For the 32-channel receive coil used the SNR penalty can become negligible when omitting detuning of the transmit coils. This not only simplifies transmit coil designs, potentially increasing their efficiency, but also enables the transmitters to be used as receivers in parallel to the receiver array, thus increasing parallel imaging performance.

Real-time assessment of potential peak local specific absorption rate value without phase monitoring: Trigonometric maximization method for worst-case local specific absorption rate determination

Purpose

Multi‐transmit MRI systems are typically equipped with dedicated hardware to sample the reflected/lost power in the transmit channels. After extensive calibration, the amplitude and phase of the signal at the feed of each array element can be accurately determined. However, determining the phase is more difficult and monitoring errors can lead to a hazardous peak local specific absorption rate (pSAR_10g) underestimation. For this purpose, methods were published for online maximum potential pSAR_10g estimation without relying on phase monitoring, but these methods produce considerable overestimation. We present a trigonometric maximization method to determine the actual worst‐case pSAR_10g without any overestimation.

Theory and Method

The proposed method takes advantage of the sinusoidal relation between the SAR_10g in each voxel and the phases of input signals, to return the maximum achievable SAR_10g in a few iterations. The method is applied to determine the worst‐case pSAR_10g for three multi‐transmit array configurations at 7T: (1) body array with eight fractionated dipoles; (2) head array with eight fractionated dipoles; (3) head array with eight rectangular loops. The obtained worst‐case pSAR_10g values are compared with the pSAR_10g values determined with a commonly used method and with a more efficient method based on reference‐phases.

Results

For each voxel, the maximum achievable SAR_10g is determined in less than 0.1 ms. Compared to the reference‐phases‐based method, the proposed method reduces the mean overestimation of the actual pSAR_10g up to 52%, while never underestimating the true pSAR_10g.

Conclusion

The proposed method can widely improve the performance of parallel transmission MRI systems without phase monitoring.

An investigation into the minimum number of tissue groups required for 7T in-silico parallel transmit electromagnetic safety simulations in the human head

PURPOSE

Safety limits for the permitted specific absorption rate (SAR) place restrictions on pulse sequence design, especially at ultrahigh fields (≥ 7 tesla). Due to intersubject variability, the SAR is usually conservatively estimated based on standard human models that include an applied safety margin to ensure safe operation. One approach to reducing the restrictions is to create more accurate subject-specific models from their segmented MR images. This study uses electromagnetic simulations to investigate the minimum number of tissue groups required to accurately determine SAR in the human head.

METHODS

Tissue types from a fully characterized electromagnetic human model with 47 tissue types in the head and neck region were grouped into different tissue clusters based on the conductivities, permittivities, and mass densities of the tissues. Electromagnetic simulations of the head model inside a parallel transmit head coil at 7 tesla were used to determine the minimum number of required tissue clusters to accurately determine the subject-specific SAR. The identified tissue clusters were then evaluated using 2 additional well-characterized electromagnetic human models.

RESULTS

A minimum of 4-clusters-plus-air was found to be required for accurate SAR estimation. These tissue clusters are centered around gray matter, fat, cortical bone, and cerebrospinal fluid. For all 3 simulated models, the parallel transmit maximum 10g SAR was consistently determined to within an error of <12% relative to the full 47-tissue model.

CONCLUSION

A minimum of 4-clusters-plus-air are required to produce accurate personalized SAR simulations of the human head when using parallel transmit at 7 tesla.

Global and peak local specific absorption rate control on parallel transmit systems using k-means SAR compression model

PURPOSE

To improve the specific absorption rate (SAR) compression model capability in parallel transmission (pTx) MRI systems.

METHODS

A k-means clustering method is proposed to group voxels with similar SAR behaviors in the scanned object, providing a controlled upper-bounded estimation of peak local SARs. This k-means compression model and the conventional virtual observation point (VOP) model were tested in a pTx MRI framework. The pTx pulse design with different SAR controlling schemes was simulated using a numerical human head model and an eight-channel 7T coil array. Multiple criteria (including RF power, global and peak local SARs, and excitation accuracy) were compared for the performance testing.

RESULTS

The k-means compression model generated a narrower overestimation bound, leading to a more accurate local SAR estimation. Among different pTx pulse design approaches, the k-means compression model showed the best trade-off between the SAR and excitation accuracy.

CONCLUSIONS

The developed SAR compression model is advantageous for pTx framework given the narrower overestimation bound and control over the compression ratio. Results also illustrate that a moderate increase of maximum RF power can be useful for reducing the maximum local SAR deposition.

Conditional safety margins for less conservative peak local SAR assessment: A probabilistic approach

Purpose

The introduction of a linear safety factor to address peak local specific absorption rate (pSAR_10g) uncertainties (eg, intersubject variation, modeling inaccuracies) bears one considerable drawback: It often results in over‐conservative scanning constraints. We present a more efficient approach to define a variable safety margin based on the conditional probability density function of the effectively obtained pSAR_10g value, given the estimated pSAR_10g value.

Methods

The conditional probability density function can be estimated from previously simulated data. A representative set of true and estimated pSAR_10g samples was generated by means of our database of 23 subject‐specific models with an 8‐fractionated dipole array for prostate imaging at 7 T. The conditional probability density function was calculated for each possible estimated pSAR_10g value and used to determine the corresponding safety margin with an arbitrary low probability of underestimation. This approach was applied to five state‐of‐the‐art local SAR estimation methods, namely: (1) using just the generic body model “Duke”; (2) using our model library to assess the maximum pSAR_10g value over all models; (3) using the most representative “local SAR model”; (4) using the five most representative local SAR models; and (5) using a recently developed deep learning–based method.

Results

Compared with the more conventional safety factor, the conditional safety‐margin approach results in lower (up to 30%) mean overestimation for all investigated local SAR estimation methods.

Conclusion

The proposed probabilistic approach for pSAR_10g correction allows more accurate local SAR assessment with much lower overestimation, while a predefined level of underestimation is accepted (eg, 0.1%).

A deep learning method for image-based subject-specific local SAR assessment

Purpose

Local specific absorption rate (SAR) cannot be measured and is usually evaluated by offline numerical simulations using generic body models that of course will differ from the patient's anatomy. An additional safety margin is needed to include this intersubject variability. In this work, we present a deep learning–based method for image‐based subject‐specific local SAR assessment. We propose to train a convolutional neural network to learn a “surrogate SAR model” to map the relation between subject‐specific B1+ maps and the corresponding local SAR.

Method

Our database of 23 subject‐specific models with an 8–transmit channel body array for prostate imaging at 7 T was used to build 5750 training samples. These synthetic complex B1+ maps and local SAR distributions were used to train a conditional generative adversarial network. Extra penalization for local SAR underestimation errors was included in the loss function. In silico and in vivo validation were performed.

Results

In silico cross‐validation shows a good qualitative and quantitative match between predicted and ground‐truth local SAR distributions. The peak local SAR estimation error distribution shows a mean overestimation error of 15% with 13% probability of underestimation. The higher accuracy of the proposed method allows the use of less conservative safety factors compared with standard procedures. In vivo validation shows that the method is applicable with realistic measurement data with impressively good qualitative and quantitative agreement to simulations.

Conclusion

The proposed deep learning method allows online image‐based subject‐specific local SAR assessment. It greatly reduces the uncertainty in current state‐of‐the‐art SAR assessment methods, reducing the time in the examination protocol by almost 25%.

Machine learning RF shimming: Prediction by iteratively projected ridge regression

PURPOSE

To obviate online slice-by-slice RF shim optimization and reduce B1+ mapping requirements for patient-specific RF shimming in high-field magnetic resonance imaging.

THEORY AND METHODS

RF Shim Prediction by Iteratively Projected Ridge Regression (PIPRR) predicts patient-specific, SAR-efficient RF shims with a machine learning approach that merges learning with training shim design. To evaluate it, a set of B1+ maps was simulated for 100 human heads for a 24-element coil at 7T. Features were derived from tissue masks and the DC Fourier coefficients of the coils' B1+ maps in each slice, which were used for kernelized ridge regression prediction of SAR-efficient RF shim weights. Predicted shims were compared to directly designed shims, circularly polarized mode, and nearest-neighbor shims predicted using the same features.

RESULTS

PIPRR predictions had 87% and 13% lower B1+ coefficients of variation compared to circularly polarized mode and nearest-neighbor shims, respectively, and achieved homogeneity and SAR similar to that of directly designed shims. Predictions were calculated in 4.92 ms on average.

CONCLUSION

PIPRR predicted uniform, SAR-efficient RF shims, and could save a large amount of B1+ mapping and computation time in RF-shimmed ultra-high field magnetic resonance imaging.

An 8-channel Tx/Rx dipole array combined with 16 Rx loops for high-resolution functional cardiac imaging at 7 T

Objective

To demonstrate imaging performance for cardiac MR imaging at 7 T using a coil array of 8 transmit/receive dipole antennas and 16 receive loops.

Materials and methods

An 8-channel dipole array was extended by adding 16 receive-only loops. Average power constraints were determined by electromagnetic simulations. Cine imaging was performed on eight healthy subjects. Geometrical factor (g-factor) maps were calculated to assess acceleration performance. Signal-to-noise ratio (SNR)-scaled images were reconstructed for different combinations of receive channels, to demonstrate the SNR benefits of combining loops and dipoles.

Results

The overall image quality of the cardiac functional images was rated a 2.6 on a 4-point scale by two experienced radiologists. Imaging results at different acceleration factors demonstrate that acceleration factors up to 6 could be obtained while keeping the average g-factor below 1.27. SNR maps demonstrate that combining loops and dipoles provides a more than 50% enhancement of the SNR in the heart, compared to a situation where only loops or dipoles are used.

Conclusion

This work demonstrates the performance of a combined loop/dipole array for cardiac imaging at 7 T. With this array, acceleration factors of 6 are possible without increasing the average g-factor in the heart beyond 1.27. Combining loops and dipoles in receive mode enhances the SNR compared to receiving with loops or dipoles only.

Electronic supplementary material

The online version of this article (10.1007/s10334-017-0665-5) contains supplementary material, which is available to authorized users.

Direct SAR mapping by thermoacoustic imaging: A feasibility study

PURPOSE

To develop a new method capable of directly measuring specific absorption rate (SAR) deposited in tissue using the thermoacoustic signal induced by short radiofrequency (RF) pulse excitation.

THEORY

A detailed model based on the thermoacoustic wave generation and propagation is presented.

METHODS

We propose a new concept for direct measurement of SAR, to be used as a safety assessment/monitoring tool for MRI. The concept involves the use of short bursts of RF energy and the measurement of the resulting thermoacoustic excitation pattern by an array of ultrasound transducers, followed by image reconstruction to yield the 3D SAR distribution. We developed a simulation framework to model this thermoacoustic SAR mapping concept and verified the concept in vitro.

RESULTS

Simulations show good agreement between reconstructed and original SAR distributions with an error of 4.2, 7.2, and 8.4% of the mean SAR values in axial, sagittal, and coronal planes and support the feasibility of direct experimental mapping of SAR distributions in vivo. The in vitro experiments show good agreement with theory (r2  = 0.52).

CONCLUSIONS

A novel thermoacoustic method for in vivo mapping of local SAR patterns in MRI has been proposed and verified in simulation and in a phantom experiment. Magn Reson Med 78:1599-1606, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

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

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. Magn Reson Med 77:374-384, 2017. © 2015 Wiley Periodicals, Inc.

High-resolution gradient-recalled echo imaging at 9.4T using 16-channel parallel transmit simultaneous multislice spokes excitations with slice-by-slice flip angle homogenization

Purpose

In order to fully benefit from the improved signal‐to‐noise and contrast‐to‐noise ratios at 9.4T, the challenges of B1+ inhomogeneity and the long acquisition time of high‐resolution 2D gradient‐recalled echo (GRE) imaging were addressed.

Theory and Methods

Flip angle homogenized excitations were achieved by parallel transmission (pTx) of 3‐spoke pulses, designed by magnitude least‐squares optimization in a slice‐by‐slice fashion; the acquisition time reduction was achieved by simultaneous multislice (SMS) pulses. The slice‐specific spokes complex radiofrequency scaling factors were applied to sinc waveforms on a per‐channel basis and combined with the other pulses in an SMS slice group to form the final SMS‐pTX pulse. Optimal spokes locations were derived from simulations.

Results

Flip angle maps from presaturation TurboFLASH showed improvement of flip angle homogenization with 3‐spoke pulses over CP‐mode excitation (normalized root‐mean‐square error [NRMSE] 0.357) as well as comparable excitation homogeneity across the single‐band (NRMSE 0.119), SMS‐2 (NRMSE 0.137), and SMS‐3 (NRMSE 0.132) 3‐spoke pulses. The application of the 3‐spoke SMS‐3 pulses in a 48‐slice GRE protocol, which has an in‐plane resolution of 0.28 × 0.28 mm, resulted in a 50% reduction of scan duration (total acquisition time 6:52 min including reference scans).

Conclusion

Time‐efficient flip angle homogenized high‐resolution GRE imaging at 9.4T was accomplished by using slice‐specific SMS‐pTx spokes excitations. Magn Reson Med 78:1050–1058, 2017. © 2016 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine.

Parallel transmission for ultrahigh-field imaging

The development of MRI systems operating at or above 7 T has provided researchers with a new window into the human body, yielding improved imaging speed, resolution and signal-to-noise ratio. In order to fully realise the potential of ultrahigh-field MRI, a range of technical hurdles must be overcome. The non-uniformity of the transmit field is one of such issues, as it leads to non-uniform images with spatially varying contrast. Parallel transmission (i.e. the use of multiple independent transmission channels) provides previously unavailable degrees of freedom that allow full spatial and temporal control of the radiofrequency (RF) fields. This review discusses the many ways in which these degrees of freedom can be used, ranging from making more uniform transmit fields to the design of subject-tailored RF pulses for both uniform excitation and spatial selection, and also the control of the specific absorption rate. © 2015 The Authors. NMR in Biomedicine published by John Wiley & Sons Ltd.

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.

Volumetric imaging with homogenised excitation and static field at 9.4 T

OBJECTIVES

To overcome the challenges of B0 and RF excitation inhomogeneity at ultra-high field MRI, a workflow for volumetric B0 and flip-angle homogenisation was implemented on a human 9.4 T scanner.

MATERIALS AND METHODS

Imaging was performed with a 9.4 T human MR scanner (Siemens Medical Solutions, Erlangen, Germany) using a 16-channel parallel transmission system. B0- and B1-mapping were done using a dual-echo GRE and transmit phase-encoded DREAM, respectively. B0 shims and a small-tip-angle-approximation kT-points pulse were calculated with an off-line routine and applied to acquire T1- and T 2 (*) -weighted images with MPRAGE and 3D EPI, respectively.

RESULTS

Over six in vivo acquisitions, the B0-distribution in a region-of-interest defined by a brain mask was reduced down to a full-width-half-maximum of 0.10 ± 0.01 ppm (39 ± 2 Hz). Utilising the kT-points pulses, the normalised RMSE of the excitation was decreased from CP-mode's 30.5 ± 0.9 to 9.2 ± 0.7 % with all B 1 (+)  voids eliminated. The SNR inhomogeneities and contrast variations in the T1- and T 2 (*) -weighted volumetric images were greatly reduced which led to successful tissue segmentation of the T1-weighted image.

CONCLUSION

A 15-minute B0- and flip-angle homogenisation workflow, including the B0- and B1-map acquisitions, was successfully implemented and enabled us to reduce intensity and contrast variations as well as echo-planar image distortions in 9.4 T images.

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.

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.

Surface coil with reduced specific absorption rate for rat MRI at 7 T

OBJECTIVE

A scaled-down slotted surface radio frequency (RF) coil was built, and the specific absorbance rate (SAR) in 100 mg of tissue (SAR100 mg) produced in a rat brain phantom was computed at 7 T.

MATERIALS AND METHODS

A slotted coil 2-cm in diameter with six circular slots was developed. Its theoretical and experimental performance was computed and compared using the signal-to-noise ratio (SNR) expression and phantom images obtained with a spin echo sequence. Electromagnetic simulations were performed using the finite integral method with saline sphere and rat brain phantoms. SAR100 mg was computed for the circular coil, by varying its radius, and was also computed for the slotted coil.

RESULTS

The slotted coil quality factor gave a twofold increment over the circular coil, and noise was reduced by 17%. The experimental SNR of the slotted coil produced a 30% improvement for points near the coil plane. The theoretical and experimental results showed substantial agreement. Axial map histograms and profiles showed greater SAR100 mg values for the circular coil than for the slotted coil.

CONCLUSIONS

The slotted surface coil offers improved performance and low SAR100 mg for rat brain imaging at 7 T. This approach may be used with new RF coils to investigate SAR in humans.

Comparison of RF body coils for MRI at 3 T: a simulation study using parallel transmission on various anatomical targets

The performance of multichannel transmit coil layouts and parallel transmission (pTx) RF pulse design was evaluated with respect to transmit B1 (B1 (+)) homogeneity and specific absorption rate (SAR) at 3 T for a whole body coil. Five specific coils were modeled and compared: a 32-rung birdcage body coil (driven either in a fixed quadrature mode or a two-channel transmit mode), two single-ring stripline arrays (with either 8 or 16 elements), and two multi-ring stripline arrays (with two or three identical rings, stacked in the z axis and each comprising eight azimuthally distributed elements). Three anatomical targets were considered, each defined by a 3D volume representative of a meaningful region of interest (ROI) in routine clinical applications. For a given anatomical target, global or local SAR controlled pTx pulses were designed to homogenize RF excitation within the ROI. At the B1 (+) homogeneity achieved by the quadrature driven birdcage design, pTx pulses with multichannel transmit coils achieved up to about eightfold reduction in local and global SAR. When used for imaging head and cervical spine or imaging thoracic spine, the double-ring array outperformed all coils, including the single-ring arrays. While the advantage of the double-ring array became much less pronounced for pelvic imaging, with a substantially larger ROI, the pTx approach still provided significant gains over the quadrature birdcage coil. For all design scenarios, using the three-ring array did not necessarily improve the RF performance. Our results suggest that pTx pulses with multichannel transmit coils can reduce local and global SAR substantially for body coils while attaining improved B1 (+) homogeneity, particularly for a "z-stacked" double-ring design with coil elements arranged on two transaxial rings.

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.

General design approach and practical realization of decoupling matrices for parallel transmission coils

PURPOSE

In a coupled parallel transmit (pTx) array, the power delivered to a channel is partially distributed to other channels because of coupling. This power is dissipated in circulators resulting in a significant reduction in power efficiency. In this study, a technique for designing robust decoupling matrices interfaced between the RF amplifiers and the coils is proposed. The decoupling matrices ensure that most forward power is delivered to the load without loss of encoding capabilities of the pTx array.

THEORY AND METHODS

The decoupling condition requires that the impedance matrix seen by the power amplifiers is a diagonal matrix whose entries match the characteristic impedance of the power amplifiers. In this work, the impedance matrix of the coupled coils is diagonalized by a successive multiplication by its eigenvectors. A general design procedure and software are developed to generate automatically the hardware that implements diagonalization using passive components.

RESULTS

The general design method is demonstrated by decoupling two example parallel transmit arrays. Our decoupling matrices achieve better than -20 db decoupling in both cases.

CONCLUSION

A robust framework for designing decoupling matrices for pTx arrays is presented and validated. The proposed decoupling strategy theoretically scales to any arbitrary number of channels. Magn Reson Med 76:329-339, 2016. © 2015 Wiley Periodicals, Inc.

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.

Comparison of simulated parallel transmit body arrays at 3 T using excitation uniformity, global SAR, local SAR, and power efficiency metrics

PURPOSE

We compare the performance of eight parallel transmit (pTx) body arrays with up to 32 channels and a standard birdcage design. Excitation uniformity, local specific absorption rate (SAR), global SAR, and power metrics are analyzed in the torso at 3 T for radiofrequency (RF)-shimming and 2-spoke excitations.

METHODS

We used a fast cosimulation strategy for field calculation in the presence of coupling between transmit channels. We designed spoke pulses using magnitude least squares optimization with explicit constraint of SAR and power and compared the performance of the different pTx coils using the L-curve method.

RESULTS

PTx arrays outperformed the conventional birdcage coil in all metrics except peak and average power efficiency. The presence of coupling exacerbated this power efficiency problem. At constant excitation fidelity, the pTx array with 24 channels arranged in three z-rows could decrease local SAR more than 4-fold (2-fold) for RF-shimming (2-spoke) compared to the birdcage coil for pulses of equal duration. Multi-row pTx coils had a marked performance advantage compared to single row designs, especially for coronal imaging.

CONCLUSION

PTx coils can simultaneously improve the excitation uniformity and reduce SAR compared to a birdcage coil when SAR metrics are explicitly constrained in the pulse design.

Local specific absorption rate (SAR), global SAR, transmitter power, and excitation accuracy trade-offs in low flip-angle parallel transmit pulse design

PURPOSE

We propose a constrained optimization approach for designing parallel transmit (pTx) pulses satisfying all regulatory and hardware limits. We study the trade-offs between excitation accuracy, local and global specific absorption rate (SAR), and maximum and average power for small flip-angle pTx (eight channels) spokes pulses in the torso at 3 T and in the head at 7 T.

METHODS

We compare the trade-offs between the above-mentioned quantities using the L-curve method. We use a primal-dual algorithm and a compressed set of local SAR matrices to design radio-frequency (RF) pulses satisfying all regulatory (including local SAR) and hardware constraints.

RESULTS

Local SAR can be substantially reduced (factor of 2 or more) by explicitly constraining it in the pulse design process compared to constraining global SAR or pulse power alone. This often comes at the price of increased pulse power.

CONCLUSION

Simultaneous control of power and SAR is needed for the design of pTx pulses that are safe and can be played on the scanner. Constraining a single quantity can create large increase in the others, which can then rise above safety or hardware limits. Simultaneous constraint of local SAR and power is fast enough to be applicable in a clinical setting.

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

Parallel transmission is a very promising candidate technology to mitigate the inevitable radio-frequency (RF) field inhomogeneity in magnetic resonance imaging at ultra-high field. 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, the MLS problem yet has been faced almost exclusively by the pulse designer with the so-called variable exchange method. In this paper, we investigate various two-stage strategies consisting of different initializations and nonlinear programming approaches, and incorporate directly the strict SAR and hardware constraints. Several schemes such as sequential quadratic programming, interior point methods, semidefinite programming and magnitude squared least squares relaxations are studied both in the small and large tip angle regimes with RF and static field maps obtained in vivo on a human brain at 7T. 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.

Correcting for strong eddy current induced B0 modulation enables two-spoke RF pulse design with parallel transmission: demonstration at 9.4T in the human brain

Successful implementation of homogeneous slice-selective RF excitation in the human brain at 9.4T using 16-channel parallel transmission (pTX) is demonstrated. A novel three-step pulse design method incorporating fast real-time measurement of eddy current induced B0 variations as well as correction of resulting phase errors during excitation is described. To demonstrate the utility of the proposed method, phantom and in-vivo experiments targeting a uniform excitation in an axial slice were conducted using two-spoke pTX pulses. Even with the pre-emphasis activated, eddy current induced B0 variations with peak-to-peak values greater than 4 kHz were observed on our system during the rapid switches of slice selective gradients. This large B0 variation, when not corrected, resulted in drastically degraded excitation fidelity with the coefficient of variation (CV) of the flip angle calculated for the region of interest being large (~ 12% in the phantom and ~ 35% in the brain). By comparison, excitation fidelity was effectively restored, and satisfactory flip angle uniformity was achieved when using the proposed method, with the CV value reduced to ~ 3% in the phantom and ~ 8% in the brain. Additionally, experimental results were in good agreement with the numerical predictions obtained from Bloch simulations. Slice-selective flip angle homogenization in the human brain at 9.4T using 16-channel 3D spoke pTX pulses is achievable despite of large eddy current induced excitation phase errors; correcting for the latter was critical in this success.

Intersubject local SAR variation for 7T prostate MR imaging with an eight-channel single-side adapted dipole antenna array

PURPOSE

Surface transmit arrays used in ultra-high field body MRI require local specific absorption rate (SAR) assessment. As local SAR cannot be measured directly, local SAR is determined by simulations using dielectric patient models. In this study, the inter-patient local SAR variation is investigated for 7T prostate imaging with the single-side adapted dipole antenna array.

METHOD

Four-dedicated dielectric models were created by segmenting Dixon water-fat separated images that were obtained from four subjects with a 1.5T scanner and the surface array in place. Electromagnetic simulations were performed to calculate the SAR distribution for each model. Radio frequency (RF) exposure variations were determined by analyzing the SAR(10g) distributions (1) with one element active, (2) using a Q-matrix eigenvalue/eigenvector approach, (3) with the maximum potential SAR in each voxel, and (4) for a phase shimmed prostate measurement.

RESULTS

Maximum potential local SAR levels for 1 W time-averaged accepted power per transmit channel range from 4.1 to 7.1 W/kg.

CONCLUSION

These variations show that one model is not sufficient to determine safe scan settings. For the operation of the surface array conservative power settings were derived based on a worst-case SAR evaluation and the most SAR-sensitive body model.

Improving SAR estimations in MRI using subject-specific models

To monitor and strategically control energy deposition in magnetic resonance imaging (MRI), measured as a specific absorption rate (SAR), numerical methods using generic human models have been employed to estimate worst-case values. Radiofrequency (RF) sequences are therefore often designed conservatively with large safety margins, potentially hindering the full potential of high-field systems. To more accurately predict the patient SAR values, we propose the use of image registration techniques, in conjunction with high-resolution image and tissue libraries, to create patient-specific voxel models. To test this, a matching model from the archives was first selected. Its tissue information was then warped to the patient's coordinates by registering the high-resolution library image to the pilot scan of the patient. Results from studying the models' 1 g SAR distribution suggest that the developed patient model can predict regions of elevated SAR within the patient with remarkable accuracy. Additionally, this work also proposes a voxel analytical metric that can assist in the construction of a patient library and the selection of the matching model from the library for a patient. It is hoped that, by developing voxel models with high accuracy in patient-specific anatomy and positioning, the proposed method can accurately predict the safety margins for high-field human applications and, therefore maximize the safe use of RF sequence power in high-field MRI systems.

Specific absorption rate intersubject variability in 7T parallel transmit MRI of the head

Patient-specific radiofrequency shimming in high-field MRI strengthens the need for online, patient-specific specific absorption rate (SAR) monitoring. Numerical simulation is currently most effective for this purpose but may require a patient-specific dielectric model. To investigate whether a generic model may be combined with a safety factor to account for variation within the population, generic SAR behavior is studied for 7T MRI of the head. For six detailed head models, radiofrequency fields were simulated for an eight-channel parallel transmit array. SAR behavior is studied through comparison of the eigenvalues/eigenvectors of the local Q-matrices. Furthermore, numerical radiofrequency shimming experiments without and with SAR constraints were performed where SAR during optimization was evaluated on a generic model. In both cases, the ability of different generic models to predict actual SAR levels was evaluated. The largest eigenvalue distribution is comparable between models. Radiofrequency shimming without constraints improves the |B +1| homogeneity while the SAR increases substantially. Imposing constraints on SAR during optimization, estimating SAR on a generic model, was effective. A safety factor of 1.4 was found to be sufficient. Generic SAR behavior makes a generic head model a practical alternative to patient-specific models and allows effective |B +1| shimming with SAR constraints.