A Mathematical Analysis of Clustering-Free Local SAR Compression Algorithms for MRI Safety in Parallel Transmission.

Parallel transmission (pTX) is a versatile solution to enable UHF MRI of the human body, where radiofrequency (RF) field inhomogeneity appears very challenging. Today, state of the art monitoring of the local SAR in pTX consists in evaluating the RF power deposition on specific SAR matrices called Virtual Observation Points (VOPs). It essentially relies on accurate electromagnetic simulations able to return the local SAR distribution inside the body in response to any applied pTX RF waveform. In order to reduce the number of SAR matrices to a value compatible with real time SAR monitoring ( << 103) , a VOP set is obtained by partitioning the SAR model into clusters, and associating a so- called dominant SAR matrix to every cluster. More recently, a clustering-free compression method was proposed, allowing for a significant reduction in the number of SAR matrices. The concept and derivation however assumed static RF shims and their extension to dynamic pTX is not straightforward, thereby casting doubt on the strict validity of the compression approach for these more complicated RF waveforms. In this work, we provide the mathematical framework to tackle this problem and find a rigorous justification of this criterion in the light of convex optimization theory. Our analysis led us to a variant of the clustering-free compression approach exploiting convex optimization. This new compression algorithm offers computational gains for large SAR models and for high-channel count pTX RF coils.

Universal nonselective excitation and refocusing pulses with improved robustness to off-resonance for Magnetic Resonance Imaging at 7 Tesla with parallel transmission.

PURPOSE: In MRI at ultra-high field, the kT -point and spiral nonselective (SPINS) pulse design techniques can be advantageously combined with the parallel transmission (pTX) and universal pulse techniques to create uniform excitation in a calibration-free manner. However, in these approaches, pulse duration is typically increased as compared to standard hard pulses, and excitation quality in regions exhibiting large resonance frequency offsets often suffer. This limitation is inherent to structure of kT -point or SPINS pulse, and likely can be mitigated using parameterization-free pulse design approaches. METHODS: The Gradient Ascent Pulse Engineering (GRAPE) algorithm was used to design parameterization-free RF and magnetic field gradient (MFG) waveforms for creating 8∘ excitation, up to 105∘ scalable refocusing and inversion, nonselectively across the brain. Simulations were performed to provide flip angle normalized root-mean-squares error (FA-NRMSE) estimations for the 8∘ and the 180∘kT -point, SPINS, and GRAPE pulses. GRAPE pulses were tested experimentally with anatomical head scans at 7T. RESULTS: As compared to kT -points and SPINS, GRAPE provided substantial improvement of excitation, refocusing, and inversion quality at off-resonance while at least preserving the same global FA-NRMSE performance. As compared to kT -points, GRAPE allowed for a substantial reduction of the pulse duration for the 8∘ excitation and the 105∘ refocusing. CONCLUSIONS: Parameterization-free universal nonselective pTX-pulses were successfully computed using GRAPE. Performance gains as compared to kT -points were validated numerically and experimentally for three imaging protocols. In its current implementation, the computational burden of GRAPE limits its use to applications where pulse computations are not subject to time constraints.

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 kT -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.

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.

Parallel-transmission-enabled magnetization-prepared rapid gradient-echo T1-weighted imaging of the human brain at 7 T.

One of the promises of Ultra High Field (UHF) MRI scanners is to bring finer spatial resolution in the human brain images due to an increased signal to noise ratio. However, at such field strengths, the spatial non-uniformity of the Radio Frequency (RF) transmit profiles challenges the applicability of most MRI sequences, where the signal and contrast levels strongly depend on the flip angle (FA) homogeneity. In particular, the MP-RAGE sequence, one of the most commonly employed 3D sequences to obtain T1-weighted anatomical images of the brain, is highly sensitive to these spatial variations. These cause deterioration in image quality and complicate subsequent image post-processing such as automated tissue segmentation at UHF. In this work, we evaluate the potential of parallel-transmission (pTx) to obtain high-quality MP-RAGE images of the human brain at 7 T. To this end, non-selective transmit-SENSE pulses were individually tailored for each of 8 subjects under study, and applied to an 8-channel transmit-array. Such RF pulses were designed both for the low-FA excitation train and the 180° inversion preparation involved in the sequence, both utilizing the recently introduced k(T)-point trajectory. The resulting images were compared with those obtained from the conventional method and from subject-specific RF-shimmed excitations. In addition, four of the volunteers were scanned at 3 T for benchmarking purposes (clinical setup without pTx). Subsequently, automated tissue classification was performed to provide a more quantitative measure of the final image quality. Results indicated that pTx could already significantly improve image quality at 7 T by adopting a suitable RF-Shim. Exploiting the full potential of the pTx-setup, the proposed k(T)-point method provided excellent inversion fidelity, comparable to what is commonly only achievable at 3 T with energy intensive adiabatic pulses. Furthermore, the cumulative energy deposition was simultaneously reduced by over 40% compared to the conventional adiabatic inversions. Regarding the low-FA k(T)-point based excitations, the FA uniformity achieved at 7 T surpassed what is typically obtained at 3 T. Subsequently, automated white and gray matter segmentation not only confirmed the expected improvements in image quality, but also suggests that care should be taken to properly account for the strong local susceptibility effects near cranial cavities. Overall, these findings indicate that the k(T)-point-based pTx solution is an excellent candidate for UHF 3D imaging, where patient safety is a major concern due to the increase of specific absorption rates.

Characterization of a two-transmon processor with individual single-shot qubit readout.

We report the characterization of a two-qubit processor implemented with two capacitively coupled tunable superconducting qubits of the transmon type, each qubit having its own nondestructive single-shot readout. The fixed capacitive coupling yields the sqrt[iSWAP] two-qubit gate for a suitable interaction time. We reconstruct by state tomography the coherent dynamics of the two-bit register as a function of the interaction time, observe a violation of the Bell inequality by 22 standard deviations after correcting readout errors, and measure by quantum process tomography a gate fidelity of 90%.

kT -points: short three-dimensional tailored RF pulses for flip-angle homogenization over an extended volume.

With Transmit SENSE, we demonstrate the feasibility of uniformly exciting a volume such as the human brain at 7T through the use of an original minimalist transmit k-space coverage, referred to as "k(T) -points." Radio-frequency energy is deposited only at a limited number of k-space locations in the vicinity of the center to counteract transmit sensitivity inhomogeneities. The resulting nonselective pulses are short and need little energy compared to adiabatic or other B 1+-robust pulses available in the literature, making them good candidates for short-repetition time 3D sequences at high field. Experimental verification was performed on three human volunteers at 7T by means of an 8-channel transmit array system. On average, whereas the standard circularly polarized excitation resulted in a 33%-flip angle spread (standard deviation over mean) throughout the brain, and a static radio-frequency shim showed flip angle variations of 17% and up, application of k(T) -point-based excitations demonstrated excellent flip angle uniformity (8%) for a small target flip angle and with sub-millisecond durations.

B1 and B0 inhomogeneity mitigation in the human brain at 7 T with selective pulses by using average Hamiltonian theory.

A novel method based on average Hamiltonian theory to design selective pulses is reported. With this tool, it is first shown how to shape the radiofrequency and gradient pulses to generate a desired rotation matrix, which is independent of the position through the slice of interest. After theoretical examination of the concept, it is applied to the strongly modulating pulses' recipe developed by the same authors and initially designed to be nonselective, to mitigate the amplitude of (excitation) radiofrequency field and amplitude of static (polarizing) field inhomogeneity problems at high field. Two in vivo human brain imaging experiments at 7 T are reported to prove the validity of the technique.

Counteracting radio frequency inhomogeneity in the human brain at 7 Tesla using strongly modulating pulses.

We report flip angle and spoiled gradient echo measurements at 7 Tesla on human brains in three-dimensional imaging, using strongly modulating pulses to counteract the transmitted radiofrequency inhomogeneity problem. Compared with the standard square pulse results, three points of improvement are demonstrated, namely: (i) the removal of the bright center (typical at high fields when using a quadrature head coil), (ii) the substantial gain of signal in the regions of low B(1) intensity, and (iii) an increased 35% signal uniformity over the whole brain at the flip angle where maximum contrast between white and gray matter occurs. We also find by means of simulations that standard BIR-4 adiabatic pulses need several times more energy to reach a similar performance at the same field strength.

Strongly modulating pulses for counteracting RF inhomogeneity at high fields.

A new pulse technique for counteracting RF inhomogeneity at high fields is reported. The pulses make use of the detailed knowledge of the voxels' B(1) and B(0) amplitude 2D histogram to generate, through an optimization procedure, gates where the flip angle is made uniform. Although most approaches to date require the use of parallel transmission, this method does not and therefore offers several advantages. The data necessary for the algorithm to determine an irradiation scheme requires only one transmit B(1) along with a B(0) inhomogeneity measurement. The use of a B(1) and B(0) amplitude 2D histogram instead of their spatial distribution also decreases substantially the complexity of the optimization problem, allowing the algorithm to find an RF solution in less than 30 s. Finally, the optimization procedure is based on an exact calculation and does not use any linear approximation. In this article, the theory behind the method in addition to spoiled gradient echo experimental data at 3T for 3D brain imaging are reported. The images obtained yield a reduction of the standard deviation of the sine of the flip angle by a factor of up to 15 around the desired value, compared to when a standard square pulse calibrated by the scanner is used.

Current to frequency conversion in a Josephson circuit.

The voltage oscillations which occur in an ideally current-biased Josephson junction were proposed to make a current standard for metrology. We demonstrate similar oscillations in a more complex Josephson circuit derived from the Cooper pair box: the quantronium. When a constant current I is injected in the gate capacitor of this device, oscillations develop at the frequency f(B)=I/2e, with e the electron charge. We detect these oscillations through the sidebands induced at multiples of f(B) in the spectrum of a microwave signal reflected on the circuit, up to currents I exceeding 100 pA. We discuss the potential interest of this current-to-frequency conversion experiment for metrology.

Benchmarking quantum control methods on a 12-qubit system.

In this Letter, we present an experimental benchmark of operational control methods in quantum information processors extended up to 12 qubits. We implement universal control of this large Hilbert space using two complementary approaches and discuss their accuracy and scalability. Despite decoherence, we were able to reach a 12-coherence state (or a 12-qubit pseudopure cat state) and decode it into an 11 qubit plus one qutrit pseudopure state using liquid state nuclear magnetic resonance quantum information processors.

Entanglement assisted metrology.

We propose a new approach to the measurement of a single spin state, based on nuclear magnetic resonance (NMR) techniques and inspired by the coherent control over many-body systems envisaged by quantum information processing. A single target spin is coupled via the magnetic dipolar interaction to a large ensemble of spins. Applying radio frequency pulses, we can control the evolution so that the spin ensemble reaches one of two orthogonal states whose collective properties differ depending on the state of the target spin and are easily measured. We first describe this measurement process using quantum gates; then we show how equivalent schemes can be defined in terms of the Hamiltonian and thus implemented under conditions of real control, using well established NMR techniques. We demonstrate this method with a proof of principle experiment in ensemble liquid state NMR and simulations for small spin systems.

Incoherent noise and quantum information processing.

Incoherence in the controlled Hamiltonian is an important limitation on the precision of coherent control in quantum information processing. Incoherence can typically be modeled as a distribution of unitary processes arising from slowly varying experimental parameters. We show how it introduces artifacts in quantum process tomography and we explain how the resulting estimate of the superoperator may not be completely positive. We then go on to attack the inverse problem of extracting an effective distribution of unitaries that characterizes the incoherence via a perturbation theory analysis of the superoperator eigenvalue spectra.