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

Designing multidimensional radiofrequency pulses for clinical application must take into account the local specific absorption rate (SAR) as controlling the global SAR does not guarantee suppression of hot spots. The maximum peak SAR, averaged over an N grams cube (local NgSAR), must be kept under certain safety limits. Computing the SAR over a three-dimensional domain can require several minutes and implementing this computation in a radiofrequency pulse design algorithm could slow down prohibitively the numerical process. In this article, a fast optimization algorithm is designed acting on a limited number of control points, which are strategically selected locations from the entire domain. The selection is performed by comparing the largest eigenvalues and the corresponding eigenvectors of the matrices which locally describe the tissue's amount of heating. The computation complexity is dramatically reduced. An additional critical step to accelerate the computations is to apply a multi shift conjugate gradient algorithm. Two transmit array setups are studied: a two channel 3 T birdcage body coil and a 12-channel 7 T transverse electromagnetic (TEM) head coil. In comparison with minimum power radiofrequency pulses, it is shown that a reduction of 36.5% and 35%, respectively, in the local NgSAR can be achieved within short, clinically feasible, computation times.     

Improved large tip angle parallel transmission pulse design through a perturbation analysis of the bloch equation

Parallel transmission has emerged as an efficient means for implementing multidimensional spatially selective radiofrequency excitation pulses. To date, most theoretical and experimental work on parallel transmission radiofrequency (RF) pulse design is based on the small‐tip‐angle approximation to the Bloch equation. The small‐tip‐angle, while mathematically compact, is not an exact solution and leads to significant errors when large‐tip‐angle pulses are designed. Methods have been proposed to overcome the limitations of the small‐tip‐angle using regularized least‐square optimization or optimal control algorithms. These methods, however, are based on further approximations to the Bloch equation or require the use of general purpose algorithms that do not capitalize fully on the dynamics of the physical model at hand. In this article, a novel algorithm for large‐tip‐angle parallel transmission pulse design is proposed. The algorithm relies on a perturbation analysis of the Bloch equation and it depicts the relationship between the excited magnetization, its deviation from the target pattern and the desired pulses. Simulations and experiments are used to validate the proposed method on a 7T 8‐channel transmit array. The results demonstrate that the perturbation analysis algorithm provides a fast and accurate approach for multidimensional large‐tip‐angle pulse design, especially when large acceleration factors and/or echo‐planar trajectories are used. Magn Reson Med, 2011. © 2011 Wiley‐Liss, Inc.     

Electrodynamic constraints on homogeneity and radiofrequency power deposition in multiple coil excitations

The promise of increased signal‐to‐noise ratio and spatial/spectral resolution continues to drive MR technology toward higher magnetic field strengths. SAR management and B₁ inhomogeneity correction become critical issues at the high frequencies associated with high field MR. In recent years, multiple coil excitation techniques have been recognized as potentially powerful tools for controlling specific absorption rate (SAR) while simultaneously compensating for B₁ inhomogeneities. This work explores electrodynamic constraints on transmit homogeneity and SAR, for both fully parallel transmission and its time‐independent special case known as radiofrequency shimming. Ultimate intrinsic SAR—the lowest possible SAR consistent with electrodynamics for a particular excitation profile but independent of transmit coil design—is studied for different field strengths, object sizes, and pulse acceleration factors. The approach to the ultimate intrinsic limit with increasing numbers of finite transmit coils is also studied, and the tradeoff between homogeneity and SAR is explored for various excitation strategies. In the case of fully parallel transmission, ultimate intrinsic SAR shows flattening or slight reduction with increasing field strength, in contradiction to the traditionally cited quadratic dependency, but consistent with established electrodynamic principles. Magn Reson Med 61:315–334, 2009. © 2009 Wiley‐Liss, Inc.     

B1+ compensation in 3T cardiac imaging using short 2DRF pulses.

The purpose of this study was to determine if tailored 2DRF pulses could be used to compensate for in-plane variations of the transmitted RF field at 3T. Excitation pulse profiles were designed to approximate the reciprocal of the measured RF transmit variation where the variation over the left ventricle was approximated as unidirectional. A simple 2DRF pulse design utilizing three subpulses was used, such that profiles could be quickly and easily adapted to different regions of interest. Results are presented from phantom and in vivo cardiac imaging. Compared with conventional slice-selective excitation, the average flip angle variation over the left ventricle (measured as the standard deviation divided by the mean flip angle) was reduced with P < 0.001 and the average reduction was 41% in cardiac studies at 3T.     

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‐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. Magn Reson Med, 2011. © 2011 Wiley‐Liss, Inc.     

Adiabatic RF pulse design for Bloch‐Siegert B mapping

The Bloch–Siegert (B–S) mapping method has been shown to be fast and accurate, yet it suffers from high Specific Absorption Rate (SAR) and moderately long echo time. An adiabatic RF pulse design is introduced here for optimizing the off‐resonant B–S RF pulse to achieve more B–S measurement sensitivity for a given pulse width. The extra sensitivity can be used for higher angle‐to‐noise ratio maps or traded off for faster scans. Using numerical simulations and phantom experiments, it is shown that a numerically optimized 2‐ms adiabatic B‐S pulse is 2.5 times more efficient than a conventional 6‐ms Fermi‐shaped B–S pulse. The adiabatic B–S pulse performance is validated in a phantom, and in vivo brain mapping at 3T and 7T are shown. Magn Reson Med 70:829–835, 2013. © 2012 Wiley Periodicals, Inc.     

Specific absorption rate benefits of including measured electric field interactions in parallel excitation pulse design

Specific absorption rate management and excitation fidelity are key aspects of radiofrequency pulse design for parallel transmission at ultra-high magnetic field strength. The design of radiofrequency pulses for multiple channels is often based on the solution of regularized least-squares optimization problems for which a regularization term is typically selected to control the integrated or peak pulse waveform amplitude. Unlike single-channel transmission, the specific absorption rate of parallel transmission is significantly influenced by interferences between the electric fields associated with the individual transmission elements, which a conventional regularization term does not take into account. This work explores the effects upon specific absorption rate of incorporating experimentally measurable electric field interactions into parallel transmission pulse design. Results of numerical simulations and phantom experiments show that the global specific absorption rate during parallel transmission decreases when electric field interactions are incorporated into pulse design optimization. The results also show that knowledge of electric field interactions enables robust prediction of the net power delivered to the sample or subject by parallel radiofrequency pulses before they are played out on a scanner.