In this work we generalized the spatial domain method for spectral-spatial parallel RF design and utilized this approach for the design of wideband uniform slab selection excitation pulses that mitigates large B1+
variation over a 600 Hz bandwidth. A significant improvement in the spectral performance was achieved over the conventional parallel RF design, at the cost of only a minor reduction in excitation uniformity at the center frequency. Given that this improvement was demonstrated in a water phantom with B1+
variation comparable to that of the largest variation observed in a recent six-subject in vivo
study at 7T which utilizes the same Tx-Rx coil array setup (15
) (signal peak-to-through ratio of ~ 3:1 in the birdcage mode), we expect the design to play an important role in improving in vivo
chemical shift imaging at high field as well as other applications needing broad-band excitations, such as water-fat imaging.
illustrates the narrow bandwidth characteristic of the spoke-based excitation when designed via conventional parallel RF technique. The bandwidth is particularly narrow for an excitation with a pulse duration of 1.76 ms. This narrowband characteristic is a direct result of the nature of the spoke excitation, whereby the final excitation profile can be thought of as a summation of the individual spoke’s excitation profiles (with accounts of the effect of the gradient lobe in between the spokes). With the conventional design technique, the individual spoke’s excitation profiles are chosen such that they combine to create a profile that is as uniform as possible at the center frequency. This is done without consideration of the performance at off-resonance frequency positions. The wideband design on the other hand, chooses individual spoke’s excitation profiles which combine well over a range of frequencies, and in doing so, trade off some in-plane spatial uniformity at the center frequency for a much wider excitation bandwidth.
In prior work described in (11
), by using MLS optimization and allowing for spatial phase variation in the excitation profile, spoke-based slice-selective excitation performance was shown to improve significantly both in term of excitation uniformity and power requirements compared to parallel RF pulses designed with conventional LS. For the design of the spectral-spatial pulse, in addition to allowing for spatial phase variation, permitting spectral phase variation is crucial to achieve the desired magnitude performance target. In , most of the spectral phase variation is from a bulk phase shift resulting from differences in spin frequency. Relaxing the target design phase both spectrally and spatially enables the incorporation of a natural spectral phase variation, avoiding designs that are ill-conditioned, and would result in very poor magnitude excitation.
tracking, the 600 Hz excitation bandwidth (~2 ppm. at 7T) achieved by the spectral-spatial spoke excitation would be sufficient in providing uniform excitation to many important metabolites in proton chemical shift imaging (CSI), for instance covering the range from 2 ppm to 4 ppm, with B0
tracking to minimize adverse effects of spatially-varying main field inhomogeneity (17
). In designing this excitation, no modification was made to the spoke gradient trajectory; therefore excitation duration of the spectral-spatial pulse was the same as the one for conventional spoke excitation.
Due to the non-convex nature of MLS optimization, global optimality of the solution cannot be guaranteed. In this work, the method presented in (11
) was used to solve the posed problem. Other methods exist, including the relaxed semi-definite programming method (18
). Future work includes an exploration of alternate means to allow for further improvements in the solution.
In the k-space trajectory design, we observed that the placements as well as the order in which the spokes are traversed affect the bandwidth of the excitation. In this work, we experimented with several possible k-space trajectories for the 4 spokes design. Two types of trajectories were examined: 1) a trajectory with a DC spoke and three surrounding spokes equally distributed on a circle centered at DC, and 2) a trajectory with four spokes equally distributed on a circle, but without a DC spoke. Various orders of the spokes’ traversal and various angular rotations of the spoke placements on the circle were examined for both types of trajectories. Based on our experimental setup, the spokes trajectory without DC sampling allowed a wider bandwidth. This type of trajectory along with the optimal traversal combination (as shown in ) was used to obtain the results presented in this work. Future work will explore the theoretical underpinnings on the placement and order of spokes and their effect to the excitation bandwidth.
The proposed spectral-spatial excitation design formulation has been utilized for the design of spoke-based wideband slab selection with B1+ mitigation. To provide a preliminary analysis of the benefit of this design methodology in increasing the bandwidth for other types of excitations, simulation of 2D spiral as well as spoke-based uniform thin-slice excitation were performed using the obtained B1 maps. For the spiral design, a 4x accelerated spiral trajectory was used with a 5×5 cm square target excitation at the center of FOV. The excitations were designed for a 3.52 ms long RF pulse, with design FOV and resolution of 18 cm and 4 mm respectively. Based on the simulation the excitation bandwidth resulting from the standard MLS design is ~100 Hz, whereas with the proposed spectral-spatial design, a bandwidth of ~500 Hz could be achieved with a minor reduction in the excitation performance at the center frequency. For the spoke-based uniform thin-slice excitation, a slice prescription of 0.5 cm was used. Employing the same k-space trajectory and time-bandwidth-product as in the previous slab selection design, the pulse duration of the excitation is 4.38 ms. With this design, the excitation bandwidth of the standard MLS design is very narrow at around 30 Hz, whereas the spectral-spatial design achieved a bandwidth of ~120 Hz, again accompanied by a minor reduction in spatial homogeneity of the excitation at the center frequency. This increase in bandwidth is not significant enough to make the pulse suitable for CSI application. However, it would improve the robustness of excitation by allowing the excitation to be much more immune to error in the B0 map estimation that is used in the designing the RF pulses.
For other types of spectral-spatial excitation specifications where finer spectral control is required, e.g. narrow band or multi-band frequency selective excitation, longer gradient trajectory would be needed to capture higher frequency components required in such designs. One possible approach for this problem is to concatenate a set of several separate spoke excitations. This is analogous to the single-channel spectral-spatial excitation described in (19
) which is based on the concatenation of sinc pulses. Future work includes design methods to determine optimal gradient trajectory for different types of parallel spectral-spatial excitations.