Spatial domain method for the design of RF pulses in multicoil parallel excitation

Abstract

Parallel excitation has been introduced as a means of accelerating multidimensional, spatially-selective excitation using multiple transmit coils, each driven by a unique RF pulse. Previous approaches to RF pulse design in parallel excitation were either formulated in the frequency domain or restricted to echo-planar trajectories, or both. This paper presents an approach that is formulated as a quadratic optimization problem in the spatial domain and allows the use of arbitrary k-space trajectories. Compared to frequency domain approaches, the new design method has some important advantages. It allows for the specification of a region of interest (ROI), which improves excitation accuracy at high speedup factors. It allows for magnetic field inhomogeneity compensation during excitation. Regularization may be used to control integrated and peak pulse power Parallel excitation was recently proposed (1,2) as a means of accelerating multidimensional selective excitation using multiple coils driven with independent waveforms. In a manner analogous to parallel imaging methods, such as sensitivity encoding (SENSE) (4) and generalized autocalibrating partially parallel acquisition (GRAPPA) (5), a reduced excitation k-space trajectory (6) can be used to achieve a desired excitation pattern by exploiting the blurring behavior of coil sensitivity patterns in the excitation k-space domain to deposit RF energy in regions that are not traversed by the trajectory. Accelerated selective excitation is useful for reducing specific absorption rate (SAR) (2), and shortening multidimensional RF pulses in such applications as compensation for B 1 and B 0 inhomogeneity (7-10). The feasibility of parallel excitation was also recently verified experimentally (11,12).Several methods currently exist for designing small-tipangle RF pulses in parallel excitation (1-3). The pioneering pulse design methods were introduced by Katscher et al. (1) and Zhu (2). The method introduced by Katscher et al. (1), dubbed transmit SENSE, is characterized by the explicit use of transmit sensitivity patterns in the pulse design process, and its formulation is based on a convolution in excitation k-space. It allows usage of arbitrary kspace trajectories. Zhu's (2) method makes explicit use of transmit sensitivity patterns, but is formulated as an optimization problem in the spatial domain, and, as described, is restricted to echo-planar k-space trajectories. Griswold et al. (3) proposed a k-space domain method that is analogous to GRAPPA imaging. It is unique in that it does not require prior determination of sensitivity patterns. Instead, it involves an extra calibration step in the pulse design process. It also appears to be restricted to echo-planar k-space trajectories.In this paper we propose an alternative RF pulse design method that is closely related to transmit SENSE (1), but is formulated in the spatial domain. It is a multicoil generalization of the iterative pulse design method proposed by Yip et al. (13), and is based on the minimization of a qua...

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

“…Using small tip‐angle approximation 10, spokes pulses optimization can be represented as a regularized MLS minimization problem through the spatial domain method 15: $\mathbf{b}=\text{arg}\hspace{0.17em}\underset{\mathrm{boldb}}{\min }\left\{\Vert \left|\mathbf{A}\mathbf{b}\right|-{\left|\mathrm{boldm}\right|\Vert }_2^2+\lambda {\Vert \mathrm{boldb}\Vert }_2^2\hspace{0.17em}\right\},$where b is a column vector of length N Tx containing the complex RF scaling factors for each of the transmit channels, A is a N vox  ×  N Tx system matrix containing the complex transmit sensitivity from each of the N Tx transmit coils in each of the N vox region of interest voxels with the phase induced from the local B 0 offset and the spokes gradient blips, m is a column vector of length N vox representing the transverse magnetization target set in each of the N vox region of interest voxels, and $\lambda$ is the Tikhonov regularization parameter as a means to regularize the global RF power. This problem can be solved efficiently by the multishift version of conjugate gradients for least‐squares (mCGLS) algorithm 43 together with the local variable exchange method 22.…”

“…To fully benefit from the improved signal‐to‐noise ratio (SNR) and contrast‐to‐noise ratio at UHF 2, 3, 4, 5, the well‐known problem of radiofrequency (RF) transmit ( ${\mathrm{normalB}}_1^{+}$) inhomogeneity 6 must be overcome first. Solutions that are currently available include novel RF coil design 7, dielectric pads 8, 9, RF pulse design 10, parallel transmission (pTx) with RF shimming 11, 12, 13, 14, and transmit sensitivity encoding (SENSE) 15, 16, 17.…”

“…Static RF shim can be considered as the special case of one spoke. The phases and amplitudes required for the sinc subpulses can be found using magnitude least‐squares (MLS) optimization 22, while taking into account the subject‐specific B 0 field distribution and complex channel‐by‐channel ${\mathrm{normalB}}_1^{+}$ sensitivity maps with the formalism of the spatial domain method 15. For multislice acquisitions, slice‐ or slab‐specific spokes pulses have been shown to be beneficial for the overall achievable homogenization in the imaging region 11, 19, 23, 24, 25.…”

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

“…In the small flip angle regime (34), the design of pTx RF pulses corresponds to solving the linear system (8):…”

“…In radiofrequency (RF) shimming, the interference of the B + 1 fields of the individual channels is optimized for excitation homogeneity (2)(3)(4)(5). Parallel transmit systems using spatially tailored RF pulses facilitate even more control of the local spin excitation within sufficiently short RF pulse durations and over a sufficient spectral range (6)(7)(8)(9). Experimental demonstrations of these techniques have been shown in recent years (10)(11)(12)(13).…”