Multi-voxel excitation using sparse pulse on significantly undersampled k-space

Introduction: 2D spatial selective RF pulse [1] is able to generate arbitrarily shaped excitation pattern, while parallel transmission [2] offers additional degrees of freedom to shorten the pulse width and reduce SAR. Both techniques have benefited the single and multi-voxel MR-spectroscopy [3, 4]. Recent years, sparse pulses [5, 6] have been developed to shorten the excitation duration by using a significantly undersampled k-space trajectory. In this work, an example of multivoxel excitation using sparse pulse is presented. The k-trajectory is designed on an undersampled k-space and represented as a Fourier Transform (FT) matrix. The RF pulse can then be designed using nonlinear Conjugated Gradient (CG) algorithm. Bloch simulation of a multi-voxel excitation is performed to demonstrate the feasibility of this method. Theory and method: To design an incoherent undersampled k-space, we used the Monto-Carlo sampling strategy to choose the k-space samples. Then an optimized kspace trajectory through all these k-space samples could be designed using the simulated annealing algorithm and discretized to Nt time samples. Also, the desired excitation pattern was discretized and rearranged to Ns spatial samples. Thus the FT matrix is expressed by a Ns×Nt system matrix A where each element ai,j is [7]: t e M i a T t i t i j i j i i j Δ = − Δ + ⋅ ] )[ ( ) ( 0 , x x k ω γ (1)