Premium
Simultaneous use of linear and nonlinear gradients for B 1 + inhomogeneity correction
Author(s) -
Ertan Koray,
Atalar Ergin
Publication year - 2017
Publication title -
nmr in biomedicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.278
H-Index - 114
eISSN - 1099-1492
pISSN - 0952-3480
DOI - 10.1002/nbm.3742
Subject(s) - nonlinear system , excitation , dimension (graph theory) , computational physics , physics , analytical chemistry (journal) , chemistry , nuclear magnetic resonance , mathematics , combinatorics , chromatography , quantum mechanics
The simultaneous use of linear spatial encoding magnetic fields (L‐SEMs) and nonlinear spatial encoding magnetic fields (N‐SEMs) in B 1 + inhomogeneity problems is formulated and demonstrated with both simulations and experiments. Independent excitation k ‐space variables for N‐SEMs are formulated for the simultaneous use of L‐SEMs and N‐SEMs by assuming a small tip angle. The formulation shows that, when N‐SEMs are considered as an independent excitation k ‐space variable, numerous different k ‐space trajectories and frequency weightings differing in dimension, length, and energy can be designed for a given target transverse magnetization distribution. The advantage of simultaneous use of L‐SEMs and N‐SEMs is demonstrated by B 1 + inhomogeneity correction with spoke excitation. To fully utilize the independent k ‐space formulations, global optimizations are performed for 1D, 2D RF power limited, and 2D RF power unlimited simulations and experiments. Three different cases are compared: L‐SEMs alone, N‐SEMs alone, and both used simultaneously. In all cases, the simultaneous use of L‐SEMs and N‐SEMs leads to a decreased standard deviation in the ROI compared with using only L‐SEMs or N‐SEMs. The simultaneous use of L‐SEMs and N‐SEMs results in better B 1 + inhomogeneity correction than using only L‐SEMs or N‐SEMs due to the increased number of degrees of freedom.