We propose single-channel head shim coils with either a helmet or a cylinder geometry. Shim current paths were designed by the stream function method with a realistic target field from a group of human subjects (n = 31). A smoothness constraint was included to decrease shim coil complexity. Helmet and cylinder shim coils with shim current amplitudes 4.2 and 6.9 A improved the standard deviation of residual magnetic field by approximately 17%, respectively.
The spatial homogeneity of the static magnetic field, B0, is one of the most fundamental and common requirements for high-quality MRI. Living organism consists of various tissues with different magnetic susceptibilities. These susceptibility differences cause magnetic field distortions, hence, image artifacts and signal degradation. In a human head, the most significant susceptibility variations are due to the air–tissue interfaces around sinuses and auditory cavities1.
Here we propose shim coil designs to reduce the image distortions in human head by using the target field method with a stream function method2. The target fields are obtained from human subjects. We add a smoothness constraint in design in order to decrease the complexity of shim current paths and to obtain a shim coil that is more practical to build. We use simulations to calculate the performance of shim coil designs with both helmet and cylinder geometries.
We used stream function method in order to design shim current paths. In this method2, a scalar field stream function is defined on the coil surface such that curl of this field corresponds to the surface current. The magnetic field was then derived from a matrix-vector formulation3,4. Given a target magnetic field, the stream function was solved from a system linear equation. In order to obtain a spatially smooth stream function, we added a constraint that maximizes the spatial smoothness of stream function values. We measured the smoothness of the stream function values by a Laplacian operator. With the estimated stream function, we took its iso-contours in order to obtain a wiring pattern of shim current paths.
Off-resonance maps were measured from 31 participants using a dual-echo gradient-recall sequence (TE1 = 2 ms, TE2 = 4.46 ms) at 3 tesla (Skyra; Siemens, Erlangen, Germany) with 2-mm isotropic resolution after a 2nd-order global shimming. The phase accrued between two echoes was calculated at each image voxel by first removing the phase related to the coil sensitivity and then taking a weighted sum across receiver channels5. The phase wrapping was reduced by the BEST-PATH algorithm6,7. An off-resonance map was estimated by the ratio between the unwrapped phase map and the difference between two TEs. Off-resonance maps from all subjects were co-registered by FSL (FMRIB, Oxford, UK) to the standard brain MNI 305 atlas (FreeSurfer, 2007) by only translation and rotation. We used the average off-resonance map across all subjects for shim coil design.
Two different coil geometries were used: (i) a helmet geometry from a magnetoencephalography (MEG) system (MEGIN, Helsinki, Finland) and (ii) a cylinder geometry (15 cm radius; 25 cm height).
We calculated the sum of squared residual inhomogeneity and standard deviation of the residual inhomogeneity in order to measure the shimming performance. These metrics were separately calculated for global and slice-selective shimming.
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