Target Audience:

MR scientists and advanced users

Outcome/Objectives:

To understand the basis underlying spherical harmonic based shimming and factors governing its importance. Based on the widespread use of multi-band (MB) imaging for fMRI and DTI, special attention is paid to how spherical harmonic shimming and dynamic updating can be utilized for MB shimming and imaging.

Results:

Spherical Harmonic Shims: Shims using spherical harmonics as their basis functions provide a set of orthogonal spatial functions which when combined create complex spatial varying magnetic fields. These fields are then used to minimize magnetic field inhomogeneities across the target regions or objects due to differences in susceptibility. Spherical harmonics are characterized by two parameters, their order and their degree, which in cartesian coordinates describes their maximal power dependence in Z and their periodicity in the X-Y plane respectively. For a given order, there are 2n+1 terms (e.g. there are 5 2nd order shims) and for a given maximal order there are (n+1)2 terms (e.g. there are 9 shims total for up to 2nd order shimming). By appropriately weighting and summing these functions complex spatial correction fields can be generated to make the target region more homogeneous. Mapping and Shimming: There are two primary factors affecting the performance of shimming procedures, the accuracy of the maps used to measure the inhomogeneity and the accuracy of the representation of the true fields generated by the shim hardware. For 3D maps of B0 inhomogeneity (most commonly used in clinical systems) the accuracy of the maps are determined by the bandwidth of the inhomogeneity that can be measured and their sensitivity to the smallest deviation. This is largely governed by the minimum and maximum evolution times used in encoding the B0 inhomogeneity. Multi-evolution time B0 mapping sequences offer the advantages of high bandwidths and high sensitivity, albeit at the cost of increased scan times. For any given maximal evolution time, noise in the data creates the statistical appearance of inhomogeneity. Thus, the choice of parameters and overall SNR can affect the apparent performance of the shims. Although the amplifiers used to control current to the shims are highly linear, imperfections in the design and manufacture of the actual shim coils can result in substantial imperfections. If these imperfections are not accounted for, convergence to optimal shim solution can be poor and in some cases the solutions can diverge. These imperfections can be represented within the same basis set as additional components to the performance of each shim channel consisting of both lower and higher order and degree terms. For 2nd and 4th order shimming, we routinely use basis sets including terms up to 6th and 10th order respectively. Shim Performance with Spherical Harmonics: With increasing order and degree, the achieved B0homogeneity will generally increase, albeit with diminishing returns when the order/degree of shim corrections approaches that present in the target ROI. Thus, for small single voxel targets (a few cc) typically 1st&2nd order shims perform quite well in most (but not all) brain regions. As the target ROI is expanded to an entire slice, a slab or the entire brain, significant advantages can be gained through the use of higher order/degree corrections. For thin to moderately thin slices (2-10mm), the overall homogeneity across the target ROI can be improved by up to 50% with 1st-4th degree shimming in comparison to 1st-2nd order shimming. For superior brain regions the overall homogeneity with 1st-4th degree shimming results in the residual inhomogeneity being dominated by the intrinsic susceptibility difference between gray and white matter. For slabs up to 4cm, similar overall fractional gains can be achieved, but will be dependent upon the exact locations of the slabs. For whole brain shims, the fractional improvement is reduced to ~25-30%. Dynamic Updating and Multiband Shimming: By extension, the overall homogeneity achieved when optimizing the shimming over a group of slices with individual setting per slice, will be generally superior to that achieved when optimizing the entire group of slices simultaneously. For 2D imaging dynamic shim updating (DSU) can be utilized. However, the widespread use of multi-band (MB) imaging, where two or more spatially disparate slices are acquired simultaneously has limited the desire/utility of optimizing homogeneity on a slice by slice basis. Thus, dynamic updating strategies are now focused on if and how the B0 homogeneity over multiple spatially disparate slices can be optimized simultaneously (MB shimming). For spherical harmonics and thin axial slices, it can be shown theoretically that the shims can be divided into two groups of shims, which are spatially degenerate, and each set can be used independently to shim a target slice with equal efficiency. The “degenerate” group of shims, has a linear dependence in the Z direction which can then be used to generate a second arbitrary shim weighting of its non-degenerate partner, enabling two spatially disparate slices to be optimized simultaneously without loss of performance in comparison to solutions for each slice independently. Thus MB=2 shimming can be achieved with equivalent performance as slice by slice (MB=1) shimming. As the MB factor increases from 2 to 4, significant gains in homogeneity are retained, but with decreasing overall improvements for 1st-4th order shimming. Thus, high order spherical harmonics can be used with advantage for up to MB=4 shimming.

Conclusions

Higher order spherical harmonics provide significant advantages for shimming for both static and dynamic solutions ranging from slices to the entire brain and multi-band shimming.

Acknowledgements

NIH R01 EB024408

References

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