Effect of degenerate spherical harmonics and a method for automatic shimming of oblique slices

Efficient eddy current characterization using a 2D image-based sampling scheme and a model-based fitting approach

PURPOSE

To propose two innovations to existing eddy current characterization techniques, which include (1) an efficient spatio-temporal sampling scheme and (2) a model-based fitting of spherical harmonic eddy current components.

THEORY AND METHODS

This work introduces a three-plane 2D image-based acquisition scheme to efficiently sample eddy current fields. Additionally, a model-based spherical harmonic decomposition is presented, which reduces fitting noise using a rank minimization to impose an exponential decay on the eddy current amplitude evolution. Both techniques are applied in combination and analyzed in simulations for their applicability in reconstructing suitable pre-emphasis parameters. In a proof-of-concept measurement, the routine is tested for its propriety to correctly quantify user-defined field dynamics. Furthermore, based on acquired precompensation and postcompensation eddy current data, the suitability of pre-emphasis parameters calculated based on the proposed technique is evaluated.

RESULTS

Simulation results derived from 500 data sets demonstrate the applicability of the acquisition scheme for the spatio-temporal sampling of eddy current fields. Compared with a conventional data processing strategy, the proposed model-based approach yields pre-emphasis parameters that reduce the average maximum residual field offset within a 10-cm-diameter spherical volume from 3.17 Hz to 0.58 Hz. Experimental data prove the proposed routine to be suitable to measure and effectively compensate for eddy currents within 10 minutes of acquisition time.

CONCLUSION

The proposed framework was found to be well-suited to efficiently characterize and compensate for eddy current fields in a one-time calibration effort. It can be applied to facilitate pre-emphasis implementations, such as for dynamic B₀ shimming applications.

Interslice current change constrained B0 shim optimization for accurate high-order dynamic shim updating with strongly reduced eddy currents

PURPOSE

To overcome existing challenges in dynamic B0 shimming by implementing a shim optimization algorithm which limits shim current amplitudes and their temporal variation through the application of constraints and regularization terms.

THEORY AND METHODS

Spherical harmonic dynamic B0 shimming is complicated by eddy currents, ill-posed optimizations, and the need for strong power supplies. Based on the fact that eddy current amplitudes are proportional to the magnitude of the shim current changes, and assuming a smoothness of the B0 inhomogeneity variation in the slice direction, a novel algorithm was implemented to reduce eddy current generation by limiting interslice shim current changes. Shim degeneracy issues and resulting high current amplitudes are additionally addressed by penalizing high solution norms. Applicability of the proposed algorithm was validated in simulations and in phantom and in vivo measurements.

RESULTS

High-order dynamic shimming simulations and measurements have shown that absolute shim current amplitudes and their temporal variation can be substantially reduced with negligible loss in achievable B0 homogeneity. Whereas conventional dynamic shim updating optimizations improve the B0 homogeneity, on average, by a factor of 2.1 over second-order static solutions, our proposed routine reached a factor of 2.0, while simultaneously providing a 14-fold reduction of the average maximum shim current changes.

CONCLUSIONS

The proposed algorithm substantially reduces the shim amplitudes and their temporal variation, while only marginally affecting the achievable B0  homogeneity. As a result, it has the potential to mitigate the remaining challenges in dynamic B0 shimming and help in making its application more readily available.

B0 magnetic field homogeneity and shimming for in vivo magnetic resonance spectroscopy

The homogenization of B₀ conditions is necessary for every magnetic resonance spectroscopy (MRS) investigation. Its direct consequence is narrow spectral lines, on which reliable separation and quantification of biochemicals, and thus experimentally obtainable metabolic information, fundamentally relies. Besides spectral linewidth, unwanted B₀ inhomogeneity also impairs other aspects of the MRS experiment, such as water suppression and editing efficiency, that rely on exact frequency definition. Therefore, experimental B₀ homogenization, called B₀ shimming, is mandatory for meaningful MRS, and high-level B₀ shimming is arguably one of the most important ingredients for successful MRS investigations. In this review, we describe the relevance of B₀ homogeneity for in vivo MRS and summarize common concepts and specific solutions for its experimental optimization.

Electrocardiogram-triggered, higher order, projection-based B₀ shimming allows for fast and reproducible shim convergence in spinal cord ¹H MRS

¹H MRS allows insight into the chemical composition of the central nervous system. However, as a result of technical challenges, it has rarely been applied to the spinal cord. In particular, the strong susceptibility changes around the spinal cord and the pulsatile flow of the cerebrospinal fluid lead to distinct B₀ field distortions which often considerably degrade the spectral quality. Hence, B₀ shimming is one of the main challenges in ¹H MRS of the spinal cord. Electrocardiogram (ECG)-triggered, higher order, projection-based B₀ shimming was introduced and compared with both conventional projection-based B₀ shimming and B₀ shimming based on ECG-triggered, three-dimensional B₀ field mapping. The linewidth of the unsuppressed water peak was used to evaluate the reproducibility and the potential improvement to B₀ homogeneity. The use of ECG-triggered projection-based B₀ shimming in combination with ECG triggering during preparation phases and triggering during acquisition of the spectra is the most robust method and thus helps to improve the spectral quality for MRS of the spinal cord.

Dynamic B0 shimming at 7 T

Dynamic slice-wise shimming improves B0 field homogeneity by updating shim coil currents for every slice in a multislice acquisition, producing better field homogeneity over a volume than can be obtained by a single static global shim. The first aim of this work was to evaluate the performance of slice-wise field-map-based second-order dynamic shimming in a human high-field 7 T clinical scanner vis-à-vis image based second order static global shimming. Another goal was to characterize eddy currents induced by second and third order shim switching. A final aim was to compare global and dynamic shimming through shim orders to elucidate the relative benefits of going to higher orders and to dynamic shim updating from a static shimming regime. An external hardware module was used to store and dynamically update slice-optimized shim values during multislice data acquisition. High-bandwidth multislice gradient echo scans with B0 field mapping and low-bandwidth single-shot echo planar scans were performed on phantoms and humans using second-order dynamic and static global shims. For the measurement of second and third order shim induced eddy currents, step response temporal phase changes of individual shims were measured and fit to shim harmonics spatially and to multiexponential decay functions temporally. Finally, an order-wise field-map-based comparison was performed with first, second and third order global static shimming, first and second order dynamic shimming, as well as combined second or third order global and first order dynamic shim. Dynamic shimming considerably improved B0 homogeneity compared to static global shimming both in phantoms and in human subjects, reducing image distortion and signal dropout. The unshielded second and third order shims generated strong B0 and self and cross-term eddy fields, with multiple time constants ranging from milliseconds to seconds. Field homogeneity improved with increasing order of shim, with dynamic shimming performing better than global shimming. Hybrid global and dynamic shimming approach yielded field homogeneity better than global static shims but worse than dynamic shims.

Dynamic Shimming of the Human Brain at 7 Tesla

Dynamic shim updating (DSU) of the zero- to second-order spherical harmonic field terms has previously been shown to improve the magnetic field homogeneity in the human brain at 4 Tesla. The increased magnetic field inhomogeneity at 7 Tesla can benefit from inclusion of third-order shims during DSU. However, pulsed higher-order shims can generate a multitude of temporally varying magnetic fields arising from eddy-currents that can strongly degrade the magnetic field homogeneity.The first realization of zero- to third-order DSU with full preemphasis and B(0) compensation enabled improved shimming of the human brain at 7 Tesla not only in comparison with global (i.e. static) shimming, but also when compared to state-of-the-art zero- to second-order DSU. Temporal shim-to-shim interactions were measured for each of the 16 zero- to third-order shim coils along 1D column projections on a spherical phantom. The decomposition into up to 3 exponentials allowed full preemphasis and B(0) compensation of all 16 shims covering 67 potential shim-to-shim interactions. Despite the significant improvements achievable with DSU, the magnetic field homogeneity is still not perfect even when updating all zero- through third-order shims. This is because DSU is still inherently limited by the shallowness of the low order spherical harmonic fields and their inability to compensate the higher-order inhomogeneities encountered in vivo. However, DSU maximizes the usefulness of conventional shim coil systems and provides magnetic field homogeneity that is adequate for a wide range of applications.

1H-MRS of the macaque monkey primary visual cortex at 7 T: strategies and pitfalls of shimming at the brain surface

Magnetic resonance spectroscopy (MRS) is ideally suited for physiology-neurochemistry experiments with the living brain and particularly for studies on the primary visual cortex (striate cortex or area V1). Yet, the highly convoluted form of the human V1 has thus far prevented the performance of MRS investigations that are spatially confined within the gray matter of this area. Typically, these studies are compromised by partial volume contaminations originating from white matter tissue, cerebrospinal fluid and other cortical areas. In this study, was exploited the relative flatness of V1 in macaques to enable single-voxel 1H-MRS from a small volume (5 x 1.6 x 5 mm3, 40 microl) that was entirely confined within the V1 gray matter of anesthetized monkeys. Linewidths of 13.5+/-1.9 Hz and 13.0+/-1.3 Hz for water and creatine, respectively, were achieved with a two-step shimming strategy for voxels at the brain surface. The quality of the obtained results paves the way for further neuroscientific research, including studies on the cortical microcircuits and the dynamic longitudinal changes occurring during cortical reorganization and plasticity.

Robust fully automated shimming of the human brain for high-field 1H spectroscopic imaging

Although a variety of methods have been proposed to provide automated adjustment of shim homogeneity, these methods typically fail or require large numbers of iterations in vivo when applied to regions with poor homogeneity, such as the temporal lobe. These limitations are largely due to 1) the limited accuracy of single evolution time measurements when full B0 mapping studies are used, and 2) inaccuracies arising from projection-based methods when the projections pass through regions where the inhomogeneity exceeds the order of the fitted parameters. To overcome these limitations we developed a novel B0 mapping method using multiple evolution times with a novel unwrapping scheme in combination with a user-defined ROI selection tool. We used these methods at 4T on 10 control subjects to obtain high-resolution spectroscopic images of glutamate from the bilateral hippocampi.

Dynamic shim updating on the human brain

Dynamic alteration of shim settings during a multi-slice imaging experiment can improve static magnetic-field homogeneity over extended volumes. In this report, a pre-emphasized dynamic shim updating (DSU) system capable of rapidly updating all non-degenerate zeroth through second-order shims is presented and applied to high-field multi-slice imaging studies on the human brain. DSU is utilized in both non-oblique and oblique slicing geometries while updating in-plane and through-slice shims. Image-based magnetic-field maps are used to quantify homogeneity improvements and comparisons are made on a slice-specific basis between static global shimming and increasing orders of shim inclusion utilized DSU. The influence of oblique slicing geometry on DSU-utilized global homogeneity is also quantified computationally. Finally, the effect of DSU on susceptibility artifact reduction in single-shot axial-sliced EPI is analyzed using experimental acquisitions.

Measurement and automatic correction of high-order B0 inhomogeneity in the rat brain at 11.7 Tesla

In vivo B(0) inhomogeneity in the rat brain at 11.7 Tesla was measured and decomposed up to the fourth-order spherical harmonic terms using an automatic slice shimming routine derived from the FLATNESS method. In vivo shimming of horizontal slices showed that significant improvement in the T(2)*-weighted echo-planar imaging was achieved after correction of all first-, second- and third-order in-slice shims. For localized proton spectroscopy, reproducible, high quality data were obtained after correcting all first- and second-order shims. The measured high-order in vivo B(0) inhomogeneity in terms of spherical harmonic terms should provide a useful guide for designing shims to meet in vivo requirements.

In vivo GABA editing using a novel doubly selective multiple quantum filter

A novel multiple quantum filtering method is proposed that uses a doubly selective pulse termed Delays Alternating with Nutations for Tailored Excitation (DANTE) for multiple quantum preparation. This method selectively prepares GABA-3 and GABA-4 into a multiple quantum state and suppresses all other resonances at 3.0 ppm in each single scan. Phantom tests demonstrated excellent GABA signal retention and complete suppression of overlapping metabolites. It is shown using numerical simulations that overlapping macromolecules are suppressed because the frequency of the first upfield 2pi rotation of the doubly selective DANTE pulse coincides with that of the macromolecules at 1.72 ppm. Excellent suppression of overlapping macromolecules was demonstrated in vivo. Using this method the concentration of GABA in the occipital lobe of healthy volunteers was measured to be 1.21 +/- 0.28 micromol/mL (mean +/-SD, N = 9).