RF shimming in the cervical spinal cord at 7 T

Purpose: Advancing the development of 7 T MRI for spinal cord imaging is crucial for the enhanced diagnosis and monitoring of various neurodegenerative diseases and traumas. However, a significant challenge at this field strength is the transmit field inhomogeneity. Such inhomogeneity is particularly problematic for imaging the small, deep anatomical structures of the cervical spinal cord, as it can cause uneven signal intensity and elevate the local specific absorption ratio, compromising image quality. This multisite study explores several RF shimming techniques in the cervical spinal cord. Methods: Data were collected from 5 participants between two 7 T sites with a custom 8Tx/20Rx parallel transmission coil. We explored two radiofrequency (RF) shimming approaches from an MRI vendor and four from an open-source toolbox


INTRODUCTION
MRI of the spinal cord (SC) is an important diagnostic tool for several pathologies, such as multiple sclerosis, 1 and traumatic injuries. 2Accurate diagnosis requires images with both high in-plane resolution and high signal-to-noise ratio (SNR), the acquisition of which can be challenging at common field strengths of 1.5 T and 3 T. Using ultrahigh field (UHF) MRI systems with a field strength of 7 T or greater, these limitations can be overcome and image quality can be improved. 3The benefits of UHF SC MRI have been demonstrated with the visualization of small anatomical structures such as nerve roots, denticulate ligaments, or blood vessels, 4,5 resulting in higher detection rates of lesions. 6,7These potential clinical benefits bring UHF MRI one step closer to a clinical routine use for central nervous system imaging. 3,8,9owever, in UHF imaging, care must be taken to address the issue of radiofrequency (RF) transmit, or B 1 + , field inhomogeneity.At lower field strengths, the characteristic RF wavelength within human tissues is greater than that of the anatomy of interest, and the B 1 + field can be considered homogeneous, or at least slowly varying.2][13][14] This limits the utility of UHF MRI, particularly for small anatomies located deep within the body, such as the cervical SC.
Parallel transmission (pTx) can be used to overcome this limitation of UHF imaging.In pTx coils, multiple transmit (Tx) elements (channels) are arranged, typically in a circular pattern, as opposed to the single element used at lower fields.These individual elements can be used in circularly polarized (CP) mode, where the same RF waveform is played out on each element, with the same amplitude, and phase offsets such that their B 1 + fields constructively add at the center of the object.Alternatively, the B 1 + field can be adjusted, or shimmed, by changing the magnitude and/or phase of the RF waveform played out for each element (static RF shimming) or changing the waveform as well (dynamic RF shimming).][18][19][20] However, despite the proliferation of bespoke 4,15,[21][22][23][24][25] and commercially available 5 coils for the cervical SC, to date, the application of RF shimming in the cervical spine at UHF has only been preliminarily investigated. 26,27n this paper, we demonstrate the feasibility and utility of participant-specific RF shimming for the cervical SC using a bespoke 8-Tx/20-receive (Rx) pTx-capable cervical spine coil.We evaluate two RF shimming approaches provided by an MRI vendor as well as four approaches implemented in the open-source Shimming Toolbox. 27We characterize B 1 + efficiency and cerebrospinal fluid (CSF) versus SC contrast on gradient echo (GRE) scans across the entire c-spine and upper thoracic region.

Participants and facilities
Five participants were scanned for this study at two sites.Two participants (30 year-old male, 31-year-old male) were scanned at the Montreal Neurological Institute (MNI, Montreal, Quebec, Canada), and 3 participants (20-year-old female, 29-year-old female, 25-year-old male) were scanned at the Massachusetts General Hospital's Athinoula A. Martinos Center for Biomedical Imaging (MGH, Charlestown, Massachusetts, USA).All data were acquired using custom 8-Tx/20-Rx cervical SC arrays 25 and 7T Magnetom Terra scanners (Siemens Healthineers, Forchheim, Germany) equipped with 2-kW/channel amplifiers.Informed consent was given before the scanning session (study approved by the Comité d'éthique de la recherche du Regroupement Neuroimagerie Québec for MNI and the Mass General Brigham institutional review board for MGH).

Sequences
Three scans were first acquired using CP mode to map the combined B 1 + field and enable the calculation of RF shim weights using the Shimming Toolbox: (1) The magnitude and phase of each Tx channel was mapped using a vendor-supplied TurboFLASH sequence (termed "tfl_rfmap" by the vendor) with a presaturation pulse, excitation flip angle (FA) = 10 SC versus CSF contrast along the cervical spine across RF shimming methods.For all scans, B 0 shim coefficients were calculated on a rectangular volume around the SC, spanning between the intervertebral disks C2/C3 down to T2/T3, and kept constant throughout the session.RF shim weights were derived from the tfl_rfmap and GRE scans as described in Section 2.1.3.Following RF shim calculation, the tfl_b1map scan and GRE scan were re-acquired for six shim conditions.For "Vendor: Volume Specific" (referred to as "volume" in the manuscript), the B 0 shim volume was defined as the region of interest (ROI) for RF shimming, and the shim weights were calculated by the scanner using a vendor-supplied approach.In "Vendor: Patient Specific" (referred to as "patient"), shim weights were likewise calculated by the scanner, but the ROI was defined as the whole FOV.Both vendor-supplied approaches aimed to minimize the coefficient of variation (CoV) within their respective ROIs.For each participant, the reference voltage was kept constant during all scans.For sub-04, the reference voltage of GRE scans was clipped at 400 V to minimize the occurrence of PALI errors.

RF shim weight calculation
RF shim weights were calculated from the CP acquisitions using the following procedure.Image data were transferred to a separate laptop.The SC was segmented from the CP mode GRE scan using the Spinal Cord Toolbox (SCT). 28The center of mass of that segmentation was then used to create a cylindrical mask of 28-mm diameter, within which RF shimming coefficients were estimated.The choice of the mask size was driven empirically, based on preliminary experiments looking at (i) the robustness of RF shimming coefficient estimation with respect to the number of voxels inside a mask, and (ii) the amount of subject motion within an approximate 1-h session.The mask was subsequently cropped between intervertebral disks C2/C3 and T2/T3 and then warped to the space of the tfl_rfmap scan.Four RF shimming algorithms were implemented in the Shimming Toolbox.The output of each algorithm is a complex set of Tx channel weights (w) that minimize the following expressions: To optimize with phase-only shimming (referred to as "phase"), the coefficient of variation (CV) of the combined B 1 + field was minimized within the ROI by adjusting the phase of each Tx channel, without taking the magnitude into account, as follows: where and w n = e i n where B + 1 n is the measured B + 1 map of Tx channel n, and ) are the SD and the mean of the shimmed B + 1 phase−only (w) map, respectively.Crucially, only the phase of the B + 1 maps is adjusted (via w n = e i n ), whereas the amplitude is left unmodified.
To optimize for CV reduction across the cord (referred to as "CoV"), the CV of the combined B 1 + field was minimized by adjusting both the phase and magnitude of each Tx channel as follows: where and w n = A n e i n .Thus, w CV red weights are calculated to minimize the CV by taking both the phase (via e i n ) and the magnitude (via A n ) of each transmit channel into account.
To optimize toward a target 20 nT/V in the ROI (referred to as "target"), a target B + 1 amplitude ("t") of 20 nT/V was used when determining the shim weights.20 nT/V was chosen based on the performance of the coil as described in Lopez-Rios et al. 25 : To optimize for SAR efficiency (referred to as "SAReff"), the local SAR, calculated from virtual observation points, was considered to increase the mean B + 1 per the square root of the maximum 10g-averaged local SAR, as follows: where w SAR eff and w target optimized both the magnitude and phase of each transmit channel.After calculation, the corresponding weights were transferred back to the scanner and applied to the corresponding Tx channels.Figure 1 illustrates the workflow for calculating RF shim weights.Total time for the RF shim

F I G U R E 1
Overview of the RF shimming procedure.The top panel shows the RF coil used for the experiments, alongside the Tx coil geometry and the electromagnetic simulation results (performed on the Gustav model using CST Studio Suite) yielding the CP mode used for this coil.The bottom panel shows the RF shimming procedure (with approximate duration).First, gradient echo (GRE) and tfl_rfmap scans are acquired (4 min 30 s).Second, these images are transferred via ethernet socket from the MRI console onto a separate laptop running the Shimming Toolbox and Spinal Cord Toolbox (< 1 s).Third, the spinal cord is automatically segmented to produce a mask that is resampled into the space of the individual coil magnitude and phase images of the tfl_rfmap scan (∼5 s).Fourth, the RF shim weights are calculated according to the defined constraints for each shim scenario (1 min total).weight calculation, including data transfer, was approximately 1 min.
All processing was performed in Python using a reproducible Jupyter Notebook (see the Data Availability Statement).The processing pipeline was applied to each subject's data and took about 2 h to run on Google Colab (without paid license; 2 Xeon CPU 2.20GHz and 12GB RAM).The key processing steps are described subsequently.

2.1.4
Anatomical T 2 *-weighted GRE Automated segmentation of the SC was performed with SCT's sct_deepseg_sc 29 on the T 2 *-weighted images acquired with the "CoV" shim mode.Vertebral levels were labeled using existing manual disc labels.Automated disc labeling methods were not robust enough due to the thick axial slices that caused poor appearance of the intervertebral discs.A mask of the CSF was generated semi-automatically: a first pass using sct_propseg (with the flag "-CSF"), 30 followed by manual correction.The images from the other shim modes were registered to the "CoV" one using a deep learning algorithm. 31After reviewing all processes using SCT's quality control module, 1 the magnitude signal of the CSF and the spinal cord was extracted slice-wise between C3 and T2 levels, smoothed (convolution with uniform filter of 50 pixels), and their ratio was computed to assess the consistency of the FA across different shim methods.
To create plots displaying participants with consistent vertebral levels along the x-axis, the x-tick positions were linearly interpolated.This interpolation was done to align with the evenly distributed distances of vertebral levels as defined by the PAM50 template. 32

B 1 + field mapping
Each tfl_b1map magnitude image (e.g., "CP," "CoV") was registered to the "CoV" GRE scan using the SliceReg algorithm. 33The computed warping field was applied to bring the GRE's segmentation and vertebral levels into each respective tfl_b1map space.The tfl_b1map relative FA map was converted into normalized units (nT/V).The B 1 + map values were extracted specifically within the segmented spinal cord.After reviewing all processes using SCT's quality control module, B 1 + values were extracted slice-wise between C3 and T2 levels and smoothed (convolution with uniform filter of 20 pixels).For each RF shimming scenario, B 1 + inhomogeneity was calculated as the CV of B 1 + values between C3 and T2.

Statistics
A one-way repeated-measures ANOVA was run to assess differences between shim methods (each being acquired on the same subjects, hence the repeated ANOVA).Post hoc analyses were performed with paired t-tests for each pair of shim methods and corrected for multiple comparisons with the Benjamini-Hochberg false discovery rate method.

RESULTS
Figure 2 shows a comparison of B 1 + efficiency maps across the tested RF shimming scenarios in 1 representative subject.Both the vendor and the custom RF shimming algorithms result in a markedly different B 1 + efficiency along the ROI compared with CP mode.In particular, vendor algorithms evaluated in this subject appear to favor CV at the expense of B 1 + efficiency.
Figure 3 shows the GRE magnitude images across the tested RF shimming scenarios in 1 representative subject.When interpreting these images in concomitance with the B 1 + maps from Figure 2, we notice the consistency between a higher B 1 + efficiency and a higher magnitude signal.
Both the vendor and custom RF shimming algorithms result in a markedly different B 1 + efficiency along the ROI compared with CP mode.In particular, vendor algorithms evaluated in this subject appear to favor CV at the expense of B 1 + efficiency.As described in Table 1, across all subjects, "patient" mode resulted in the lowest B 1 + homogeneity, whereas "volume" resulted in the highest homogeneity, and "CoV", "phase", "target", and "SAReff" shim modes showed higher B 1 + homogeneity than "CP" mode, with both vendor-supplied methods showing low B 1 + efficiency.
The B 1 + efficiency measured in the SC from C3 to T2 vertebral levels across participants is shown in Figure 4A.Overall, we observe the same trend across participants, with the "CP", "CoV", and "SAReff" shim modes showing the highest B 1 + efficiency, and the "patient" and "volume" modes showing the lowest B 1 + efficiency.Aggregate statistics are described in Table 1 (column "B 1 + efficiency") and confirm the observed trends.Results of ANOVA and post hoc analyses are available as Table S1.An intriguing observation is that for sub-02, and to a lesser extent in sub-04, the "target" algorithm failed to achieve its goal + efficiency for one participant (sub-05) across all seven RF shimming conditions.The top left panel shows the tfl_b1map magnitude image with an overlay of the mask that was used to perform RF shimming.Text inserts show the mean (in nT/V) and CV (in %) of B 1 + efficiency along the spinal cord between C3 and T2.

F I G U R E 3
Gradient echo (GRE) magnitude signal intensity for one participant (sub-05) across RF shimming conditions.The colormap adjustment is the same across all images.The differences in B 1 + efficiency along the cord between the various RF shimming conditions results in signal intensity differences.Visual contrast between CSF and spinal cord (SC) is affected, with "volume" showing poor visual contrast compared with, for example, the "CP" or "SAReff" modes.

T A B L E 1
Summary statistics of B 1 + homogeneity (lower is better), B 1 + efficiency (higher is better), and CSF/cord contrast (higher is better) in the spinal cord between C3 and T2 vertebral levels (included).  of a 20 nT/V average.Conversely, the "SAReff" algorithm appeared to come closer to this mean value.Looking at the online output from Shimming Toolbox, for sub-02 and sub-04, the mean B 1 + within the SC were, respectively, 19.3 nT and 19.0 nT/V, which is close to the target.However, the RFshim ROI was based on a noisy and aggressively masked tfl_rfmap sequence, whereas the evaluation ROI was based on the tfl_b1map, which could explain the discrepancies between the target versus measured B 1 + values.
Figure 4B shows the CSF-to-SC ratio measured from the GRE scan in the SC from C3 to T2 vertebral levels across participants.Overall, we observe the same trend across participants, with the "CoV", "volume", and "target" shim modes showing the highest CSF/SC contrast,  To match the x-ticks across subjects, the C2-C3 and the T2-T3 intervertebral discs of each subject were aligned with that of the PAM50 template, 32 and the curves were scaled along the x-axis to match this alignment.
(A) (B) and the "SAReff" and "CP" modes showing the lowest contrast.Aggregate statistics are described in Table 1 (column "CSF/cord contrast") and confirm the observed trends.
Results of ANOVA and post hoc analysis are available as Table S2.

DISCUSSION AND CONCLUSIONS
To make full use of the benefits of 7 T MRI for SC imaging, the inherent drawback of B 1 + field inhomogeneity needs to be overcome.In this work, we presented the feasibility and utility of using static RF shimming for SC imaging across two 7 T systems.Several vendor-based and automatic ROI-customized shim algorithms were evaluated.

Evaluation metrics
Before delving into method comparisons, it is essential to first outline the evaluation metrics used.The first metric, Tx homogeneity, reflects the variability of the B 1 + field within the target imaging region.Achieving uniform FAs across this ROI is crucial, notably to ensure a consistent contrast throughout the ROI.Generally, enhancing B 1 + homogeneity is possible with increased input power, although hardware limitations, such as the maximum capacities of the RF amplifier for peak and average power, cap this improvement.This leads to our second metric, Tx efficiency, which gauges the efficacy of the RF field produced in the specified region relative to the input power.
The third metric involves the CSF/cord contrast derived from a GRE magnitude image.This is a particularly pragmatic metric, because the contrast between CSF and the SC is crucial for subsequent image analyses and interpretations, such as the precise segmentation of the SC to measure indicators of conditions like cord atrophy.Ideally, if both tissues are subjected to the same FA, the contrast should remain constant along the superior-inferior (S-I) direction.Thus, examining variations in CSF/cord contrast along the S-I direction offers an indirect measure of B 1 + homogeneity.Although the average CSF/cord contrast along the S-I axis is also significant, it is influenced by the T 1 relaxation properties of the tissues and the FA that optimizes contrast.Consequently, if the GRE scans were conducted with a higher or lower FA, the average contrast for each evaluated shimming method could have varied.Because the optimal FA for maximizing contrast was not established in this study, conclusions cannot be drawn about the shimming method that maximizes contrast.Instead, evaluations should concentrate on the variations in contrast along the S-I axis, as this serves as an indicator of B 1 + homogeneity.

Comparison of RF shimming methods
Vendor-based approaches ("patient," "volume") were restricted by the possibility to optimize the ROI within which RF shim coefficients are calculated.In the "patient" approach, the optimization ROI is the full FOV, which leads to an inhomogeneous excitation within the cord (Table 1), whereas in the "volume" approach, a rectangular ROI can be specified and resulted in the best B 1 + homogeneity across all methods.However, a rectangle is an imperfect fit for the anatomy of the spinal cord.The cervical SC is naturally curved and surrounded by other tissues and the trachea.Within this study, we found it challenging to draw a rectangle that included all of the SC but did not include any air or surrounding tissue, thereby biasing the shimming algorithm.The comparison of RF shim performance between a rectangular ROI and an ROI that tightly follows the curvature of the spine is illustrated on Figure S1.Another drawback of vendor solutions is the opaque nature of the shimming algorithm and its cost function.We observed that the "volume" approach tended to improve B 1 + homogeneity at the cost of B 1 + efficiency, whereas the "patient" approach performed poorly for both B 1 + homogeneity and efficiency.
Custom RF shimming methods ("CoV", "phase", "target", and "SAReff") implemented in the vendoragnostic Shimming Toolbox can overcome these limitations.The "CoV" method produced the highest CSF/SC contrast on T 2 *-weighted scans, and the lowest variation of that contrast along the S-I axis.Using the Spinal Cord Toolbox, the SC can be segmented to derive an ROI that tightly fits the cord area for an optimal calculation of RF shimming coefficients.Previous studies undertook a similar segmentation based approach for optimizing B 0 shimming in the SC. 27,34The optimization algorithms and their cost functions implemented in Shimming Toolbox are fully open source and transparent to the user and could be extended or modified at will.
We observed that changes in B 1 + efficiency and homogeneity result in similar changes in visual image quality, with low-efficiency RF shim methods ("volume") resulting in less apparent signal, whereas high-efficiency methods ("SAReff", "CoV") result in more apparent signal in GRE scans.B 1 + homogeneity influenced the variation of CSF/SC contrast, thus the "CoV", due to its high efficiency and homogeneity, the highest contrast showed the least variation.Patient motion, particularly motion between the scans used to map the B 1 + field and the acquisition of RF shimmed scans, was a potential source of errors in our study.Although patient motion was minimized using careful instruction and immobilization during our study, it was not actively mitigated.To minimize the potential impact, a large, 28-mm-diameter mask was chosen for RF shimming.Post-scan visual inspection of the GRE scans revealed that the SC was within this mask for all RF shimming scenarios and all participants.
The performance of the "CP" mode was similar to that of the patient-specific "SAReff" method, which is likely because the "CP" mode of both coils was calculated to maximize B 1 + efficiency.However, what we did find surprising, is how good the "CP" mode was across all subjects (for both sites), despite it being fixed across subjects.We would have expected better performance for the "SAReff" model, as it provides personalized shim solutions for each individual.This suggests interesting follow-up research hypotheses: Are personalized shim solutions not as good in practice because of the difficulty in obtaining robust and reliable B 1 + maps?Is it because of excessive noise and/or subject motion?Given how good performances are on "CP" mode across subjects, does that suggest that shim solutions based on universal pulses would be a promising solution for spinal cord applications at 7 T (see also the following discussion)?

Differences between sites
We noticed some differences between sites.Notably, the CSF/cord contrast (Figure 4B) curves are fairly similar within sites (MGH, sub-01, sub-02, and sub-03; MNI, sub-04 and sub-05), but the trends are different between the two sites.More specifically, for MGH subjects, the contrast is increasing toward the lower vertebral levels, whereas the MNI subjects show the opposite trends.Despite the two sites being equipped with a coil that followed the same design and construction protocol, especially in terms of Tx dipole sizes and locations, the two coils are not exactly the same.Essentially, the MNI coil housing has two layers of dielectric materials (total thickness: 6.2 mm) between the Tx and Rx arrays, which were removed from the MGH design.However, the measured S-parameters and the simulated electromagnetic fields are very similar between both coils.Other possible sources of discrepancies between the two sites include the subjects' body mass index (sub-04 and sub-05 are larger), positioning (sub-04 and sub-05 show exhibit more lordosis), and breathing (sub-04 and sub-05 exhibit more respiratory-related artifacts), which could have affected the reliability of the B 1 + maps, especially in the upper thoracic levels.

Limitations and future studies
In this study, we used a configuration of eight transmit dipoles positioned in a single row around the neck area.
Research suggests that a design incorporating multiple rows of transmit elements, similar to those used in earlier C-spine coil designs, 15 has the potential to significantly enhance RF shimming due to the better complementarity of coil elements along the S-I axis. 35,36Expanding coverage areas, such as the head and neck, would largely benefit from a 16-channel Tx system, as shown by May et al. 37 However, such a system would incur higher costs.Evaluation of the different shim approaches in terms of SAR was not part of our study, and SAR information was not collected at MGH.For comparison, we show the SAR of the GRE scans for our representative subject (sub-05) in Table S3.We observe that "volume" resulted in the lowest head-only 10-s averaged SAR, whereas "patient" resulted in the second-highest SAR, following "SAReff."Further studies may investigate the effects of RF shimming on SAR, based on electromagnetic simulations and scanner side measurements.
The current workflow of the Shimming Toolbox would benefit from better interoperability with vendor-specific consoles, especially to reduce time required for data transfer.Nonetheless, the proprietary nature of vendor software poses a challenge to achieving transparent and cross-platform reproducibility.In this context, the development of vendor-neutral acquisition platforms 38,39 offers a promising solution by facilitating a more open and interoperable environment for research and clinical applications.
Another consideration is the choice of B 1 + mapping sequence.Here, we used the TurboFLASH sequence, which offers fast acquisition times at the cost of sensitivity to motion, susceptibility artifacts, and a limited dynamic range for B 1 + field strength measurement, affecting its accuracy and reliability in certain scenarios.Alternative sequences can be explored and compared in future studies for SC applications, such as the dual excitation angle method (DREAM), 40 the actual flip-angle imaging (AFI). 41lice-wise RF shimming would also be an interesting avenue for the SC, as demonstrated in the brain, 20 especially for sequences acquired axially with large slice thicknesses, as is often the case in quantitative MRI SC protocols.
Our study focused on tailoring the B 1 + field to the individual participants to achieve specific B 1 + constraints (homogeneity, target B 1 + value, minimum SAR, etc.).A complementary approach can be found in Universal Pulses, 42 where instead of participant-specific tailoring, pulses are designed to create homogeneous excitation across a wide range of participants.Universal Pulses have been demonstrated for imaging the brain, 42 heart, 43 and SC. 44,45n conclusion, this study compared various RF shimming methods for SC imaging at 7 T, across two different sites.The "CP", "CoV", and "SAReff" shim modes showed the highest B 1 + efficiency, and the vendor-based "patient" and "volume" modes showed the lowest B 1 + efficiency.The "CoV" method produced the highest CSF/cord contrast on T 2 *-weighted scans.The study's findings highlight the potential of RF shimming to advance 7T MRI's clinical utility for central nervous system imaging by enabling more homogenous and efficient SC imaging.Future studies may explore the feasibility of applying static RF shimming to other UHF MRI that are adversely affected by signal inhomogeneity, such as functional MRI. 46

Note:
The mean and SD, respectively, correspond to the average and standard deviation computed along the spinal cord of each participant.Each cell represents the mean ± standard deviation across participants.The best values are highlighted in bold.

F
signal ratio from the gradient-echo scan (B) across subjects and across different RF shimming conditions.Data were measured in the spinal cord from C3 to T2 vertebral levels.