Multi‐echo–based fat artifact correction for CEST MRI at 7 T

CEST MRI is influenced by fat signal, which can reduce the apparent CEST contrast or lead to pseudo‐CEST effects. Our goal was to develop a fat artifact correction based on multi‐echo fat–water separation that functions stably for 7 T knee MRI data.


INTRODUCTION
CEST MRI is a promising contrast for better investigation of multiple diseases due to its metabolic weighting. 1One application of huge interest is knee CEST MRI for arthritic patients.The main research focus of knee CEST MRI is gagCEST, [2][3][4] which is weighted by the concentration of glycosaminoglycans and is thus a potential marker for the degeneration of articular cartilage.However, evaluations of synovial fluid and serum showed that the concentrations of other metabolites (e.g., glucose, Cho, lactate, and lipids) also differ across different types of arthritic diseases. 5,6Additionally, associations between various metabolites, for example, lactate and glutamine, and the synovitis scores of osteoarthritic patients were recently noted. 7Hence, evaluations of various CEST contrasts in tissues such as the synovial fluid or membrane are of interest for noninvasive investigation of arthritic diseases.However, certain challenges complicate the use of knee CEST MRI in clinical research settings.In addition to motion as well as B 0 as B 1 field inhomogeneities, the presence of fat signal also compromises the CEST contrast.In the presence of fatty tissue, the CEST contrast is strongly affected by the superimposed fat signal, which can even lead to pseudo-CEST effects for certain saturation frequencies. 8,9The tissues of interest in knee imaging such as cartilage, synovial fluid, or a pathologically thickened synovial membrane are located close to fatty tissues such as articular fat pads and bone marrow.Therefore, they are prone to fat-related artifacts caused by partial volume effects or chemical shift.Thus, a correction of fat-related artifacts seems crucial to achieving robust and reproducible CEST contrasts.
Different methods to correct for fat influences have already been investigated, including fat suppression pulses, 9 water excitation, 10,11 multi-echo-based fat-water separation (FWS), 12,13 and a Z-spectrum-based model approach. 14Whereas fat suppression pulses and water excitation mainly target the main fat resonance (at approximately −3.4 ppm), FWS methods with a multi-peak fat model can theoretically correct for influences from all fat resonances.This can be especially relevant for the evaluation of CEST contrasts close to additional fat resonances (e.g., close to 1 ppm) and in the case of strong B 0 field inhomogeneities. 106][17] To reduce the degrees of freedom, these algorithms typically assume a fixed fat peak model that is estimated based on spectroscopic measurements.However, for an optimal correction of Z-spectra, the frequency-dependent saturation of fat signal by the CEST saturation must be considered.This was demonstrated by Zhao et al. 12 for CEST MRI in the breast at 3 T.To correct for saturation of the fat signal, they used a voxel-wise fitting of the magnitude signal with a fat model adapted to the local saturation subsequent to FWS with a hierarchical iterative decomposition of water and fat with echo asymmetry and least squares estimation (IDEAL) with R * 2 correction. 16ltrahigh field strengths play an important role in CEST MRI due to the increased spectral resolution and SNR.However, at ultrahigh field strengths, multi-echo-based FWS becomes more challenging due to the high resonance frequency, which leads to a time reduction of one phase cycle between fat and water.Therefore, the achievable echo spacing of a normal gradient echo (GRE) sequence does not allow for a full sampling of the oscillation behavior, which leads to multiple local optima.Additionally, B 0 inhomogeneities become stronger at high field strengths, which increases the risk of fat-water swaps.
To provide a more stable CEST contrast evaluation for knee imaging, the goal of this work was to develop a stable algorithm for FWS that includes an adaptive fat model for CEST MRI at 7 T.The functionality of our approach is shown based on simulations and phantom measurements.To evaluate the potential of the optimized multi-echo-based FWS compared to faster single-echo measurements, the results were compared to two published methods for fat correction of single-echo CEST MRI measurements at 7 T: a Gaussian fat saturation pulse and a Z-spectrum-based correction model. 14Comparison results are shown for both phantom measurements and in vivo knee CEST MRI.In this work, we focused on the application of knee CEST MRI with a low-power CEST saturation that is weighted to metabolites with medium exchange rate such as relayed nuclear Overhauser effect (rNOE) and amides including glutamine.However, the investigated fat correction methods are independent of the CEST saturation scheme and can be translated to other CEST weightings such as gagCEST, or to other applications such as abdominal or breast imaging.

Adaptive fat-water separation
Our proposed FWS algorithm was designed for data acquired with a magnetization-prepared multi-echo GRE sequence with monopolar readout.To obtain stable FWS results, we utilized six TEs.To optimize the TEs for the FWS, we calculated the effective number of signal averages, which is a measure of the noise performance of the FWS, for various echo spacings, and first TEs with an algorithm provided in the ISMRM (International Society for Magnetic Resonance in Medicine) FW Toolbox 18,19 (Figure S1).Based on our findings, we selected TEs that maximize the effective number of signal averages of the FWS while keeping the echo spacing as short as possible with the used pulse sequence.Reaching an echo spacing slightly below 0.5 ms, which would be optimal for FWS, was not possible with the utilized GRE sequence and chosen resolution.
For the used sequence and in the presence of fat and water signal, the signal in a voxel q at an TE t can be described by the simplified model 16,20 : where  w∕f,q denote the total water and fat signal, Δ 0,q the B 0 inhomogeneity in Hz, and R * 2,q the overall transverse decay rate within the voxel.The fat signal contains N different components with resonance frequencies Δ n relative to water and relative signal magnitudes a n .It is defined that ∑ N n=1 a n = 1.For a sequence without magnetization preparation, a n is constant throughout the entire image under the assumption that the composition of all fat tissue is identical.However, in the case of CEST saturation, fat resonances close to the chosen saturation frequency become partially saturated.Thus, a n changes dependent on the saturation frequency but also throughout the image due to the variation of the saturation with the B 0 and B 1 + distribution.The saturation of each single fat component n can be described by the Bloch equations.
Figure 1 illustrates our proposed approach for correcting CEST spectra using a FWS with an adaptive fat model, which accounts for this local saturation of the fat signal.As first step, we performed the FWS for the CEST images with far off-resonant saturation (−300 ppm), called M 0 , which were acquired for normalization of the Z-spectra.Because the fat signal is not saturated in this case, a regular FWS without local variation of the fat model was used.
To mitigate the risk of fat-water swaps, we demodulated the phase of the complex signal S(t) prior to FWS with an initial estimation of the off-resonance map Δ 0,init .It was calculated based on the complex Z-spectrum data of the first echo by voxel-wise finding the minimum of the phase unwrapped Z-spectra and calculating its deviation from the scanner frequency.In the case of dominant fat signal, the minimum was assumed to correspond to the main fat resonance and was calculated relative to −3.4 ppm.
To reduce noise at tissue boundaries, all values in the Scheme of the adaptive FWS algorithm.First, the signal of the first TE is used to calculate an initial off-resonance map Δ 0,init .The complex signal of the M 0 scans is demodulated with this fieldmap before applying the graph cut algorithm for FWS.Based on the resulting Δ 0 and a measured rB 1, the saturation of the single fat contributions is calculated for each CEST offset.With the known parameters and assuming that the field inhomogeneities are constant for all CEST scans, the problem reduces to a linear problem that can be solved for the water  w and fat  f signal contributions.The fat signal-corrected spectra can be calculated from the water images.FWS, fat-water separation; M 0 , far off-resonant saturated CEST scan for normalization of Z-spectra; Δ 0 , off-resonance map; Δ 0,init , initial guess off-resonance map;  w∕f water/fat signal; rB 1 , relative B 1 + map.
resulting Δ 0,init map with a deviation greater than 0.05 ppm compared to the median of the surrounding 5 × 5 region were replaced by utilizing MatLab's imfill function (MATLAB R2017b, MathWorks, Natick, MA).Subsequently, the Δ 0,init map was filtered with a 2D Gaussian filter with a SD of one voxel.Finally, the signal of the M 0 scans was demodulated voxel-wise by multiplying it by the inverse phase given by Δ 0,q,init : The demodulated signal S ′ (t) was then parsed into a FWS algorithm.We utilized a graph cut algorithm followed by an additional gradient descent as implemented in the ISMRM FW Toolbox. 17The algorithm calculates the separated water and fat signal  w∕f, , as well as a R * 2 and off-resonance map Δ 0,dem .We acquired two M 0 scans per CEST measurement: one at the beginning and one at the end of each measurement.For more robustness, we used the voxel-wise mean value of R * 2 and Δ 0,dem from both scans for the further evaluation.To obtain the total off-resonance Δ 0 of the unmodulated data S(t), we summed Δ 0,dem and Δ 0,init .
The calculated Δ 0 and a measured relative B 1 + map (rB 1 ) were used to obtain the adaptive fat model for each voxel and offset.The saturation of each fat resonance n was described by the Bloch equations 21 : where Assuming that Δ 0,q and R * 2,q are constant during one CEST acquisition and with the known adaptive fat model F q (t) = ∑ N n=1 a n,q exp(i 2 Δ n t), Equation (1) reduced to a linear problem for all other CEST scans: This voxel-wise linear equation system was solved for  w and  f , resulting in water and fat images for all CEST offsets.The fat-corrected CEST spectra were calculated from the absolute values of the water-only  w images.
The proposed 7 T-optimized approach was inspired by the self-adapting multi-peak method (SMPM) published by Zhao et al. for 3 T CEST data. 12The SMPM also differentiates the cases of the M 0 scans and CEST scans with potential fat saturation.In the first step, the FWS of the M 0 scans is performed.In the second step, the obtained R * 2 and Δ 0 maps are used to determine the locally varying fat model and perform the adaptive FWS for the scans with CEST saturation.In contrast to our approach, the FWS is performed in both steps by using a hierarchical IDEAL algorithm with R * 2 correction. 16The results for  w∕f and R * 2 of the hierarchical IDEAL algorithm are further refined by subsequently performing a voxel-wise fit of the magnitude signal.This voxel-wise fit allows the integration of the locally varying fat model for the CEST scans.The adaptive fat model was also based on the Bloch equations.However, instead of preknown R 2 values, the R * 2 values obtained by the FWS were used to describe the T 2 decay during the CEST saturation for all fat resonances.To compare our 7 T-optimized approach to the SMPM, we reimplemented the SMPM as described in the publication, except for two alterations to increase comparability.The first step of the SMPM was also performed on the phase-demodulated data.In the second step, the Δ 0 map was kept fixed to the result from the FWS of the M 0 scans to provide better stability of the hierarchical IDEAL algorithm for CEST offsets with strong water saturation.
Additional to the SMPM, we compared our approach to FWS with a fixed fat model.Therefore, we performed the same processing steps as in the adaptive case but without varying the fat model.
To evaluate the need for six TEs, we additionally performed the FWS for all volunteers regarding only the first three TEs with and without including R * 2 correction into the FWS.

Single-echo fat artifact correction methods
To compare the potential of the multi-echo-based FWS to fat artifact correction methods based on faster single-echo acquisition, we compared it to two published single-echo correction methods: acquisition with a Gaussian fat saturation pulse and a postprocessing correction model based on information contained in the Z-spectrum. 14or fat saturation, a Gaussian fat saturation pulse with a 110 • flip angle (FA) followed by gradient spoiling was played out in between CEST saturation and readout.
The Z-spectrum-based correction model utilizes the idea that remaining signal after CEST saturation at the water frequency is caused by fat signal.The model suggested by Zimmermann et al. 14 assumes that the water signal at direct water saturation is completely saturated (assumption 1) and also that the lipid signal is not saturated at direct water saturation or other spectral regions of interest (assumption 2).Under these assumptions, the fat signal for each voxel and CEST offset ⃗ F q (Δ) is given by the residual signal at direct water saturation ⃗ S q (Δ DS ) and can be subtracted from the total signal ⃗ S q (Δ) to obtain the water-only signal: With a known off-resonance map Δ 0 , the signal at the position of direct water saturation ⃗ S q (Δ DS ) can be estimated by interpolating the Z-spectrum.With this information, Equation ( 5) can be directly solved resulting in the complex water-only signal.In contrast to the originally suggested implementation, we utilized Δ 0,init , as described in the previous section, to determine the spectral position of direct water saturation instead of finding the minimum of the real part of the Z-spectrum.

Simulations
To verify the functionality of our algorithm, we performed simulations of the signal in image space.The CEST spectra and saturation of the fat signal were simulated with Bloch-McConnell equations 22  For the fat pools, the same T 2 and T * 2 values as for the water pool were used, and a T 1 relaxation time of 550 ms was assumed.Fat resonances were chosen as seven-peak model based on literature, 23 with Δ n = [−3.70,−3.30, −3.01, −2.57, −2.35, −1.83, 0.71] ppm and relative amplitudes a n = [0.0847,0.6257, 0.0707, 0.0952, 0.0662, 0.0159, 0.0418].
The simulation was performed for different combinations of rB 1 , Δ 0 , initial phases of the overall signal, and fat fractions as 2D image with dimensions of 41 × 41 voxels.Readout effects on the magnetizations, as well as chemical shift artifacts, were neglected.The simulated spectra were corrected for B 0 inhomogeneities after fat correction with the ground truth Δ 0 map.

Phantom and in vivo experiments
For phantom measurements, a water-filled container was used containing six vials with 0%, 5%, 10%, 25%, 50%, and 75% volume fractions of peanut oil emulsified with agar solution (3% w/v), as described in Ref. 24 The phantom contained no CEST agent.To compare the fat correction methods in vivo, five volunteers (28 ± 4 years, three male, two female) were recruited under the approval of the local ethics committee.All subjects gave informed written consent to participate in the study.
All measurements were performed at a 7 T MRI scanner (Magnetom Terra, Siemens Healthcare, Erlangen, Germany) with a 1 Tx/28 Rx knee coil (Quality Electrodynamics, Mayfield Village, OH).
To calculate the fat model for the phantom, a STEAM sequence with TE = 20 ms, TR = 4000 ms, mixing time = 10 ms, BW = 4000 Hz, voxel size of 10 mm 3 , and 32 averages was measured within the 75% oil vial.The spectrum was evaluated with a nine-peak AMARES fit (Advanced Method for Accurate, Robust, and Efficient Spectral Fitting) performed in jMRUI 5.2. 26,27To estimate the T 1 and T 2 relaxation times of the peanut oil, a second phantom measurement was performed with a 100% oil solution.For the in vivo measurements, the fat model was defined based on literature values described by Ren et al. in the human calf at 7 T. 23 It provided resonance frequencies and relative signal amplitudes for the seven most prominent fat resonances, as well as T 1 and T 2 values for six of these resonances.We used the mean of the published values within bone marrow and subcutaneous fat to define the initial seven-peak fat model.For the fat resonance without reported relaxation times, T 1 was assumed as 500 ms and T 2 as 57.5 ms.

Z-spectrum postprocessing and quantitative evaluation
After fat correction, all CEST spectra were corrected for B 0 inhomogeneities.For the phantom data, an off-resonance map calculated based on the minima of the spectra that were fat-corrected using our adaptive FWS approach was used.For the in vivo data, the B 0 correction was based on the output Δ 0 map of the FWS.The asymmetric MT ratio (MTR asym ) was calculated as the difference of both sides of the Z-spectrum that was normalized with the first M 0 scan.To provide a reference spectrum for the phantom measurements, the Z-spectra of the agarose-only vial were B 1 -corrected to the mean rB 1 of each fat fraction vial using a three-point correction as described by Windschuh et al. 28 For this purpose, additional CEST measurements with B 1,rms = 0.6 μT and 2.4 μT were used.
To statistically evaluate the in vivo knee data, tissue regions of interest (ROIs) within the gastrocnemius muscle, the anterior femoral articular cartilage, and the retropatellar synovial fluid were drawn based on the PD-weighted images.The ROIs are shown in Figure S2.

RESULTS
Figure 2 shows a representative spectrum of the measured fat signal in phantom.The corresponding fat model parameters used as initial fat model for the FWS are provided in Table S1.The measured relaxation times within the 100% fat vial were T 2 = (150 ± 6) ms and T 1 = (506 ± 23) ms.
As shown in Figure 3, FWS was prone to fat-water swaps for knee imaging with the used measurement parameters, especially in the case without patient-specific B 0 shim calculated based on an individually acquired off-resonance map.However, even with additional B 0 shimming, minor swaps occurred in regions with strong off-resonances.Demodulating the signal with an off-resonance map calculated based on the Z-spectrum prior to FWS eliminated fat-water swaps in the results.The demodulation reduced the range of the effective off-resonance map treated by the graph cut FWS algorithm to ±150 Hz (Figure S3).
The fat-uncorrected spectra in simulation (Figure 4) and phantom (Figure 5) demonstrate the effect of increasing fat contributions on the Z-spectrum.Although the height of the main fat peak at approximately −3.5 ppm increased with increasing fat fraction, the height of the overall spectrum decreased, as can be seen at the water resonance (0 ppm).For high fat fractions (≥50%), effects of the fat resonances around 2.6 and 0.5 ppm also became Representative 1 H spectrum within the 75% peanut oil vial, showing nine detectable fat resonances with their respective resonance frequencies Δ n relative to water.The corresponding relative peak areas are shown in Table S1, frequency offset Results of the graph cut FWS of the M 0 scan for one exemplary volunteer for two B 0 shim settings: (A) the system default shim without individual optimization, and (B) a patient specific shim optimized on an individually measured off-resonance map with the vendor routine.For each setting, the magnitude image of the first TE (TE 1, upper left), the initial guess of the field map based on the Z-spectra Δ 0,init (lower left), as well as the resulting water and fat magnitude images and Δ 0 map without (upper row) and with (lower row) prior demodulation with Δ 0,init are shown.For both shim settings, fat-water swaps occurred in regions with strong B 0 deviations (orange circles).The swaps were eliminated by prior demodulation.visible in the Z-spectra.The decrease in the overall spectral height led to a decrease of the MTR asym , as can be seen for the CEST effect around 1.0 ppm in the simulated data.FWS with the graph cut algorithm and a fixed fat model showed good restoration of the positive side of the Z-spectrum and around the water peak but overcorrected the fat influences between 2 and 4 ppm at higher fat fractions (>25%).The SMPM correction method by Zhao et al. with an adaptive fat model based on an additional magnitude fitting showed good correction for low fat fractions but gave unstable results in the regions of the fat resonances at higher fat fractions (see also Figure S4).For our 7 T phantom measurements, the results were worse than with the fixed model approach.Our modified approach combining the graph cut FWS algorithm using the complex imaging data with an adaptive fat model showed the best results overall.However, in the phantom measurements, slight deviations from the expectation were still observed, especially for high fat fractions.It should be noted that for high fat fractions, the quality of the fat Comparison on simulated data of our proposed method, a graph cut FWS combined with an adaptive fat model based on the complex data, to already published multi-echo FWS approaches: a graph cut FWS with a fixed fat model and the SMPM, as suggested by Zhao et al., for 3 T 12 .The plots show the Z-spectra and MTR asym for fat fractions of 5%, 25%, 50%, and 75% for the simulated data.Reference shows the ground truth water-only signal.Our approach combining the graph cut algorithm with an adaptive model showed strongly improved fat correction compared to the SMPM or fixed fat model for higher fat fractions (≥50%).MTR asym asymmetric magnetization transfer ratio; SMPM, self-adapting multi-peak method.

F I G U R E 5
Comparison within phantom of our proposed method, a graph cut FWS combined with an adaptive fat model based on the complex data, to already published multi-echo FWS approaches: a graph cut FWS with a fixed fat model and the SMPM as suggested by Zhao et al. for 3 T 12 .The plots show the Z-spectra and MTR asym for fat fractions of 5%, 25%, 50%, and 75% within ROIs within the different flasks of the phantom.Reference shows the spectrum within the 0% fat vial that was B 1 -corrected to the rB 1 of the other vials for the phantom.Although all versions performed well for low fat fractions (25%), the SMPM showed unstable performance in spectral regions of fat resonance for higher fat fractions.
artifact correction showed a dependence on the number of included fat peaks and their assumed T 1 and T 2 relaxation times (Figures S5 and S6A).Using a single-peak model led to a less accurate correction.Reducing the number of used TEs to five, four, or three echoes slightly decreased the quality of the correction for high fat volume fractions (75%) but still provided comparable results for lower fat volume fractions (Figure S6B).This was confirmed when comparing the in vivo data evaluated by using six echoes to only using the first three echoes with or without T *

F I G U R E 6
Comparison of contrast correction with FWS using three or six TEs with and without T * 2 correction included in the FWS.correction for the FWS (Figure 6).Although no deviations in the fat-corrected contrast at 1 ppm could be observed, the contrast at 3.5 ppm showed slight differences.As visible from the exemplary images (Figure 6B), the contrast was slightly overcorrected close to tissue edges when using only three echoes, especially for the case of including the T * 2 correction.This corresponds to the regions with higher fat volume fractions.Also within the muscle, the contrast was corrected to slightly higher values consistently across all volunteers.By using only three echoes, the proposed method could also be applied to data with doubled in-plane resolution achieving comparable results (Figure S7).
Our optimized adaptive FWS approach was compared to basic Gaussian fat saturation and the Z-spectrum-based correction model (Figures 7 and 8).All three methods reduced the main fat influence on the CEST spectrum, as can be seen by the restoration of the water peak in the spectra and the reduced magnitude signal in the M 0 image in regions with higher fat fractions (Figure 7A).However, the quality of the fat saturation pulse showed a spatial dependence, as visible in the M 0 and MTR asym (−3.5 ppm) images (Figure 8).Within the central region of the 75% oil vial, the fat suppression pulse led to an unexpected behavior of the magnetization, which resulted in a failed normalization of the Z-spectra.In the outer regions of the vial, the Z-spectra appeared normal.However, the fat saturation was incomplete, as could be seen by an incomplete restoration of the water peak and remaining deviations around −3.5 ppm.The Z-spectrum-based approach gave robust results in restoring the water resonance throughout the entire phantom.Due to its model assumption of perfect on-resonant saturation of the water signal, an overcorrection of the signal is visible.Because no saturation of the fat signal is assumed in this model, the spectrum is not properly corrected in regions of fat resonances.FWS resulted in the best overall spectral correction, as can be clearly seen in the MTR asym contrast image at −3.5 ppm.Although the FWS performed better for high fat fractions with a deviation of only 5.1% MTR asym (−3.5 ppm) to the expected value of zero compared to the fat saturation pulse with a deviation of 22%, it was still not able to perfectly correct the fat influences.Similar to the phantom, the Gaussian fat saturation pulse showed inhomogeneous fat saturation in knee measurements in vivo (Figure 9).In some regions such as the synovial fluid, even overshoots in the Z-spectrum around −3.5 ppm can be noted.The MTR asym contrast showed strong pseudo-CEST effects around −3.5 ppm for the uncorrected and Z-spectrum-based approach, especially for small structures in between fatty tissue such as the anterior femoral cartilage.This was heavily improved by utilizing our adaptive FWS approach; for example, the MTR asym (3.5 ppm) within the cartilage ROI increased from −7.5% (fat saturation) and −8.6% (Z-spectrum-based) to −1.5%.Only minor differences in the correction approaches could be seen in the MTR asym for other spectral regions.The most prominent change in the Comparison within phantom of the proposed multi-echo FWS to two single-echo fat artifact correction methods: a Gaussian fat saturation pulse, and a Z-spectrum-based correction method.(A) shows the mean spectra in the vials with 5%, 25%, 50%, and 75% fat fraction; (B) the corresponding mean MTR Asym ; and (C) the mean and SD within the vials for the spectral amplitude at 0 ppm and the MTR asym at 1.0 and −3.5 ppm.Reference shows values of the water-only vial B 1 + -corrected to the rB 1 within the other vials.As expected from the model assumptions, the Z-spectrum-based approach did not correct the signal close to fat resonances but showed good correction in other parts of the spectrum.Accordingly, the approach is not suitable for asymmetry analysis close to fat resonances.FWS showed the best spectral correction around fat resonances and also was closest to the expected value at direct water saturation (0 ppm).
MTR asym (1 ppm) images is the increased contrast to noise ratio (CNR) when using the adaptive FWS due to using multiple echoes.These effects were consistently observed over all five volunteers, as shown in Figure 10.The mean MTR asym (3.5 ppm) was clearly higher for the FWS and fat saturation than without correction or with the Z-spectrum-based approach for all tissue types.Thereby, the fat saturation showed the highest values, which is consistent with the overshoot observed in the single spectra.The spread of the mean values of all volunteers was reduced when using the adaptive FWS.For the mean MTR asym (1 ppm), a slight increase in the contrast compared to the uncorrected data could be noted with all fat artifact correction methods, especially in cartilage and the synovial fluid.The SD of the MTR asym within the muscle ROI (Figures S8) was smaller for the adaptive FWS than for the other approaches at both 3.5 and 1 ppm.In the other tissues, the SD was comparable for all methods.

DISCUSSION
Achieving good FWS for 7 T knee data proved to be challenging.Even when using the graph cut algorithm, which is reported to be robust against B 0 inhomogeneities, 17 fat-water swaps were apparent in the resulting water and fat images in vivo.This is related to large B 0 field inhomogeneities (up to 500 Hz) apparent in our knee measurements, which could only partially be improved with available vendor B 0 shimming routines.Additionally, the Pseudo CEST effects around −3.5 ppm visible in the cartilage and synovial fluid for the uncorrected and Z-spectrum-based approach could be reduced using the adaptive FWS.used echo spacing was longer than one phase oscillation of the fat and water signal, which increases the risk of an incorrect fieldmap estimation.However, we were able to stabilize the FWS by using a demodulation with an initial guess off-resonance map based on the Z-spectral data.This approach works similarly to the proposal by Sharma et al. 29 or Diefenbach et al., 30 which used a demodulation with an estimated off-resonance map based on an approximated susceptibility map to improve the FWS.Our estimate of the off-resonance map based on the spectral data inherently includes further field components such as the shim field without requiring prior knowledge of hardware or tissue properties.
The SMPM FWS suggested for 3 T did not show stable results for our 7 T data and performed even worse than nonadaptive FWS.The poor performance of the voxel-wise Boxplots showing the mean within ROIs (see Figure S2) within muscle, articular cartilage, and synovial fluid over all five volunteers exemplarily for the MTR asym contrast at 3.5 ppm (A) and 1.0 ppm (B).The data is shown for the fat uncorrected data as well as the Gaussian fat saturation (FS), the Z-spectrum-based correction (spectrum), and our adaptive FWS approach.For the uncorrected data and Z-spectrum-based approach, an increased MTR asym at 3.5 ppm was visible for all tissue types.FS, fat saturation; spectrum, Z-spectrum-based magnitude fit at 7 T is most likely related to the relatively large echo spacing compared to the dephasing time of fat and water signal, which increases the number of local optima.Using the full complex data instead of only the magnitude combined with assuming constant field inhomogeneities for all offsets stabilized the estimation of the water signal.Nevertheless, reducing the echo spacing could further improve the method in the future, especially the robustness of the off-resonance map estimation, which could lower the need for an initial fieldmap estimation.Switching to a bipolar readout mode was not sufficient to achieve a echo spacing in the optimal range of ∼0.5 ms for our sequence and measurement parameters.One possibility to reduce the effective echo spacing is to use a multi-shot acquisition with different TEs per shot, which was shown to result in good FWS in morphological 7 T MRI. 31 However, this approach is impractical for CEST MRI due to the need to repeat the CEST preparation, which would result in strongly increased measurement times.An alternative solution could be a time-interleaved acquisition with interleaving acquisitions with different TEs within one shot. 32However, this increases the duration of the readout train, which has comparable limitations to increasing the TR to incorporate a multi-echo acquisition.Alternatively, the CEST preparation could be combined with a radial readout with ultrashort TEs, as was recently proposed for pH-weighted CEST MRI. 33,34This would also allow a reduction of TR, which is markedly longer for multi-echo acquisitions compared to single-echo acquisitions.The long TR is a limitation of our approach because it prolongs the overall readout time.This is problematic in CEST MRI because the longer magnetization decay during the readout results in less CEST weighting and more image blurring.Thus, our FWS approach might be limited for use in 3D or high-resolved CEST MRI.This is problematic for most clinical applications, for which a 3D coverage with higher resolution is desirable.However, our results suggest that even with only three echoes being used for the FWS, good fat artifact correction results can be achieved, which enabled us to increase the in-plane resolution without further increasing TR.This can help translate our method to higher resolved clinical applications without overly elongating the readout train.Additionally, the FOV could be reduced to gain higher resolution without the need to change TE or TR for applications that focus on cartilage evaluation and are insensitive to folding artifacts in the subcutaneous tissue.The longer TR also increases measurement time compared to single-echo methods.For our sequence, the total acquisition time was increased by about 24% for incorporating six echoes.However, averaging over multiple echoes increased the CNR, which is beneficial for high-resolution CEST MRI.
Although outperforming the other methods for overall fat artifact correction in the Z-spectra, the adaptive FWS still was not able to achieve optimal correction for high fat fractions (>50%).This could be caused by imperfections within the measurement data such as phase errors due to eddy currents but also by inaccuracies of the signal model.One limitation of the chosen signal model is the assumption of only one R * 2 per voxel.Although this prevents ambiguity of the fit parameters, it introduces an error especially in cases with a strong deviation of water and fat T * 2 .The simulation results also showed that erroneous assumptions on the relaxation times of the single fat resonances slightly influence the correction accuracy.Additionally, the assumption of one overall fat model is not necessarily true in vivo, where the fat composition might vary between tissues such as the bone marrow and subcutaneous fat.However, published values state that these variations are rather small 23 and can thus be expected to have a negligible impact.Yet, it is known that the frequency shift between fat and water varies with temperature and pH. 35This was neglected in our approach but could be included in the future by adding one further fit parameter. 36Our results using the fat saturation pulse showed strong spatial dependence, which is related to B 1 + and B 0 inhomogeneities.This could be improved by utilizing parallel transmit or spatial-spectral pulses. 37,38e demonstrated that the proposed adaptive FWS approach can successfully reduce pseudo rNOE effects in knee imaging.Whereas lower SD of the MTR asym (3.5 ppm) within single volunteers, especially in muscle tissue, is at least partially explained by the higher SNR due to multiple echoes being used, the lower variation of the mean contrasts in between volunteers hints that FWS might lead to more reproducible contrasts.Overall, we conclude that our FWS approach is advantageous compared to fat saturation and the Z-spectrum-based correction method for the analysis of rNOE effects, in case of asymmetry analysis, or for applications in which high fat signal contributions are expected.

CONCLUSION
Our work demonstrated the feasibility of FWS with an adaptive fat model for correction of fat artifacts in CEST MRI at 7 T.With the chosen TEs, an initial estimation of the off-resonance map, and prior knowledge of the composition of the fat signal, good fat artifact correction across the entire Z-spectrum is possible even for very high fat fractions of 75%.FWS with an adaptive fat model provided better fat artifact correction than Gaussian fat saturation or a Z-spectrum-based correction approach, especially on the downfield side of the Z-spectrum.

ACKNOWLEDGMENTS
The present work was performed in partial fulfillment of the requirements for obtaining the degree "Dr.rer.Nat." at the Friedrich-Alexander-University (FAU) Erlangen-Nürnberg.Parts of this work were presented at the ISMRM workshop on Ultra-High Field MR (Lisbon, Portugal, 2022).Open Access funding enabled and organized by Projekt DEAL.
was chosen for the measurements is marked by the red cross.shows the results when using the full 9-peak fat-model, with only the five most prominent fat peaks, with only the main fat-peak, and using all 9 fat-peaks but assuming different T 2 relaxation times for each peak based on the variation described in (23).(B) shows the results with the full 9-peak fat-model when using only the first 3 to 6 echo times.Changes in the quality of the fat artifact correction were mainly observed for high fat volume fractions.FIGURE S7.Example of the CEST contrasts and spectra for a measurement acquired with in-plane resolution of 0.8 mm × 0.8 mm without fat correction and with the adaptive FWS.The FWS was performed based on three echoes without R * 2 correction.To achieve the higher resolution the echo spacing had to be increased to 2.4 ms.The CEST CNR for a 2D single slice measurement with this high resolution showed to be rather low.However, the adaptive FWS still performed well and was able to correct the pseudo CEST effects around −3.5 ppm.FIGURE S8.Boxplots showing the standard deviation within ROIs (see Figure S2) within muscle, articular cartilage, and synovial fluid over all five volunteers exemplarily for the MTR asym contrast at 3.5 ppm (A) and 1.0 ppm (B).The data is shown for the fat uncorrected data as well as the Gaussian fat saturation (FS), the Z-spectrum-based correction (spectrum) and the proposed adaptive FWS approach.The standard deviation of the contrasts within each ROI was comparable or lower with the FWS than with the other approaches for all cases.TABLE S1.Resonance frequencies Δ n and relative peak areas a n for the nine detectable fat resonances of the 1 H spectrum measured within the 75% peanut oil vial with the stimulated echo acquisition mode (STEAM) acquisition.
(A) and (B) show the exemplary MTR Asym images at 1.0 ppm and 3.5 ppm of an exemplary volunteer comparing the case of three echoes without T * 2 correction, three echoes or six echoes with T * 2 correction to the case of no fat artifact correction (uc).(C) and (D) show the boxplots of the mean values in the three defined ROIs in muscle, cartilage, and synovial fluid for all five volunteers for both contrasts.Although the correction results for all three cases are comparable for MTR Asym (1 ppm), slight deviations can be seen for MTR Asym (3.5 ppm), especially in muscle and at tissue boundaries.ROI, region of interest; uc, uncorrected; MTR asym , mean MTR Asym within ROI.

F I G U R E 7
Comparison within phantom of the proposed multi-echo FWS to two single-echo fat artifact correction methods: a Gaussian fat saturation pulse, and a Z-spectrum-based correction method.(A) The water M 0 image, (B) the MTR asym at 1 ppm, and (C) the MTR asym at the main fat resonance at −3.5 ppm.With the fat saturation pulse, the fat signal was reduced compared to the uncorrected data.However, not the complete fat signal was removed, and the efficiency spatially varied with B 0 and B 1 + inhomogeneities.The MTR asym maps with FWS are closest to the expectation of zero CEST contrast.

F I G U R E 9
Comparison of the fat artifact correction methods in vivo for one representative volunteer: (A) the water M 0 image; (B) MTR asym contrast at 1 ppm; (C) MTR asym contrast at 3.5 ppm; and (D) mean Z-spectrum and corresponding MTR asym within ROIs in muscle, articular cartilage, and synovial fluid.The chosen ROIs are shown in orange on the uncorrected M 0 image (upper left).As can be seen in the water M 0 image, the fat saturation pulse showed incomplete and inhomogeneous fat saturation in the bone marrow and subcutaneous fat.

FIGURE S2 .
Regions of interest in the gastrocnemius muscle (green), the anterior femoral articular cartilage (yellow), and the retropatellar synovial fluid (red) as used in the quantitative method evaluation are shown for all five volunteers overlaid on the corresponding sagittal slice of the fat saturated proton-density-weighted image.FIGURE S3.Difference maps of the final off-resonance map and the initial off-resonance map shown in Figure3: Δ 0,graph cut = Δ 0 − Δ init .These maps corresponds to the additional change in the Δ 0 estimation caused by the graph cut + gradient descent FWS algorithm after demodulation.The maps are shown for both shimming cases displayed in Figure3: (A) the system default shim, and (B) the patient specific optimized shim.For both cases, the additional off-resonance provided by the graph cut FWS was in the range of up to ±150 Hz.FIGURE S4. (A)The off-resonance Δ 0 , initial phase  0 , and rB 1 distribution as used in the simulations.(B) Spatially dependent results of the different FWS methods (fixed fat model, SMPM, adaptive fat model) for the simulated data with a fat signal fraction of 50%.The graphic shows the absolute difference of the corrected spectral value Z(Δ) and the ground truth value of the water only signal Z GT (Δ) for CEST saturation at −3.5, 1.0, and 0.0 ppm.While the FWS with a fixed fat-model showed a constant error of the correction around −3.5 ppm, the SMPM showed a spatial dependency.With our adaptive FWS approach the best overall correction was achieved.FIGURE S5.Simulation results showing the influence of the T 1 and T 2 relaxation times used in the fat model as well as an error in the assumed chemical shift in between fat and water on the fat artifact correction results with the adaptive FWS.To make the effects visible, the results are shown for a high fat fraction of 75%.The simulations were performed as described in the main paper, however distinct T 1 and T 2 relaxation times were assumed for the single fat resonances based on literature(23).(A) and (D) show the Z-spectra and MTR Asym results of the adaptive FWS separation when using the T 2 value of the main fat resonance for all fat resonances in the adaptive fat model and when additionally assuming an error of 10% of the used T 2 value.(B) and (E) show the results when wrongly assuming T 1 in the same way.(C) and (F) show the results when the resonance frequencies of the assumed fat model were shifted by minus 0.05 and 0.1 ppm relative to the water resonance.The evaluation shows that using wrong relaxation times or resonance frequencies in the fat model results in inaccuracies in the fat artifact correction, especially between −2 and −4 ppm.However, these inaccuracies are small compared to the error of the uncorrected case.FIGURE S6.Influence of the chosen fat model (A) and the number of used echoes (B) on the adaptive FWS in phantom for fat volume fractions of 5%, 25%, 50%, and 75%.(A)