A comparison of static and dynamic ∆B₀ mapping methods for correction of CEST MRI in the presence of temporal B₀ field variations

1 INTRODUCTION

High and ultrahigh static magnetic fields (B₀) provide advantages that are critical for the quality of CEST MRI results. Not only the SNR, but also the chemical specificity are significantly improved, because the spectral separation between the resonances of interest increases. The CEST also benefits from a prolonged storage of saturation in bulk water due to longer T₁, which facilitates its sensitivity. Furthermore, CEST works particularly well in the slow to intermediate exchange regime (k_sw < ∆ω_S, where k_sw is the exchange rate from the labile proton pool to the bulk water pool and ∆ω_S the solute proton pool frequency offset (which is proportional to B₀)). Under this condition, spectral resonances of interest can be much better distinguished from the direct saturation of water. This regime is increasingly met at higher B₀ even for rapidly exchanging protons.1, 2

On the other hand, local B₀ inhomogeneities (∆B₀) are more severe at higher B₀, causing regionally dependent frequency shifts in Z-spectra. This complicates quantification in CEST. The applied frequency-selective CEST saturation pulses at ∆ω_RF are shifted away from the targeted nominal frequency offset (∆ω) by δω = ∆ω_RF - ∆ω = ∆B₀/γ (γ being the gyromagnetic ratio), which is proportional to the local ∆B₀.2 Even with optimized B₀ shimming protocols prior to the experiments, a retrospective ∆B₀ correction is generally needed, in which the Z-spectrum of each voxel is centered at the water resonance (0 ppm). A highly accurate ∆B₀ correction is particularly important when studying exchanging compounds very close to water (e.g., glucose, lactate, myo-inositol).3-6 Zaiss et al. recently reported substantial pseudo-CEST effects for dynamic CEST at 3 T from B₀ alterations (~1% per 7-Hz drift).7

The simplest approach for a ∆B₀ correction is to determine the water resonance frequency from the Z-spectrum (from here on this approach is termed “CEST-minZ”).8-10 This works well only when the applied saturation power is low and the magnetization transfer contrast from semisolid macromolecules and CEST effect close to the water resonance can be neglected.8, 9, 11 In addition to this limitation, CEST-minZ requires the full sampling of a high-spectral-resolution Z-spectrum, which increases the scan time (i.e., the spectral range covering the water peak cannot be excluded). In vivo CEST measurements with higher saturation power and more accurate ∆B₀ correction can be achieved by acquiring an external ∆B₀ map. Water saturation shift referencing is probably the most widely used method to acquire such an external ∆B₀ map for CEST data processing. In WASSR, a matching CEST pulse sequence is acquired as a prescan, but with low saturation power and targeting only a narrow range of offsets around 0 ppm with high spectral resolution.12 Alternatively, a prescanned ∆B₀ map can be obtained from the phase difference of at least two gradient-echo images acquired at different echo times (here termed “GRE-2TE”).13-18

All these three established ∆B₀ correction methods, (A) CEST-minZ, (B) WASSR, and (C) GRE-2TE, estimate the water resonance frequency for a single time point and correct every z-spectral point by applying the same shift (δω). This shift may not necessarily be representative for all points of the CEST spectrum, as they are acquired at different times. Consequently, all three methods share the drawback of being prone to errors due to temporal changes in the B₀ field over the course of a CEST experiment. Such temporal ∆B₀ fluctuations may arise from system instabilities [primarily heating of magnet’s gradient coils by heavy duty cycles19 or heating of passive shims20], from cardiac or respiratory effects21 or subject movement.22 Some previous studies performed at 3 T have reported drifts ranging from of 1.2 Hz/min to 5 Hz/min after a series of functional MRI or diffusion weighted imaging scans.23-25 Larger drifts are expected at higher B₀ (e.g., at 7 T periodic B₀ fluctuations of up to ~4 Hz due to respiration are already detectable even far away from the lungs).26-29

In this paper, three dynamic ∆B₀ correction methods, which integrate the ∆B₀ mapping as part of the CEST sequence, are proposed; two of them via the phase generated by the CEST readout itself and the third by an interleaved 2D EPI navigator. They allow temporal fluctuations in B₀ to be mapped and compensated for each individual Z-spectral point separately. The accuracy of this B₀ mapping and its impact on CEST correction are compared for these dynamic approaches and to three established static methods (i.e., CEST-minZ, WASSR, and GRE-2TE) for CEST analysis close to water.

2 THEORY

2.1 Chemical exchange in the presence of B₀ inhomogeneities

At present, the most common CEST quantification metric is the asymmetric magnetization transfer ratio (MTR_asym). The purpose of CEST asymmetry analysis is to separate the asymmetric CEST contribution from the symmetric components (e.g., direct water saturation).30-32 This analysis is performed by subtraction of the magnitude signal on one side of the Z-spectrum from its mirrored side1, 2:

(1)

where S₀ and S_sat correspond to reference and labeled magnitude signals, respectively. Here the MTR_asym would be equal to the proton transfer ratio expression considered in the two-pool exchange model if the water saturation were caused purely by exchange and in the absence of ∆B₀.33-35 However, when the frequency is shifted by δω, the proton transfer ratio can be redefined as36:

(2)

where η is a modulation factor that fully compensates the proton transfer ratio and ∆MTR is the MTR offset used to compensate MTR_asym. The factor η can be further derived as:

(3)

It can be seen from Equation (3) that the modulation comes from the labeling coefficient α and spillover factor σ. In the denominator, both terms are dependent on the frequency shift δω with respect to the solute resonance frequency offset ∆ω_S, making η strongly sensitive to ΔB₀. It has previously been shown that inaccurate ∆B₀ corrections can be erroneously interpreted as CEST effects, especially at frequencies close to the water resonance where the slope of the Z-spectrum is steep because of direct saturation of bulk water.37

2.2 Static ∆B₀ correction

The three state-of-the-art static approaches for ∆B₀ correction compared in this study are:

(A) CEST-minZ

The water resonance frequency is intrinsically determined from the Z-spectrum of each voxel (i.e., using magnitude images from a CEST experiment), by finding the minimum signal intensity value after a smoothing-splines interpolation in the spectral domain.9, 10, 38

(B) WASSR

The WASSR uses an additional CEST sequence (i.e. prescan) with high spectral resolution over a narrow frequency range and low saturation power, in which CEST and MTC contributions are considered negligible, allowing the reference frequency to be estimated from the dominating direct water saturation. Similar to CEST-minZ, WASSR utilizes only magnitude images, but the water resonance is determined by fitting the water peak with a Lorentzian curve, from which the central frequency of water can be estimated.12

(C) GRE-2TE

The GRE-2TE approach calculates the ∆B₀ maps from the difference of two gradient-echo-based phase images acquired at echo times TE₁ and TE₂13:

(4)

where is the phase image acquired at echo time (j), by channel (l), in this case from the gradient-echo pre-scan (see Figure 1). For multichannel coils, the coil combination can be performed calculating the sum over the channels of the weighted channel-wise phase difference (i.e., the sum Hermitian-inner product)14:

(5)

where symbolizes the angle of the complex data, and are the magnitude images, and and are the phase images for a given channel acquired at echo times TE₁ and TE₂.

2.3 Dynamic ∆B₀ correction

The three methods that we propose to use for CEST ∆B₀ correction integrate dynamic B₀ estimation as part of the CEST sequence, construct a ∆B₀ map for each saturation frequency offset (∆ω) applied in the CEST labeling module, and allow the independent ∆B₀ correction of each individual Z-spectral point.

(D) CEST-GRE-2TE

The CEST-GRE-2TE method calculates the ∆B₀ maps from multichannel dual-echo data in the same way as the static method GRE-2TE. The main difference is that the commonly used single-echo readout of the CEST sequence is replaced by a dual-echo readout. Thereby, the magnitude/phase from the prescan in Equation (5) is replaced by the CEST data, which are intrinsically generated immediately after the CEST-labeling module (see Figure 1).

(E) CEST-GRE-1TE

Similar to CEST-GRE-2TE, this method derives ∆B₀ maps from phase data from the CEST sequence, although in this case only a single echo is needed. This is possible if we assume that the phase offset per channel (Φ_RX,l) is time-invariant, in which case a single estimation of Φ_RX,l, calculated from a dual-echo prescan (e.g., the same used for method GRE-2TE) is sufficient. This has been demonstrated to hold even at 7 T and where there is significant head motion.39, 40 The phase offsets are calculated using:

(6)

This approach enables the calculation of dynamic ∆B₀ maps from single-echo readouts by correcting the phase images per channel before calculating the weighted averaged phases over the channels. The ∆B₀ maps can hence be derived as:

(7)

where and are the magnitude and phase images per channel, acquired from the CEST readout at a single echo time for each frequency offset.

(F) NAV-EPI-2TE

In contrast to using the intrinsic magnitude/phase information of the CEST-weighted images, the NAV-EPI-2TE method uses dual-echo data in Equation (5), which are additionally acquired before each saturation module via a 2D multishot EPI navigator (see Figure 1).

3 METHODS

The accuracy of all six ∆B₀ correction methods and any possible bias on the intrinsic dynamic mapping methods (i.e., CEST-GRE-2TE and CEST-GRE-1TE) was first investigated in a homogeneous polydimethylsiloxane oil phantom (Siemens AG, Munich, Germany). In such a phantom, MTR_asym should ideally be 0% in the absence of magnetization transfer (MT) from semisolid or CEST agents. Subsequently, each method was tested on five healthy volunteers (three males, two females; mean age 34 ± 4 years) after Ethics Committee approval by the Medical University of Vienna and informed consent was obtained.

All phantom scans were performed for a single slice with 1.7 × 1.7 × 6 mm³ spatial resolution over a field of view of 220 × 220 mm² with a spectral resolution of 0.11 ppm. For the volunteer scans, the field of view was 270 × 270 mm² with a resolution of 2.1 × 2.1 × 6 mm³, and the frequency offset increments were 0.15 ppm. Details on imaging parameters are listed in the following and in Table 1. Imaging parameters were matched wherever possible.

3.2 Dynamic ∆B₀ corrections

4. For CEST-GRE-2TE, the more commonly used single-echo readout of the CEST sequence was replaced by two readouts with doubled receiver bandwidth (e.g., 780 Hz/Px instead of 390 Hz/Px).

5. The CEST-GRE-1TE could be acquired with no change to the conventional single-echo readout of the CEST sequence. However, to prevent bias in the comparison, data from TE₂ of the GRE readout post CEST labeling were simply ignored and the ∆B₀ mapping used only data from TE₁. The required coil offset maps, which were assumed to be time-invariant,39, 40 were obtained from the GRE pre scan.

6. For NAV-EPI-2TE, a navigator was placed before each CEST-labeling module as shown in Figures 1 and 2. The number of k-space lines (i.e., echoes) collected in each shot of the EPI navigator was set to 4 to minimize geometric distortions and a readout bandwidth of 2442 Hz/Px used to reduce fat-water chemical shift to 0.4 mm, resulting in a ~1-s navigator duration. This could be further shortened by increasing the number of k-space lines per shot (e.g., from 4 up to 128). The delay between the ∆B₀ mapping with the navigator and CEST data sampling illustrated in Figure 2 was assumed to be negligible.

4 RESULTS

The accuracy of dynamic B₀ estimation via CEST-GRE-2TE and CEST-GRE-1TE was compromised when the CEST-labeling pulses were applied close to water. Figure 3 shows how the ∆B₀ maps of phantom experiments were apparently corrupted by saturation RF trains applied at ∆ω < |0.33| ppm. On the other hand, NAV-EPI-2TE presented unaffected ∆B₀ maps over the whole saturation ∆ω range.

Figure 4 presents the accuracy of ∆B₀ maps for the different correction methods by evaluating deviations from the 0% MTR_asym that was expected for a phantom containing no MTC or CEST agents. The GRE-2TE generated the most homogeneous MTR_asym map (i.e., although comparable to WASSR, the one that had the lowest spatial variability) among the static methods with minimal offset from 0% MTR_asym compared to WASSR. Among the dynamic methods, CEST-GRE-2TE resulted in the most accurate MTR_asym maps, with spatial variability similar to GRE-2TE. The methods, CEST-GRE-1TE and NAV-EPI-2TE, on the other hand, led to slight spatial gradients in MTR_asym maps, and ~40% to 60% higher variability than for CEST-GRE-2TE. The third row of Figure 2 illustrates that most of these differences become negligible for ∆ω = ±[1–2] ppm.

For in vivo experiments, MT effects and other confounding factors cannot be neglected, so ∆B₀ mapping accuracy cannot be evaluated. However, rows 2 to 4 of Figure 5 show how the differences between correction methods gradually diminish the further the integration ranges ∆ω are from the water resonance. This indicates that in vivo CEST is sensitive to ∆B₀ over a wider range of ∆ω than the phantom experiments. The ∆B₀ corrections via static methods were generally inferior to those using the dynamic methods for ∆ω = ±[0.3–1.0] ppm (Figure 5). The CEST-GRE-1TE slightly underestimated B₀ compared to CEST-GRE-2TE, thereby producing artificial MTR_asym increases, while the MTR_asym maps corrected by NAV-EPI-2TE showed a gradient from posterior left to anterior right direction (consistent with the phantom experiments).

Figure 6 shows the variation in B₀ over time and the effect of this on the corrected MTR_asym curves within a ROI placed in a white matter (WM) region of volunteer V3, for both minimum field change and the imposed frequency drift. The dynamic mapping methods successfully followed the B₀ evolution and corrected each Z-spectral point independently before the MTR_asym analysis. All static methods, on the other hand, resulted in severely underestimated (~1/3 for CEST-minZ) or overestimated (~3 times for WASSR and GRE-2TE) MTR_asym values.

The ΔB₀-corrected color-coded MTR_asym maps derived from the scan-rescan experiment are presented in Figure 7 for volunteer V4. For the CEST sequence with induced frequency drift, the MTR_asym contrast after ΔB₀ correction via CEST-minZ was underestimated, while WASSR and GRE-2TE ΔB₀ correction led to the opposite effect. On the contrary, all dynamic methods compensated for this drift efficiently. The CEST-GRE-2TE and NAV-EPI-2TE achieved MTR_asym maps with the most similar contrasts with and without induced frequency drift (ROI-averaged errors of 0.001%/Hz and 0.002%/Hz drift, respectively), while CEST-GRE-1TE showed slightly higher deviation (e.g., error of 0.006%/Hz), but was still superior to all the static approaches.

The results of the comparison among all five healthy volunteers (V1-V5) for the dynamic ΔB₀ correction methods CEST-GRE-2TE and NAV-EPI-2TE are presented in Figure 8. The MTR_asym maps derived by CEST-GRE-2TE and NAV-EPI-2TE were highly consistent between acquisitions with/without artificially induced frequency drift for all subjects.

5 DISCUSSION

In this study, we have investigated the applicability of three dynamic ∆B₀ mapping methods for correction of CEST, which integrate ∆B₀ mapping in the CEST measurement. In contrast to static correction methods, each Z-spectral point can be adjusted independently to compensate for temporal B₀ changes such as those arising from system instabilities. Static and dynamic correction performance were evaluated and compared focusing on the ΔB₀ mapping accuracy and bias of MTR_asym maps in the human brain at 7 T, first in the absence and then in the presence of a frequency drift.

Previous studies have evaluated the accuracy of static ∆B₀ correction of CEST-weighted maps by multiecho methods,15-18 while studies proposing dynamic methods to correct for temporal ∆B₀ changes have only recently emerged.46, 47

Windschuh et al. proposed a method to correct each Z-spectral point independently retrospectively, combining phase images from a single-echo GRE CEST readout and a prescan to calculate relative ∆B₀ maps (WASABI).46 However, development work is still needed to improve the stability of this approach, which was significantly affected by the RF saturation pulses even at ∆ω ≈ 1 ppm from the water resonance. In contrast, the intrinsic dynamic correction methods we propose here (CEST-GRE-2TE and CEST-GRE-1TE) were affected by the CEST labeling only within a narrow range of ∆ω < |0.3| ppm, most likely because of low SNR of the saturated CEST images.

Windschuh et al. estimated the error of the MTR_asym (1.1 ppm) to be on average 0.18%/Hz drift. This is in good agreement with the deviations of MTR_asym (0.3–1.1 ppm) between acquisitions with and without induced B₀ drift found in our study (e.g., 0.21%/Hz and 0.18%/Hz corrected by WASSR and GRE-2TE, respectively). The spatial inhomogeneity cannot be directly compared, since the surface of the ROI over the measured cartilage on the knee in the study by Windschuh et al. was much smaller than that covered here, in the brain.

Simegn et al. proposed a prospective motion and ∆B₀ correction of glycoCEST by updating the zero-order and first-order shim gradients for each CEST offset acquisition using a 3D version similar to that of our navigator.47 However, they did not show any ∆B₀ map or provide any information about the remaining local inhomogeneities of higher than first-order within the CEST volume after correction, and hence did not attempt to apply any further postprocessing steps.

The metric MTR_asym, which is highly sensitive to frequency shift errors close to the water resonance,12 has been used to assess the quality of the ∆B₀ correction methods in a similar way to the previously proposed Symmetric Analysis of Z-Spectra (SAS).48 The static GRE-2TE and the dynamic CEST-GRE-2TE methods resulted in MTR_asym maps with lowest spatial variability and mean values closest to 0% for the phantom experiments. This indicates that these two methods lead to the most accurate ∆B₀ correction among the static and dynamic approaches.

The in vivo results showed comparable corrected CEST-weighted signal distribution between the static methods GRE-2TE and WASSR. In contrast, the dynamic methods showed the following divergences: 1) the MTR_asym maps corrected by GRE-CEST-2TE achieved similarly homogeneous distribution to the static methods; and 2) corrections performed by CEST-GRE-1TE and NAV-EPI-2TE resulted in an overall positive MTR_asym offset and a slight spatial gradient in the anterior-posterior direction (frequency encoding direction) relative to GRE-CEST-2TE, respectively. These effects could arise from delays of the applied gradients and could be corrected by acquiring the same scan with opposite image readout orientation.49, 50

The scan-rescan experiment revealed very high consistency between ΔB₀-corrected MTR_asym maps with and without frequency drift for all subjects when using GRE-CEST-2TE and NAV-EPI-2TE for all volunteers. The B₀ estimation by GRE-CEST-1TE corrected the frequency drift, but less efficiently than the other two dynamic methods. Further investigations would be necessary to identify the source of this deviation; however, the known nonlinear phase evolution in white matter (due to specific tissue microstructure) could be a potential contributor.51

In our study, the accuracy of multiecho ∆B₀ mapping was dependent not only on the ∆TE between the two echoes, as reported previously,16 but also on the actual values set for each TE and their receiver bandwidths. We had to optimize the TE settings experimentally to eliminate erroneous B₀ offsets and spatially linear B₀ gradients (mostly in the readout encoding direction) in phantoms prior to the CEST experiments. For routine use, it will be important to achieve accurate ∆B₀ mapping for any CEST sequence setting without previous optimization. For similar reasons we also used only monopolar readout gradients, although GRE-CEST-2TE and GRE-2TE should benefit from bipolar readout gradients. We have also refrained from performing additional corrections for any other confounding effects such as motion, B₁ inhomogeneities, semisolid MT, water relaxation, T₂-dependent spillover or nuclear Overhauser enhancement exchange to prevent introducing factors that could make it difficult to isolate B₀-related effects.52-60 Of course these should be used when applying accurate CEST quantification in (patient) studies.

In the future, the proposed dynamic methods could be additionally combined with real-time motion correction by extending the navigator to 3D as previously applied in MRI and MRSI.47, 52-55 Thereby, artifacts due to motion and B₀-instabilities could be simultaneously mitigated. Although not investigated here, other CEST quantification routines such as Lorentzian or Bloch fitting61-63 would also be likely to benefit from the presented dynamic ∆B₀ correction, since B₀ is usually included as a fitting parameter.

6 CONCLUSION

We have presented three dynamic ∆B₀ correction methods for CEST MRI that successfully mapped and compensated for B₀ changes for each individual Z-spectral point. Improved correction performance in the presence of frequency drift was demonstrated by comparison with established static approaches. Among them, the self-correcting properties of CEST-GRE-2TE made it the most reliable and easiest to implement. Implementation of an interleaved navigator (NAV-EPI-2TE) was more complicated, but allowed improved dynamic ∆B₀ correction even close to water, but not better than CEST-GRE-2TE for typically investigated frequency ranges.

Dynamic B₀ corrections for CEST are another important step toward more reliable clinical CEST MRI without the need for (lengthy) prescans or for acquisition of additional Z-spectral points near water (as required for CEST-minZ), lending itself particularly to dynamic CEST MRI.