On the transmit field inhomogeneity correction of relaxation‐compensated amide and NOE CEST effects at 7 T

High field MRI is beneficial for chemical exchange saturation transfer (CEST) in terms of high SNR, CNR, and chemical shift dispersion. These advantages may, however, be counter‐balanced by the increased transmit field inhomogeneity normally associated with high field MRI. The relatively high sensitivity of the CEST contrast to B 1 inhomogeneity necessitates the development of correction methods, which is essential for the clinical translation of CEST. In this work, two B 1 correction algorithms for the most studied CEST effects, amide‐CEST and nuclear Overhauser enhancement (NOE), were analyzed. Both methods rely on fitting the multi‐pool Bloch‐McConnell equations to the densely sampled CEST spectra. In the first method, the correction is achieved by using a linear B 1 correction of the calculated amide and NOE CEST effects. The second method uses the Bloch‐McConnell fit parameters and the desired B 1 amplitude to recalculate the CEST spectra, followed by the calculation of B 1‐corrected amide and NOE CEST effects. Both algorithms were systematically studied in Bloch‐McConnell equations and in human data, and compared with the earlier proposed ideal interpolation‐based B 1 correction method. In the low B 1 regime of 0.15–0.50 μT (average power), a simple linear model was sufficient to mitigate B 1 inhomogeneity effects on a par with the interpolation B 1 correction, as demonstrated by a reduced correlation of the CEST contrast with B 1 in both the simulations and the experiments.

interpolation-based approach to correct Z-spectra and CEST contrast for B 1 inhomogeneity. 23 In this approach, the densely sampled Z-spectra are acquired at at least two different B 1 levels, and B 1 correction of Z-spectra and isolated CEST contrast is achieved by spline interpolation of the multiple B 1 data to a B 1 of interest. However, this approach may not be possible in a clinical setting, where the scan time is very limited.
In this work, two methods that require only one CEST dataset at a particular B 1 level and a relative B 1 map as a reference are compared. Both methods rely on fitting the multi-pool Bloch-McConnell equations 24 to the densely sampled Z-spectra using a B 1 map as a reference. In the first method, an assumption is made about a linear relationship of CEST effects with B 1 . The B 1 correction is achieved by using a linear B 1 correction of the calculated amide and NOE CEST effects. The second method is based on an assumption that the Bloch-McConnell estimated fit parameters other than B 1 are independent of the actual B 1 . The estimated fit parameters and the desired B 1 amplitude are used to recalculate the Z-spectra followed by the calculation of B 1 -corrected amide and NOE CEST effects.
Both approaches were first evaluated in simulated data and subsequently tested in data from healthy human brain. T 2 = 1 s/10 μs, pool size ratio 11%, exchange rate 50 Hz, chemical shift −2.4 ppm). Even though the NOE effect (−3.5 ppm) was shown to be composed of multiple fine structures, 13 we chose to approximate it with the single offset due to the use of short pulses with high bandwidth in this work. Due to large insensitivity of simulations to T 1 values of other than water pools, the T 1 of amide-CEST, NOE and MT was fixed to 1 s, as suggested previously. 27 The sequence parameters used in the simulations are the same as in the data acquisition (see later), except for the B 1 level extended up to 1.8 μT (average power). The simulations were based on the assumption that there are only four pools in the system and that the only interactions are with water.

| Data acquisition
In this report, we made a retrospective analysis of the data in Reference 23 . In vivo experiments were performed on a 7 T MR whole-body system (Magnetom; Siemens, Erlangen, Germany) using a Tx/Rx head coil (Tx, one channel; Rx, 24 channels). The CEST protocol was as follows 28 : saturation consisted of a train of 120, 15 ms Gaussian pulses interleaved with a GR-spoiler, duty cycle 60%; for readout a singleshot 2D gradient echo sequence (GRE) was used with GRAPPA acceleration factor 2, T R /T E /FA = 7.4 ms/3.6 ms/10°, matrix 128 × 128, slice thickness 5 mm. Total scan time was 4 min 7 s. Z-spectra were sampled at 66 frequency offsets distributed unevenly between ±500 ppm (500 ppm offset was used for normalization). The CEST sequence was performed at eight different B 1 levels: 0.14, 0.29, 0.43, 0.50, 0.58, 0.65, 0.72, and 0.80 μT. B 1 level refers to the nominally set, average power of the saturation pulse throughout the paper. B 0 inhomogeneity was corrected using the WASSR method. 29 A 2D flip-angle map was based on a single-shot GRE sequence: a rectangular preparation pulse (2 ms) with nominal flip angle 90°, T E / T R = 2.42 ms/5000 ms. The transmitter voltage and thus the nominal B 1 values were calibrated on the basis of this flip angle map. A relative map of irradiation amplitude (rB 1 (x, y)) was produced by the normalization of this flip-angle map by the nominal flip angle. The actual irradiation amplitude B 1 in each pixel (x, y) was assigned employing the relative B 1 map rB 1 (x, y) by B1(x, y) = rB1(x, y)B1 , nom, where B 1,nom is the nominal B 1 value as chosen in the protocol settings. A T 1weighted anatomical image was used to produce white matter (WM) and grey matter (GM) masks in FSL (FMRIB v6.0, UK).

| Fitting Bloch-McConnell equations to the data
The four (water, amide-CEST, NOE and MT) and six (water, amide-CEST, NOE, MT, amine-CEST 23 and NOE* 22 ) pool Bloch-McConnell equations were used to fit the simulated and the in vivo Z-spectra, respectively. The data was fitted at a single B 1 level at any given time. Since the saturation duration in the employed sequence is less than water T 1 , the saturation duration was taken into account in data fitting. 25 The choice of six pools to fit the in vivo Z-spectra was based on the results of fitting a few test Z-spectra by incrementing the number of pools and monitoring the goodness-of-fit statistics. Increasing the number of pools from four to six reduced the sum of squared errors by 50% (F-test, p < 0.01). The fitting was done employing a non-linear least squares constrained optimization algorithm (lsqcurvefit function in MATLAB) and using the pool parameters 26,[30][31][32][33] in Table 1. The goodness of fit was examined using Curve Fitting Toolbox™ in MATLAB with the following metrics: (i) the sum of squared errors; (ii) R-square; (iii) adjusted R-square; and (iv) root mean squared error.
The only parameters fixed in the fit were the actual B 1 (Equation 1) and T 1 (set to unity) for all pools except water.
To correct for the effects of the traditional MT and direct water saturation, the amide-CEST effect size (contribution to the Z-spectrum) was quantified by the pool difference method using the inverse metrics 34,35 : where MTR Rex,amide is the effect size of the cytosolic amides,  Finally, the B 1 -corrected effect size of amide and NOE is isolated using Equation 2.

| Linear model B 1 correction
The first and the second steps of the linear B 1 correction algorithm are identical to those of the BE B 1 correction algorithm ( Figure 1). In the 10 000 50 X 0 , LB and UB represent the initial guess and lower and upper bounds, respectively. third step, the effect size of amide and NOE is isolated using Equation 2 and a linear B 1 correction is achieved by division of the isolated effects by the relative B 1 .

| Comparison with interpolation-based B 1 correction
Both B 1 correction algorithms analyzed in this work were compared with the ideal interpolation-based B 1 correction approach. 23 The contrast maps of amide and NOE were generated at all B 1 levels as describedin theflowchart(Figure1, Steps 1 and 2) and using Equation2 to extract the effect sizes. The 3 | RESULTS

| Numerical simulations
In Figure  There are noticeable rotation effects for MTR Rex,amide at a B 1 above 0.8 μT. [38][39][40] The concept of the BE B 1 correction is shown in Figure 3, where a series of Z-spectra was simulated in the B 1 range 0.1-0.5 μT and subsequently fitted using BEs ( Figure 3A). The BE fit parameters from

| Experimental results
The experimentally derived B 1 dependence of MTR Rex,amide and MTR Rex,NOE is plotted in Figure 5. As predicted in the simulations At this power level, the effect size of amide and NOE is reduced by 15% and 10%, respectively, relative to their corresponding maxima. In  data, resulting in a very broad distribution, which can also be seen by visual inspection of the images in Figure 7B.    ). B, Same as A for the colored markers, but the colored solid lines represent BEcorrected spectra recalculated at a B 1 of 0.43 μT (assumed to be nominal B 1 level) using the corresponding fitting parameters from A. A Gaussian noise of 1% (of the signal at 500 ppm) was added to the simulated data.  Figure 3A), the linear model B 1 -corrected (isolated from Figure 3A with the subsequent linear B 1 correction), and the BE B 1 -corrected (isolated from Figure 3B) MTR Rex,amide effect size as a function of B    The perfectly fitted simulated spectra ( Figure 3A) and the visual inspection of the overlapping BE B 1 -corrected CEST spectra ( Figure 3B) suggest that fixing only one B 1 parameter in the BEs and allowing the FIGURE 8 The histograms of the images shown in Figure 7B. A,B, WM and GM, respectively, for MTR Rex,amide . C,D, WM and GM, respectively, for MTR Rex,NOE . The box and whiskers above each histogram contain values of 25-75% and 9-91%, respectively. rest to vary within reasonable constraints is sufficient to fit and correct the CEST spectra for B 1 inhomogeneity in this low B 1 range, 0.1-0.5 μT. However, care must be taken since the similarity between the BE B 1 -corrected spectra does not guarantee that they contain similar CEST features, i.e. MTR Rex,amide and MTR Rex,NOE , which are of interest and should be isolated from the spectra. Therefore, for the fair comparison of both B 1 correction algorithms, we chose to compare them in terms of the B 1 -corrected MTR Rex,amide and MTR Rex,NOE effects.
The BEs incorporate the effect of chemical exchange and are known to describe the exchange-mediated processes precisely. 24 However, many parameters are correlated, e.g. T 2 and k, k and M 0 , 41  The interpolation B 1 correction method 23 can be considered an ideal B 1 correction approach due to its applicability to any in vivo system at any B 1 level. Therefore, all contrast maps generated, uncorrected, linearly and BE B 1 corrected, were compared with those produced by the interpolation (Figure 7B). Only the linearly B 1corrected maps of both MTR Rex,amide and MTR Rex,NOE effects resemble those generated by the interpolation in terms of the image quality and the effect size, which further validates our assumption of a linear B 1 correction in the low B 1 regime (Figure 8 and Figure 9). For more detailed analysis of the interpolation B 1 correction approach, e.g. number of B 1 levels, image quality, etc., the interested reader is referred to the original work by Windschuh et al. 23  However, a linear model is no longer valid at this high power ( Fixing water T 1 , however, did not improve the performance of the BE B 1 -correction algorithm. In this manuscript, the strong linear correlation between M 0 (concentration) and k (exchange rate), which is difficult to decouple, 41 has been exploited to our advantage. For the same effect size (amide or NOE) a low fitted M 0 will be compensated by a high fitted k and vice versa. The B 1 correction algorithms in this work apply to the effect size (a product of M 0 and k), and so the individual parameters are less relevant as long as the BEs fit the original data.
Despite the fact that the linear B 1 correction algorithm was shown only on healthy brain, it is expected to be applicable to pathological tissue as well. Abnormally high water T 1 expected in tumors will scale the CEST effect, 34,35 but the linear B 1 dependence of amide-CEST and NOE effects at low power levels will not change with water T 1 (Supporting Information SI1, Figure S1). The same is true for different CEST saturation parameters, e.g. saturation duration and duty cycle, as long as the average power, which takes account of the CEST saturation parameters, 43 is low (0.1-0.5 μT). A change in water T 1 and CEST saturation parameters may, however, cause a variation in amide-CEST and NOE signal losses using the linear assumption when compared with measuring the effects at optimal B 1 levels.
In this work, we opted for the use of the multi-pool BE to extract amide and NOE features from CEST data as it is the only approach that intrinsically incorporates the sequence parameters, e.g. B 1 and other CEST saturation prepulse parameters, and the physiological parameters, e.g. metabolite concentration and pH-dependent exchange rate of labile protons with water. Yet, we expect the linear B 1 correction to be applicable to the other methods used for amide and NOE isolation such as the three point method 44 , the Lorentzian difference method, 13,45 and multiple Lorentzian fitting 23,46 .

| LIMITATIONS
The