# Efficient optimization of chemical exchange saturation transfer MRI at 7 T using universal pulses and virtual observation points

Thaddée Delebarre, Vincent Gras, Franck Mauconduit, Alexandre Vignaud, Nicolas Boulant, Luisa Ciobanu

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## To cite this version:

Thaddée Delebarre, Vincent Gras, Franck Mauconduit, Alexandre Vignaud, Nicolas Boulant, et al. Efficient optimization of chemical exchange saturation transfer MRI at 7 T using universal pulses and virtual observation points. Magnetic Resonance in Medicine, 2023, 90, pp.51 - 63. 10.1002/mrm.29617. hal-05120924

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Submitted on 19 Jun 2025

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RESEARCH ARTICLE

Magnetic Resonance in Medicine

# Efficient optimization of chemical exchange saturation transfer MRI at 7 T using universal pulses and virtual observation points

Thaddée Delebarre ID

Vincent Gras ID

Franck Mauconduit ID

Alexandre Vignaud ID

Nicolas Boulant ID

Luisa Ciobanu ID

NeuroSpin, UMR CEA/CNRS 9027, Paris-Saclay University, Gif-sur-Yvette, France

**Correspondence**

Luisa Ciobanu, NeuroSpin, UMR CEA/CNRS 9027, Paris-Saclay University, Gif-sur-Yvette, France.

Email: luisa.ciobanu@cea.fr

**Funding information**

Agence Nationale de la Recherche, Grant/Award Number: ANR-19-CE17-0008; Fondation Leducq, Grant/Award

Number: NEUROVASC7T

**Purpose:** To optimize the homogeneity of the presaturation module in a Chemical Exchange Saturation Transfer (CEST) acquisition at 7 T using parallel transmission (pTx).

**Theory and Methods:** An optimized pTx-CEST presaturation scheme based on precomputed universal pulses was designed. The optimization was performed by minimizing the L2-norm between the effective $B_{1,RMS}^+$ and a given target while imposing energy constraints under virtual observation points (VOPs) supervision. The proposed method was evaluated through simulations and experimentally, both in vitro, on a realistic human head phantom, and in vivo, on healthy volunteers. The results were compared with circular polarization (CP) presaturation and other pTx approaches previously proposed. All experiments were conducted on a 7 T MRI scanner using a commercial 8Tx/32Rx head coil.

**Results:** The simulations show that the proposed pTx strategy boosted with VOPs is superior to the CP mode and existent pTx approaches. While the best results are obtained with subject specific pulses, the gain provided by the use of VOPs renders the universal pulses superior to tailored pulses optimized under vendor provided Specific Absorption Rate (SAR) management. In the phantom, the glucose MTR$_{asym}$ map was significantly more homogeneous than with CP (root mean square error [RMSE] 17% vs. 30%). The efficiency of the method for in vivo hydroxyl, glutamate and rNOE weighted CEST acquisitions was also demonstrated.

**Conclusion:** The use of a pTx presaturation scheme based on universal pulses optimized under VOP SAR management is significantly benefiting CEST imaging at high magnetic field.

**KEYWORDS**

chemical exchange saturation transfer, magnetization transfer asymmetry, parallel transmission, tailored pulses, universal pulses, virtual observation points
# 1 | INTRODUCTION

Chemical Exchange Saturation Transfer (CEST)¹ imaging is an MRI technique that enables the detection of certain compounds by taking advantage of the chemical exchange between their labile protons and the bulk water protons. Selectively irradiating the exchangeable protons results in a partial saturation of the water magnetization, which is proportional to the concentration of the compound. Prolonged irradiation durations lead to signal amplification and the detection of low concentrations, below those observable in standard NMR and MRI. The compounds detectable by CEST typically contain functional groups such as hydroxyl (-OH), amide (-NH) and amine (-NH₂).² Additionally, sequences developed for CEST imaging allow the detection of mobile macromolecules through relayed Nuclear Overhauser Enhancement (rNOE) effects.³⁻⁵ In the brain, CEST has been employed for the imaging of several important moieties, promoting its use for preclinical and clinical applications. Most prevalent applications are based on amide proton transfer or the detection of two main brain metabolites, glutamate (gluCEST) and glucose (glucoCEST), and include: the assessment of stroke, the characterization of gliomas and the diagnosis of neurological disorders.⁶⁻¹⁶

The increased availability of high and ultra-high magnetic fields promises to broaden the range of CEST applications as the technique benefits significantly from the high sensitivity, the large chemical shift dispersion and the increased water $T_1$ relaxation time attainable by increasing the $B_0$ field.¹⁷ However, before CEST imaging can become a routine technique in clinical settings, several challenges must be overcome. Imaging at high magnetic fields faces increased $B_0$ and $B_1^+$ inhomogeneities¹⁸ and significant radiofrequency (RF) energy deposition in tissues.¹⁹ Several algorithms have been proposed for the correction of $B_0$ and $B_1^+$ inhomogeneities, either independently,²⁰,²¹ or simultaneously.²²,²³ Because the CEST contrast is strongly dependent on the saturation RF amplitude,²⁴ most of these methods require multiple acquisitions, at several $B_1^+$ values, and eventually additional $B_1^+$ mapping, lengthening the total acquisition time.

An elegant solution for mitigating the $B_1^+$ inhomogeneity is to use parallel transmission (pTx).²⁵ pTx uses multiple RF channels which can be controlled independently. The combined, effective $B_1^+$ is homogenized by carefully designing the spatial and temporal profiles of the RF waveforms for each individual channel. The benefit of pTx for CEST imaging at 7 T has been demonstrated. In the Multiple interleaved mode saturation (MIMOSA) method,²⁶ the authors use a combination of two modes presenting spatial complementary without taking into consideration the exact $B_1^+$ spatial distributions. An additional gain in

saturation quality has been obtained by using pre-acquired $B_1^+$ maps to find the optimal parameters for individual modes by solving an optimization problem,²⁷,²⁸ with the drawback of increasing the complexity and the workload during the exam. Importantly, current common practice consists in monitoring the Specific Absorption Rate (SAR) by using a very conservative power threshold, provided by the vendor. This approach, as we detail in the manuscript, limits the pTx performance as compared to more realistic SAR-based RF monitoring strategies.

In this work, we design a presaturation CEST module based on precomputed Universal Pulses²⁹ (UP), while ensuring near optimal use of the pTx hardware and the multitransmit RF coil. This approach can be easily brought to clinics as the pulses are designed offline, avoiding time-consuming, subject-specific optimization. While the use of UPs has been reported previously for anatomical and functional imaging, this is the first time they are used for CEST acquisitions. Moreover, we show that the efficiency of the CEST presaturation pulse train is enhanced by managing the energy deposition using Virtual Observation Points (VOPs).³⁰,³¹ We evaluate the performance of this design using numerical simulations, as well as in vitro and in vivo CEST measurements.

# 2 | THEORY

## 2.1 | pTx pulse design

Ideal CEST presaturation pulses produce a spatially uniform saturation for a given RF amplitude and at a specific frequency. To this end, our approach is to find the pTx pulse parameters which minimize the distance (L2 norm) between the effective $B_{1,RMS}^+$ and a given target. The effective RF amplitude of an RF waveform of duration $T_s$ can be expressed as:²⁶

$$B_{1,RMS}(\mathbf{r}) = \sqrt{\frac{1}{T_s} \int_0^{T_s} B_1^2(\mathbf{r}, t) \, dt.} \quad (1)$$

The magnitude of a single RF pulse, $B_1(\mathbf{r}, t)$, can be decomposed into a space-dependent component and a time-dependent component. For a specific channel $i$, we denote the spatially dependent component by $B_{1,i}(\mathbf{r})$ (also known as transmit sensitivity) expressed in Tesla/Volt, and the time-dependent component by $V_i(t)$, expressed in Volt. Using a vector formalism, we write $\mathbf{b}_1(\mathbf{r})$ and $\mathbf{V}(t)$ to denote, respectively, these quantities for all channels, where $\mathbf{b}_1(\mathbf{r})$ is obtained with a $B_1^+$ mapping sequence and $\mathbf{V}(t)$ is the result of an optimization, as detailed below. With these notations, the combined effect of $N_c$ transmit channels can be written:
$$B_1^A(\mathbf{r}, t) = \sum_{i=1}^{N_c} V_i^A(t) b_{1,i}(\mathbf{r}) = \mathbf{V}^A(t)\mathbf{b}_1(\mathbf{r}). \quad (2)$$

In Equation (2), the subscript A identifies a complete set of RF parameters for all channels and will be referred to as “mode A.” Given two modes, A and B, of the same duration ($T_{pulse}$), and shape, we can write $\mathbf{V}^A(t) = \mathbf{p}^A \times w(t)$ and $\mathbf{V}^B(t) = \mathbf{p}^B \times w(t)$, where $w(t)$ is the same normalized waveform for each channel and $\mathbf{p}^A$ and $\mathbf{p}^B$ are complex weights (units of V) to be optimized for mode A and mode B, respectively. By plugging the expression of $B_1(\mathbf{r}, t)$ from Equation (2) in Equation (1) we obtain:

$$B_{1,RMS}(\mathbf{r}) = w_{RMS} \sqrt{\frac{(\mathbf{p}^A \mathbf{b}_1(\mathbf{r}))^2 + (\mathbf{p}^B \mathbf{b}_1(\mathbf{r}))^2}{2}}, \quad (3)$$

where

$$w_{RMS} = \sqrt{\frac{1}{T_{pulse}} \int_{0}^{T_{pulse}} w^2(t) dt.} \quad (4)$$

Using the framework described above, we pose the following minimization problem, which aims to find an optimal set of modes to reach a given $B_{1,RMS}^+$ under the RF energy deposition constraints that are detailed hereafter:

$$\mathbf{p}^A, \mathbf{p}^B = \arg \min_{\mathbf{p}^A \mathbf{p}^B} \| \mathbf{B}_{1 \text{ RMS target}} - \mathbf{B}_{1 \text{ RMS}} \|_2$$

$$\text{s.t.} \quad c_{\text{global}}(\mathbf{p}^A, \mathbf{p}^B) \le \text{SAR}_{\text{global,max}} \quad (5)$$

$$c_{\text{local,m}}(\mathbf{p}^A, \mathbf{p}^B) \le \text{SAR}_{\text{local,max}}, \quad 1 \le m \le N_{\text{VOP}}$$

This optimization must be subject to energy deposition constraints. The vendor-provided SAR management strategy, so-called protected mode, sets limits on total and per channel power, namely $P_{total} < 8$ W and $P_{channel} < 1.5$ W, respectively. While these constraints guarantee compliance with the first-level SAR mode, they over-restrict the maximum RF power and can be a limitation for some applications, including CEST. To relax these constraints and, therefore, to improve the optimization in Equation (5), a VOP management of the local SAR was used. VOPs are a set of judiciously chosen SAR matrices allowing for a conservative estimation of the maximum local SAR in the head in real time.31 Such a VOP set is usually obtained by compression30 of one or more full SAR models representing tens of thousands of SAR matrices (one per voxel of the numerical head model). The number of VOPs in our case32 was 190, allowing manageable RF pulse design algorithms in pTx. The use of this SAR monitoring approach for the optimization leads to the following constraints: $P_{total} < 16$ W, $P_{channel} < 3$ W (set by the coil manufacturer), SAR$_{local} < 10$ W/kg, and SAR$_{global} < 3.2$ W/kg.

# 3 | METHODS

## 3.1 | Experimental setup

All measurements were conducted on a whole-body investigative 7 T MR system (Magnetom 7 T, Siemens Healthineers) equipped with a Nova head coil with eight transmit and 32 receive channels (Nova Medical).

For in vitro experiments, a two-compartment, realistic head shape phantom (Figure S1) was three-dimensional printed with high-temperature resin following the design from Jona et al.,33 but 10% smaller due to printing constraints. The two compartments of the phantom were filled with 10 mM D-glucose in 2.5% agarose (inner compartment), and 15 mM creatine in 2.0% agarose (outer compartment). (Note: no creatine CEST experiments were performed in this study). In order to mimic human brain tissue characteristics we adjusted the pH to 7.0 and added, in both compartments, 4 g/L NaCl and 0.064 mM Dotarem (for a $T_1$ relaxation time of 1600 ms). 4 mM sodium azide was also added to avoid bacterial degradation. To ensure uniform distribution, all components were fully dissolved in distilled water and thoroughly mixed before adding agarose to the solution. Before the experiments, the phantom was warmed up to 37 °C by placing it in a hot oven for 24 h.

For the in vivo experiments, seven healthy volunteers (between 22 and 52 years old, two female and five male) were recruited after providing informed written consent. No glucose administration was performed before the acquisitions. The study was approved by the local institutional review board.

## 3.2 | CEST acquisitions

### 3.2.1 | Tailored and universal pTx pulse design

For in vitro experiments, tailored pulses (TP) were designed specifically for the phantom used. Following a $B_0$ measurement performed using a three-dimensional-GRE protocol, a $B_1^+$ map was acquired with an in-house made interferometric turbo-FLASH sequence called XFL34 (5 mm isotropic resolution, matrix size 40 × 64 × 40). This $B_1^+$ map was used for the optimization in Equation (5).

For in vivo acquisitions, TPs were designed for each volunteer following an identical procedure. In addition, UPs were also used for the in vivo acquisitions. The use of UPs presents the advantage of an offline design while still offering excellent $B_1^+$ uniformization capability, comparable to TPs.29 For designing UPs a composite matrix $\mathbf{b}_1(\mathbf{r})$ was built by concatenating $B_1^+$ maps from a large database
<figure><img src="image_3.png" /><figcaption>FIGURE 1 Diagram of the chemical exchange saturation transfer pulse sequence showing the events during one repetition time. The colored pulses, A and B, are pairs of parallel transmission pulses. Each pair is played *N* times before spoiling and echo-planar imaging readout to produce an effective saturation time of $T_{sat} = 2N \times T_{pulse}$.</figcaption></figure>

of subjects. Our database consists of 26 subjects,³⁵ with 13 randomly selected maps serving as optimization group and 13 others as evaluation group.

The pulse optimization was done in MATLAB (Mathworks, version 9.7, R2019b) using an interior-point solving algorithm (Intel Core i7-9850H CPU at 2.60 GHz, 32.0 Go RAM). For TPs, calculated using only one $B_1^+$ map, the average computational time was 13 s, while for UPs, calculated using 13 $B_1^+$ maps, it was 22 s.

### 3.2.2 | Pulse sequence setup

The pTx optimized pulses, either TPs or UPs, were integrated in a modified EPI sequence as shown in Figure 1. The saturation was performed using a train of $2 \times N$ pulses consisting of two interleaved modes (mode A, mode B, mode A, ..., mode B). Immediately after saturation, gradient spoilers were applied in all three directions. The excitation pulse of the EPI module was used in the standard circularly polarized (CP) mode. For five volunteers, a single axial slice was imaged at position $z = +15$ mm from the isocenter, for the other two volunteers, three axial slices were imaged at $z = +15, +40$ and $-40$ mm from the isocenter. The other experimental parameters were set as follows: echo time = 34 ms, repetition time = 2500 ms, FOV = $3.4 \times 3.4 \text{ mm}^2$, slice thickness = 4 mm, flip angle = 78°, matrix size = $64 \times 64$. For spectral selectivity considerations, the shape of the saturation pulses was Gaussian with a Hanning window for which $B_{1,mean}^+ = 0.74 B_{1,RMS}^+$. The standard deviation (SD) of the Gaussian was chosen to be 12.5 ms in order to minimize the second lobe of the pulse spectrum. The length of each saturation pulse was 50 ms.

Hydroxyl-weighted CEST acquisitions were performed with 20 presaturation pulses (10 A-B pairs) of target $B_{1,RMS}^+ = 1.5 \mu\text{T}$, for an effective saturation time of 1 s.¹⁴ Forty-two measurements were performed with saturation offsets equally spaced between -5 and 5 ppm and one,

for normalization, at -10 ppm, ending up with a total acquisition time of 2 min 5 s.

For glutamate-weighted CEST acquisitions, the presaturation RF amplitude was set to $B_{1,RMS}^+ = 3 \mu\text{T}$ and only 16 pulses were employed for an effective saturation time¹¹ of 800 ms. Because of the higher RF amplitude target, the repetition time was increased to TR = 5000 ms in order to maintain a similar duty cycle and be able to obtain good saturation homogeneity. 42 acquisitions were performed, 41 with frequency offsets between -5 and 5 ppm and one at -10 ppm, setting the scan time to 3 min 50 s.

For $B_0$ correction, a WAter Saturation Shift Referencing²⁰ strategy was used. The water saturation shift referencing acquisition was performed using the same presaturation pulses as for the CEST but scaled to reach $B_{1,RMS}^+ = 0.15 \mu\text{T}$. The presaturation module, with an effective duration of 500 ms, was applied at 21 frequency offsets equally spaced between -1 and 1 ppm. All other imaging parameters were identical with those for the CEST acquisition except for TR, which was set to 1.5 s.

For the exams performed on volunteers, an anatomical image, necessary for segmentation, was also acquired using an MP2RAGE sequence³⁶ (repetition time = 6000 ms, inversion times = 800 ms / 2700 ms, bandwidth = 240 Hz, flip angle = 4°, 0.8 mm isotropic resolution, matrix size = 300 × 320 × 190).

Following the above-described protocols, hydroxyl-weighted CEST acquisitions were performed using CP, MIMOSA, and optimized pTx pulses (with TPs for phantom and UPs in vivo). If the SAR constraints allowed it, the spatially averaged saturation RF amplitude, $B_{1,RMS}^+$, of MIMOSA and CP were kept at the same level as the UPs (made on the evaluation dataset). Otherwise, the magnitude of MIMOSA and CP pulses was scaled down to reach the maximum allowed SAR (see Table S1). The two MIMOSA modes had the same amplitude. The TP and UP pulses were optimized on a 10 mm-thick slab, centered on the imaged slice. In vivo glutamate-weighted CEST acquisitions were also performed but only using pTx with UPs.

## 3.3 | Data analysis

A retrospective motion correction (image to image) was performed on in vivo CEST acquisitions using SPM12. An extrapolation of movement for frequencies between -0.75 and 0.75 ppm was done to avoid registration of low-intensity images. After the motion correction, a $B_0$ correction was made using the water saturation shift referencing acquisition. Specifically, the water peak was fitted with a Lorentzian curve and the acquired Z spectra to be corrected were linearly interpolated and shifted by the
same value as that required to bring the center of the fitted Lorentzian curve to 0 ppm. To produce various CEST weighted maps, the Magnetization Transfer Asymmetry (MTR<sub>asym</sub>) was computed voxel by voxel according to:

$$MTR_{asym}(\Delta\omega) = \frac{S(-\Delta\omega) - S(\Delta\omega)}{S_{ref}}. \quad (6)$$

For each volunteer, we produced glutamate and hydroxyl-weighted CEST maps as well as an rNOE map (using the hydroxyl-weighted CEST acquisition as saturation parameters are close<sup>3,14</sup>) by calculating MTR<sub>asym</sub> at $\Delta\omega$ of 3 ppm, $1.25 \pm 0.25$ ppm and $-4$ ppm, respectively. A composite image was finally produced by overlaying the CEST maps on the anatomical image. For the statistical analysis, the white and gray matter were segmented with SPM12.

# 4 | RESULTS

## 4.1 | Pulse scheme efficiency

The first pulse optimization result was that increasing the number of modes beyond two does not significantly improve $B_{1,RMS}^+$ homogeneity, as observed previously by Leitão et al.<sup>28</sup> We therefore only focused on the optimization of two modes. Typical TPs optimized for hydroxyl-weighted CEST acquisitions for a given volunteer are shown in Figure 2A. While the optimization does not result in a trivial solution, we note that, due to the combined optimization of the two modes, the spatial distributions of the $B_{1,RMS}^+$ show spatial complementarity (Figure 2B).

$B_{1,RMS}^+$ maps obtained on the evaluation dataset using Equation (3) for both UPs and CP are shown in Figure S2

(the optimization was performed using hydroxyl-weighted CEST presaturation parameters). UPs provide a much more homogeneous saturation than CP. The root mean square error (RMSE), computed as the ratio of the difference between the target and the effective $B_{1,RMS}^+$ (Equation (3)) to the $B_{1,RMS}^+$ target, decreases from 28% to 7.7% when using UPs compared to the CP mode. The UPs also perform more evenly across subjects, the SD of intersubject RMSE being 2.2 times smaller than with CP.

Figure 3A shows the simulated performance of CP, MIMOSA,<sup>26</sup> UPs and TPs for a volume saturation when the optimization was performed under protected mode or VOP supervision. The $B_{1,RMS}^+$ RMSE is plotted as a function of $B_{1,RMS}^+$ target $\sqrt{\text{DC}}$, with DC = $\frac{T_{\text{sat}}}{T_R}$ (duty cycle). This representation is justified by the fact that, by increasing the TR, an optimized pulse can be scaled up (higher $B_{1,RMS}^+$) while still respecting the energy constraints.

In Figure 3, two regimes stand out. For low energy deposition (low duty cycle), the protected and VOP SAR management strategies perform similarly. For higher duty cycle, starting at $B_{1,RMS}^+\sqrt{\text{DC}} = 0.9 \ \mu\text{T}$, the use of VOPs allows maintaining a constant RMSE while the optimization under protected mode breaks down. In this regime, the UPs and TPs perform similarly. MIMOSA benefits less than the other pTx pulses from VOP supervision, most likely due to the similarity with the CP mode. Of particular interest in practice, we note that the local SAR supervision enables shorter TRs without sacrificing saturation homogeneity. In Figure 3B we show that optimizing pulses on a slab can dramatically reduce the RMSE while the trends observed for different pulses in Figure 3A are maintained.

For the study in case, for the hydroxyl-weighted CEST and glutamate-weighted CEST acquisitions performed with the parameters presented in the Methods section, the

<figure><img src="image_4.png" /><figcaption>FIGURE 2 (A) Magnitude and phase of optimized tailored pulses for a chemical exchange saturation transfer presaturation targeting hydroxyl protons. Each color represents one channel. (B) Spatial distribution of the effective $B_{1,RMS}^+$ for the two modes.</figcaption></figure>
<figure><img src="image_5.png" /><figcaption>FIGURE 3 $B_{1,RMS}^{+}$ root mean square error (RMSE) of circular polarization (CP), MIMOSA, tailored pulses (TPs) and universal pulses (UPs) under different optimization and energy management strategies. TPs were designed subject-by-subject on the evaluation data-set. Lines represent the average performance while colored areas are bounded by the minimum and maximum RMSE. (A) Comparison of CP, MIMOSA, UPs and TPs for a whole brain optimization under protected mode (PM) or virtual observation points (VOPs) SAR management. (B) Comparison of CP, MIMOSA, UPs and TPs for an axial slab ($z = +15 \pm 5$ mm) optimization under VOP management. The two arrows point to the values on the abscissa corresponding to experimental protocols described in the Methods section (red for hydroxyl-weighted chemical exchange saturation transfer, blue for glutamate-weighted CEST).</figcaption></figure>

<table><caption>TABLE 1 Performance summary of different presaturation strategies for hydroxyl-weighted CEST and glutamate-weighted CEST acquisitions in the study (optimization performed on a slab).</caption><thead><tr><th rowspan="2"></th><th rowspan="2"></th><th colspan="4">Protected mode</th><th colspan="4">VOP supervision</th></tr><tr><th>CP</th><th>MIMOSA</th><th>UP</th><th>TP</th><th>CP</th><th>MIMOSA</th><th>UP</th><th>TP</th></tr></thead><tbody><tr><td rowspan="5">Hydroxyl CEST</td><td>P<sub>total</sub> (W)</td><td>8.0</td><td>8.0</td><td>8.0</td><td>8.0</td><td>8.0</td><td>12</td><td>15</td><td>13</td></tr><tr><td>P<sub>channel</sub> (W)</td><td>1.0</td><td>1.0</td><td>1.2</td><td>1.3</td><td>1.0</td><td>1.5</td><td>2.7</td><td>2.2</td></tr><tr><td>SAR<sub>local</sub> (W/kg)</td><td>10</td><td>6.6</td><td>6.0</td><td>4.7</td><td>10</td><td>9.6</td><td>9.4</td><td>8.8</td></tr><tr><td>SAR<sub>global</sub> (W/kg)</td><td>1.2</td><td>1.2</td><td>1.2</td><td>1.2</td><td>1.2</td><td>1.7</td><td>1.8</td><td>1.8</td></tr><tr><td>RMSE (%)</td><td>25.3</td><td>21.4</td><td>19.3</td><td>18.3</td><td>25.3</td><td>9.3</td><td>8.1</td><td>3.9</td></tr><tr><td rowspan="5">Glutamate CEST</td><td>P<sub>total</sub> (W)</td><td>8.0</td><td>8.0</td><td>8.0</td><td>8.0</td><td>8.0</td><td>12</td><td>12</td><td>16</td></tr><tr><td>P<sub>channel</sub> (W)</td><td>1.0</td><td>1.0</td><td>1.0</td><td>1.3</td><td>1.0</td><td>1.5</td><td>1.5</td><td>2.7</td></tr><tr><td>SAR<sub>local</sub> (W/kg)</td><td>10</td><td>6.6</td><td>6.0</td><td>4.9</td><td>10</td><td>10</td><td>10</td><td>10</td></tr><tr><td>SAR<sub>global</sub> (W/kg)</td><td>1.2</td><td>1.2</td><td>1.2</td><td>1.2</td><td>1.2</td><td>1.8</td><td>1.7</td><td>2.2</td></tr><tr><td>RMSE (%)</td><td>35.7</td><td>33.1</td><td>31.4</td><td>30.3</td><td>35.7</td><td>17.9</td><td>8.70</td><td>6.93</td></tr></tbody></table>

Notes: The values highlighted in orange are capped by the constraints under both the protected mode and VOPs. The values highlighted in blue are allowed under VOP supervision but forbidden under protected mode.

Abbreviations: CEST, chemical exchange saturation transfer; CP, circular polarization; RMSE, root mean square error; TP, tailored pulses; UP, universal pulses; VOP, virtual observation points.
<figure><img src="image_6.png" /><figcaption>FIGURE 4 (A) $B_{1,RMS}^{+}$ simulation results for the two modes of a specific tailored pulse (TP) optimized on the phantom. (B) Simulated $B_{1,RMS}^{+}$ maps for circular polarization (CP) and for the combination of the TP modes shown in (A). (C) Experimental $MTR_{asym}$(1.25 ppm) maps obtained on the phantom with CP and TP.</figcaption></figure>

values of $B_{1,RMS}^{+}$ target $\sqrt{\text{DC}}$ are 1.03 and 1.3 $\mu$T, respectively (see arrows in Figure 3B). Under these conditions, the performances of the different pulses, optimized on a slab, are summarized in Table 1. The RMSE is drastically reduced using VOP supervision as it leverages the degrees of freedom of both the amplitude and phase, allowing higher RF amplitudes than the protected mode. More specifically, it allows UPs to achieve an RMSE three to four times smaller than CP and up to two times smaller than MIMOSA. For hydroxyl and glutamate acquisitions, TPs perform better than UPs, with, as noted before, the disadvantage of requiring a subject-specific optimization.

## 4.2 | In vitro CEST results

For the phantom, simulated $B_{1,RMS}^{+}$ maps corresponding to the two TP modes are shown in Figure 4A and their combination in Figure 4B (right). In Figure 4B

we also show the simulated $B_{1,RMS}^{+}$ map for CP (left). According to these $B_{1,RMS}^{+}$ simulations, pTx significantly improves the homogeneity of the saturation compared to CP with an eight times smaller RMSE (4% vs. 32%). As expected, the $MTR_{asym}$ map experimentally obtained with TP (Figure 4C) is also more homogeneous, with an RMSE of 17% versus 30% with CP.

Figure 5 shows the Z-spectra obtained in two different regions of interest (ROIs), one located in the center of the phantom, the other in the posterior region exhibiting low $B_{1}^{+}$ with CP. Across the phantom, the CP pulse leads to changes in the width of the Z-spectra with a full width at half maximum (FWHM) doubled between ROI 1 and ROI 2 (Figure 5A). When the presaturation is performed with TP, the Z-spectrum is constant across the phantom. The $MTR_{asym}$ obtained with TP matches well the simulation results obtained for a saturation RF amplitude of 1.5 $\mu$T (Figure 5B). An almost identical $MTR_{asym}$ value is obtained at 1.25 ppm, in both ROIs with TP while CP leads to much higher values in ROI 1 compared to ROI 2.

For TP, the SNR of the $MTR_{asym}$ map reaches 20 on average across the slice. Given the 10 mM glucose concentration in the phantom, we expect, for typical brain glucose concentrations of 1 mM, an SNR of 2 (assuming only glucose CEST contribution).

## 4.3 | In vivo CEST results

### 4.3.1 | Hydroxyl-weighted CEST

We studied the homogeneity of in vivo hydroxyl-weighted CEST maps obtained with UPs and CP CEST presaturation.

The results obtained on four volunteers, shown in Figure 6, are consistent with those from simulations and in vitro measurements. Specifically, the hydroxyl-weighted CEST maps obtained with UPs present overall higher $MTR_{asym}$ values than those with CP, especially at the borders of the brain. We can note that with CP, the low saturation at the borders of the brain leads to a strong rNOE effect and, as a result, to a negative $MTR_{asym}$ value. It can be also noted that in the center of the brain, CP and UPs show similar values of $MTR_{asym}$, thanks to the comparable saturation values. Figure 6B shows $B_{1,RMS}^{+}$ obtained with UPs for each subject. The average $B_{1,RMS}^{+}$ RMSE is 13%, giving therefore an improvement of a factor 2 compared to the saturation obtained with CP. The corresponding flip angle maps computed as in Zu et al.³⁸ are shown in Figure 6C. For completeness, we show the $B_{1,RMS}^{+}$ maps for individual modes in Figure S3.

The observations above are supported by Figure 7. In Figure 7A, we note, for all subjects, a higher $MTR_{asym}$
<figure><img src="image_7.png" /><figcaption>FIGURE 5 (A) Experimental and simulated Z-spectra in the phantom. Using a tailored pulse (TP), the spectra in the two ROIs are almost superimposed, as expected. This is, however, not the case for circular polarization (CP) due to the $B_1^+$ brightening effect in ROI 1 and signal dropout in ROI 2. The simulated Z-spectrum (black line) is almost identical to those obtained with TP. (B) MTR<sub>asym</sub> calculated in the ROIs shown in (A), demonstrating identical glucose MTR<sub>asym</sub> values when using TP. The colored areas are delineated by the SD of the signal in the respective ROIs. MTR<sub>asym</sub> (black line) agrees well with the TP results. The simulations were performed with the Bloch-McConnell solver “bm_sim_fit” available at www.cestsources.org and included the four glucose hydroxyl-groups with characteristic parameters as in Khlebnikov et al.<sup>37</sup> The chemical exchange saturation transfer saturation was modeled with 20 identical Gaussian-Hanning pulses scaled to reach 1.5 µT $B_{1,RMS}^+$.</figcaption></figure>

value with a more homogeneous distribution with UPs than with CP. As it is shown in Figure 7B, and 7C, for UPs, the median and the full width at half maximum of the MTR<sub>asym</sub> are four times higher and 40% narrower, respectively. The MTR<sub>asym</sub> median for different brain regions, gray matter, white matter and central part, is shown in Figure 7D. The UPs provide a high and constant median value in all the different regions. CP gives, like UPs, a 2% MTR<sub>asym</sub> value in the center of the brain, but the values in white matter and gray matter are significantly lower with a near 0% MTR<sub>asym</sub> median.

In Figure 8 we compare the performances of CP, MIMOSA, and UP on two volunteers at three locations from the isocenter (z = +15, +40 and -40 mm). Both the MTR<sub>asym</sub> (Figure 8A) and the $B_{1,RMS}^+$ (Figure 8B) maps demonstrate that UP outperforms the other two approaches in all three slices. For all three methods, the inhomogeneity in MTR<sub>asym</sub> for the lower slice (z = -40 mm) is stronger than that expected based on the $B_{1,RMS}^+$ maps, due to, nonetheless, strong B<sub>0</sub> inhomogeneities in this brain region. Compared to CP, MIMOSA provides a significant improvement in $B_{1,RMS}^+$ in the central (z = +15 mm) and the lower slices (z = -40 mm). For the upper slice, however, MIMOSA leads to a strong $B_{1,RMS}^+$ on the

edge of the brain and suffers from a dropout in the center of the brain. For all three slices, and especially for the upper slice, UP provides the most homogeneous $B_{1,RMS}^+$ (see Tables S1 and S2).

### 4.3.2 | Other CEST contrasts

rNOE and glutamate-weighted CEST weighted maps, acquired using UPs are shown in Figure 9. Consistent with our hydroxyl-weighted CEST results, these maps show good contrast across the brain. The rNOE maps present an average MTR<sub>asym</sub> of 4% in gray matter and 7.5% in white matter which is similar to average values reported in the literature.<sup>3-5</sup> The glutamate-weighted maps show a gray matter contrast in agreement with that reported by Debnath et al.<sup>39</sup> In the white matter, we note very low MTR<sub>asym</sub> values, even negative, most likely because we did not perform a magnetization transfer correction.<sup>39</sup>

Average hydroxyl, rNOE, and glutamate MTR<sub>asym</sub> values, for each volunteer, are presented in Table S2. The UP parameters used for the acquisitions of the maps in Figures 6 and 9 are given in Tables S3 and S4.
<figure><img src="image_8.png" /><figcaption>FIGURE 6 (A) Comparison of MTR<sub>asym</sub> maps obtained with circular polarization (CP) and universal pulses (UPs) on four volunteers. The MTR<sub>asym</sub> maps are overlaid on T<sub>1</sub> weighted anatomical images. With UP presaturation, the MTR<sub>asym</sub> does not suffer of dropout in peripheral areas. (B) B<sup>+</sup><sub>1,RMS</sub> and (C) flip angle maps corresponding to the UP images in (A).</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>FIGURE 7 Distribution statistics of the MTR<sub>asym</sub>(1.25 ± 0.25 ppm) obtained in vivo (n = 4 volunteers) for circular polarization (CP) and universal pulses (UP) CEST presaturation. (A) MTR<sub>asym</sub> distribution across subjects. (B) MTR<sub>asym</sub> median across subjects. (C) MTR<sub>asym</sub> full width at half maximum. (D) Median MTR<sub>asym</sub> for segmented regions, gray matter (GM), white matter (WM), and a central part of the white matter (Center).</figcaption></figure>
<figure><img src="image_10.png" /><figcaption>FIG URE 8 (A) MTR<sub>asym</sub> and (B) B<sub>1,RMS</sub><sup>+</sup> maps obtained on two subjects using circular polarization (CP), MIMOSA and universal pulses (UP) optimized for hydroxyl-weighted chemical exchange saturation transfer acquisitions. Three slices were imaged at positions +40 mm, +15 mm and -40 mm from isocenter.</figcaption></figure>

**5** | DISCUSSION

In this study, we propose and evaluate a pTx-based method to mitigate $B_{1,RMS}^{+}$ inhomogeneity effects on the CEST contrast occurring in human brain at 7 T. The developed CEST presaturation scheme is composed of two interleaved modes and optimized using transmit sensitivity maps. We show that this method works not only when tailoring the CEST presaturation pulse to the subject-specific $B_1^+$ map but also when using a fixed CEST *universal* presaturation pulse optimized offline on a collection of $B_1^+$ maps. Additionally, the use of VOPs for SAR management allows a significant gain in CEST presaturation uniformity. The VOP boost could also be used for TR reduction, as one can design pulses minimizing SAR deposition while keeping

the inhomogeneity of $B_{1,RMS}^{+}$ under a given threshold. Our simulations show that such an approach enables TRs two times shorter than when using the protected mode SAR management strategy.

We note that the use of subject specific TPs optimized under VOP energy management constraints has been reported recently for magnetization transfer imaging<sup>28</sup> with similar performance as that presented in this manuscript. From a practical point of view, the approach introduced here, the use of UPs and VOPs, brings a substantial improvement as it considerably simplifies the workflow in a clinical setting. Our simulations show that, while the UPs are outperformed by TPs, they perform better than CP and other pTx approaches. This high level of performance, the absence of in-line optimization
<figure><img src="image_11.png" /><figcaption>FIGURE 9 (A) In vivo rNOE and (B) glutamate-weighted CEST MTR<sub>asym</sub> maps obtained with UP CEST presaturation overlaid on T<sub>1</sub> weighted anatomical images. (The images in the fourth column come from different subjects due to a technical problem during the first rNOE data acquisition.)</figcaption></figure>

and the improved $B_1^+$ robustness to subject motion provides an opportunity to bring CEST MRI closer to clinical applications. To further improve $B_1^+$ homogeneity, our method can be combined with a $B_1^+$ correction strategy<sup>21</sup> requiring however additional scans, and therefore increasing the acquisition time. As an example, using a one-point $B_1^+$ correction, we obtained an average of 7% increase in intra-tissue homogeneity for the hydroxyl-weighted MTR<sub>asym</sub> maps presented in Figure 6 (see Figures S4 and S5).

We implemented our solution in a single slice, two-dimensional sequence, making the optimization on a slab possible, in order to design a more efficient saturation but our approach can also be used for three-dimensional CEST acquisitions. As the efficiency of the solution depends on the variability of $B_1^+$ profile in the optimization region, the performance can change drastically from one region of interest to another. As mentioned by Leitao et al.,<sup>28</sup> optimized pTx methods (and it is also the case of the one presented here) can greatly benefit from the development of coils with a larger number of transmission channels or increased complementarity between channels. The presented implementation takes advantage of pTx only for the CEST presaturation module but the excitation can also be performed in pTx mode in order to enhance the flip-angle homogeneity and the SNR as in Libert et al.<sup>40</sup> In vivo imaging is inevitably susceptible to subject motion, which can have deleterious effects on

CEST contrast maps.<sup>41</sup> Given the two-dimensional single slice acquisitions performed in this study, only an in-plane correction could be applied, while large, out-of-plane motions, if existent, would remain uncorrected. The implementation of a three-dimensional method, which will overcome this drawback, is underway.

This study aims to enable endogenous glucose weighted CEST imaging. While our in vivo data is supported both by in vitro and simulation results, the MTR<sub>asym</sub> maps presented reflect several CEST signals. Robust separation of different metabolic contributions remains a major challenge for CEST imaging and it is beyond the scope of this paper. The presented approach can also be used to perform dynamic glucose<sup>42,43</sup> studies. Moreover, by acquiring data only at strategically chosen frequency offsets in order to minimize the acquisition time, metabolic functional imaging studies, similar to those performed in rodents,<sup>44</sup> are conceivable.

## 6 | CONCLUSION

This work presents an optimized CEST presaturation scheme mitigating $B_{1,RMS}^+$ inhomogeneities even for high saturation-time/repetition-time ratio by taking advantage of the VOP framework to fully exploit the potential of pTx. The UPs perform much better than the CP mode, and, compared to subject specific TPs present the advantage
of offline optimization. Using UPs, the hydroxyl-weighted CEST MTR<sub>asym</sub> values obtained were, on average, four times higher and with 40% narrower distribution than those obtained with a conventional CP CEST pre saturation.

## ACKNOWLEDGMENTS

This work has received financial support from the ANR (fMETAMR project, ANR-19-CE17-0008) and Leducq Foundation (large equipment Equipement de Recherche et Plateformes Technologiques program, NEUROVASC7T project).

## ORCID

Thaddée Delebarre https://orcid.org/0000-0002-9933-5374

Vincent Gras https://orcid.org/0000-0002-4997-2738

Franck Mauconduit https://orcid.org/0000-0002-0128-061X

Alexandre Vignaud https://orcid.org/0000-0001-9203-0247

Nicolas Boulant https://orcid.org/0000-0003-2144-2484

Luisa Ciobanu https://orcid.org/0000-0001-6932-6859

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## SUPPORTING INFORMATION

Additional supporting information may be found in the online version of the article at the publisher's website.

**Figure S1.** The realistic head phantom used for in vitro experiments. (A) Photographs of the phantom, inner (left),

and outer (right) compartments. (B) MR localizer images showing the sagittal (left), coronal (middle), and axial (right) planes.

**Figure S2.** $B_{1,RMS}^{+}$ distribution obtained on the evaluation data set (13 $B_{1}^{+}$ maps independent from those used to design the universal CEST presaturation pulses) using CP vs UPs. For both strategies, the target $B_{1,RMS}^{+}$ was 1.5 μT and the other presaturation parameters were those for hydroxyl-weighted CEST.

**Figure S3.** $B_{1,RMS}^{+}$ maps for the two modes, used to acquire the datasets in Figure 6 and obtained with an UP optimized for hydroxyl-weighted CEST.

**Table S1.** (A) Average $B_{1,RMS}^{+}$ and (B) $B_{1,RMS}^{+}$ RMSE corresponding to the maps shown Figure 8A.

**Table S2.** Average (over the entire slice) MTRasym (%) values from hydroxyl, rNOE and glutamate-weighted CEST, measured at 1.25 ± 0.25 ppm, -4 ppm, and 3 ppm, respectively. The values in the table correspond to the four datasets presented in Figure 6. Glutamate-weighted CEST acquisitions were not performed in CP mode.

**Table S3.** Parameters of the UP designed for hydroxyl-weighted CEST, optimized on an axial slab positioned at $z = +15$ mm from isocenter and used for the acquisition of images in Figures 6 and 8.

**Table S4.** Parameters of the UP designed for glutamate-weighted CEST, optimized on an axial slab positioned at $z = +15$ mm from isocenter and used for the acquisition of images in Figure 9B.

**Figure S4.** Hydroxyl-weighted CEST images obtained with UP presaturation (top row) and with UP-presaturation and one-point B1 correction (bottom row). The $B_{1}$ correction was performed as in Windschuh et al.²¹

**Figure S5:** Histograms of hydroxyl-weighted MTRasym values in grey matter (GM) and white matter (WT) corresponding to the CEST maps shown in Figure S4. The standard deviations ($\sigma$) of the distributions show, on average, a 7% decrease upon $B_{1}$-correction.

**How to cite this article:** Delebarre T, Gras V, Mauconduit F, Vignaud A, Boulant N, Ciobanu L. Efficient optimization of chemical exchange saturation transfer MRI at 7 T using universal pulses and virtual observation points. *Magn Reson Med.* 2023;90:51-63. doi: 10.1002/mrm.29617