# Effect of the spin-locking B radiofrequency field strength on the signal enhancement with Magic Sandwich Echo sequence

Eloïse Mougel, Hélène Ratiney, Eric van Reeth, Kevin Tse Ve Koon, Olivier

Beuf, Denis Grenier

<figure><img src="image_1.png" /></figure>

## ► To cite this version:

Eloïse Mougel, Hélène Ratiney, Eric van Reeth, Kevin Tse Ve Koon, Olivier Beuf, et al.. Effect of the spin-locking B radiofrequency field strength on the signal enhancement with Magic Sandwich Echo sequence. Journal of Magnetic Resonance, 2025, 381, pp.107973. 10.1016/j.jmr.2025.107973. hal-05352136

HAL Id: hal-05352136

https://hal.science/hal-05352136v1

Submitted on 19 Nov 2025

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Distributed under a Creative Commons Attribution 4.0 International License
1 **Effect of the spin-locking B₁ radiofrequency field strength on the signal**
2 enhancement with Magic Sandwich Echo sequence

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4 Eloïse MOUGEL¹, Hélène RATINEY¹*, Eric VAN REETH¹, Kevin TSE VE KOON¹, Olivier

5 BEUF¹, Denis GRENIER¹.

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7 ¹INSA Lyon, Université Claude Bernard Lyon 1, CNRS, Inserm, CREATIS UMR 5220, U1294,

8 F-69621, LYON, France

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12 **e-mail address, corresponding author:**

13 helene.ratiney@creatis.insa-lyon.fr*

14 eloisemougel@gmail.com

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16 **Present/permanent address:**

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18 CREATIS- CNRS UMR 5220, Inserm U1294

19 INSA Lyon, Bâtiment Léonard de Vinci (401)

20 21 avenue Jean Capelle

21 69621 Villeurbanne Cedex, FRANCE.

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**Abstract**

Contrast methods based on dipolar coupling are of great interest for imaging tissues containing large macromolecules, such as myelin. Most of these conventional methods deal with various “relaxation” phenomena influenced by dipolar coupling such as inhomogeneous magnetization transfer. In this work we propose to investigate the benefit of using another method, called magic sandwich echo (MSE), which allows direct modulation of the dipolar coupling ($H_d$) as described by the work of Matsui and the Redfield theory. To verify the potential of this method in biological tissue, we first proposed an experimental model for dipolar coupling modulation in an *ex vivo* tendon (as a highly anisotropic tissue) and used it to prove $H_d$ modulation by varying the amplitude of the spin-lock radiofrequency pulse of this sequence. We then proposed a potential *in vivo* usable metric, directly related to the residual amount of $H_d$, which we called MaSteR for Magic sandwich echo to Stimulated echo ratio, as it is based on the ratio of the signal acquired with the MSE sequence and a stimulated echo sequence. First, we show that the higher $H_d$, the more effective the spin-lock radiofrequency amplitude. We measured with MaSteR that the change in radiofrequency amplitude allowed us to distinguish between different $H_d$ intensities, with a greater MaSteR when $H_d$ is higher.

**Keywords**

magic angle, magic sandwich echo sequence, dipolar interaction, stimulated echo sequence, binomial RF pulse.

**Highlights**

* Experimental design to modulate $H_d$ effect in *ex vivo* tissue.

* Validation of $H_d$ modulation by adjusting the amplitude of the spin-lock radiofrequency pulse in the MSE sequence.

* New metric directly related to $H_d$ modulation, usable *in vivo* to determine $H_d$ amplitude.
# 1. Introduction

Dipolar interaction is strongly correlated with the rotational mobility of molecules. In the case of macromolecules, their size substantially restricts this rotational mobility and in the case of small molecules like water, their movement is limited by their macromolecular environment. Several $^1$H contrast imaging methods based on the observation of the residual dipolar interaction have been used in different biological tissue [1–4]. Particularly, recent applications of inhomogeneous magnetization transfer (ihMT) have shown promising results as imaging biomarkers for the diagnosis in multiple sclerosis [5]. This method relies on magnetization transfer and isolates dipolar order arising from non-averaged dipolar interactions. IhMT shows strong specificity for myelin [6,7] and its alteration [8,9]. Additionally a recent paper has shown that ihMT could also be applied on tendon and other material [10]. In contrast, Magic Sandwich Echo method (MSE) has formerly been designed for solid state imaging [11], and thus it has mainly been applied to “solid”-like tissues such as tendon, cartilage and muscle, and has seldom been used in the brain. These two methods differ in numerous aspects, but they are related. MSE modulates with an RF spin lock the dipolar Hamiltonian ($H_d$) that is directly responsible for dipolar coupling in the tissue, whereas ihMT is based on a magnetization transfer property, i.e. relaxation. IhMT contrast is influenced by dipolar order relaxation, whereas MSE contrast is driven by the dipolar coupling between the spins and therefore both are related to dipolar order. Here we hypothesize MSE could be useful in estimating the underlying pool of dipolar interactions. Additionally, this paper contributes to further investigations into the MSE method, aiming to enhance its suitability as a diagnostic tool [12,13]. Indeed, the implementation of this MSE sequence on an MRI scanner remains a challenge, as it requires careful management of the radiofrequency field strength of the spin-lock ($B_{1sl}$).

As described by Redfield [14], MSE method relies on the application of a strong $B_{1sl}$ which will imposes a modulation of the dipolar Hamiltonian in the double tilted rotary frame (DTRF), that we call in the following $B_{1sl}$-induced modulation of $H_d$. When the intensity of the RF field becomes greater than the intensity of dipolar field as demonstrated by Redfield [14], the value of the residual dipolar Hamiltonian in the DTRF, $H_{dDTR}$, can be arbitrarily set regarding $B_{1sl}$ amplitude between -1/2 and 1 times its value in the classic rotating frame (CRF) $H_d$ [15], as we will more detailed in the theoretical consideration §2.2 of the present manuscript.
Judicious alternation of the signal evolution in the CRF and DTRF allows the generation of an echo free of dipolar interaction. The most classical use of this property was shown in Matsui's work [11], by applying to the system a spin-lock (Fig.1.A) of sufficient amplitude to compete with the coherence loss mechanism in the DTRF [16] and set $H_{dDTR}$ to $-H_d/2$ for a $2\tau$ duration. $\tau$ duration is calculated from the free evolution in the CRF. At the echo time ($3\tau$), the total dipolar interaction effect then verifies $\tau \times H_d + 2\tau (-\frac{H_d}{2}) = 0$. If $B_{1sl}$-induced modulation is sufficient to reach $-H_d/2$ [11], otherwise a residual dipolar interaction still remains. As demonstrated by Redfield, when $B_{1sl}$ is higher than the spin-spin interaction, the RF can modulate the dipolar interaction. This statement can only be verified empirically on such complex systems as are biological tissues where $H_d$ intensity is unknown. It is therefore necessary to carefully study the influence of $B_{1sl}$ on modulating $H_d$ and the subsequent echo amplitude and to interpret the contrast provided by this sequence. Regatte et al. [13] have studied in depth the effect of $B_{1sl}$ on apparent relaxation in the MSE sequence. To go further, we suggest a method for investigating the effect of $B_{1sl}$ amplitude on $H_d$ to highlight the correlation between $H_d$ and the contrast provided by this sequence for a fixed echo time ($3\tau$). To quantify this process, we use the classic stimulated echo sequence (STE) [17] as a reference because it is formally a MSE sequence with $B_{1sl} = 0$ $\mu$T.

The contributions of this paper focus on two key elements: the implementation of an experimental setup capable of adjusting the magnitude of the residual $H_d$ by modifying the sample orientation (angle-induced modulation of $H_d$) and the development of methods for evaluating the signal modulation associated with $B_{1sl}$-induced modulation of $H_d$. From this experimental setup, we studied the impact of the $B_{1sl}$ amplitude on the echo amplitude (and thus on the reduction of the dipolar coupling effects). We established experimental limits on the utilization of the MSE sequence. We finally introduced and studied a straightforward metric for echo amplitude modulation, referred to as MaSteR which stands for the ratio between the signal intensity of MSE and STE acquisition, providing insights into the extent of $H_d$.

## 2. Theoretical considerations on $H_d$ modulations

### 2.1. Angle-induced modulation of $H_d$
According to the literature, dipolar hamiltonien is described by this equation:

$$H_d \approx d/2 (1 - 3 \cos^2(\theta)) \quad \text{eq.1}$$

where d is the dipole-dipole coupling constant and θ is the angle between the dipole and the main axis (along B₀). The magnitude of H₉ is especially influenced by the orientation relative to B₀ (θ). A tendon sample, being at the same time rich in macromolecular content and very anisotropic, is a good candidate to obtain different H₉ regimes of its water content just by a physical rotation of the sample. Hence, according to eq.1, we proposed to modulate the macroscopic dipolar interaction present in the tissue between -d and d/2 just by changing the orientation of the sample with respect to B₀. An angle close to the magic angle (54.7°) and 128° would give a minimal H₉ contribution (H₀MA), while other orientations would result in a significant H₉ effect.

## 2.2. B₁sl-induced modulation of H₉

The role of B₁sl in MSE was theorized first by Rhim [15]. It was then exploited by Matsui [11], with the introduction of this new sequence called magic sandwich echo based on the Takegoshi's works [18]. In this sequence, they introduced the use of a spin lock, which should modulate H₉, as it is stated in Redfield's theory [14]. If B₁ >> ΔB₀, H₀DTR is [15]:

$$H_{0DTR} = \frac{1}{2}(3 \cos^2(\theta_{eff}) - 1) H_9 \quad \text{eq.2,}$$

which means that H₀DTR can be modulated between +H₉ and -H₉/2 in the double tilted rotating frame as a function of effective angle Θₐff, describing inclination of the effective field with respect to the B₀ field.

This property is then exploited by using a B₁sl with a specific timing in the MSE sequence. We postulate that for a given value of B₁sl, we will have three different scenarios depending on the intensity of dipolar interaction acting on water molecules near macromolecules:

i) If there is no dipolar interaction (or negligible effect), B₁sl has no effect and the acquired signal is not increased by an MSE sequence compared with an STE sequence (i.e. a MSE sequence with B₁sl = 0 μT).

ii) If the dipolar interaction has an effect but is weaker than B₁sl, B₁sl modulates H₉ and eventually, if B₁sl is high enough, cancels H₉ and the signal might be enhanced relative to an STE sequence.
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iii) If the dipolar interaction is stronger than $B_{1sl}$, $B_{1sl}$ fails to modulate $H_d$. $H_d$ effect remains and the signal is not enhanced in an MSE sequence compared to an STE sequence.

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# 3. Material and Methods

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## 3.1. Experimental setup and analysis to identify different $H_d$ regimes

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### 3.1.1 Experimental setup and sample preparation

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All measurements were performed with a 4.7 T Oxford Magnet coupled to Bruker AV-1 hardware on ex vivo-tendon samples. A 10 × 8 × 8-mm³ frozen sample of beef knee tendon was cut and immersed in saline at room temperature for 1 hour to reach 20°C before starting the experiment. Sample was then placed in a device (Fig.1.C) that allowed rotation around an axis perpendicular to the $B_0$ axis thus changing $\theta$. In the first configuration, the tendon fiber was orientated along $B_0$. Angle of the sample was then manually increased by ~15° steps between each MR acquisition, providing measurements with different amounts of $H_d$ (§2.1). Acquisitions were done with RapidBioMed quadrature TX/RX 32 mm RF coil.

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### 3.1.2. Sequence design and MR acquisition protocol for validation of experimental setup

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First automatic Bruker adjustment was performed. Then, for each orientation of the tendon sample, a FLASH (gradient echo) sequence was used to measure the relative angle $\theta$ to the first orientation of the sample. For each orientation, the angle is then a posteriori evaluated using ImageJ software. A non-localized spectroscopic stimulated echo sequence (STE) (Fig.1.B) was used to measure the $H_d$ modulation on the stimulated echo. This sequence contained three identical non-selective gaussian-$\pi$/2 pulses of 0.34 ms and 8050-Hz bandwidth. $3\tau$ parameter was set to 35 ms, such as $\tau = 11.67$ ms, we also tested two other $3\tau$ duration (77 and 144 ms) (Appendix A1). Signal was acquired immediately after the last RF pulse for 150 ms with a sampling rate of 4 kHz and no spoiler gradient was used during the mixing time, and one average. The duration between two acquisitions was set to 6 s.

### 3.1.3 Fitting strategy

According to the STE coherence pathway, as no spoiler was applied during mixing time, temporal signal provided 3 echoes (Fig.2). Plotting maxima of the first two echoes as a function of $\theta$ angle are sufficient to assess the $H_d$ modulation (between -d and -d/2, according to eq.1).
Indeed, echo 1 amplitude was influenced by the dipolar interaction, as it came from the spin echo pattern, so echo 1 amplitude was sufficient to extract the $|H_d|$ modulation. In particular, we identified that the signal amplitude was influenced by magnetic susceptibility effects when the sample was rotated. Hence, a model taking into account the dipolar interaction and magnetic susceptibility effect was used to fit the modulation of the echo 1 signal:

$$ \text{Model fit}_{dip+\chi} = C + D \times \left( 1 - \left| \frac{(1-3 \cos^2((\theta-A)\times\frac{\pi}{180}))}{2} \right| \right) - B \times \left( (\theta-A) \times \frac{\pi}{180} - \frac{\pi}{2} \right)^2 \quad \text{eq.3} $$

with the constants C fixing a nominal signal level, D scaling the $H_d$ component, B scaling the susceptibility component (the choice of the polynomial function is presented in Appendix A2) and A being a correcting angle (i.e., accounting for the uncertainty in the initial absolute angle of sample orientation with respect to $B_0$). For comparison, a model containing only the dipolar part is also applied to the first echo.

According to MacDonald's work [19], echo 2 is a solid echo through the third $\pi/2$ and is therefore free of dipolar interaction; this echo amplitude could therefore be used as a control for echo amplitude modulation by the dipolar interaction. Thus, eq.3 is also applied for fitting echo 2 data for verification of the absence of modulation.

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## 3.2. MSE sequence implementation and spin lock effect

### 3.2.1. MSE Sequence implementation and MR protocol

In this section, the non-localized spectroscopic version of the MSE was used to focus on the link between $B_{1sl}$ and the dipolar interaction. Hence no spatial encoding gradient was used in this sequence, providing a sequence closer to the original NMR version. The three non-selective gaussian- $\pi/2$ pulses were parameterized with a duration of 0.34 ms and a large excitation bandwidth of 8050 Hz, which allows to reduce the duration between the second $\pi/2$ pulse maximum and the beginning of the spin-lock RF pulse. A first order binomial shape (corresponding to a pulse of constant magnitude and a phase inversion in the middle of its duration) was used for the spin-lock pulse (Fig.1.A). Finally, the acquisition started immediately after the last radiofrequency $\pi/2$ pulse of the MSE with the same characteristics as in the previous section (150 ms with a 4kHz sampling rate).

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One series of acquisition on the same ex vivo tendon sample (see section 3.1.1), consisted of eight different $B_{1sl}$ amplitudes (0.1, 1, 7, 24, 53, 90, 131, 167 µT) was executed

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just after the STE acquisition for each angle and for each orientation (section 2.2.1). Other sequence parameters were the same as in section 3.1.2: a $3\tau = 35$ ms echo time and one average. The delay between two acquisitions was set to 6 s. Note that when $B_{1sl} = 0$ µT, the sequence is totally equivalent to the STE acquisition.

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### 3.2.2. Analysis of the effectiveness of $B_{1sl}$-induced $H_d$ modulation

#### 3.2.2.1. Measuring MSE signal modulation with regard to sample orientation

The data measured with this protocol were analyzed in two different ways to assess the efficiency of $B_{1sl}$ to attenuate the dipolar interaction in the echo.

Firstly, according to case (i) of §2.2, if the effect of $H_d$ is minimal, $B_{1sl}$ has no effect and, therefore, the amplitude of the echo measured with the minimal effect of the dipolar interaction, $H_{dMA}$ (see §2.1), can be used as a reference to determine the effectiveness of $B_{1sl}$. The ratio of the amplitudes defined by $\text{SMSE}(H_d, B_{1sl})/\text{SMSE}(H_{dMA}, B_{1sl})$ is directly related to the intensity of the residual $H_d$ and therefore directly related to the efficiency of $B_{1sl}$ in removing $H_d$. With a very low residual $H_d$ (a complete cancellation of the effect of the $H_d$) we should find a ratio equal to 1. This corresponds to an intensity of $B_{1sl}$ sufficient to cancel out the $H_d$ (case (ii) in §2.2). Thus, by rotating the sample, it is possible to study the effectiveness of $B_{1sl}$ in suppressing $H_d$. This allows determining the minimum $B_{1sl}$ to begin modulating $H_d$ as well as the $B_{1sl}$ required to cancel $H_d$. However, this method of determining the efficiency of $B_{1sl}$ in suppressing $H_d$ cannot be used in vivo, as there is no true way of rotating the subject relative to $B_0$.

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#### 3.2.2.2. MSE signal modulation for a specific spin lock intensity: MaSteR definition

To go further, we determine a protocol to estimate the $B_{1sl}$ efficiency in vivo: As noted above, the stimulated echo sequence is strictly equivalent to our sequence when $B_{1sl} = 0$ µT (i.e. with no $B_{1sl}$-induced modulation of $H_d$) and as such it appears as a good reference (Fig.1.B) for the same orientation $\theta$. One can hence estimate the MSE/STE signal relative change ratio (MaSteR) which is correlated to the effect of $B_{1sl}$ on the echo amplitude:

$$MaSteR(3\tau) = (S_{MSE}(3\tau) - S_{STE}(3\tau))/S_{STE}(3\tau) \quad \text{eq.4}$$

with $S_{MSE}$ the signal obtained with the MSE sequence at $3\tau$, and $S_{STE}$ the signal obtained with the MSE sequence at $3\tau$ when $B_{1sl} = 0$ µT.

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Behavior of MaSteR can be interpreted according to the three scenarios presented in §2.2:
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i) If there is no $H_d$, MaSteR should be close to 0 and constant by increasing $B_{1sl}$, as SMSE should be equivalent to $S_{STE}$.

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ii) If $H_d$ is weaker than $B_{1sl}$, $H_{dDTR}$ should be modulated from $+H_d$ to $-1/2H_d$ by increasing $B_{1sl}$.

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For lower $B_{1sl}$, modulating $H_d$ will have a cumulative effect on the echo amplitude, resulting in a smaller signal with the MSE sequence than with the STE sequence. So, when $B_{1sl}$ starts modulating $H_d$, $S_{MSE}$ should be much smaller than $S_{STE}$, and thus MaSteR should be negative.

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Then increasing $B_{1sl}$ should change $H_{dDTR}$ from $+H_d$ to $-1/2H_d$, and thus so gradually reduce the effect of $H_d$ in $S_{MSE}$, so $S_{MSE}$ should increase and so should MaSteR. As long as $B_{1sl}$ does not modulate $H_d$ to negative value, $S_{MSE}$ should be less than $S_{STE}$ and MaSteR should therefore be negative. When $B_{1sl}$ is sufficient to start reversing the effect of $H_d$ in echo, MaSteR should become positive.

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iii) If $H_d$ is stronger than $B_{1sl}$, $B_{1sl}$ is unable to modulate $H_d$, and so SMSE should remain unchanged and equal to $S_{STE}$, thus MaSteR should be constant and equal to 0.

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# 4. Results

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## 4.1. Validation of the experimental setup to obtain different $H_d$ in the same sample of tendon

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The model given by eq.3 fits the amplitude modulation of echo 1 well, while it does not really fit the amplitude modulation of echo 2 (Fig.3). On the one hand, the dipolar interaction strongly dominates the modulations of the echo 1, as expected. On the other hand, the susceptibility contributes slightly to the modulation, and it is much smaller than the dipolar contribution, with an effect at least 5-fold smaller. The amplitude of echo 2 remains slightly modulated by $H_d$ (Fig.3.B) for $3\tau = 35$ ms, however this modulation is almost negligible at higher $3\tau$ (Appendix A1). This weak modulation for $3\tau = 35$ ms can be explained by the overlapping of the residual signal of echo 1 under echo 2 for $3\tau = 35$ ms. Thus, the modulation of $H_d$ mainly affects echo 1 and we can therefore use the modulation of this first echo to track the $H_d$ effect.

These observations validate this experimental setup of rotating the tendon sample to obtain different $H_d$ regimes. Furthermore, this model shows that the angles for each orientation are slightly off from the *a priori* estimated angle.
Based on the modulation of echo 1 and regarding these fitting (Fig.3.A), it is possible to identify at least two $H_d$ regimes: a weak $H_d$ regime, where echo has the maximum amplitude, and a strong $H_d$ regime, where echo has the lowest amplitude. The minimum echo modulation corresponds to the weak $H_d$ regime, and the higher modulation is associated to the strong $H_d$ regime. Hence three different orientations of the sample were identified for the weak $H_d$ group and seven orientations for the strong $H_d$ group (respectively points in blue and green in Fig.3.A). In addition, we can identify the orientation giving the lowest modulation (here the third angle ~50°). This angle is close to the so called “magic angle”, which we will take in the next section (§4.2.) as a reference for the minimal effect of dipolar interaction and which we will call $H_{dMA}$. In the next, we will use these different $H_d$ regimes to evaluate the effect of the $B_l$ spin lock field strength by calculating the MaSteR (§4.3.), which would be useful for in vivo measurements.

## 4.2. Echo amplitude evolution in MSE for increasing $B_{1sl}$ as reference measurement

In agreement with observation with STE sequence (corresponding to $B_{1sl} = 0$ µT), three echoes were visualized for the smallest $B_{1sl}$ (Fig.4), whereas only the echo 1 should remain in MSE sequence. This situation arises for a $B_{1sl} > 24$ µT and the expected signal increase with $B_{1sl}$ can be observed after a transition. Hence, we first observed a signal amplitude decrease when $B_{1sl}$ increases from 0 to 24 µT, before obtaining an increase of the echo 1 signal amplitude when $B_{1sl}$ continued to increase from 24 µT to 167 µT (according to case (ii) §2.2 the $S_{MSE}$ increases with $B_{1sl}$, when $B_{1sl}$ is sufficient high to modulate $H_d$). For $B_{1sl} < 24$ µT, the amplitude of echo 1 seemed to decrease as the other two echoes moved towards the echo 1 (Fig.4), due to a resulting phase mixing between echoes. When echoes 2 and 3 had completely fused with echo 1, the amplitude of echo 1 started to grow because $B_{1sl}$ had become high enough to start modulating $H_d$. Hence in Fig.5 we observed the $S_{MSE}/S_{MSE}(H_{dMA}=0)$ ratio increase as $B_{1sl}$ increases, and this $B_{1sl}$-induced modulation of $H_d$ starts with $H_{dDTR} = +H_d$ and goes to $H_{dDTR} = -H_d/2$. Nevertheless, in Fig.5, we can note a strong hardware limitation. Even for the largest $B_{1sl}$ amplitude achievable with our RF system, the echo signal intensity never reached the signal for zero $H_d$ (and $S_{MSE}/S_{MSE}(H_{dMA}=0)$ remained less than 1), meaning that the dipolar interaction present in the sample was too strong to be canceled by the RF available.
### 4.3. Effect of $B_{1sl}$ on the MaSteR

In line with the previous paragraph, we found similar behavior with MaSteR (Fig.6), namely a decrease in MaSteR followed by an increase in MaSteR for each $H_d$ regime. According to case (ii) in §3.2.2.2., for a $B_{1sl}$ just above $H_d$, $B_{1sl}$-induced $H_d$ modulation begins with $H_{dDTR} = +H_d$; consequently, this cumulative effect in the $H_d$ residual gives the $H_d$ residual higher than without $B_{1sl}$ and a $S_{MSE}$ much lower than $S_{STE}$. MaSteR thus decreases and becomes negative. While the theory of MaSteR in case (ii) §3.2.2.2 indicates that MaSteR should be negative because $S_{MSE}$ is lower than $S_{STE}$ when $B_{1sl}$ starts modulating $H_d$, it does not explain what exactly happens during the decrease before $B_{1sl}$ starts modulating $H_d$. Indeed according to case (iii) in §3.2.2.2, when $B_{1sl}$ is not strong enough relative to $H_d$, MaSteR should remain constant, but a jump between $S_{MSE} = S_{STE}$ amplitude and a lower $S_{MSE}$ amplitude when $B_{1sl}$-induced $H_d$ modulation begins is not expected in NMR physics. We therefore expect instead a continuous transition between these two states. The observations made in Fig.4, with the fusion of echoes occurring during this transition regime, provide a clue for interpreting the decrease in MaSteR. By continuing to increase $B_{1sl}$, $B_{1sl}$-induced $H_d$ modulation goes towards $H_{dDTR} = -H_d/2$, and MaSteR therefore increases as expected since $H_d$ residual is getting smaller and smaller (case (ii) in §3.2.2.2). However, as $B_{1sl}$ is restricted, the highest $B_{1sl}$ gives incomplete cancellation of $H_d$ residual. As MaSteR $\le 0$ even for the highest $B_{1sl}$, we have assessed that $S_{MSE}$ is always less than or equal to $S_{STE}$, otherwise MaSteR should be positive. This means that even the highest $B_{1sl}$ is unable to reverse the sign of $H_d$. As MaSteR is close to 0, $B_{1sl}$-induced $H_d$ modulation results in $H_d \sim 0$ for the highest $B_{1sl}$, which corresponds to a residual $H_d$ identical to the $H_d$ residual without $B_{1sl}$, so $S_{MSE} = S_{STE}$.

We identified two different behaviors, function of the $H_d$ strength (Fig.6A. and Fig.6.B. for strong and weak $H_d$ respectively). We observed that the required amplitude of $B_{1sl}$ needed to observe a MaSteR increase is approximately 1 µT when $H_d$ is weak (Fig.6.B) and greater than 7 µT for higher $H_d$ value (Fig.6A). This is in line with Redfield's theory, which indicates that $B_{1sl}$-induced $H_d$ modulation starts when $B_{1sl} \gg H_d$. When $H_d$ is weak, minimal $B_{1sl}$ required to modulate $H_d$ is lower than when $H_d$ is strong.

Finally, MaSteR seems to be a good indicator of the $H_d$ intensity. For the last five measured points (highest $B_{1sl}$), the curvature of the MaSteR plots behaved differently according
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to $H_d$ strength. For weak $H_d$, MaSteR seems to reach a maximum for the highest $B_{1sl}$ values, but
seems to continue to increase for strong $H_d$. Additionally, the average value of MaSteR over
the five highest magnitudes of $B_{1sl}$ (Fig.7) was significantly different between weak $H_d$ and
strong $H_d$ (paired t-test: t = 7.78, p<0.001, performed with JASP software v.2). Ultimately,
when $B_{1sl}$ was high enough, the MaSteR reflected the $H_d$ strength. Thus, in the same way the
ratio $S_{MSE}/S_{MSE}(H_{dMA} \sim 0)$ did, MaSteR appears to be an indicator of $H_d$ removal with the
advantage of being able to be used without angle a priori on $H_{dMA} \sim 0$. MaSteR would therefore
be more generic than other ratios to assess $B_{1sl}$ at a fixed echo time (3τ), especially in vivo.

# 5. Discussion

## 5.1. Toward the implementation for imaging using MaSteR

While Matsui's MSE sequence was originally designed so that the $B_{1sl}$ amplitude would
be intense enough to fully set $H_d$ residual to 0, we have shown empirically that even using
smaller values of $B_{1sl}$, the MSE sequence can provide a useful information reflecting $H_d$
intensity and can be available through the MaSteR. In the original implementation of this
sequence, the biggest issue might be the SAR limitation, due to the high $B_{1sl}$ required to fully
refocus $H_d$. However, MaSteR could provide an alternative of SAR limit as it can provide
information on $H_d$ with a smaller $B_{1sl}$. It will be interesting for further application, especially
on clinical MRI, to perform SAR simulation.

Although this is not specifically highlighted by Regatte *et al.* [13] as they do not discuss
the $B_{1sl}$ threshold providing an $H_d$ modulation, their use of the MSE sequence with a relatively
low $B_{1sl}$ gave interesting results, on tendon. Indeed, in their study, they also acquired data at
4.7T, on tendon, but they applied a $B_{1sl}$ up to ~43 µT which, for our setup, seemed just enough
to start observing signal modulation on the tendon, but not sufficient to completely remove $H_d$
effect, even if $H_d$ was low. Interestingly, under these conditions, they observed relaxation time
differences raising the contrast between area with fast and slow relaxation. In line with our
present results, contrast generated with MSE sequence could also be seen in terms of a strong
$H_d$ and weak $H_d$, respectively. Ultimately, comparison with this other study confirmed that
MSE, in an imaging version with weak $B_{1sl}$, could discriminate between strong $H_d$ and weak $H_d$
in the same sample. However, previous approaches differ radically from the present study, as
they focused on evaluating effect of $B_{1sl}$ for different 3τ durations, required to measure
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relaxation maps. Here we go a step further and focus on the specific $H_d$ modulation in MSE signal at a fixed $3\tau$ duration. Our results illustrate how MaSteR is recommended for this purpose and provides a contrast proportional to $H_d$ in this context.

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The ability of MaSteR to discriminate $H_d$ modulation only, free from other interactions therefore shows that MaSteR could be an interesting tool to visualize $H_d$ intensity, in a medical context. Following some calibration and adapting the sequence for imaging or localized spectroscopy, it might provide information on macromolecular content of specific tissues like myelin as an example. Particularly, the transition from an ineffective $B_{1sl}$ to an effective one could be a “signature” of dipolar coupled macromolecular content. However, for now it appears more of a support tool for other methods than a directly applicable *in vivo* method, and further investigation would be required to evaluate the gain over other reference methods.

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## 5.2. MaSteR as support for other methods to inform on $H_d$

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MaSteR appears then to be an original method providing information on $H_d$ strength in tissues, and the only method that directly correlated with $H_d$ intensity. Another method, such as ihMT [5], is based on magnetization transfer between different pools. This indirect method is influenced by dipolar order via $T_{1D}$ relaxation, by the size of the dipolar reservoir and by the frequency offset, and the physical origin of the contrast remains partially understood [20,21]. Hence, a comparison between MaSteR and ihMT contrasts, could be carried out to study the correlation between $T_{1D}$ and $H_d$. Such comparison could be done in preclinical study as SAR is less of a limit than in a clinical study.

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## 6. Conclusion

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In this original work, we showed that the $B_{1sl}$ magnitude is a crucial parameter when using the MSE sequence, which should be mentioned when this sequence is used. We introduced the MaSteR parameter as a new technique to identify the minimum $B_{1sl}$ magnitude to start modulating $H_d$. As MaSteR appears an effective parameter to discriminate between different amounts of $H_d$, it could be then further used to measure macromolecule contents *in vivo*.

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Figures:

<figure><img src="image_3.png" /></figure>

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**Figure 1:** (2 columns) **Chronogram of MSE and STE sequences and setup used for these experiments.** A. Spectroscopic MSE sequence: this sequence is defined with the timing $\tau$, with the $\pi/2$ pulse phases $\phi1, \phi2, \phi4=x$ and $\phi3=y$. An echo is created at time $3\tau$. B. STE Sequence: this sequence is formally equivalent to the MSE sequence above with the $B_{1sl}$ amplitude set to zero. C. Setup used to rotate the tendon sample. Angle $\theta$ corresponds to the rotation of the sample from $B_0$ axis.

<figure><img src="image_4.png" /></figure>

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**Figure 2:** (1 column) **Absolute value of the signal acquired with the STE sequence** for two different sample's angles (relative to the original orientation aligned along $B_0$) corresponding to two different $H_d$ amplitudes. We can identify the first two echoes expected in this temporal window. Echo 1 is the stimulated echo and echo 2 is a simple solid echo, respectively.
<figure><img src="image_5.png" /></figure>

<table><caption>**Figure 3:** (2 columns) Amplitude of the first and second echo signal acquired with STE sequence as a function of the relative orientation of the sample with respect to $B_0$ for $3\tau = 35$ ms. A. First echo data are plotted in green dot. Red dotted line is the fit using the model containing the dipolar and susceptibility effects described in eq.3. The yellow dashed line represents the fit with only $H_d$. Data for the echo 2 (solid echo) (blue square dots) is plotted as a function of the relative angle with respect to the initial position (along $B_0$). Fitting of the second echo amplitude with eq.3 is plotted on the graph (green dashed line) and gives a coefficient D close to 0. Based on the Dip + χ model and signal modulation, strong $H_d$ and weak $H_d$ regimes are determined *a posteriori*. B. Zoom on the echo 2 data.</caption><thead><tr><th rowspan="2">Echoes<br>Model</th><th colspan="2">Echo 1</th><th colspan="2">Echo 2</th></tr><tr><th>Dip + χ</th><th>Dip</th><th>Dip + χ</th><th>Dip + χ</th></tr></thead><tbody><tr><td>A (angle correction)</td><td>-9.65</td><td>-10.90</td><td>-10.73</td><td>-10.73</td></tr><tr><td>B (susceptibility)</td><td>1.32<sup>E4</sup></td><td>-</td><td>1.38<sup>E3</sup></td><td>1.38<sup>E3</sup></td></tr><tr><td>C (nominal signal)</td><td>7.80<sup>E4</sup></td><td>9.74<sup>E4</sup></td><td>1.90<sup>E4</sup></td><td>1.90<sup>E4</sup></td></tr><tr><td>D (dipolar)</td><td>6.95<sup>E4</sup></td><td>5.05<sup>E4</sup></td><td>5.91<sup>E3</sup></td><td>5.91<sup>E3</sup></td></tr></tbody></table>
<figure><img src="image_6.png" /><figcaption>Figure 4: (1.5 column) Amplitude of the signal of tendon for $3\tau = 35$ ms and a strong $H_d$ (corresponding to an adjusted angle $\theta \sim 10^\circ$ relative to the original orientation aligned along $B_0$) with different $B_{1sl}$ field strength. The signal acquisition starts immediately after the last $\pi/2$ RF using a MSE sequence with different magnitude of spinlock. When $B_{1sl}$ is zero, the first stimulated and second solid echoes are refocused. When $B_{1sl}$ increases, the second echo gradually disappears.</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>Figure 5: (1 column) Effect of $B_{1sl}$ amplitude on echo MSE amplitude normalized by the echo amplitude obtained when $H_{dMA}$ is close to 0 (= the fourth angle, indicated by a star) as a function of the sample's angle. The ratio increases for each orientation associated with high $H_d$ as $B_{1sl}$ increases. Nevertheless, for the largest value of $B_{1sl}$ accessible (167 µT on our coil/system) we observe that the amplitude of the echo strongly affected by high $H_d$ values does</figcaption></figure>
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not reach 1, which means that the B<sub>Imax</sub> is not yet strong enough to completely remove the dipolar interaction in this tendon sample.

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<figure><img src="image_8.png" /></figure>

<figure><img src="image_9.png" /></figure>

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**Figure 6:** (2 columns) **Behavior of the MaSteR function of B<sub>Isl</sub> intensity** for different sample orientation (adjusted angle, relative to the original orientation aligned along *B*₀) at 3τ = 35ms. MaSteR shows the capacity of MSE to remove dipolar interaction as a function of *B*<sub>Isl</sub>. The ability of the spin lock to modulate *H*<sub>d</sub> differs as a function of *H*<sub>d</sub> intensity. Panels A show a specific MaSteR behavior for strong *H*<sub>d</sub> plotted as a function of *B*<sub>1</sub> in a logarithmic axis. Panels B show specific MaSteR behavior for weak *H*<sub>d</sub> plotted as a function of *B*<sub>1</sub> amplitude expressed in a logarithmic axis.

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<figure><img src="image_10.png" /></figure>

<figure><img src="image_11.png" /></figure>

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**Figure 7:** (2 columns) **Average of MaSteR over the 5 highest values of B<sub>Isl</sub> and the standard error of the mean over the 5 highest values with varying orientation of the sample (A) and mean between the two groups (6 strong *H*<sub>d</sub> and 3 weak *H*<sub>d</sub>) (B).** MaSteR is correlated to the absolute

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$H_d$ magnitude. Weak and strong $H_d$ are represented in blue and green, respectively. Two groups are significantly different according to a two-sample t-test ($t = 7.78$, $p<0.001$).

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## Appendix

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### Appendix A1: comparison of different model to fit to the signal intensity in the experimental setup

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For comparison of the dipolar modulation, we acquired data for two other echo times.

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We note no modulation of echo 2 as expected for $3\tau = 77$ and 144 ms. (Fig.A1.1).

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<figure><img src="image_12.png" /></figure>

<figure><img src="image_13.png" /></figure>

<table><thead><tr><th rowspan="2">Echoes<br>Model</th><th colspan="2">Echo 1</th><th colspan="2">Echo 2</th></tr><tr><th>Dip + χ</th><th>Dip</th><th>Dip + χ</th><th>Dip</th></tr></thead><tbody><tr><td>A</td><td>-9.85</td><td>-11.59</td><td>-18.54</td><td>-19.59</td></tr><tr><td>B</td><td>6.07<sup>£3</sup></td><td>-</td><td>7.51<sup>£7</sup></td><td>7.19<sup>£8</sup></td></tr><tr><td>C</td><td>4.02<sup>£4</sup></td><td>4.90<sup>£4</sup></td><td>5.91<sup>£3</sup></td><td>1.19<sup>£3</sup></td></tr><tr><td>D</td><td>2.54<sup>£4</sup></td><td>1.71<sup>£4</sup></td><td>4.56<sup>£2</sup></td><td>1.84<sup>£2</sup></td></tr></tbody></table>

<figure><img src="image_14.png" /></figure>

<figure><img src="image_15.png" /></figure>

<table><thead><tr><th rowspan="2">Echoes<br>Model</th><th colspan="2">Echo 1</th><th colspan="2">Echo 2</th></tr><tr><th>Dip + χ</th><th>Dip</th><th>Dip + χ</th><th>Dip</th></tr></thead><tbody><tr><td>A</td><td>-12.83</td><td>-13.92</td><td>-19.59</td><td>-19.59</td></tr><tr><td>B</td><td>1.34<sup>£3</sup></td><td>-</td><td>7.19<sup>£8</sup></td><td>7.19<sup>£8</sup></td></tr><tr><td>C</td><td>2.05<sup>£4</sup></td><td>2.24<sup>£4</sup></td><td>1.19<sup>£3</sup></td><td>1.19<sup>£3</sup></td></tr><tr><td>D</td><td>5.55<sup>£3</sup></td><td>3.75<sup>£3</sup></td><td>1.84<sup>£2</sup></td><td>1.84<sup>£2</sup></td></tr></tbody></table>

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**Figure A1.1** (2 columns) Models fit to the data acquired for other echo times with STE sequence. A. data acquired for $3\tau = 77$ ms B. data acquired for $3\tau = 144$ ms. We can observe the very small dipolar modulation of Echo 2, and the poor fitting of the Dip + $\chi$ model to the echo 2 data.

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## Appendix A2: Susceptibility effect on signal as a function of the angle

Susceptibility participates in the signal modulation when the sample rotates. In the literature[22], on a cylindrical model with $B_0$ along z the susceptibility influences the field and can be decomposed in both contributions. The first acts inside the cylinder, and the field follows this expression:

$$ \vec{B}_{in}(\theta, \phi) = \begin{pmatrix} \cos(\phi) \frac{1+X}{1+\frac{X}{2}} B_0 \sin(\theta) \\ -\frac{1+X}{1+\frac{X}{2}} B_0 \sin(\theta) \sin(\phi) \\ B_0 \cos(\theta) (1+X) \end{pmatrix}, $$

with X the sample susceptibility, the angle to z and the angle around the z axis.

The second contribution operates outside the cylinder and is not influenced by the susceptibility. The field is then described by:

$$ \vec{B}_{out}(\theta, \phi) = \begin{pmatrix} B_0 \sin(\theta) \cos(\phi) + B_0 \sin(\theta) \frac{\frac{X}{2}}{1+\frac{X}{2}} \left(\frac{a}{\rho}\right)^2 (\cos(2\phi) \cos(\phi) + \sin(2\phi) \sin(\phi)) \\ -B_0 \sin(\theta) \sin(\phi) + B_0 \sin(\theta) \frac{\frac{X}{2}}{1+\frac{X}{2}} \left(\frac{a}{\rho}\right)^2 (\sin(2\phi) \cos(\phi) - \cos(2\phi) \sin(\phi)) \\ B_0 \cos(\theta) \end{pmatrix} $$

By integrating on both populations: inside (1) and outside (2), the signal is given by:

$$ s(t, \theta) = \rho_1 \int_0^{2\pi} \int_a^b e^{i2\pi(\Delta B_{in}(\theta, \phi, z))\gamma t} d\phi dz + \rho_2 \int_0^{2\pi} \int_a^b e^{i2\pi(\Delta B_{out}(\theta, \phi, z))\gamma t} d\phi dz \quad (\text{eq.A1.1}), $$

with b-a equals at the height of the considered cylinder. The results are plotted on the figure A2 with maxima software. We note that the signal value is minimal when the angle is perpendicular to $B_0$. The signal response approaches a square-like model visualized on figure A2.1.b.
<figure><img src="image_16.png" /></figure>

<figure><img src="image_17.png" /></figure>

**Figure A2.1:** (1 column) Simulation of the susceptibility effect on the signal. a. The signal is plotted using eq.A1.1 as a function of the angle θ. b. The signal is plotted using eqA1.1 as a function of the angle θ for a 3τ duration of 35ms. A quadratic function (red curve) fits well the signal modulated by the susceptibility as a function of the angle.

**Acknowledgments:** This work was performed within the framework of the LABEX PRIMES (ANR- 11-LABX-0063) of Université de Lyon. This material is based upon work done on the ISO 9001:2015 PILoT facility.

**Author contributions:** CRediT:

Conceptualization: DG, EM

Formal analysis: EM, HR

Investigation: EM

Methodology: EM, DG, HR, KTVK, EVR

Funding Acquisition: OB, DG

Resources: OB, DG

Writing – original draft: EM, DG, HR

Writing – review and editing: EM, DG, HR, KTVK, OB, EVR
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