# Quantitative muscle water T2 mapping using RF phase-modulated 3D gradient echo imaging

Eléonore Vermeulen, Pierre-yves Baudin, Marc Lapert, Benjamin Marty

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Eléonore Vermeulen, Pierre-yves Baudin, Marc Lapert, Benjamin Marty. Quantitative muscle water T2 mapping using RF phase-modulated 3D gradient echo imaging. Magnetic Resonance in Medicine, 2025, 10.1002/mrm.30545. hal-05073884

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# Quantitative muscle water T2 mapping using RF phase-modulated 3D gradient echo imaging

Eléonore Vermeulen¹, Pierre-Yves Baudin¹, Marc Lapert², and Benjamin Marty¹

¹NMR Laboratory, Neuromuscular Investigation Center, Institute of Myology, Paris, France,

²Siemens Healthcare SAS, Courbevoie, France

**Corresponding author:**

Name: Eléonore Vermeulen

Mail: e.vermeulen@institut-myologie.org

Address: Institute of Myology, Bâtiment Babinski, Groupe Hospitalier Pitié-Salpêtrière, 47-83
boulevard Vincent Auriol, 75651 Paris Cedex 13

**ORCID**

Eléonore Vermeulen: https://orcid.org/0000-0002-8030-4623

Pierre-Yves Baudin: https://orcid.org/0000-0001-8955-4648

Benjamin Marty: https://orcid.org/0000-0002-4983-647X

Word count: 5077

Keywords: MRI, muscle imaging, water T2, radiofrequency spoiling
**Purpose:** To propose a motion robust 3D sequence for water T2 (T2H2O) estimation in skeletal muscle tissues.

**Methods:** A T2H2O estimation method is proposed, using ten image volumes acquired with a partially spoiled gradient echo (pSPGR) sequence, varying the RF phase-cycling increment and prescribed flip angle. The complex signal evolution is fit with a bi-component water/fat model to extract T2H2O and account for B1 and fat fraction confounders. Accuracy and precision were evaluated using numerical simulations. Cartesian and radial implementations of the sequence were tested. In phantoms, results were compared with reference spectroscopic and multi-spin echo imaging techniques. Several in vivo experiments evaluated robustness to B1 field inhomogeneities, sensitivity to physiological and pathological variations in T2H2O on the thigh muscles.

**Results:** In phantoms, T2H2O values were highly correlated with reference spectroscopy and multi spin echo values (R² > 0.8). In vivo, T2H2O values were correlated with reference values in healthy controls (R² = 0.69) and pathological muscles (R² = 0.87) and were not affected by B1 inhomogeneities (R² = 0.06). In the tongue muscle, a significant reduction in the standard deviation of T2H2O values was observed using the radial compared to the Cartesian pSPGR sequence (-28 %).

**Conclusion:** The proposed approach provides efficient 3D T2H2O estimation in skeletal muscle, including small moving organs like the tongue. This broadens the range of accessible targets for characterizing heterogeneous impairment of muscle tissue, while retaining durations compatible with clinical research.
# 1. Introduction

Magnetic resonance imaging is a versatile non-invasive technique that can be used to monitor skeletal muscle thanks to its excellent soft tissue contrast, providing precise anatomical and structural measurements which are crucial for monitoring the natural history of neuromuscular disorders (NMD) and evaluate innovative treatments (1). Quantitative MRI (qMRI) is increasingly used as an outcome measure in clinical trials for these diseases (2,3). The intramuscular fat fraction (FF) and water-T2 relaxation time ($T_{2H2O}$) are typically measured to assess disease severity and active muscle damage, respectively (1,4–6).

Muscle microstructural changes, such as inflammation, necrosis, or edema, often precede irreversible muscle-fat replacement in many pathologies. $T_{2H2O}$ serves as a sensitive biomarker for these changes, reflecting alterations in water content, compartmentation, and mobility (7,8) and has proven effective in detecting early muscle alterations in various NMDs (3,9). Measuring global $T_2$ instead of $T_{2H2O}$ in the presence of fat can introduce bias due to differing $T_2$ values of fat and water (10), making water-fat separation crucial for accurately assessing muscle damage. Additionally, muscle alterations are unevenly distributed along the muscle length (11), which renders 3D imaging beneficial in longitudinal studies to minimize inter-scan variability compared to 2D multi-slice imaging.

Most conventional muscle qMRI methods use Cartesian k-space sampling, which is highly motion-sensitive compared to non-Cartesian encoding schemes, such as radial (10). This raises challenges in imaging muscles like swallowing muscles, which are involved in vital functions and often deteriorate in specific NMDs, such as oculopharyngeal muscular dystrophy, myotonic dystrophy, or inclusion body myositis (11,12). Therefore, developing a motion-insensitive method for 3D $T_{2H2O}$ mapping with a clinically feasible acquisition time is essential, as it could enable various applications in the field of NMDs.

Muscle water transverse relaxation time is often determined using standard 2D multi spin echo (MSE) acquisitions and single or multi-exponential fitting of the signal decay (13). Other fitting approaches use more accurate signal modeling using Bloch or extended phase-graph (EPG) simulations to overcome the inherent bias caused by B1 inhomogeneities to the transverse relaxation decay (14–16). However, high-energy deposition associated with the MSE sequence restricts its scope to 2D imaging, with limited spatial resolution that may impede longitudinal follow-up studies or the study of small muscles at 3T.

MR sequence designs relying on various steady state gradient echo (GRE) acquisitions have demonstrated their ability to produce fast 3D multi-parametric maps (17–20), making them an excellent option for fast and high-resolution qMRI of the skeletal muscles. In particular,
radiofrequency (RF) phase-modulated (or partially spoiled) GRE (pSPGR) steady state signal can be sensitized to T2 (21). This sequence uses standard RF spoiling based on a quadratic variation of the phase of the RF pulses, providing an image contrast dependent on the applied phase increment. Analytical formulas have been proposed for the signal intensity as a function of the sequence and tissue parameters (21–23). Recent Bloch simulation-based studies have shown a strong and monotonic dependence of the phase of the steady state signal on T2, with low dependence on T1 using very small RF phase increments (from 2° to 4°), enabling fast T2 mapping from a few GRE phase images (24,25). Wang et al. (25) combined this method with chemical shift-encoded acquisition to perform T2H2O measurements in the spleen. However, high B1+ heterogeneities expected at high field in the lower limbs, especially at the thighs level, could interfere with the resulting T2H2O if not accounted for, as demonstrated by Seginer et al (24), who used acquisitions at different flip angles to simultaneously retrieve T2 and B1. Quantitative imaging using configuration states (QuICS) (26,27) introduced a dictionary approach to estimate several parameters, including T2 from a series of pSPGR with different RF phase increments and flip angle, fitting the whole complex signal. However, this method does not account for the presence of fat due to muscle fatty replacement. MRI sequences designed for muscle applications typically rely on spectrally selective fat suppression to reduce the effect of fatty replacement on retrieved T2, but this approach has known limitations in completely removing the fat signal (13,28,29).

In this work, we propose a bi-component EPG dictionary approach to estimate muscle T2H2O from a series of 3D pSPGR acquisitions with different RF flip angles and phase increments, including the confounding effects of FF and B1 into the signal model. We made a series of EPG simulations of the generated steady state signal for different sequence, tissue, and experimental parameters including T2H2O, B1 and FF. After optimizing the acquisition parameters, we compared the obtained sequence with reference methods both in vitro and in vivo. Finally, we demonstrated the feasibility of high-resolution 3D T2H2O mapping in the lower limb and tongue muscles at 3.0 T, on healthy volunteers and one subject with NMD.
## 2. Methods

### 2.1. Partially spoiled gradient echo sequence

In pSPGR sequences, RF spoiling introduces a quadratic increase in the phases of consecutive RF pulses. The sequence acquisition scheme, including both Cartesian and radial acquisitions, is described in **Figure 1**. The spoiler's gradient trajectory was set to fix the spoiler's direction (in the Gx direction) and moment.

### 2.2. Numerical simulations

#### 2.2.1. EPG algorithm for bi-component signal modeling

The steady state signal of pSPGR sequence applied in mixture of water and fat protons was computed using a differentiable EPG simulation, available on github (https://github.com/py-baudin/epgpy). A 6-peak model was used for an accurate representation of the lipid signal (30), with single fat relaxation times values ($T_{2fat}$ and $T_{1fat}$) for the different components of the spectrum. The steady state signal (S) was modeled as:

$$S = wEPG(T1_{H2O}, T2_{H2O}, B0, B1, \alpha, \phi, N) + f \sum_{k=1}^{6} c_k EPG(T1_{fat}, T2_{fat}, \delta_k, B0, B1, \alpha, \phi, N)$$

with:

$f, w$: water and fat proton densities

$c_k$: relative amplitude of k-th fat peak within the fat model

$\delta_k$: frequency of k-th fat peak within the fat model

$\alpha$: nominal RF flip angle

$\phi$: RF spoiling increment

$N$: number of repetitions

$B1$: attenuation factor due to RF inhomogeneities

$B0$: static field inhomogeneities

We assessed the number of repetitions of the pSPGR scheme required to reach a steady state for various combinations of sequence and tissue parameters.
### 2.2.2. Effect of tissue parameters variations and field inhomogeneities on pSPGR steady state

To evaluate the sensitivity of pSPGR to different tissue parameters and experimental conditions, we simulated the complex steady state signal for $\alpha=15^{\circ}$ and $\phi$ evenly distributed between -15$^{\circ}$ and 15$^{\circ}$ obtained with different $T_{2H2O}$, B1, FF, $T_{1H2O}$, and B0 values. Parameters ranges were $T_{2H2O}$ between 25 and 70 ms, B1 between 0.7 and 1.3, FF between 0 and 60%, $T_{1H2O}$ between 1000 and 1500 ms, B0 between -100 and 100 Hz.

### 2.2.3. Sequence design and optimization

In order to accurately estimate $T_{2H2O}$ and distinguish its effects from potential confounding factors, such as B1 inhomogeneities and FF variations, multiple acquisition points are required. These acquisitions should ensure robust signal separation and improve the reliability of parameter estimation, particularly under varying tissue and experimental conditions. For the present proof-of-concept study, the choice was made to use 10 volumes so that acquisition time remains in the same range of the standard 2D MSE acquisitions performed in neuromuscular studies. TE and TR were set to minimum to minimize the examination time and maximize signal amplitude. The same TR and TE were used for all the acquisitions. The flip angle $\alpha$ limits were set at 5 and 35$^{\circ}$.

The sequence parameters $\phi$ and $\alpha$ of each pSPGR acquisition were optimized using the differentiable EPG operators implemented in the `epgpy` library via a Cramer-Rao lower bound (CRLB) minimization (31,32,26). The cost function (CF) was defined as the CRLB of the signal with respect to the following parameters: signal magnitude, FF, $T_{1H2O}$, B1 and $T_{2H2O}$, summed over three different B1 values (0.8-1-1.2). The CRLB provides the highest achievable precision for the estimators of the parameters and was estimated as:

$$CRLB = \mathrm{Tr}(W \cdot FIM^{-1})$$

with FIM representing the Fisher information matrix and diagonal weighting matrix $W = \text{diag}[1, 1/T_{2H2O}^2, 1/B_{1H2O}^2, 1/T_{1H2O}^2, 1/0.5^2]$ set to balance the relative CRLB of each parameter equally. FIM was computed as:

$$FIM = \frac{1}{\sigma^2} J^T J$$

where $\sigma^2$ is the variance of the Gaussian noise (we used $\sigma^2 = 1$), and $J$ is the Jacobian matrix of the signal for the parameters to estimate. The CRLB was then minimized using Sequential Least Squares Programming (SLSQP) (33) for solving nonlinear objective functions. Further theoretical details
related to the CRLB formulation and optimization strategy are provided in the supplementary materials (Supplementary material S1 and S2).

## Bi-component dictionary fitting

A bi-component dictionary searching method was used for solving the inverse problem of estimating the tissue parameters given the observed steady state signals of a series of pSPGR volumes acquired at different $\phi$ and $\alpha$. Since the acquisition parameters have been set, the expression presented in 2.1 can be expressed as follows:

$$S = \tilde{w}_{\text{EPG}}(T1_{\text{H2O}}, \tilde{T2}_{\text{H2O}}B0, \tilde{B1}_{\text{B1}}, \underline{\alpha}, \underline{\phi}, N) + f \sum_{k=1}^{6} c_k \text{EPG}(T1_{\text{fat}}, T2_{\text{fat}}, \delta_k, B0, \tilde{B1}_{\text{B1}}, \underline{\alpha}, \underline{\phi}, N)$$

where the parameters varying between acquisition points are underlined, the parameters that are estimated are marked with a tilde above, and all other parameters are fixed.

Each dictionary index (i) is associated with a pair of (T2H2O, B1) values, and constituted by two signals: a water one ($D_w^i$) which depends on T2H2O and B1, and a fat one ($D_f^i$) which depends solely on B1. The dictionary was generated for a range of different T2H2O values (from 10 to 70 ms, step size of 1 ms), B1 attenuation values (between 0.5 and 1.5, step size of 0.025). T1fat, T2fat and T1H2O were fixed to 390, 130 and 1220 ms, respectively. T1fat, and T1H2O values were fixed according to literature at 3T (34,35), while T2fat value was set according to experimental measurements performed in the subcutaneous fat of healthy volunteers (Figure S5). Images were processed voxel-wise. The complex signal evolution was fitted by an exhaustive search into the bi-component dictionary to obtain T2H2O and B1 estimates, using a phase-constrained least squares linear regression (36) for the weights of the water and fat components. The optimal parameters T2H2O, B1 and amplitudes of water and fat signals were determined by solving the following problem:

$$\operatorname{argmin}_{w,f,\varphi_0} \left\| S - [D_w^i D_f^i]^* e^{i\varphi_0} \right\|^2$$

Where S is the acquired signal at a given voxel, column vectors $D_w^i$ and $D_f^i$ are respectively the complex water and fat signals of the i-th dictionary entry, w and f the real amplitudes of water and fat signals and initial phase $\varphi_0$, a phase offset dependent on the off-resonance frequency, common to the water and fat components (36,37).
### 2.2.4. In silico evaluation: effect of input parameters on T<sub>2H2O</sub> accuracy

Numerical simulations were conducted to assess the impact of the fixed values for T<sub>2fat</sub>, T<sub>1H2O</sub>, and T<sub>1fat</sub> on the quantification of T<sub>2H2O</sub> and FF. Signals were generated with T<sub>1H2O</sub> = 1220 ms, T<sub>1fat</sub> = 390 ms; T<sub>2fat</sub> = 130 ms, B1 = 1, Δf = 0 Hz, T<sub>2H2O</sub> ranging from 20 to 70 ms and FF varying from 0.01 to 0.6. Each dataset was processed using our method with modified values for T<sub>2fat</sub>, T<sub>1H2O</sub>, and T<sub>1fat</sub>, ranging from -10 % to +10 % difference from the nominal values. Mean errors between the estimated and nominal values of T<sub>2H2O</sub> and FF were then computed for each dataset.

Numerical simulation experiments were conducted to assess the robustness of T<sub>2H2O</sub> quantification to B1 and FF changes and to demonstrate the relevance of fitting these parameters for muscle applications. The sequence was simulated for SNR ranging from 5 to 70, T<sub>2H2O</sub> from 20 to 70 ms and 4 sets of tissue parameters (B1/FF = 1/0, 1/0.2, 0.8/0, 0.8/0.2) using 10000 samples per tested signal. Three dictionary settings were tested: A) fitting T<sub>2H2O</sub> with FF fixed to 0 and B1 to 1; B) fitting FF and T<sub>2H2O</sub> with B1 fixed to 1; C) fitting FF, T<sub>2H2O</sub> and B1. The mean of absolute error on T<sub>2H2O</sub> estimation was calculated for each setting.

## 2.3. Experimental validation

### 2.3.1. Sequence implementation

Experimental data were acquired on a 3T scanner (Magnetom Prisma<sup>Fit</sup>, Siemens Healthineers, Erlangen Germany) using a flexible body matrix coil for the thighs and legs experiments, a 15-channel knee coil for the phantom experiments or a 20-channel head and neck coil for the tongue experiments.

The commercial Cartesian VIBE sequence was modified to allow flexible user control of the quadratic RF phase increment φ (resolution = 0.1°) and the moment of spoiling gradient (resolution = 1). A slice-selective excitation was used and a GRAPPA acceleration factor of 2 was applied.

For radial acquisitions, a custom 3D stack-of star radial GRE sequence was implemented in the same way. Radial data were reconstructed offline using the BART toolbox, using parallel imaging and compressed sensing reconstruction (38). A non-selective excitation was used. The golden-angle radial trajectory was undersampled using 150 radial spokes per partition.

For the VIBE based sequence, TR/TE=5.5/2.25 ms, for the radial GRE sequence, TR/TE=6.6/1.94 ms. For both sequences, a spoiling gradient was added in the Gx direction, corresponding to a 2π-dephasing of the signal.
## 2.4. Phantom evaluation

A 15-vial phantom was used to evaluate the accuracy of T<sub>2H2O</sub> measurements and their sensitivity to fat content. The phantom contained emulsions of peanut oil and water. The water phase was prepared with MnCl<sub>2</sub> diluted in a 0.9 % NaCl solution, adjusted for physiological T<sub>2</sub> values, and included 2.0 % agarose. Peanut oil was added in varying portions ranging from 0 to 40% w/w.

The reference MRS T<sub>2H2O</sub> value was determined in each vial by single-voxel spectroscopy (SVS) using the stimulated echo acquisition mode (STEAM) at 14 different TEs: [20, 27, 36, 45, 54, 63, 81, 90, 108, 135,162, 198, 243, 288] msec, with voxel size = 16 × 16 × 16 mm<sup>3</sup>, Tacq = 26 s per TE. T<sub>2H2O</sub> values were extracted by fitting the evolution of the water resonance's amplitude to an exponential model using Matlab trust-region fitting algorithm (40). The reference FF values were determined applying the 3-point Dixon method (39) to a 3D-GRE sequence with three TEs (2.75/3.95/5.95 ms).

The parameters of the pSPGR sequence were: pixel size, 0.8 × 0.8 mm²; 48 slices, slice thickness 5 mm, and the optimal φ and α as determined by the CRLB optimization. FOV, 175 × 350 mm² for Cartesian and 204 × 204 mm² for radial pSPGR sequence. The total acquisition times were 4min 40 s for Cartesian pSPGR and 7min50s for the radial pSPGR sequence.

For the imaging techniques, mean and standard deviation of T<sub>2H2O</sub> values were extracted from circular regions of interest (ROIs) drawn within each vial. For spectroscopy, fitted coefficients with 95 % confidence bounds were extracted. Pearson correlations were used for comparison.

### 2.4.1. In vivo experiments

Volunteer and patient examinations were conducted in accordance with our institutional guidelines (Comité de Protection des Personnes Ile de France VI) and written informed consent was obtained from all subjects.

Reference imaging T<sub>2H2O</sub> values were obtained via a 2D 17-TE MSE (TEs from 9.5 to 161 ms, 5 slices) image series fitted by 2-component dictionary searching with EPG simulated entries (14). The same FF 3D-GRE reference was used as in vitro.

Several proof-of-concept experiments were conducted:

i. We acquired Cartesian pSPGR and MSE data from the legs of eight healthy volunteers (4 women, mean age = 40 ± 11 years). Using the pSPGR acquisitions, we estimated T<sub>2fat</sub> in the subcutaneous fat with a single-component model, assuming a FF of 1 to parametrize the fat signal in the bi-component model. We then calculated T<sub>2H2O</sub> values using bi-component dictionary matching in the different muscles (tibialis anterior, extensor digitorum, peroneus, gastrocnemius medialis,
gastrocnemius lateralis and soleus) and compared these values with those estimated from the reference MSE acquisitions. MSE parameters were the following: pixel size, 1.3 × 1.3 mm²; 5 slices, slice thickness 10 mm; TR = 3000 ms, Tacq = 3 min 41s. The mean signal-to-noise ratio (SNR) was also evaluated in ensuring the relevance of the simulations (Figure S6).

ii. In the thighs of a 24-year-old healthy man, we compared the B1 values computed by our approach to the reference B1 values obtained using the constructor's B1 mapping sequence (41) (turbo flash with sequence parameters: FOV = 350 × 175 mm², spatial resolution = 5.5 × 5.5 mm², 3 slices, slice thickness = 10 mm, TE/TR = 1.78/2000 ms, FA = 8°, Tacq = 4 s).

iii. To access the reproducibility of the pSPGR $T_{2H2O}$ measurements, six healthy volunteers (one woman, mean age = 33 ± 7 years) were scanned twice, with the subject removed from the scanner between both scans. The coefficients of variation on $T_{2H2O}$ were measured in individual muscles.

iv. We demonstrated the sensitivity of the Cartesian pSPGR method to physiological $T_{2H2O}$ variations by conducting an eccentric exercise protocol designed to induce noticeable changes in $T_{2H2O}$ in leg muscles. A 39-year-old woman was asked to perform double leg calf raise until muscle exhaustion and was scanned at the leg level before and immediately after the exercise. We compared the difference in $T_{2H2O}$ response using the MSE and the pSPGR quantification methods for the peroneus, the gastrocnemius medialis and tibialis anterior muscles.

v. To showcase the potential of our method for quantitatively assessing muscular disease, we acquired Cartesian pSPGR-based $T_{2H2O}$ maps in a 48-year-old woman with anorexia nervosa, a rare neuromuscular disorder, as a complement to an ongoing clinical study that included MSE. We compared $T_{2H2O}$ values obtained by both methods using Pearson correlations.

vi. The Cartesian pSPGR method was compared to the 3D stack-of star radial pSPGR method and the standard MSE to image the tongue muscle in five healthy volunteers (1 women, mean age = 44 ± 17 years). For this protocol, all acquisitions had a FOV of 200 × 200 × 192 mm³ and in plane resolution of 0.8 × 0.8 × 3 mm³. Tongue muscles were manually delineated on anatomical images, and we assessed $T_{2H2O}$ distribution for each subject using the three qMRI approaches.
# 3. Results

## 3.1. In silico evaluation

### 3.1.1. Effect of tissue parameters variations and field inhomogeneities on pSPGR steady state

The number of repetitions of the pSPGR acquisition required to reach a steady state for different sequence parameters is shown in **Figure S3-A**. Based on these results, we decided to evaluate the signal after 500 repetitions in all subsequent numerical simulations and for dictionary generation.

The magnitude and phase of the pSPGR steady-state signal are shown in **Figure 2** for small RF phase increments with varying T<sub>2H2O</sub>, B1, FF, T<sub>1H2O</sub> and B0 at a flip angle of α = 15°. Changes in T<sub>2H2O</sub>, B1, and FF affected both signal phase and magnitude, while the phase showed minimal dependence on T<sub>1H2O</sub>. Variations in B0 caused a constant phase shift. Similar results for flip angles of α = 5° and 25° are presented in **Figure S4**.

### 3.1.2. Sequence optimization

The final optimized sequence parameters were φ = [0.3, 0.3, -1.1, 0.3, 2.1, -2.1, 3, -2.6, 2.8, -2.6] ° and α= [6.5, 7, 25, 26, 8, 8, 17, 13, 16, 16] °, which were used in all subsequent simulations and acquisitions. **Figure S3-B** shows that these parameters achieve a steady state for typical water and fat signals after a few hundred repetitions.

### 3.1.3. Effect of input T<sub>1H2O</sub>, T<sub>1fat</sub> and T<sub>2fat</sub> errors on T<sub>2H2O</sub> quantification

The influence of fixed input parameters T<sub>1H2O</sub>, T<sub>1fat</sub> and T<sub>2fat</sub> on T<sub>2H2O</sub> estimation accuracy is illustrated in **Figure 3**. Variations in T<sub>1H2O</sub> had minimal impact, with less than 0.1 % error for a 10 % change. In contrast, fat relaxation parameters caused errors exceeding 10 % in T<sub>2H2O</sub> estimation for a 10 % variation in T<sub>1fat</sub> or T<sub>2fat</sub> at high FF values (> 0.6).

### 3.1.4. Effect of B1 and FF variations on T<sub>2H2O</sub> quantification

Using Monte Carlo simulations, we estimated the mean absolute error in T<sub>2H2O</sub> estimation as a function of SNR and of the number of estimated parameters (**Figure 4, A-C**). For signals with FF = 0.3, ignoring fat in the model caused large errors (>10 ms). Adding FF fitting reduced errors but still exceeded 5 ms with strong B1 variations. By fitting both B1 and FF, accurate T<sub>2H2O</sub> values were recovered across the entire range of values for signals with SNR > 20, even under low B1. At SNR = 11
40 and T<sub>2H2O</sub> = 30 ms, the mean T<sub>2H2O</sub> values for the four signals were 30.08 ± 1.85, 30.16 ± 3.14, 30.11 ± 2.20, and 30.16 ± 3.55 ms. Different FF values produced widely different signals (**Figure 4**, **D**).

3.2. Phantom validation

The mean T<sub>2H2O</sub> values measured by the pSPGR approach in the different vials of the phantom were highly correlated to the multi-TE SVS reference, with Pearson coefficient of determination (R<sup>2</sup>) higher than 0.85; despite greater dispersion of T<sub>2H2O</sub> values as the SNR of the water signal decreases with the increasing fat fraction. The mean FF values were highly correlated to the references Dixon (R<sup>2</sup> > 0.9) as shown in **Figure 5**. Despite the observed bias between the Cartesian and radial implementations (mean difference ± 95 % limits of agreement: - 4.9 ± 4.9 ms), the correlation with the reference method remained consistent.

3.3. In vivo T2<sub>H2O</sub> mapping

3.3.1. Leg T2<sub>H2O</sub> mapping at rest

T<sub>2H2O</sub> values extracted on the six leg muscles averaged over the eight volunteers using both the MSE
and the pSPGR methods are presented in **Table 1**. The values from individual muscle ROIs correlated
between methods (R<sup>2</sup> = 0.69), with a systematic bias for the pSPGR approach (mean difference ± 95 %
limits of agreement: -10.78 ± 1.50 ms).

3.3.2. Confounding effects

The B1, T<sub>2H2O</sub> and FF maps computed using the Cartesian pSPGR sequence in the thighs of a healthy subject are displayed in **Figure 6.A** along with the maps obtained using the reference sequences (turbo flash, MSE and multi-TE GRE, respectively). Across the entire thigh region, B1 values computed using pSPGR and the reference turbo flash sequence were significantly correlated (p < 0.05, R<sup>2</sup> = 0.843, **Figure 6.B**). Additionally, pixel-wise analysis showed only a weak but significant correlation between B1 and pSPGR T<sub>2H2O</sub> values (p < 0.05, R<sup>2</sup> = 0.065, **Figure 6.C**). Despite significant B1 inhomogeneities across the thighs, T<sub>2H2O</sub> values remained homogenous, as illustrated in **Figure 6.D**.

3.3.3. Muscle T2<sub>H2O</sub> repeatability
The observed coefficients of variation upon repeating the Cartesian and radial pSPGR $T_2_{H2O}$ measurements on 6 volunteers were equal to 0.63±0.56ms and 0.58±0.34ms. Bland-Altman plots between the measurements is also displayed in **Figure S7**.

### 3.3.4. Muscle $T_2_{H2O}$ variations after an eccentric exercise protocol

The $T_{2_{H2O}}$ maps obtained before and after eccentric exercise using the Cartesian pSPGR and MSE approaches are shown in **Figure 7.A**. Both methods indicated post-exercise activation of the peroneus muscle. The variations were consistent between pSPGR and MSE, with $T_{2_{H2O}}$ increasing by 14% and 13% in the peroneus and decreasing by 7% and 6% in the tibialis anterior and by 2% and 1% in the gastrocnemius medialis, respectively (**Figure 7.B**).

### 3.3.5. $T_{2_{H2O}}$ Mapping in a subject with a neuromuscular disease

$T_{2_{H2O}}$ maps obtained with the Cartesian pSPGR and MSE approaches for a patient with a muscular disease are shown in **Figure 8**. $T_{2_{H2O}}$ values from different muscle ROIs demonstrated a strong correlation between the methods ($R^2 = 0.87$), with a bias toward lower values using the pSPGR approach (11.39 ± 0.67 ms).

### 3.3.6. $T_{2_{H2O}}$ mapping of the tongue muscle

FF maps of the tongue muscles obtained using the Dixon method, Cartesian pSPGR, and radial pSPGR methods are shown in **Figure 9**, along with $T_{2_{H2O}}$ maps obtained from MSE and both pSPGR sequences. Mean $T_{2_{H2O}}$ values in the tongue muscle were 40.1 ± 2.1 ms with the MSE method, 22.3 ± 2.2 ms with the Cartesian pSPGR method, and 23.2 ± 2.4 ms with the radial pSPGR method. The radial encoding scheme improved mapping quality, revealing small anatomical features of the lingual septum in the FF maps. Additionally, $T_{2_{H2O}}$ distributions were significantly narrowed across five volunteers (mean standard deviation: MSE: 5.64 ± 1.33 ms, Cartesian pSPGR: 5.39 ± 1.22 ms, radial pSPGR: 3.87 ± 0.97 ms).
## 4. Discussion

In this study, we demonstrated that a series of 3D pSPGR acquisitions can be used to quantify T2<sub>H2O</sub> values in skeletal muscle. We validated the proposed approach's domain of validity using numerical simulations and Monte Carlo analyses. We compared the accuracy of this method in phantoms against the gold standard spectroscopic method. Several proof-of-concept in vivo experiments were conducted to evaluate the approach's robustness to B1 field inhomogeneities, its sensitivity to physiologically and pathophysiological induced T2<sub>H2O</sub> variations, and its applicability in rarely studied regions such as the tongue muscle. In contrast to the reference MSE approach, typically used to measure T2<sub>H2O</sub> in the skeletal muscle tissues, the pSPGR method is based on fast gradient echo, enabling 3D maps to be acquired in times compatible with clinical research.

3D T2 quantification using pSPGR acquisitions has been previously applied in quantitative brain imaging (22). However, adapting this method for muscle applications, especially for patients with neuromuscular diseases, required addressing muscle degeneration and muscle replacement by fat. Our study demonstrated through numerical simulations that the steady state reached by pSPGR acquisitions is highly dependent on the FF. In a previous study of pSPGR T2<sub>H2O</sub> measurements in the lower limb muscles (23), a standard fat suppression method was proposed to eliminate the lipid contribution. However, magnetic B0 and B1 inhomogeneities, particularly at 3T, can cause incomplete or inconsistent fat suppression across the entire field of view, which is often large in muscle imaging applications (14,29). To overcome this challenge, we utilized the QuICS principle, using the complex steady state signal from multiple pSPGR acquisitions to extract various parameters (27,26).

We proposed an optimal acquisition protocol minimizing the CRLB of different variables and a bi-component dictionary matching approach to simultaneously derive T2<sub>H2O</sub>, FF and B1 in the muscle from 10 pSPGR acquisitions. We showed that some variables, such as T1<sub>H2O</sub>, T1<sub>fat</sub>, T2<sub>fat</sub>, and B0, could be fixed without significantly affecting the accuracy of T2<sub>H2O</sub> quantification. However, accurately determining FF and B1 was essential for maintaining the precision of T2<sub>H2O</sub> measurements. The use of a multi-peak fat model combined with relaxation times differences model provides sufficiently different fingerprints between water and fat, where MSME may encounter challenges differentiating signals that demonstrate exponential behavior (42).

In in vivo results, we observed a systematic bias between the T2<sub>H2O</sub> values determined by the pSPGR approach and the standard MSE method, with the pSPGR method yielding lower values. Similar differences between T2 measurements obtained by MSE and gradient echo-based methods have been reported in various applications (23,24,26). Specifically, in muscle imaging, the MSE method is known to overestimate T2 values compared to the gold standard spectroscopic approach (43). In this study, the observed bias could be due to chemical exchanges within the muscle tissue. Further analysis
is required to understand the relationship between the obtained values and muscle T2<sub>H2O</sub> compartmentalization, especially using the pSPGR method, which could enhance our understanding of the mechanisms highlighted by this biomarker.

Despite the observed bias in T2<sub>H2O</sub> values, we demonstrated that the pSPGR method can detect T2<sub>H2O</sub> variations in the same proportions as the MSE sequence in different physiological and pathophysiological contexts, while offering better spatial resolution and increased coverage. For instance, we investigated the muscle response to an intense eccentric exercise paradigm in a healthy volunteer, which was previously shown to increase T2<sub>H2O</sub> values (23,44). We observed that the exercise induced similar proportions of T2<sub>H2O</sub> changes with both the standard MSE and the pSPGR quantification approaches in the activated muscles. Likewise, T2<sub>H2O</sub> values measured in the patient with a neuromuscular disorder were highly correlated between the two techniques. These initial in vivo observations need further validation in dedicated follow-up studies.

The increased spatial resolution and coverage of the pSPGR approach, compared to the standard MSE acquisition, provides access to muscles that are otherwise difficult to assess. Additionally, we increased the versatility of the pSPGR acquisition by implementing a radial k-space encoding, making it suitable for imaging muscle groups often significantly affected by motion, such as swallowing muscles. As exemplified in the tongue imaging proof-of-concept, the 3D stack-of-star radial pSPGR method overcomes many limitations of the MSE approach, making it a prime candidate for use in clinical research on these critical targets in neuromuscular disorders. The strong correlation between fat fraction measurements from the reference Dixon and the pSPGR approach in phantoms suggests that approach could be used for multi-parametric FF and T2<sub>H2O</sub> MRI. However, further validation is needed, especially in patients with significant fat replacement.

Several limitations of this study need to be acknowledged. First, the optimization method chosen for the sequence parameters, which involved minimizing the CRLB of selected variables, could be improved. By making the optimization sensitive to B1, a confounding factor rather than a parameter intended for measurement, the sequence may have become too sensitive to B1. It might have been more appropriate to use a cost function that directly minimizes the estimation error in T2<sub>H2O</sub>. Furthermore, the optimal number of points will need to be determined, as the choice of 10 points was arbitrary. Additionally, non-Cartesian undersampled acquisition schemes induce spatially dependent noise-like artifacts that are ignored by the CRLB cost function (32,45). Further work is needed to adapt the optimization framework to account for non-Cartesian schemes and potentially improve the precision of T2<sub>H2O</sub> measurements. A more comprehensive evaluation of the impact of the imaging acceleration methods, such as GRAPPA, or the radial undersampling factor applied in the pSPGR sequences should also be conducted in vivo.
Another limitation of this study is the use of a fixed lipid spectrum and relaxation times in the bi-component model, based on literature data and subcutaneous fat measurements. The model assumes a 6-peak spectral lipid profile with fixed amplitudes, chemical shifts, and a single T2fat value, relying on the similarity between subcutaneous and intramuscular fat. The observed variability of T2fat in healthy subjects supports this assumption. Furthermore, previous studies have shown that the T2fat of infiltrated muscle is similar to that of subcutaneous fat (46). However, recent findings indicate that subcutaneous fat may contain up to 10% water, which our model did not account for (16). Incorrect fat modeling, including an inaccurate T2fat value, could interfere with T2H2O quantification. This issue must be carefully evaluated in future studies to determine whether the fixed lipid model can be reliably applied to pathological conditions. In addition, while the tongue proof of concept showed the pSPGR 3D radial stack-of-star method overcomes many of the limitations of the typical MSE approach, there was no comparison with an implementation of a MSE sequence with a radial readout.

In conclusion, consistent with our findings from the numerical simulations and in good agreement with reference measurements, the proposed technique, efficiently estimates T2H2O in the context of skeletal muscle studies. This method is compatible with the clinical research workflow. Future evaluations in larger patient cohorts will be conducted to explore its potential in patients with various neuromuscular disorders.

## Acknowledgements

This study was funded by ANR-20-CE190004.
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Tables

<table><caption>Table 1: Mean T2<sub>H2O</sub> values measured in the leg muscles of healthy volunteers.</caption><thead><tr><td>Muscle</td><td>MSE T2<sub>H2O</sub> (ms)</td><td>pSPGR T2<sub>H2O</sub> (ms)</td></tr></thead><tbody><tr><td>tibialis anterior</td><td>32.8 ± 1.6</td><td>22.1 ± 0.8</td></tr><tr><td>extensor digitorum</td><td>33.1 ± 1.2</td><td>22.3 ± 1.6</td></tr><tr><td>peroneus</td><td>33.8 ± 1.7</td><td>22.7 ± 1.4</td></tr><tr><td>gastrocnemius medialis</td><td>34.0 ± 1.7</td><td>23.5 ± 1.4</td></tr><tr><td>gastrocnemius lateralis</td><td>33.6 ± 1.5</td><td>22.8 ± 1.3</td></tr><tr><td>soleus</td><td>34.6 ± 0.8</td><td>23.7 ± 1.0</td></tr></tbody></table>
Figure legends

<figure><img src="image_2.png" /><figcaption>Figure 1: Diagram of the (A) Cartesian (B) Radial 3D pSPGR sequence. The pulse phase follows a quadratic pattern.</figcaption></figure>

<figure><img src="image_3.png" /><figcaption>Figure 2: pSPGR steady-state signal magnitude and phase over the range of small phase increments φ for various tissues and field parameters. For all simulations, TR/TE=5.5/2.25 and flip angle=15°. When not varying, T2H2O=25 ms, B1=1, FF=0, T1H2O=1220 ms and B0=0 Hz.</figcaption></figure>
<figure><img src="image_4.png" /><figcaption>Figure 3: Influence of input parameters (A) T1<sub>H2O</sub>, (B) T1<sub>fat</sub>, (C) T2<sub>fat</sub> on the accuracy of T2<sub>H2O</sub> estimated using the proposed method for a variation up to 10 % from the nominal values. Mean error for T2<sub>H2O</sub> ranging from 20 to 70 ms. ΔT2<sub>H2O</sub> was quantized in 15 bins between the min and max values.</figcaption></figure>
<figure><img src="image_5.png" /><figcaption>Figure 4: Simulation results of T<sub>2H2O</sub> estimation using (A) 1-parameter (B) 2-parameter and (C) 3-parameter fitting models. The mean absolute relative error from 10.000 repetitions, ΔT<sub>2H2O</sub> is shown as a function of SNR, using Monte Carlo simulations with (column 1) B1 = 1 and FF = 0, (column 2) B1 = 1 and FF = 0.5, (column 3) B1 = 0.8 and FF = 0, (column 4) B1 = 0.8 and FF = 0.3. ΔT<sub>2H2O</sub> was quantized in intervals of 0.1ms. (D) Magnitude and phase of mean signals and predictions for SNR=40 for the 3-parameter fitting model. x-axis labels correspond to the acquisition points. The parameters pairs (α, φ) are in the following order: (6.5, 0.3), (7, 0.3), (25, -1.1), (26, 0.3), (8, 2.1), (8, -2.1), (17, 3), (13, -2.6), (16, 2.8), (16, -2.6).</figcaption></figure>
<figure><img src="image_6.png" /><figcaption>Figure 5: (A) T2<sub>H2O</sub> and (B) FF map (central axial slice) obtained on 5 vials of the multi-vial phantom using the proposed Cartesian method. (C): Linear regression between T2<sub>H2O</sub> computed from the proposed method and the reference spectroscopy (MRS-STEAM) (D) Linear regression between FF computed from the proposed method and the reference Dixon method. The solid lines represent the linear regression fit. (E) Magnitude and phase of mean signals and predictions in 2 vials at different oil fat fraction with the mean signal and prediction calculated in an ROI of n=121 voxels from Cartesian pSPGR acquisitions.</figcaption></figure>
<figure><img src="image_7.png" /><figcaption>Figure 6: (A) Quantitative maps obtained in the thighs of a 24-year-old healthy volunteer using the proposed pSPGR sequence and the reference TFL, MSE and Dixon for B1, T2H2O and FF, respectively. (B) Linear correlation between B1 values derived from the TFL and the proposed pSPGR approaches (R² = 0.843), the solid blue line represents the linear regression fit. (C) Linear correlation between T2H2O and B1 values derived from pSPGR approach (R² = 0.065), the solid blue line represents the linear regression fit. (D) Profiles of T2H2O and B1 across the rectangular portion (5-pixel thick line) plot in (A)</figcaption></figure>
<figure><img src="image_8.png" /><figcaption>Figure 7: (A) T2<sub>H2O</sub> maps obtained from the pSPGR and the reference MSE approaches before and after eccentric exercise in the leg of a healthy volunteer. In axial view, yellow dotted lines indicate the muscles of interest. In the coronal view, dotted red lines correspond to the location of 4 of the 5 MSE slices. (B) Distribution of normalized T2<sub>H2O</sub> changes measured in the different muscles using both approaches.</figcaption></figure>
<figure><img src="image_9.png" /><figcaption>Figure 8: (A) Three slices of the T2<sub>H2O</sub> maps obtained in one leg from a subject with anoctaminopathy. The left gastrocnemius medialis muscle was totally replaced with fat. (B) Correlation between pSPGR and MSE T2<sub>H2O</sub> values across all muscles of each leg. (C) Bland-Altman plot between the proposed method and reference MSE methods.</figcaption></figure>
<figure><img src="image_10.png" /><figcaption>Figure 9: (A) Fat fraction maps obtained in the tongue of a healthy volunteer using the three different methods: Dixon (left), pSPGR Cartesian (middle), and pSPGR radial (right). The lingual septum (shown by red arrow) is visible in both the radial pSPGR and Dixon FF maps. (B) T2<sub>H2O</sub> maps obtained from the same volunteer using the three different methods: MSE (left), pSPGR Cartesian (middle), pSPGR radial (right), overlaid on the corresponding anatomical volume. (C) T2<sub>H2O</sub> distribution observed in the delineated region for each subject.</figcaption></figure>