Bi-component T1ρ and T2 Relaxation Mapping of Skeletal Muscle In-Vivo

The goal of this paper was to evaluate the possibility of bi-component T1ρ and T2 relaxation mapping of human skeletal muscle at 3 T in clinically feasible scan times. T1ρ- and T2-weighted images of calf muscle were acquired using a modified 3D-SPGR sequence on a standard 3 T clinical MRI scanner. The mono- and biexponential models were fitted pixel-wise to the series of T1ρ and T2 weighted images. The biexponential decay of T1ρ and T2 relaxations was detected in ~30% and ~40% of the pixels across all volunteers, respectively. Monoexponential and bi-exponential short and long T1ρ relaxation times were estimated to be 26.9 ms, 4.6 ms (fraction 22%) and 33.2 ms (fraction: 78%), respectively. Similarly, the mono- and bi-exponential short and long T2 relaxation times were 24.7 ms, 4.2 ms (fraction 15%) and 30.4 ms (fraction 85%) respectively. The experiments had good repeatability with RMSCV < 15% and ICC > 60%. This approach could potentially be used in exercise intervention studies or in studies of inflammatory myopathies or muscle fibrosis, permitting greater sensitivity and specificity via measurement of different water compartments and their fractions.

increases linearly with the number of points, so a trade-off must be made between image acquisition time and measurement accuracy. As shown in Fig. 1b, the improvement from 10 to 15-time points is negligible (less than 2%) considering the 50% increase in the total scan time. Hence, in this study, 10 TSL/TE points were selected for the in-vivo experiment. As shown Fig. 1c and d, the estimation errors are higher for shorter long and longer short components. The effect of component fractions on the estimation is shown in Fig. 1e and f. The component with higher fraction is estimated more accurately than the one with a smaller fraction.
In vivo experiment. Figure 2 shows a representative slice of a scan with TSL = 2 ms in axial, sagittal, and coronal planes and the regions of interests (ROIs) in which the relaxation components were estimated. A representative example of T1ρ and T2 maps are shown in Fig. 3a1-d1 and Fig. 3a2-d2 respectively. The summary of descriptive statistics calculated across eight participants in each ROI is summarized in  [28.4-55.2 ms], respectively. The short component has lower fraction than the long relaxing component. In this study, we observed that a biexponential fit is a better describes the T1ρ and T2 relaxation decay than a monoexponential model. As shown in Fig. 4a, since the monoexponential fit appears as a straight line in logarithmic scale, the deviation of the data points from the line indicates the existence of more than one exponential term 16 in the model. Moreover, the biexponential fit has smaller residuals than the monoexponential fit which confirm that it can better represent the relaxation decay.
Statistical Analysis. Figure 5 shows the comparison between T1ρ and T2 relaxation time in different muscle ROIs. The Wilcoxon rank sum test results showed that the global mono and long T1ρ relaxation components were significantly higher than T2 relaxation. The gender difference analysis results for T1ρ and T2 relaxation components revealed that the short T2 relaxation component was significantly greater in male participants than the female participants. In addition, the Kruskal-Wallis test was applied to investigate the difference between different ROIs. The results showed that there is a statistically significant difference in monoexponential T1ρ (P < 0.001) and T2 (P = 0.0038) in different ROIs. No significant difference was observed in biexponential components. The pairwise comparison between ROIs is shown in Table 2. Figure 6 shows the ICC and RMSCV across three participants. The ICC > 60% and RMSCV < 15% on all the regions show the good reliability and repeatability of this study.

Discussion
In this paper, we presented a 3T MRI technique for in-vivo, bi-component T1ρ and T2 analysis of calf muscle. Five ROIs were defined in the muscle and T1ρ, and T2 relaxation times were measured in each ROI. The calf muscle chemical composition consists of intra-(~25%) and extracellular water (~75%), contractile proteins (~20%:  myosin, actin, tropomyosin/troponin, myoglobin) and other components (~5%: salts, phosphates, ions, glycogen, and macronutrients). The short components are thought to be related to the tightly bound macromolecular (collagen, contractile proteins, and other components, etc.) and intracellular water compartments; while the long relaxation component corresponds mainly to the loosely bound water (extracellular/vascular). The results showed that biexponential fitting might better present and distinguish the different relaxation times in the muscle due to different water compartments. The estimated monoexponential relaxations were comparable to the other studies 3,13 . The monoexponential estimated T1ρ was higher than T2. To the best of our knowledge this comparison has not been reported for the calf muscle, however, our results trend are in agreement with other tissues such as articular cartilages [17][18][19][20] in which T1ρ > T2.
The existence of three relaxation components was shown in previous studies using Carr-Purcell-Meiboom-Gill (CPMG) sequence 21,22 . Saab et al. 21 reported the in vivo multi-component T2 relaxations in flexor digitorum profundus muscle while Cole et al. 22 measured the T2 relaxation in rat muscle. These three components have been related to the hydration shell of macromolecules, intracellular water, and extracellular water, respectively [21][22][23] . In a study performed by Araujo et al. 24 the existence of the biexponential relaxation behavior (e.g., an intermediate

ROI Relaxation Type T mono (ms) T short (ms) F short (%) T long (ms) F long (%) Ratio (%)
GM  and a long components) has been confirmed for T2 relaxation time using a localized 2D-ISIS-CPMG sequence. However, no short component has been detected due to long TE's used in the sequence 24 . In contrast, our method can measure a short component and provide 3D volumetric maps. Recently, Araujo et al. 2 proposed a UTE sequence to measure the short T2 components. Only the short component was measured due to the short TEs used in this study. The total acquisition time to acquire one scan with 7 TE values was 7 min, 49 s. They measured T2 in only one thick (6 mm) slice while we acquired 3D volumetric scans. However, our method cannot detect very short T2 due to using TE of 3.78 ms in the readout. Due to the SAR limitation in the T1ρ experiment, the longest TE/TSL in our study was 55 ms. Hence; our long component is close to the third component, and our short component is close to the first component calculated in Saab study. Moreover, the smaller slice thickness (2 ms) in our study in comparison with Saab study (10 mm) leads to lower partial volume effect (PVE).
To the best of our knowledge, biexponential T1ρ measurement of muscle has only been done on animals. For example, a biexponential analysis of T1ρ in rat muscles was reported by Yuan et al. 15 . The mono, short and long T1ρ were measured as (~30-33 ms), (~9-11 ms) and (~37-41 ms), respectively. The short and long fractions were (~12-20%) and (~80-88%). 25 temporal points from TSL = 1 ms to 60 ms were acquired in this study at the cost of increasing the total acquisition time to ~30 minutes 15 . Our T 1ρ estimations using 10 TSLs acquired in 15 minutes scans are in good agreement with this study. The difference is probably due to the higher temporal resolution in Yuan study.
The selection of TR can affect the T1ρ and T2 estimation due to the T1 relaxation. We evaluated this effect using Bloch simulation. Our simulation showed that there is ~5% difference between the T1ρ or T2 estimation error with TR = 1500 ms and TR = 5000 ms. Considering the longer acquisition time of TR = 5000 ms, we considered this error as negligible.
The fatty infiltration of muscular occurring in some cases such as atrophy and muscular dystrophy does not affect the relaxation time since the fat signal was suppressed in the scans by exciting only the water with a binomial RF excitation pulse 25,26 .
Our study has some limitations. The biexponential condition of 4T short < T long can produce some bias. We chose this condition based on the suggestion in Juras study 27 .
Field inhomogeneities also affected the estimation since the spin-locking in T1ρ imaging is very sensitive to B 0 and B 1 inhomogeneities. To compensate this effect, as described in our previous studies 26 , we used spin-lock phase  alteration and a refocusing pulse for B 1 and B 0 compensation, respectively. In addition, the manual shimming was performed to further correct the field inhomogeneities. Our results showed a homogenous B 0 (ΔB0 < ±5 Hz) and B 1 changes less than ±50 Hz across ROIs. However, the compensation techniques used in this study may not be successful for scanning large volumes such as gluteus muscle or covering inhomogeneous regions such as arms and dorsal muscles. Moreover, the binomial RF excitation pulse is not robust in the presence of large inhomogeneities, and hence, the fatty infiltration may affect the estimation. Further studies in the large volumes muscles and, in the presence of fatty infiltration are warranted to evaluate the performance of our method. The magic angle effect related to dipolar interactions of fiber orientation with respect to B 0 may affect the T 1ρ and T 2 values. The spins decay monoexponentially when the tissue's orientation to B 0 is about 55°2 8 , though T 1ρ is relatively less sensitive than T 2 to this effect 29 .
Finally, we expect an elevation in relaxation components due to a muscular disease such as muscle fibrosis. However, only a small number of asymptomatic participants were scanned in this study and further validation in patients with fibrosis is warranted.
In conclusion, in this study, we showed the feasibility of in vivo measurement of bi-exponential T1ρ and T2 relaxation of human calf muscle in clinically feasible scan times. Our method could potentially be used in intervention exercise studies or in studies of inflammatory myopathies or muscle fibrosis, permitting greater sensitivity and specificity via measurement of different water compartments and their fractions.
is the MRI signal intensity at time t (TSL in T1ρ and TE in T2 imaging), S 0 is initial value, a i is the fraction of i th exponential term with the assumption of ∑ = = a 1 i M i 1 , and N is the additive noise. Assuming S 0 = 1, to express biexponential decay (M = 2), the equation can be written as: where T s and T l are long and short relaxing components, respectively. The long (a l ) and short (a s ) fractions can be expressed in percentage as F l = 100 × a l ⁄(a l + a s ) and F s = 100 × a s ⁄ (a l+ a s ), respectively. To estimate the relaxation time constants and their fractions, the MR signal must be acquired at several time points. Under given signal to noise ratio (SNR), the smaller number of points is desired to minimize the scan time. To determine the adequate range and number of points for successful estimation, Mont Carlo simulation 30 was performed for 1000 random noise trail with normal distribution N(0,σ). The SNR was defined as SNR = 1/σ. The estimation errors were calculated for each noise trail as: where y a and y e are the actual and estimated values, respectively. The average of errors in 1000 trial was reported in percentage as the Monte Carlo simulation result.
In-vivo MRI acquisition. The study was approved by the institutional review board (IRB). All methods were performed in accordance with the relevant guidelines and regulations, and all of the participants signed a written informed consent prior to MRI scanning. Four females (age: 26 ± 3 years, BMI: 22 ± 1 kg/m 2 ) and four male participants (age: 30 ± 3 years and BMI: 24 ± 2) with no signs of muscle pains or history of lower leg muscle injuries were recruited for this study. Additionally, follow-up scans were acquired from three participants two weeks after their first scan. 3D T1ρ and T2-weighted MR scans were taken on a 3T whole-body clinical MRI scanner (Prisma, Siemens Healthcare, Erlangen, Germany) with a 15-channel Tx/Rx knee coil (QED, Cleveland OH). 3D-Cartesian turbo-flash (TFL) sequence was used after T1ρ or T2 preparation module as readout followed by a delay for T1 restoration. The sequence timing diagram is shown in Fig. 7. Fat-suppressed T1ρ-and T2-weighted scans were acquired in the sagittal plane at 10 different TSL/TEs including 2, 4, 6, 8, 10, 15, 25, 35, 45, and 55 ms (Fig. 2). The total scans time to acquire both T1ρ and the T2-weighted data set was 29 min, 30 s. The sequence acquisition parameters were as follows: TR/TE = 1500 ms/3.78 ms, flip angle = 8°, field of view (FOV) = 140 mm 2 , matrix size 256 × 128 × 64, slice thickness = 2 ms, GRAPPA 31 acceleration factor (AF) = 3. The spin-lock frequency (FSL) of 500 Hz was used in T1ρ preparation module.
In the final biexponential estimation the pixels where 4T short < T long were excluded from the analysis 27 .
Statistical analysis. The statistical analysis was performed using JMP statistical software (JMP ® , Version 13 SAS Institute Inc., Cary, NC, 1989NC, -2007. Wilcoxon rank sum test was applied to compare T1ρ and T2 relaxation components as well as gender difference. T1ρ and T2 relaxation components were also compared in different ROIs using the Kruskal-Wallis test. The repeatability studies were performed on three participants by repeating the scans after two weeks. The coefficient of variation (CV) for each participant was calculated as σ µ = CV (4) where µ and σ are the mean and standard deviation of the estimated components from two scans, respectively. The root-mean-squared CV (RMSCV) was then calculated across three subjects to evaluate the inter-subject repeatability: where σ b 2 and σ w 2 are the between and within subjects variances, respectively.
Data availability. The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request. Figure 7. The imaging sequence timing diagram with (a) T 1ρ and (b) T 2 preparation, 3D turbo-Flash readout, and T1 recovery delay. To compensate the effect of B 1 inhomogeneities, the spin-lock pulse was divided into four segments with alternative phase. The refocusing pulse was applied between two pairs to compensate the B 0 inhomogeneities. One phase line from all slices was acquired after applying the preparation module (partition loop). After a delay for T1 restoration, another preparation module was applied to acquire the next phase line (phase loop).