Chemical shift-encoded imaging (CSEI) is a common quantitative magnetic resonance imaging (MRI) method for fat–water separation and measurement of fat content in numerous body parts, such as the liver and skeletal muscles (1–5). In skeletal muscles, fatty infiltration has been related to, for example, insulin resistance and various neuromuscular diseases (6–11). The location of fat accumulation within the muscle has also been shown to be important (6), as some muscle groups are more likely to accumulate fat (12). Depending on the muscle group involvement, the outcome of some neuromuscular diseases can show a large variability (11, 13). In addition, different neuromuscular diseases show different fat infiltration patterns of the muscle groups. By detecting these patterns, it might be easier to identify a specific disease (11, 14). To enable and simplify the distinction between the different muscle groups, and between inter- and intramuscular fat, high-resolution fat fraction (FF) images are desirable. CSEI is a validated method for fat quantification purposes (4, 15), and it has previously been used for skeletal muscle applications (1, 2, 5).
Previously, fat quantification methods based on differences in fat and water T2 (16) rather than chemical shifts have been suggested for applications in skeletal muscles (17, 18). With T2-based methods, there is a possibility of obtaining information on FF and T2 relaxation times simultaneously (18). This would offer more information about the status of the disease, as a change in muscle T2-relaxation time has been shown to reflect the activity and progress of neuromuscular diseases (13, 19), complementing the information about the fat infiltration degree that primarily serves as a severity indicator (14). Moreover, there are several challenges associated with the CSEI technique, particularly when high resolution is required, which may be addressed by using T2-based methods. For example, increasing the resolution increases the minimal achievable interecho time which may have a negative impact on the CSEI fat quantification accuracy (20). In addition, it is common that fat/water swaps are present in FF images when using CSEI.
To obtain both the amplitudes and the T2-relaxation times of the fat, as well as the water component of the signal, a nonlinear least squares (NLLS) fitting method is commonly used (21, 22). However, NLLS has known problems with estimating the parameters correctly when 1 component is considerably larger than the other (23, 24). As a consequence, it may be difficult to measure low FFs using NLLS. In such cases, a fitting method based on Bayesian probability theory could be an alternative, as it has also been shown to be more robust against noise compared with NLLS (25). Bayesian fitting models have been proposed for other MRI applications such as intra-voxel incoherent motion imaging (26) and myelin water fraction estimations (27), but have, to the best of our knowledge, not yet been evaluated for fat quantification purposes.
The aim of this study was to examine the accuracy and noise performance of 3 different T2-based fat quantification methods, using high-resolution MRI for low FFs in healthy volunteers, and compare it with CSEI. The first T2-based method uses fixed T2-relaxation times of both water and fat as described by Kan et al. (17). The second method uses only a fixed fat T2-relaxation time to study the possibility of obtaining a simultaneous T2 map of water. The third method is based on Bayesian probability theory as described by Barbieri et al. (26), in which neither relaxation time is fixed. In this study, the muscular FF was measured in the calf of healthy volunteers, and simulations were made to study possible biases in the estimation of the FF using the T2-based methods.
In total, 10 healthy volunteers, 3 males (mean age, 28 years; range 25–30 years) and 7 females (mean age, 28 years; range, 24–32 years), were recruited and scanned with the approval from the regional ethical board. Informed consent was obtained from all volunteers.
MRI Data Acquisition
All measurements were acquired using a 3 T scanner (MAGNETOM Trio, Siemens Healthineers, Erlangen, Germany) and a 6-element body matrix coil. All data were obtained at 2 matrix sizes, 128 × 128 and 512 × 512, keeping the field of view constant at 280 × 280 mm2 and thus acquiring data at low- and high-spatial resolution. A single 6-mm transversal slice was collected for each acquisition, centered at the widest part of the left calf of each volunteer.
A multi-echo gradient echo (MGRE) sequence with 6 echoes was used for the CSEI method. To avoid T1 bias, a long repetition time (TR = 500 milliseconds) and a small flip angle (12°) were used. By estimating the number of signal averages as a function of interecho spacing, echo times (TEs) were chosen to obtain as small interecho spacing for the highest number of signal averages value as possible. The bandwidth (BW) was then set as low as possible without affecting the interecho time. In this way, a minimal interecho time with a high noise performance was ensured. With the first TE set to the shortest possible, the following parameters were used: TE1/ΔTE = 1.11/1.56 milliseconds (low resolution), TE1/ΔTE = 2.57/3.92 milliseconds (high resolution), BW = 1776 Hz/px (low resolution), and BW = 651 Hz/px (high resolution). Acquiring 1 average, the scanning times were 1 minute 6 seconds (low resolution) and 4 minutes 18 seconds (high resolution). From 1 subject, additional high-resolution CSEI images were collected with 2, 3, and 9 averages that had scanning times of 8 minutes 34 seconds, 12 minutes 50 seconds, and 38 minutes 29 seconds, respectively.
For the T2-based methods, 32 multi-echo spin echo (MESE) images were acquired with a 180° refocusing pulse and the following settings: TR = 2000 milliseconds, ΔTE = 9.2 milliseconds (low and high resolution), BW = 425 Hz/px (low resolution), BW = 391 Hz/px (high resolution), and number of averages = 1. To avoid long acquisition times, parallel imaging (GRAPPA) was used with an acceleration factor of 2. The resulting scan times were 2 minutes 36 seconds (low resolution) and 9 minutes (high resolution).
The methods used in this study are summarized in Figure 1. All calculations were performed using MATLAB (r2017a, The MathWorks, Inc., Natick, MA).
Chemical Shift-Encoded Imaging
The FF was calculated using a complex and magnitude-based iterative multiecho water–fat separation algorithm (28), with a multipeak fat model (29) and a joint T*2 estimation (30). Using 6 echoes (30), the FF was calculated using the following equation:
T2-Relaxation Time-Based Imaging
Two of the T2-based methods use a fixed T2-relaxation time of fat (T2,F), of which 1 uses a fixed T2-relaxation time of water (T2,W) as well. To obtain these values, a monoexponential fit of the signal decay was carried out voxel by voxel, resulting in a T2 map. For each volunteer, individual T2,F and T2,W values were then calculated as the mean value within corresponding regions of interest (ROIs), which were drawn in subcutaneous fat and muscle tissue, respectively (Figure 2). The ROI of fat was drawn to include as much of the subcutaneous fat as possible, avoiding visible blood vessels. In 1 volunteer, the subcutaneous fat layer was too thin for ROI definition. For this volunteer, the mean T2,F of the rest of the volunteers was calculated and used instead. The muscle ROI was drawn in a small part of tibialis anterior without any visible fat to minimize fat bias in the estimation of T2,W. Echoes 2–16 were used for all estimations using MESE data. The first echo was excluded owing to stimulated echo effects present in all other echoes, whereas the last echoes were excluded to reduce noise bias.
Two-Parameter Fit—Fixed T2,F and T2,W.
Using the estimated T2,F and T2,W values from the monoexponential fit, the amplitudes of water W and fat F could be calculated by a simple linear regression, as described by Kan et al. (17). The signal model is given by using the following equation:
Three-Parameter Fit—Fixed T2,F.
Using the same signal model [equation (2)] as in the 2-parameter fit and fixed T2,F value, T2,W, W, and F were estimated using a trust region-based NLLS fitting algorithm.
Bayesian Fitting Method.
An alternative to exponential fitting is using a Bayesian probability method (31). Here, all four parameters (T2,W, T2,F, W, and F) are estimated simultaneously using the method described by Barbieri et al. (26) using the MATLAB function slicesample. The signal model is given by the following equation:4).
Fat Fraction Calculation and T1-Correction
Owing to the long T1-relaxation time of muscle tissue and the desire to keep the acquisition times feasibly low, all the T2-based fat quantification methods described in the above sections were corrected for T1-relaxation bias. The T1-relaxation times T1,W = 1420 milliseconds and T1,F = 371 milliseconds (16) were used to correct the water and fat signal amplitudes according to FT1corr = F/[1 − exp(−TR/T1,F)] and WT1corr = W/[1 − exp(−TR/T1,W)], respectively. Hence, the FF can be described using the following equation:
To compare the 4 methods, 3 ROIs were drawn in the calf muscles of all 10 volunteers following the outlines of tibialis anterior, soleus, and gastrocnemius (Figure 2). Small areas with fat–water swaps in the high-resolution FF images calculated with CSEI were excluded from the ROIs. If the fat–water swap extended over a large area covering most of the muscle such that no swap-free ROI could be defined, the entire muscle group was excluded from further analysis.
Mean signal-to-noise ratios (SNRs) of the collected MGRE and MESE magnitude images were calculated as SNR = 0.655 · S/σ where 0.655 is due to the Rayleigh distribution of the noise in magnitude images (32) and σ is the standard deviation of the background noise. The SNR of both subcutaneous fat and muscle tissue was calculated. To calculate the standard deviation of the background noise of the MESE data, the ROIs were placed near the edge of the images where the g-factor was expected to be close to 1.
Wilcoxon signed-rank tests and Bland–Altman analysis were performed to compare the estimated FFs within the ROIs using the 2-parameter fit, 3-parameter fit, Bayesian fit, and high-resolution CSEI, to the FFs calculated with low-resolution CSEI.
Simulations were conducted to investigate the effects of incorrect T2 estimations, of incorrect signal amplitude, and of noise on the calculated FF. In all simulations, a biexponential model [equation (2)] was used to describe the signal decay using T2,W = 40 milliseconds and T2,F = 160 milliseconds as true T2-relaxation times. Signals from 5 different FFs (2%, 5%, 10%, 30%, and 95%) were simulated, each with 20 echoes. The signal amplitude at t = 0 was set to 1.
To study the effect of inaccurate T2-relaxation times, simulations were performed by using incorrect T2,W and T2,F in the 2-parameter fit method and incorrect T2,F in the 3-parameter fit method. T2,W was set to vary between 22 and 42 milliseconds and T2,F was set to vary between 70 and 260 milliseconds. No noise was added to the signal.
In the Bayesian fitting method, the effect of using an inaccurate S0 value was studied by varying the S0 value between 0.8 and 1.2. No noise was added, and each calculation was carried out 1000 times.
The effect of noise was studied in all 3 T2-based methods by altering the SNR of the simulated signal. The true T2-relaxation times were used to generate a noise-free signal. Complex Gaussian noise was then added to the signal before calculating the magnitude value. The effect was studied at 5 different SNR levels (20, 50, 150, 300, and 600), defined at t = 0. Each simulation was carried out 1000 times.
The estimated mean T2-relaxation times and standard deviations of muscle (tibialis anterior) and fat (subcutaneous fat), using the monoexponential fit, the 3-parameter fit, and the Bayesian fit are presented in Figure 3. The 3-parameter fit estimated a lower value of T2,W compared with the monoexponential fit and the Bayesian fit. The estimated T2,W from all three methods were independent of matrix size.
Example FF images of all 4 methods can be seen in Figure 4. In contrast to the T2-based methods, the high-resolution CSEI produced an FF image with a noise level that concealed the anatomy of the calf. Although all 3 T2-based methods produced FF images in which the different muscles were distinguishable, the estimated FFs were different between the methods. Because the high-resolution CSEI images with a single average (Figure 4) had a low SNR, additional high-resolution MGRE images were acquired with more averages from 1 volunteer (data not shown). Although SNR naturally increased with the number of averages, the noise level was still obscuring the anatomy of the muscles when using 9 averages.
Scatter plots and Bland–Altman plots of the methods are presented in Figure 5. The linear regression parameters and corresponding confidence intervals are shown in Table 1. Owing to fat–water swaps in the estimated FF images using high-resolution CSEI, results from 3 volunteers were excluded. Compared with the low-resolution CSEI method as reference, the 2-parameter fit was able to estimate the muscle FF accurately, showing only a small overestimation of FFs >3%. High-resolution CSEI overestimated the lower FFs and underestimated the higher FFs of the muscles, whereas the 3-parameter fit consistently overestimated the FF. The Bayesian fitting method showed an underestimation that increased with the FF. In Table 1, the mean values and the standard deviations of the estimated FFs of gastrocnemius, soleus, and tibialis anterior and the corresponding P-values of all volunteers and image resolutions are presented. All calculated mean FFs obtained from the 3-parameter fit, at both high and low resolution, significantly (P < .05) overestimated the FFs obtained from the reference method in comparison with the 2-parameter fit in which no significant differences were found.
In Figure 6, the acquired signal decay of 3 voxels of low- and high-resolution MESE images and the fitted curves of the 3 T2-methods are depicted. All 3 methods performed equal at high FF, whereas at lower FFs (∼17% and 3%), the estimated signals differ. The 3-parameter fit results in a slower decaying signal compared with the other 2 methods, whereas the Bayesian method results in a faster decaying signal.
The mean SNRs of the single average MESE (second echo)/MGRE (first echo) images of all volunteers were 919/250 (low resolution, muscle), 2048/208 (low resolution, fat), 214/71 (high resolution, muscle), and 449/63 (high resolution, fat). Because the SNR varies over the MESE images owing to parallel imaging, these values represent SNR when the g-factor is close to 1.
The simulated effect on the estimation of FF when using incorrect T2,W and T2,F, respectively, is shown in Figure 7. In both cases, an underestimation of T2-relaxation time resulted in an overestimation of the FF, whereas an overestimation of T2-relaxation time resulted in an underestimation of FF. The 3-parameter fit was more sensitive to errors in T2,F compared with the 2-parameter fit. At higher FFs, it was more important that T2,F was estimated correctly, whereas a correct T2,W was more important at low FFs. For the Bayesian fit, the effect of using an incorrect S0 value, as well as the standard deviation of the estimated FF, is shown in Figure 8. Using an underestimated S0 value resulted in an underestimation of the FF, and an overestimated S0 value resulted in an overestimated FF. However, the effect of using an overestimated S0 value was greater than that using an underestimated one. Lower FFs (2%–5%) were less sensitive for incorrect S0 compared with higher FFs (10%–30%). This can also be seen by looking at the standard deviation that was larger for higher FFs.
In Figure 9, the simulated effect of noise is shown as the difference between the estimated and true FFs and the standard deviation of the estimated FF of each of the 3 T2-based methods. The accuracy of both the 2- and 3-parameter fits increased with SNR (except for FF = 95% using the 3-parameter fit). The 2-parameter fit was less sensitive to noise than the 3-parameter fit. The Bayesian fit was more affected by noise at higher SNR compared with the NLLS-based methods. As the SNR increased, the standard deviation decreased for all methods and FFs.
In this work, 3 T2-based approaches (2-parameter fit, 3-parameter fit, and a Bayesian probability method) have been studied and compared with CSEI in terms of their capability to correctly estimate low FFs using high-resolution images. This was carried out through a study on healthy volunteers and by simulations. All T2-based methods provided high-resolution FF images in which it was possible to delineate the different muscles of the calf. With respect to the estimated FFs, the 2-parameter fit showed best agreement to the reference method.
Even though the measured mean FF of high-resolution CSEI in vivo corresponded well with the low-resolution CSEI, the high noise level of the images made it impossible to differentiate any anatomy within the muscle fascia, and therefore, it was difficult to locate potential fat accumulations of the muscles. After acquiring 9 averages, thus increasing SNR, it was still not possible to separate the different muscles of the calf. Using an even larger number of averages to increase SNR further could increase the possibility of differentiating the different muscles groups, but this would result in infeasibly long acquisition times. SNR may also be increased by using a larger flip angle (33). This would, however, require a correction for the T1-bias, including an estimation of the true flip angle map, and it would therefore introduce an additional source of error. As low-resolution CSEI was used as a reference method, this approach was thus not used. Another way to increase SNR is to acquire 3D MGRE data. In this study, we chose to collect 2D MGRE images for comparison with 2D MESE images. Because only 1 slice was needed, a 2D acquisition allowed for a longer TR and a larger flip angle compared with a 3D acquisition of the same total scan time.
Problems with fat–water swaps occurred in some of the estimated FF images of the high-resolution CSEI owing to the long TE needed. All high-resolution CSEI data from 3 subjects had to be excluded because of this. The interecho time of high-resolution CSEI may be reduced by means of bipolar or interleaved data acquisition. However, these approaches are associated with problems with phase errors (28, 34–37). Thus, a single acquisition monopolar readout was chosen to avoid any bias of our reference method.
The estimated T2-relaxation times of muscle tissue and subcutaneous fat in this study correspond well with T2-relaxation values of healthy volunteers from literature [T2,W = 32−40 milliseconds and T2,F = 133-154 milliseconds (16, 17, 38–40)], although the Bayesian fitting model results in a slightly overestimated T2,F. The measured FFs also agree with previously published data, that is, measured FFs ranging between 1.2% and 3.6% (tibialis anterior), 2.5% and 3.3% (soleus), and 0.91% and 5.0% (gastrocnemius) by using MRI and magnetic resonance spectroscopy fat quantification methods (40–43). Estimation of FF using T2-based techniques has been conducted in previous studies (17, 18). However, these studies have studied higher FFs (>5%) not comparable with the results of this study.
The importance of high SNR in the estimation of T2-relaxation times has been studied previously (44). Here, we simulated the effect of noise on fat quantification using T2-based methods and found that the 2- and 3-parameter fit overestimated the FF at lower SNRs. This could be explained by the fact that the presence of noise might be interpreted by the 3-parameter fit as fat signal, as T2,F > T2,W. Using correct T2-values was also shown to be of importance when using the 2- or 3-parameter fit, particularly for water, to measure low FFs correctly. Owing to a high lowest SNR (∼200) of the acquired MESE data, SNR may not be the main issue for the 2- and 3-parameter fit at low and intermediate FFs. Instead, incorrect T2 values are a more probable cause of bias. Like the NLLS-based methods, the Bayesian fit performed better as SNR increased. Simulations also showed that using a correct S0 value is important for obtaining an accurate estimation of the FF, particularly for intermediate FFs. The simulated Bayesian fit resulted in a larger standard deviation compared with the NLLS-based methods, suggesting that the Bayesian fitting method, using the slicesample algorithm as described in this work, might be less robust. Although this contradicts previous results (25), the used Bayesian probability approaches are not identical and might therefore not be comparable. In addition, the number of estimated parameters is larger in the Bayesian fit compared with the 2-parameter fit which affects the robustness.
Although the 2-parameter fit resulted in accurate FFs compared with low-resolution CSEI, it depends on whether it is possible to obtain both T2,F and T2,W without any contamination, that is, fluid accumulation due to edema or extramyocellular and intramyocellular fat. It has also been reported that T2,W varies between muscle groups (40). Using a T2,W calculated from an ROI placed in 1 muscle group could therefore result in incorrect FFs in other muscles. In this study, one volunteer had too little available subcutaneous fat, making it impossible to draw a ROI to obtain an individual T2,F. Alternatively, one could use T2-relaxation times obtained from literature. However, simulations in this study suggest that it is important to use correct T2-relaxation times to avoid biases. A fat quantification method without the need of ROIs, like the Bayesian method, might therefore be preferred.
Owing to varying T2-values between the muscles, one might expect that keeping T2,W fixed would result in less accurate FF calculation compared with estimating T2,W together with W and F. Both the in vivo results and the simulations suggested that this was not the case, as the 3-parameter fit overestimated the FF, and was more sensitive to incorrect T2-relaxation times. A recent paper instead described the fat signal decay using a biexponential model, that is, a triexponential model for the total (water and fat) signal (18). It is possible that a biexponential description of the fat signal could improve the results of the NLLS methods in this study. For the Bayesian method, a triexponential signal model has also been studied for intravoxel incoherent motion applications (45), which could be adapted for fat quantification purposes. Another source of error might be the use of only 1 T2-relaxation time to describe the fat signal decay, although it consists of several composites, each with an individual T2-relaxation time (29).
Although the Bayesian fit slightly underestimated the FF compared with low-resolution CSEI, there are numerous advantages with the method. For example, all volunteers could be evaluated independent of the amount of subcutaneous fat, as the method is not dependent on the ROI definition. Additional advantages are the possibility of obtaining T2,W maps and that no user input is needed. Further investigations to improve the performance of the Bayesian fit using slicesample are needed, including the choice of the number of echoes to include in the calculations, estimation of S0, smoothing level of the parameter probability density functions, and number of generated samples and burn-in factor in the slicesample algorithm.
Several drawbacks with the T2-based methods that were used in this study were found. First, the effect of B1-inhomogeneties was not accounted for, assuming perfect T2 decay of the signal over the course of the MESE acquisition. Methods suggested in previous studies include dismissing voxels where large B1-inhomogeneites are present by obtaining a B1-map by an additional data acquisition (18) and using a method based on extended phase graphs (46). Second, owing to the long T1-relaxation time of muscle tissue, an impractically long TR (>4 seconds) is needed to avoid T1 bias. Alternatively, as was done here, a T1-correction can be performed in the postprocessing steps. In this study, T1-relaxation times obtained from the literature were used to correct for T1 bias. This can introduce errors if the true T1-relaxation times are different from the ones obtained from the literature. Using individual T1-relaxation times could possibly improve the correction, but it will require additional data acquisition. Third, owing to the long acquisition times of MESE images, parallel imaging had to be used to reduce the scan time. This caused varying noise levels and therefore varying SNR over the images.
Several other drawbacks and limitations of the study were identified during this work. The study was conducted in healthy subjects only, and no pathological fat accumulation was seen. Thus, the range of FFs investigated was likely to be lower than that of a patient group. Phantom studies are not included, as it was not possible to construct a phantom which worked for all methods simultaneously. A completely fair comparison of the precision of the various methods was not possible, as they were acquired using different acquisition times and the number of estimated parameters differed between the methods. However, the effect of increasing the acquisition time of high-resolution MGRE images to that of MESE was investigated in 1 subject and it was found to still result in a high noise level and inferior image quality.
In conclusion, all the T2-based methods could produce high-resolution FF images of the calves of healthy volunteers, where the FF was 1%–6%. The 2-parameter fit showed the best quantitative agreement to low-resolution CSEI. The method can thus be an alternative to CSEI when the latter method fails to produce high-resolution FF images owing to low SNR or fat–water swaps. However, the NLLS-based methods are sensitive to incorrect T2-values, particularly T2,W for low FFs. Although the Bayesian fit avoids this particular limitation, further development is needed before it can be used for accurate fat quantification.