Introduction
Chemical shiftencoded 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, highresolution 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 T_{2} (16) rather than chemical shifts have been suggested for applications in skeletal muscles (17, 18). With T_{2}based methods, there is a possibility of obtaining information on FF and T_{2} relaxation times simultaneously (18). This would offer more information about the status of the disease, as a change in muscle T_{2}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 T_{2}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 T_{2}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 intravoxel 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 T_{2}based fat quantification methods, using highresolution MRI for low FFs in healthy volunteers, and compare it with CSEI. The first T_{2}based method uses fixed T_{2}relaxation times of both water and fat as described by Kan et al. (17). The second method uses only a fixed fat T_{2}relaxation time to study the possibility of obtaining a simultaneous T_{2} 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 T_{2}based methods.
Methodology
Subjects
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 6element 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 mm^{2} and thus acquiring data at low and highspatial resolution. A single 6mm transversal slice was collected for each acquisition, centered at the widest part of the left calf of each volunteer.
A multiecho gradient echo (MGRE) sequence with 6 echoes was used for the CSEI method. To avoid T_{1} 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: TE_{1}/ΔTE = 1.11/1.56 milliseconds (low resolution), TE_{1}/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 highresolution 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 T_{2}based methods, 32 multiecho 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).
Fat/WaterSeparation Methods
The methods used in this study are summarized in Figure 1. All calculations were performed using MATLAB (r2017a, The MathWorks, Inc., Natick, MA).
Figure 1.
Schematic view over the used methods (chemical shiftencoded imaging [CSEI], 2parameter fit, 3parameter fit, and Bayesian fit) and the corresponding outputs.
Chemical ShiftEncoded Imaging
The FF was calculated using a complex and magnitudebased 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:
where the complexvalued
F and
W are the estimated fat and water signals, respectively. T
_{1} bias was avoided by using a low flip angle acquisition.
T_{2}Relaxation TimeBased Imaging
Two of the T_{2}based methods use a fixed T_{2}relaxation time of fat (T_{2,F}), of which 1 uses a fixed T_{2}relaxation time of water (T_{2,W}) as well. To obtain these values, a monoexponential fit of the signal decay was carried out voxel by voxel, resulting in a T_{2} map. For each volunteer, individual T_{2,F} and T_{2,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 T_{2,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 T_{2,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.
Figure 2.
The regions of interest (ROIs) used for calculating T_{2,W} and T_{2,F} (dashed line), and the fat fraction (FF) in 3 calf muscles (solid line): gastrocnemius, soleus, and tibialis anterior.
TwoParameter Fit—Fixed T_{2,F} and T_{2,W}.
Using the estimated T_{2,F} and T_{2,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:
where
S is the measured signal at TE
t, and
T_{2,F} and
T_{2,W} are kept fixed.
ThreeParameter Fit—Fixed T_{2,F}.
Using the same signal model [equation (2)] as in the 2parameter fit and fixed T_{2,F} value, T_{2,W}, W, and F were estimated using a trust regionbased NLLS fitting algorithm.
Bayesian Fitting Method.
An alternative to exponential fitting is using a Bayesian probability method (31). Here, all four parameters (T_{2,W}, T_{2,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:
where
S_{0} denotes the signal at
t = 0 and
f denotes the FF in the range [0, 1]. To obtain
S_{0}, linear regression was performed on linearized data, ln(
S), in each voxel. However, owing to the biexponential form of the signal decay, ln(
S) is not linear. To compensate for this, ln(
S) was weighted by the signal amplitude
S, making the fit rely mostly on the earlier echoes of the signal. Water and fat amplitudes,
W =
S_{0}(1 −
f) and
F =
S_{0}f, respectively, were calculated before correcting for T
_{1} bias and calculating FF as described by equation (
4).
Fat Fraction Calculation and T_{1}Correction
Owing to the long T_{1}relaxation time of muscle tissue and the desire to keep the acquisition times feasibly low, all the T_{2}based fat quantification methods described in the above sections were corrected for T_{1}relaxation bias. The T_{1}relaxation times T_{1,W} = 1420 milliseconds and T_{1,F} = 371 milliseconds (16) were used to correct the water and fat signal amplitudes according to F_{T1corr} = F/[1 − exp(−TR/T_{1,F})] and W_{T1corr} = W/[1 − exp(−TR/T_{1,W})], respectively. Hence, the FF can be described using the following equation:
Because the MGRE data were collected with a low flip angle, no correction for T
_{1} bias was needed for CSEI.
Data Analysis
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 highresolution 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 swapfree ROI could be defined, the entire muscle group was excluded from further analysis.
Mean signaltonoise 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 gfactor was expected to be close to 1.
Wilcoxon signedrank tests and Bland–Altman analysis were performed to compare the estimated FFs within the ROIs using the 2parameter fit, 3parameter fit, Bayesian fit, and highresolution CSEI, to the FFs calculated with lowresolution CSEI.
Simulations
Simulations were conducted to investigate the effects of incorrect T_{2} 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 T_{2,W} = 40 milliseconds and T_{2,F} = 160 milliseconds as true T_{2}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 T_{2}relaxation times, simulations were performed by using incorrect T_{2,W} and T_{2,F} in the 2parameter fit method and incorrect T_{2,F} in the 3parameter fit method. T_{2,W} was set to vary between 22 and 42 milliseconds and T_{2,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 S_{0} value was studied by varying the S_{0} 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 T_{2}based methods by altering the SNR of the simulated signal. The true T_{2}relaxation times were used to generate a noisefree 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.
Results
Volunteer Study
The estimated mean T_{2}relaxation times and standard deviations of muscle (tibialis anterior) and fat (subcutaneous fat), using the monoexponential fit, the 3parameter fit, and the Bayesian fit are presented in Figure 3. The 3parameter fit estimated a lower value of T_{2,W} compared with the monoexponential fit and the Bayesian fit. The estimated T_{2,W} from all three methods were independent of matrix size.
Figure 3.
The mean and standard deviation of T_{2,W} (A) within an ROI placed in tibialis anterior and T_{2,F} (B) within an ROI placed in the subcutaneous fat, of all volunteers (except one in the monoexponential fit) at high and lowresolution imaging.
Example FF images of all 4 methods can be seen in Figure 4. In contrast to the T_{2}based methods, the highresolution CSEI produced an FF image with a noise level that concealed the anatomy of the calf. Although all 3 T_{2}based methods produced FF images in which the different muscles were distinguishable, the estimated FFs were different between the methods. Because the highresolution CSEI images with a single average (Figure 4) had a low SNR, additional highresolution 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.
Figure 4.
Fat fraction maps of a calf calculated at low and high resolution, using four methods: CSEI, 2parameter fit, 3parameter fit, and Bayesian fit.
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 highresolution CSEI, results from 3 volunteers were excluded. Compared with the lowresolution CSEI method as reference, the 2parameter fit was able to estimate the muscle FF accurately, showing only a small overestimation of FFs >3%. Highresolution CSEI overestimated the lower FFs and underestimated the higher FFs of the muscles, whereas the 3parameter 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 Pvalues of all volunteers and image resolutions are presented. All calculated mean FFs obtained from the 3parameter fit, at both high and low resolution, significantly (P < .05) overestimated the FFs obtained from the reference method in comparison with the 2parameter fit in which no significant differences were found.
Figure 5.
To the left: Scatter plots showing the estimated FF of highresolution CSEI (A), 2parameter fit (B), 3parameter fit (C), and Bayesian fit (D). Each plot shows data points that represent the mean FF within an ROI (3 muscles measured for each volunteer), the linear regression fit (dashed), and the identity line (solid). To the right: Bland–Altman plots of highresolution CSEI (E), 2parameter fit (F), 3parameter fit (G), and Bayesian fit (H), showing the mean difference (solid) and 1.96 standard deviations (dashed).
Table 1.
Mean Estimated Fat Fraction and Standard Deviation Between Volunteers, Using All 4 Methods, in Gastrocnemius, Soleus, and Tibialis Anterior Muscles

CSEI 
2Parameter Fit 
3Parameter Fit 
Bayesian Fit 
128 × 128

Fat fraction (%) 
Gastrocnemius 
3.39 ± 0.97 
2.70 ± 1.95 
5.13 ± 1.60 
1.99 ± 0.59 

— 
(P = 0.43) 
(P = 9.1 · 10^{−3}) 
(P = 1.3 · 10^{−3}) 
Soleus 
4.15 ± 1.16 
4.48 ± 1.03 
6.22 ± 0.98 
2.32 ± 0.37 

— 
(P = 0.38) 
(P = 1.0 · 10^{−3}) 
(P = 2.2 · 10^{−3}) 
Tibialis anterior 
1.80 ± 0.65 
1.32 ± 0.67 
4.02 ± 0.44 
1.5 ± 0.15 

— 
(P = 0.19) 
(P = 1.8 · 10^{−4}) 
(P = 0.62) 
Linear regression parameters 
Intercept 
— 
−0.62 
2.1 
0.91 


(CI = −1.7–0.45) 
(CI = 1.4–2.8) 
(CI = 0.65–1.2) 
Slope 
— 
1.1 
0.92 
0.33 


(CI = 0.78–1.4) 
(CI = 0.71–1.1) 
(CI = 0.26–0.41) 
R^{2}

— 
0.64 
0.75 
0.74 
Bland–Altman 
Mean (limits of agreement) 
— 
−0.32 (−2.5, 1.9) 
1.9 (0.44, 3.3) 
−1.2 (−3.0, 0.68) 
512 × 512

Fat fraction (%) 
Gastrocnemius 
3.30 ± 0.58 
4.00 ± 2.03 
6.75 ± 1.52 
2.51 ± 0.60 

(P = 0.63) 
(P = 0.52) 
(P = 2.5 · 10^{−4}) 
(P = 9.1 · 10^{−3}) 
Soleus 
3.38 ± 0.56 
4.42 ± 1.20 
6.81 ± 0.95 
2.51 ± 0.39 

(P = 0.38) 
(P = 0.43) 
(P = 3.3 · 10^{−4}) 
(P = 2.2 · 10^{−3}) 
Tibialis anterior 
2.54 ± 0.62 
1.71 ± 0.68 
4.79 ± 0.56 
1.68 ± 0.21 

(P = 5.8 · 10^{−4}) 
(P = 0.73) 
(P = 1.8 · 10^{−4}) 
(P = 0.68) 
Linear regression parameters 
Intercept 
2.2 
−0.19 
3.4 
1.1 

(CI = 1.6–2.9) 
(CI = −0.95–0.58) 
(CI = 2.8–4.0) 
(CI = 0.82–1.4) 
Slope 
0.29 
1.1 
0.87 
0.35 

(CI = 0.09–0.48) 
(CI = 0.91–1.4) 
(CI = 0.68–1.1) 
(CI = 0.27–0.44) 
R^{2}

0.34 
0.79 
0.76 
0.73 
Bland–Altman 
Mean (limits of agreement) 
0.18 (−2.0, 2.4) 
0.24 (−1.3, 1.8) 
3.0 (1.7, 4.3) 
−0.91 (−2.7, 0.90) 
In Figure 6, the acquired signal decay of 3 voxels of low and highresolution MESE images and the fitted curves of the 3 T_{2}methods are depicted. All 3 methods performed equal at high FF, whereas at lower FFs (∼17% and 3%), the estimated signals differ. The 3parameter fit results in a slower decaying signal compared with the other 2 methods, whereas the Bayesian method results in a faster decaying signal.
Figure 6.
The acquired and fitted signal decay of 3 voxels with different FFs are shown for the lowresolution (A–C) and highresolution (D–F) MESE images.
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 gfactor is close to 1.
Simulations
The simulated effect on the estimation of FF when using incorrect T_{2,W} and T_{2,F}, respectively, is shown in Figure 7. In both cases, an underestimation of T_{2}relaxation time resulted in an overestimation of the FF, whereas an overestimation of T_{2}relaxation time resulted in an underestimation of FF. The 3parameter fit was more sensitive to errors in T_{2,F} compared with the 2parameter fit. At higher FFs, it was more important that T_{2,F} was estimated correctly, whereas a correct T_{2,W} was more important at low FFs. For the Bayesian fit, the effect of using an incorrect S_{0} value, as well as the standard deviation of the estimated FF, is shown in Figure 8. Using an underestimated S_{0} value resulted in an underestimation of the FF, and an overestimated S_{0} value resulted in an overestimated FF. However, the effect of using an overestimated S_{0} value was greater than that using an underestimated one. Lower FFs (2%–5%) were less sensitive for incorrect S_{0} compared with higher FFs (10%–30%). This can also be seen by looking at the standard deviation that was larger for higher FFs.
Figure 7.
The difference between the true and estimated FFs when using incorrect T_{2,W} (A) and incorrect T_{2,F} (B) in the 2parameter fit and when using incorrect T_{2,F} (C) in the 3parameter fit. The true T_{2,W} and T_{2,F} are 40 milliseconds and 160 milliseconds, respectively.
Figure 8.
The simulated effect of using an incorrect S_{0} value in the Bayesian fitting method showing the difference between the estimated and true FF (left), and the standard deviation of 1000 estimations (right).
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 T_{2}based methods. The accuracy of both the 2 and 3parameter fits increased with SNR (except for FF = 95% using the 3parameter fit). The 2parameter fit was less sensitive to noise than the 3parameter fit. The Bayesian fit was more affected by noise at higher SNR compared with the NLLSbased methods. As the SNR increased, the standard deviation decreased for all methods and FFs.
Figure 9.
The difference between estimated FF and true FF equal to 2%, 5%, 10%, 30%, and 95% at different signaltonoise ratios (SNRs) (20, 50, 150, 300, and 600) using the 2parameter fit (A), the 3parameter fit (B), and the Bayesian fit (C). The corresponding standard deviations of 1000 estimations using the 2parameter fit (D), the 3parameter fit (E), and the Bayesian fit (F) are also shown. The mean SNR of the collected MESE images (512 × 512) in muscle and fat is shown in the first plot (A). At low FF, all 3 methods overestimate the FF in the presence of a high noise level. The difference between estimated and true FF, of the 3parameter fit outside the shown interval in (B) are: −40.9% (SNR = 20) and −27.8% (SNR = 50). The corresponding standard deviation not shown in (E) is ±41.4% and ±39.0%, respectively.
Discussion
In this work, 3 T_{2}based approaches (2parameter fit, 3parameter fit, and a Bayesian probability method) have been studied and compared with CSEI in terms of their capability to correctly estimate low FFs using highresolution images. This was carried out through a study on healthy volunteers and by simulations. All T_{2}based methods provided highresolution FF images in which it was possible to delineate the different muscles of the calf. With respect to the estimated FFs, the 2parameter fit showed best agreement to the reference method.
Even though the measured mean FF of highresolution CSEI in vivo corresponded well with the lowresolution 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 T_{1}bias, including an estimation of the true flip angle map, and it would therefore introduce an additional source of error. As lowresolution 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 highresolution CSEI owing to the long TE needed. All highresolution CSEI data from 3 subjects had to be excluded because of this. The interecho time of highresolution 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 T_{2}relaxation times of muscle tissue and subcutaneous fat in this study correspond well with T_{2}relaxation values of healthy volunteers from literature [T_{2,W} = 32−40 milliseconds and T_{2,F} = 133154 milliseconds (16, 17, 38–40)], although the Bayesian fitting model results in a slightly overestimated T_{2,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 T_{2}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 T_{2}relaxation times has been studied previously (44). Here, we simulated the effect of noise on fat quantification using T_{2}based methods and found that the 2 and 3parameter fit overestimated the FF at lower SNRs. This could be explained by the fact that the presence of noise might be interpreted by the 3parameter fit as fat signal, as T_{2,F} > T_{2,W}. Using correct T_{2}values was also shown to be of importance when using the 2 or 3parameter 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 3parameter fit at low and intermediate FFs. Instead, incorrect T_{2} values are a more probable cause of bias. Like the NLLSbased methods, the Bayesian fit performed better as SNR increased. Simulations also showed that using a correct S_{0} 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 NLLSbased 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 2parameter fit which affects the robustness.
Although the 2parameter fit resulted in accurate FFs compared with lowresolution CSEI, it depends on whether it is possible to obtain both T_{2,F} and T_{2,W} without any contamination, that is, fluid accumulation due to edema or extramyocellular and intramyocellular fat. It has also been reported that T_{2,W} varies between muscle groups (40). Using a T_{2,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 T_{2,F}. Alternatively, one could use T_{2}relaxation times obtained from literature. However, simulations in this study suggest that it is important to use correct T_{2}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 T_{2}values between the muscles, one might expect that keeping T_{2,W} fixed would result in less accurate FF calculation compared with estimating T_{2,W} together with W and F. Both the in vivo results and the simulations suggested that this was not the case, as the 3parameter fit overestimated the FF, and was more sensitive to incorrect T_{2}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 T_{2}relaxation time to describe the fat signal decay, although it consists of several composites, each with an individual T_{2}relaxation time (29).
Although the Bayesian fit slightly underestimated the FF compared with lowresolution 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 T_{2,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 S_{0}, smoothing level of the parameter probability density functions, and number of generated samples and burnin factor in the slicesample algorithm.
Several drawbacks with the T_{2}based methods that were used in this study were found. First, the effect of B_{1}inhomogeneties was not accounted for, assuming perfect T_{2} decay of the signal over the course of the MESE acquisition. Methods suggested in previous studies include dismissing voxels where large B_{1}inhomogeneites are present by obtaining a B_{1}map by an additional data acquisition (18) and using a method based on extended phase graphs (46). Second, owing to the long T_{1}relaxation time of muscle tissue, an impractically long TR (>4 seconds) is needed to avoid T_{1} bias. Alternatively, as was done here, a T_{1}correction can be performed in the postprocessing steps. In this study, T_{1}relaxation times obtained from the literature were used to correct for T_{1} bias. This can introduce errors if the true T_{1}relaxation times are different from the ones obtained from the literature. Using individual T_{1}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 highresolution 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 T_{2}based methods could produce highresolution FF images of the calves of healthy volunteers, where the FF was 1%–6%. The 2parameter fit showed the best quantitative agreement to lowresolution CSEI. The method can thus be an alternative to CSEI when the latter method fails to produce highresolution FF images owing to low SNR or fat–water swaps. However, the NLLSbased methods are sensitive to incorrect T_{2}values, particularly T_{2,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.
Acknowledgments
This research was supported by Magnus Bergvalls stiftelse and Direktör Albert Påhlssons Stiftelse.
Disclosure: No disclosures to report.
Conflict of Interest: The authors have no conflict of interest to declare.
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Research Articles
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TOMOGRAPHY, September 2017, Volume 3, Issue 3:153162
DOI: 10.18383/j.tom.2017.00011
HighResolution MR Imaging of Muscular Fat Fraction—Comparison of Three T2Based Methods and Chemical ShiftEncoded Imaging
Lena Trinh^{1}, Emelie Lind^{1}, Pernilla Peterson^{1}, Jonas Svensson^{1}, Lars E. Olsson^{1}, Sven Månsson^{1}
Abstract
Chemical shiftencoded imaging (CSEI) is the most common magnetic resonance imaging fat–water separation method. However, when high spatial resolution fat fraction (FF) images are desired, CSEI might be challenging owing to the increased interecho spacing. Here, 3 T_{2}based methods have been assessed as alternative methods for obtaining highresolution FF images. Images from the calf of 10 healthy volunteers were acquired; FF maps were then estimated using 3 T_{2}based methods (2 and 3parameter nonlinear least squares fit and a Bayesian probability method) and CSEI for reference. In addition, simulations were conducted to characterize the performance of various methods. Here, all T_{2}based methods resulted in qualitatively improved highresolution FF images compared with highresolution CSEI. The 2parameter fit showed best quantitative agreement to lowresolution CSEI, even at low FF. The estimated T_{2}values of fat and water, and the estimated muscle FF of the calf, agreed well with previously published data. In conclusion, T_{2}based methods can provide improved highresolution FF images of the calf compared with the CSEI method.
Introduction
Chemical shiftencoded 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, highresolution 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 T_{2} (16) rather than chemical shifts have been suggested for applications in skeletal muscles (17, 18). With T_{2}based methods, there is a possibility of obtaining information on FF and T_{2} relaxation times simultaneously (18). This would offer more information about the status of the disease, as a change in muscle T_{2}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 T_{2}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 T_{2}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 intravoxel 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 T_{2}based fat quantification methods, using highresolution MRI for low FFs in healthy volunteers, and compare it with CSEI. The first T_{2}based method uses fixed T_{2}relaxation times of both water and fat as described by Kan et al. (17). The second method uses only a fixed fat T_{2}relaxation time to study the possibility of obtaining a simultaneous T_{2} 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 T_{2}based methods.
Methodology
Subjects
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 6element 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 mm^{2} and thus acquiring data at low and highspatial resolution. A single 6mm transversal slice was collected for each acquisition, centered at the widest part of the left calf of each volunteer.
A multiecho gradient echo (MGRE) sequence with 6 echoes was used for the CSEI method. To avoid T_{1} 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: TE_{1}/ΔTE = 1.11/1.56 milliseconds (low resolution), TE_{1}/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 highresolution 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 T_{2}based methods, 32 multiecho 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).
Fat/WaterSeparation Methods
The methods used in this study are summarized in Figure 1. All calculations were performed using MATLAB (r2017a, The MathWorks, Inc., Natick, MA).
Figure 1.
Schematic view over the used methods (chemical shiftencoded imaging [CSEI], 2parameter fit, 3parameter fit, and Bayesian fit) and the corresponding outputs.
Chemical ShiftEncoded Imaging
The FF was calculated using a complex and magnitudebased 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:
(1)
T_{2}Relaxation TimeBased Imaging
Two of the T_{2}based methods use a fixed T_{2}relaxation time of fat (T_{2,F}), of which 1 uses a fixed T_{2}relaxation time of water (T_{2,W}) as well. To obtain these values, a monoexponential fit of the signal decay was carried out voxel by voxel, resulting in a T_{2} map. For each volunteer, individual T_{2,F} and T_{2,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 T_{2,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 T_{2,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.
Figure 2.
The regions of interest (ROIs) used for calculating T_{2,W} and T_{2,F} (dashed line), and the fat fraction (FF) in 3 calf muscles (solid line): gastrocnemius, soleus, and tibialis anterior.
TwoParameter Fit—Fixed T_{2,F} and T_{2,W}.
Using the estimated T_{2,F} and T_{2,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:
(2)
ThreeParameter Fit—Fixed T_{2,F}.
Using the same signal model [equation (2)] as in the 2parameter fit and fixed T_{2,F} value, T_{2,W}, W, and F were estimated using a trust regionbased NLLS fitting algorithm.
Bayesian Fitting Method.
An alternative to exponential fitting is using a Bayesian probability method (31). Here, all four parameters (T_{2,W}, T_{2,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:
(3)
Fat Fraction Calculation and T_{1}Correction
Owing to the long T_{1}relaxation time of muscle tissue and the desire to keep the acquisition times feasibly low, all the T_{2}based fat quantification methods described in the above sections were corrected for T_{1}relaxation bias. The T_{1}relaxation times T_{1,W} = 1420 milliseconds and T_{1,F} = 371 milliseconds (16) were used to correct the water and fat signal amplitudes according to F_{T1corr} = F/[1 − exp(−TR/T_{1,F})] and W_{T1corr} = W/[1 − exp(−TR/T_{1,W})], respectively. Hence, the FF can be described using the following equation:
(4)
Data Analysis
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 highresolution 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 swapfree ROI could be defined, the entire muscle group was excluded from further analysis.
Mean signaltonoise 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 gfactor was expected to be close to 1.
Wilcoxon signedrank tests and Bland–Altman analysis were performed to compare the estimated FFs within the ROIs using the 2parameter fit, 3parameter fit, Bayesian fit, and highresolution CSEI, to the FFs calculated with lowresolution CSEI.
Simulations
Simulations were conducted to investigate the effects of incorrect T_{2} 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 T_{2,W} = 40 milliseconds and T_{2,F} = 160 milliseconds as true T_{2}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 T_{2}relaxation times, simulations were performed by using incorrect T_{2,W} and T_{2,F} in the 2parameter fit method and incorrect T_{2,F} in the 3parameter fit method. T_{2,W} was set to vary between 22 and 42 milliseconds and T_{2,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 S_{0} value was studied by varying the S_{0} 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 T_{2}based methods by altering the SNR of the simulated signal. The true T_{2}relaxation times were used to generate a noisefree 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.
Results
Volunteer Study
The estimated mean T_{2}relaxation times and standard deviations of muscle (tibialis anterior) and fat (subcutaneous fat), using the monoexponential fit, the 3parameter fit, and the Bayesian fit are presented in Figure 3. The 3parameter fit estimated a lower value of T_{2,W} compared with the monoexponential fit and the Bayesian fit. The estimated T_{2,W} from all three methods were independent of matrix size.
Figure 3.
The mean and standard deviation of T_{2,W} (A) within an ROI placed in tibialis anterior and T_{2,F} (B) within an ROI placed in the subcutaneous fat, of all volunteers (except one in the monoexponential fit) at high and lowresolution imaging.
Example FF images of all 4 methods can be seen in Figure 4. In contrast to the T_{2}based methods, the highresolution CSEI produced an FF image with a noise level that concealed the anatomy of the calf. Although all 3 T_{2}based methods produced FF images in which the different muscles were distinguishable, the estimated FFs were different between the methods. Because the highresolution CSEI images with a single average (Figure 4) had a low SNR, additional highresolution 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.
Figure 4.
Fat fraction maps of a calf calculated at low and high resolution, using four methods: CSEI, 2parameter fit, 3parameter fit, and Bayesian fit.
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 highresolution CSEI, results from 3 volunteers were excluded. Compared with the lowresolution CSEI method as reference, the 2parameter fit was able to estimate the muscle FF accurately, showing only a small overestimation of FFs >3%. Highresolution CSEI overestimated the lower FFs and underestimated the higher FFs of the muscles, whereas the 3parameter 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 Pvalues of all volunteers and image resolutions are presented. All calculated mean FFs obtained from the 3parameter fit, at both high and low resolution, significantly (P < .05) overestimated the FFs obtained from the reference method in comparison with the 2parameter fit in which no significant differences were found.
Figure 5.
To the left: Scatter plots showing the estimated FF of highresolution CSEI (A), 2parameter fit (B), 3parameter fit (C), and Bayesian fit (D). Each plot shows data points that represent the mean FF within an ROI (3 muscles measured for each volunteer), the linear regression fit (dashed), and the identity line (solid). To the right: Bland–Altman plots of highresolution CSEI (E), 2parameter fit (F), 3parameter fit (G), and Bayesian fit (H), showing the mean difference (solid) and 1.96 standard deviations (dashed).
Table 1.
Mean Estimated Fat Fraction and Standard Deviation Between Volunteers, Using All 4 Methods, in Gastrocnemius, Soleus, and Tibialis Anterior Muscles
i] Pvalues are given for the comparison against low resolution CSEI. Confidence intervals (CI) are given at a significance level of 0.05.
In Figure 6, the acquired signal decay of 3 voxels of low and highresolution MESE images and the fitted curves of the 3 T_{2}methods are depicted. All 3 methods performed equal at high FF, whereas at lower FFs (∼17% and 3%), the estimated signals differ. The 3parameter fit results in a slower decaying signal compared with the other 2 methods, whereas the Bayesian method results in a faster decaying signal.
Figure 6.
The acquired and fitted signal decay of 3 voxels with different FFs are shown for the lowresolution (A–C) and highresolution (D–F) MESE images.
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 gfactor is close to 1.
Simulations
The simulated effect on the estimation of FF when using incorrect T_{2,W} and T_{2,F}, respectively, is shown in Figure 7. In both cases, an underestimation of T_{2}relaxation time resulted in an overestimation of the FF, whereas an overestimation of T_{2}relaxation time resulted in an underestimation of FF. The 3parameter fit was more sensitive to errors in T_{2,F} compared with the 2parameter fit. At higher FFs, it was more important that T_{2,F} was estimated correctly, whereas a correct T_{2,W} was more important at low FFs. For the Bayesian fit, the effect of using an incorrect S_{0} value, as well as the standard deviation of the estimated FF, is shown in Figure 8. Using an underestimated S_{0} value resulted in an underestimation of the FF, and an overestimated S_{0} value resulted in an overestimated FF. However, the effect of using an overestimated S_{0} value was greater than that using an underestimated one. Lower FFs (2%–5%) were less sensitive for incorrect S_{0} compared with higher FFs (10%–30%). This can also be seen by looking at the standard deviation that was larger for higher FFs.
Figure 7.
The difference between the true and estimated FFs when using incorrect T_{2,W} (A) and incorrect T_{2,F} (B) in the 2parameter fit and when using incorrect T_{2,F} (C) in the 3parameter fit. The true T_{2,W} and T_{2,F} are 40 milliseconds and 160 milliseconds, respectively.
Figure 8.
The simulated effect of using an incorrect S_{0} value in the Bayesian fitting method showing the difference between the estimated and true FF (left), and the standard deviation of 1000 estimations (right).
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 T_{2}based methods. The accuracy of both the 2 and 3parameter fits increased with SNR (except for FF = 95% using the 3parameter fit). The 2parameter fit was less sensitive to noise than the 3parameter fit. The Bayesian fit was more affected by noise at higher SNR compared with the NLLSbased methods. As the SNR increased, the standard deviation decreased for all methods and FFs.
Figure 9.
The difference between estimated FF and true FF equal to 2%, 5%, 10%, 30%, and 95% at different signaltonoise ratios (SNRs) (20, 50, 150, 300, and 600) using the 2parameter fit (A), the 3parameter fit (B), and the Bayesian fit (C). The corresponding standard deviations of 1000 estimations using the 2parameter fit (D), the 3parameter fit (E), and the Bayesian fit (F) are also shown. The mean SNR of the collected MESE images (512 × 512) in muscle and fat is shown in the first plot (A). At low FF, all 3 methods overestimate the FF in the presence of a high noise level. The difference between estimated and true FF, of the 3parameter fit outside the shown interval in (B) are: −40.9% (SNR = 20) and −27.8% (SNR = 50). The corresponding standard deviation not shown in (E) is ±41.4% and ±39.0%, respectively.
Discussion
In this work, 3 T_{2}based approaches (2parameter fit, 3parameter fit, and a Bayesian probability method) have been studied and compared with CSEI in terms of their capability to correctly estimate low FFs using highresolution images. This was carried out through a study on healthy volunteers and by simulations. All T_{2}based methods provided highresolution FF images in which it was possible to delineate the different muscles of the calf. With respect to the estimated FFs, the 2parameter fit showed best agreement to the reference method.
Even though the measured mean FF of highresolution CSEI in vivo corresponded well with the lowresolution 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 T_{1}bias, including an estimation of the true flip angle map, and it would therefore introduce an additional source of error. As lowresolution 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 highresolution CSEI owing to the long TE needed. All highresolution CSEI data from 3 subjects had to be excluded because of this. The interecho time of highresolution 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 T_{2}relaxation times of muscle tissue and subcutaneous fat in this study correspond well with T_{2}relaxation values of healthy volunteers from literature [T_{2,W} = 32−40 milliseconds and T_{2,F} = 133154 milliseconds (16, 17, 38–40)], although the Bayesian fitting model results in a slightly overestimated T_{2,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 T_{2}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 T_{2}relaxation times has been studied previously (44). Here, we simulated the effect of noise on fat quantification using T_{2}based methods and found that the 2 and 3parameter fit overestimated the FF at lower SNRs. This could be explained by the fact that the presence of noise might be interpreted by the 3parameter fit as fat signal, as T_{2,F} > T_{2,W}. Using correct T_{2}values was also shown to be of importance when using the 2 or 3parameter 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 3parameter fit at low and intermediate FFs. Instead, incorrect T_{2} values are a more probable cause of bias. Like the NLLSbased methods, the Bayesian fit performed better as SNR increased. Simulations also showed that using a correct S_{0} 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 NLLSbased 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 2parameter fit which affects the robustness.
Although the 2parameter fit resulted in accurate FFs compared with lowresolution CSEI, it depends on whether it is possible to obtain both T_{2,F} and T_{2,W} without any contamination, that is, fluid accumulation due to edema or extramyocellular and intramyocellular fat. It has also been reported that T_{2,W} varies between muscle groups (40). Using a T_{2,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 T_{2,F}. Alternatively, one could use T_{2}relaxation times obtained from literature. However, simulations in this study suggest that it is important to use correct T_{2}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 T_{2}values between the muscles, one might expect that keeping T_{2,W} fixed would result in less accurate FF calculation compared with estimating T_{2,W} together with W and F. Both the in vivo results and the simulations suggested that this was not the case, as the 3parameter fit overestimated the FF, and was more sensitive to incorrect T_{2}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 T_{2}relaxation time to describe the fat signal decay, although it consists of several composites, each with an individual T_{2}relaxation time (29).
Although the Bayesian fit slightly underestimated the FF compared with lowresolution 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 T_{2,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 S_{0}, smoothing level of the parameter probability density functions, and number of generated samples and burnin factor in the slicesample algorithm.
Several drawbacks with the T_{2}based methods that were used in this study were found. First, the effect of B_{1}inhomogeneties was not accounted for, assuming perfect T_{2} decay of the signal over the course of the MESE acquisition. Methods suggested in previous studies include dismissing voxels where large B_{1}inhomogeneites are present by obtaining a B_{1}map by an additional data acquisition (18) and using a method based on extended phase graphs (46). Second, owing to the long T_{1}relaxation time of muscle tissue, an impractically long TR (>4 seconds) is needed to avoid T_{1} bias. Alternatively, as was done here, a T_{1}correction can be performed in the postprocessing steps. In this study, T_{1}relaxation times obtained from the literature were used to correct for T_{1} bias. This can introduce errors if the true T_{1}relaxation times are different from the ones obtained from the literature. Using individual T_{1}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 highresolution 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 T_{2}based methods could produce highresolution FF images of the calves of healthy volunteers, where the FF was 1%–6%. The 2parameter fit showed the best quantitative agreement to lowresolution CSEI. The method can thus be an alternative to CSEI when the latter method fails to produce highresolution FF images owing to low SNR or fat–water swaps. However, the NLLSbased methods are sensitive to incorrect T_{2}values, particularly T_{2,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.
Notes
[2] Abbreviations:
CSEI
Chemical shiftencoded imaging
FF
fat fraction
MRI
magnetic resonance imaging
NLLS
nonlinear least squares
MGRE
multi echo gradient echo
TR
repetition time
TE
echo time
BW
bandwidth
MESE
multi echo spin echo
T_{2,F}
T_{2}relaxation time of fat
T_{2,W}
T_{2}relaxation time of water
ROI
regionofinterest
SNR
signaltonoise ratio
Acknowledgments
This research was supported by Magnus Bergvalls stiftelse and Direktör Albert Påhlssons Stiftelse.
Disclosure: No disclosures to report.
Conflict of Interest: The authors have no conflict of interest to declare.
References
Journal Information
Journal ID (nlmta): tom
Journal ID (publisherid): TOMOG
Title: Tomography
Subtitle: A Journal for Imaging Research
Abbreviated Title: Tomography
ISSN (print): 23791381
ISSN (electronic): 2379139X
Publisher: Grapho Publications, LLC (Ann Abor, Michigan)
Article Information
Self URI: media/vol3/issue3/pdf/tomo03153.pdf
Copyright statement: © 2017 The Authors. Published by Grapho Publications, LLC
Copyright: 2017, Grapho Publications, LLC
License (openaccess, http://creativecommons.org/licenses/byncnd/4.0/):
This is an open access article under the CC BYNCND license (http://creativecommons.org/licenses/byncnd/4.0/).
Publication date (print): September 2017
Volume: 3
Issue: 3
Pages: 153162
Publisher ID: TOMO201700011
DOI: 10.18383/j.tom.2017.00011
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