Fat quantification with IDEAL gradient echo imaging: Correction of bias from T1 and noise

Authors

  • Chia-Ying Liu,

    Corresponding author
    1. Department of Radiology, University of Wisconsin-Madison, Madison, WI, USA
    2. Department of Medical Physics, University of Wisconsin-Madison, Madison, WI, USA
    • Department of Radiology, J5/M150, CSC, University of Wisconsin, 600 Highland Avenue, Madison, WI 53792-3252
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  • Charles A. McKenzie,

    1. Department of Radiology, Beth Israel-Deaconess Medical Center and Harvard Medical School, Boston, MA, USA
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  • Huanzhou Yu,

    1. Global Applied Science Laboratory, GE Healthcare, Menlo Park, CA, USA
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  • Jean H. Brittain,

    1. Global Applied Science Laboratory, GE Healthcare, Madison, WI, USA
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  • Scott B. Reeder

    1. Department of Radiology, University of Wisconsin-Madison, Madison, WI, USA
    2. Department of Medical Physics, University of Wisconsin-Madison, Madison, WI, USA
    3. Department of Biomedical Engineering, University of Wisconsin-Madison, Madison, WI, USA
    4. Department of Medicine, University of Wisconsin-Madison, Madison, WI, USA
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Abstract

Quantification of hepatic steatosis is a significant unmet need for the diagnosis and treatment of patients with nonalcoholic fatty liver disease (NAFLD). MRI is capable of separating water and fat signals in order to quantify fatty infiltration of the liver (hepatic steatosis). Unfortunately, fat signal has confounding T1 effects and the nonzero mean noise in low signal-to-noise ratio (SNR) magnitude images can lead to incorrect estimation of the true lipid percentage. In this study, the effects of bias from T1 effects and image noise were investigated. An oil/water phantom with volume fat-fractions ranging linearly from 0% to 100% was designed and validated using a spoiled gradient echo (SPGR) sequence in combination with a chemical-shift based fat-water separation method known as iterative decomposition of water and fat with echo asymmetry and least squares estimation (IDEAL). We demonstrated two approaches to reduce the effects of T1: small flip angle (flip angle) and dual flip angle methods. Both methods were shown to effectively minimize deviation of the measured fat-fraction from its true value. We also demonstrated two methods to reduce noise bias: magnitude discrimination and phase-constrained reconstruction. Both methods were shown to reduce this noise bias effectively from 15% to less than 1%. Magn Reson Med 58:354–364, 2007. © 2007 Wiley-Liss, Inc.

The importance of fatty infiltration (hepatic steatosis) in the progression of diffuse liver disorders is well documented (1–4). Nonalcoholic fatty liver disease (NAFLD) is a condition with increasing recognition as the most common cause of chronic liver disease, afflicting an estimated 14% to 30% of the general population (2, 5) in the United States. NAFLD is closely linked with insulin resistance and is thought by many to be the hepatic manifestation of the “metabolic syndrome.” In an important subset of patients with NAFLD, steatosis progresses to inflammation and fibrosis, a condition known as nonalcoholic steatohepatitis (NASH). Up to 3% of all Americans may be afflicted with NASH; of these, 27% progress to end-stage cirrhosis and 12% die of liver failure (4, 6, 7).

The earliest manifestation and hallmark of NAFLD/NASH is steatosis. However, accurate and early diagnosis of steatosis is difficult because its assessment relies on liver biopsy (8, 9). Unfortunately, the utility of biopsy, the current gold standard, is very limited. Steatosis can have a heterogeneous distribution, and nontargeted liver biopsy has very high sampling variability (8). In addition, histological evaluations of steatosis are graded on a subjective scale. A distinct disadvantage of liver biopsy is that it is an invasive procedure with a risk of morbidity or mortality. Rates of complication vary with procedures, ranging from 1.3% to 20.2%, approximately 1% to 3% of patients require hospitalization (9). Quantitative assessment of hepatic steatosis using noninvasive imaging techniques is highly desirable for the diagnosis and evaluation of fatty liver disease. Such a method could be performed frequently to track the evolution of steatosis in clinical trials for the evaluation of new drugs in the treatment of hepatic steatosis (10, 11). Accurate quantification of steatosis could also enhance the statistical power of drug trials, greatly reducing the number of patients needed to determine drug therapy effectiveness.

Preliminary MRI using chemical shift based techniques (12–16) to generate in-phase and out-of-phase images has been clinically studied for quantification of liver fat content (17–19). However, this approach suffers from a natural ambiguity; as noted by Hussein et al. (19), fat-fractions greater than 50% cannot be distinguished easily from fat-fractions less than 50%; for example, a fat-fraction of 30% causes the same signal dropout as a 70% fat-fraction. It is difficult to determine fat-fraction over a range of 0% to 100% unless the water and fat signals are fully separated. Unfortunately, true separation of water and fat with in/out phase imaging is highly sensitive to magnetic field inhomogeneities (12), and requires more advanced imaging and reconstruction methods (13–16).

Regardless of the fat-water separation imaging technique, different relaxation times between water and fat result in a significant bias in the estimate of fat-fraction. This occurs because the shorter T1 of fat causes a relative signal amplification of fat compared to water. For example, the T1 of fat and water in the liver at 1.5T are approximately 343 ms and 586 ms, respectively (20). Consequently, true fat-fraction images cannot be obtained in the presence of T1 weighting. The effect of T2* must also be considered in diseased livers with iron overload, even though it can be ignored in normal livers for short-TE gradient echo imaging. Although we have demonstrated the ability to correct for shortened T2* (21), for the purposes of this work, we will ignore the effects of T2*, and report T2* compensation methods in hepatic iron overload elsewhere.

In addition to the relaxation effects, the influence of image noise must also be considered. For most fat-water separation methods, which use complex images to separate water and fat, the subsequent calculation of fat-fraction is based on magnitude fat and water images. Noise bias is introduced in areas with low signal due to the skewed noise distribution from the magnitude operation. This effect will have great clinical importance in low fat content regions affecting the diagnosis of mild steatosis.

A multipoint chemical-shift–based fat-water decomposition technique known as iterative decomposition of water and fat with echo asymmetry and least squares estimation (IDEAL) (16, 22, 23) has been shown to be a robust method for separation of water and fat signals. IDEAL uses asymmetric phase shifts (θ = –π/6+πk, π/2+πk, 7π/6+πk, k = integer, echo times [TE] = θ/(2πΔf), where Δf is the chemical shift between fat and water, which is approximately –210 Hz at 1.5T and –420 Hz at 3.0T), to improve the effective number of signal averages (NSA) noise performance to the maximum possible value of 3 over the entire range of fat-water proportions (16, 22, 24). NSA is equivalent to the signal-to-noise ratio (SNR) of three averaged images and can be used to describe the noise performance in the fat-water separation algorithm (13, 16). The largest obstacle to volumetric quantification of hepatic fat content with MRI is the need to acquire all the necessary data within one reasonable breath-hold duration to avoid movement artifacts, which corresponds to ∼30 s in the young and healthy population, but perhaps significantly less in the disease population. Spoiled gradient recalled echo (SPGR) is a commonly used sequence for three-dimensional (3D) volumetric liver imaging. IDEAL has been combined with parallel imaging (25) and incorporated with multiecho SPGR sequence (26) to further accelerate scan time, permitting image acquisition over the whole liver in a short breathhold. The multiecho SPGR sequence in combination with the IDEAL reconstruction provides breathheld acquisitions over the entire liver and reliable fat-water separated images, and is therefore an excellent choice for accurate fat quantification.

The purpose of our study was to investigate the effects of T1 and noise bias on fat quantification and to propose solutions to avoid these biases. We first describe the sources of these biases, potential solutions for correction, and then demonstrate the effectiveness of the proposed algorithm with IDEAL-SPGR water-fat separation methods. Quantitative analysis using a fat/water phantom was performed for evaluation of the small flip angle and dual flip angle approaches to reduce T1 bias. The bias created by image noise was studied using a water phantom and methods including magnitude discrimination and phase-constrained approaches were examined.

THEORY

Definition of Fat-Fraction

Triglycerides are the primary component of accumulated lipids, all of which is contained within intracellular vacuoles of hepatocytes in steatotic livers (27). The NMR spectrum of intracellular lipid consists of multiple fatty acid peaks including olefinic (-CH = CH-), methylene (-(CH2)n-), and methyl (-CH3) protons (28, 29). Olefinic protons are unsaturated lipids and have a chemical shift of 5.35 ppm, which is close to that of water (4.65 ppm). Therefore, signal from olefinic protons will contribute to water images in chemical shift imaging methods. However, only the signals from methylene (1.3 ppm) and methyl (0.9 ppm) protons are of clinical significance in diagnosis of hepatic steatosis, directly reflecting the concentration of fatty acids that accumulate in patients with insulin resistance. Accordingly we define true fat-fraction as,

equation image(1)

where Mw and Mf are water and fat (-CH2- and -CH3 groups only) proton densities respectively. In MRI, we measure water and fat signal intensities to represent their proton densities (ignoring relaxation effects). Hence, the apparent (or signal) fat-fraction can be defined according to

equation image(2)

In Eq. [2], the water (Sw) signal includes contributions from olefinic protons and fat (Sf) signal contains only methylene and methyl groups. Using this definition, the fat-fraction is reflected accurately and provides a useful scale between 0% and 100%. System effects such as coil sensitivity are normalized out through the use of the fat-fraction, providing system independent results.

If the percentage of signal from the olefinic protons relative to the total fat, κ, is known, the fat-fraction can be easily corrected as

equation image(3)

For example, consider ηs = 0.5 and κ = 10% (a reasonable assumption according to Yeung et al. (29)). Without the correction from Eq. [3], there will be a 2.6% decrease of the apparent fat-fraction, a relatively small error, for this “worst-case” scenario. For the purposes of describing the effects of T1 and noise bias in this work, the effects of the olefinic peaks will be ignored.

Although the definition we described above represents the true proton density fat-fraction, it may not correspond to the volume fraction of lipids within a voxel due to small differences between the proton densities of triglycerides and water. We believe that the proton density fraction of fat may be a more meaningful and practical definition, since it is a measure that is independent of relaxation parameters (T1, T2*), and is therefore independent of pulse sequence acquisition parameters.

Confounding T1 Effects on Fat-Fraction

The water signal Sw for SPGR depends on T1w, T2w*, α, the repetition time (TR), the echo time (TE), and the proton density Mw as given by Eqs. [4] and [5] (for fat) (30, 31),

equation image(4)
equation image(5)

In fast imaging techniques, TE is relatively short compared to the T2* of the species in question (TE ≈ 4–7 ms and T2* ≈ 26 ms in normal liver (32)). For the purpose of this work, T2* effects can be ignored, although in patients with concomitant iron overload and steatosis, T2* may become important and can be incorporated into the IDEAL signal model (21). The fat signal fraction ηs, which depends on Sw and Sf, will also depend on flip angle when the T1 values of fat and water are unequal. This implies that ηs will be different from the true fat-fraction, η, as described by Eqs. [1] and [2].

The simulated fat/water signal behavior (assuming Mw = Mf, in Fig. 1a) and fat signal fractions (Fig. 1b) for a given TR = 10 ms, T1f = 343 ms, and T1w = 586 ms at 1.5T (20) of various flip angles demonstrate this effect, which the larger the flip angle, the more deviation of the fat-fraction from its true value.

Figure 1.

a: Simulated fat and water signal behavior vs. flip angles using SPGR sequence with TR = 10 ms, T1w = 586 ms, and T1f = 343 ms and assuming the same fat/water proton densities. b: Simulated fat-fraction of various flip angles. The deviation of the signal fraction from the true value decreases with decreasing flip angle. A maximum error of 23% was calculated with a 30° flip angle, while there is only 4% error with a 5° flip angle, at equal amounts of fat and water.

Figure 2 demonstrates 3D IDEAL-SPGR fat-signal fraction images acquired in a patient with known steatosis. Fat-fraction from the same region of interest varies significantly (29–45%) with flip angle (5°–30°) due to T1 effects as discussed above. Without T1 correction, this error will lead to severe inaccuracy in the diagnosis of hepatic steatosis.

Figure 2.

Fat-signal fraction images acquired with 3D IDEAL-SPGR in a patient with known steatosis. Apparent fat-fraction from the same region of interest varies (29–45%) with flip angle (5° to 30°) used in imaging acquisitions. This large bias is due to difference in T1 between water and fat signals.

Small Flip Angle Approach

The proton densities can be calculated correctly if the T1 of both water and fat are known. The measured signal intensity (Sw, Sf), and the known flip angle α, allows Mw and Mf to be calculated as follows,

equation image(6)
equation image(7)

However, T1 values are unknown in general and may vary in different disease states, particularly in the presence of iron or copper deposition (33, 34). T1 mapping is not part of routine clinical assessment owing to the lengthy scan times associated with the T1 measurements (35). To reduce the influence of the T1 dependence of the SPGR sequence on fat quantification, a small flip angle may be used. This is due to the first order Taylor expansion with respect to small α in Eq. [4], i.e., cosα≈1, sinα≈α which simplifies the signal relation to Sw≈Mwα. Hence the flip angle term cancels in the fat-fraction calculation and the two definitions in Eqs. [1] and [2] are equal:

equation image(8)

SNR performance must be considered when small flip angles are used because SNR of an SPGR acquisition decreases rapidly at small flip angles (Fig. 1a). For example, using a flip angle of 5° will reduce the signal by 46% and 33% from the maximum amplitudes of fat and water, respectively. Figure 3a shows the results of a Monte Carlo simulation (3000 trials) that plots the SD of the fat-fraction (noise) caused by the addition of zero-mean Gaussian noise added to both the water and fat signals. For a specified SNR value, the SD of the noise was determined by measuring the signal from water at the Ernst angle (Smath image), with Tmath image = 586 ms, TR = 10 ms, αErnst = 11°, ie: σ=SNR/Smath image. For all simulations in Fig. 3a, the true fat-fraction is fixed at 0.5, and the SD on the fat-fraction was calculated from the 3000 trials to estimate the noise (error) that would be introduced into the fat-fraction estimate for various flip angles and overall image SNR levels.

Figure 3.

a: Simulated noise (SD) of the fat-fraction estimated after the addition of Gaussian noise added to water and fat signals, using a Monte Carlo simulation (3000 trials for each fat-fraction calculation, with TR = 10 ms, T1w = 586 ms, and T1f = 343 ms) as a function of flip angle, assuming a true fat-fraction of 0.5. The SD of the fat-fraction is plotted as a percentage of the true fat-fraction. The SD of the noise is determined for a given SNR value (= 5, 10, and 30) based on the water signal at its Ernst angle (10.5°, TR = 10 ms, T1w = 586 ms). The minimum noise on the fat-fraction estimate occurs at a flip angle of 12° for all SNR values. The fast rise of the curves below 5° indicates the increasing error in the fat-fraction estimation at low SPGR signal levels. Without consideration of T1 bias, a flip angle of 12° gives the optimal noise performance in the fat-fraction estimations. b: Calculated fat-fraction bias at different flip angles from the same simulation. Bias is the difference in the true fat-fraction (0.5) and the calculated fat signal fraction, which is confounded by the differences in T1 between water and fat. Bias on fat-fraction bias is independent of image SNR.

Unlike Fig. 3a, which plots the noise estimate of the fat-fraction, Fig. 3b plots the bias of fat-fraction estimates for at different flip angles from the same simulation. The bias is the difference between the true fat-fraction of 0.5 and the fat signal fraction (calculated using Eq. [2] with confounding T1 effects). The calculated bias in fat-fraction is independent of SNR, since the bias is simply the difference in true fat-fraction (0.5) and the fat-signal fraction, which is skewed by T1 effects.

From Fig. 3a, we see that a flip angle of 12° gives optimal SNR performance, with the lowest noise on the fat-fraction estimate for all simulated SNR levels (5–30). This occurs because the overall signal levels from both water and fat are highest near this flip angle, and the overall noise on the calculated fat-fraction is lowest at this flip angle. However, using a 12° flip angle leads to considerable bias (4.5%) as is seen in Fig. 3b. Reducing the flip angle, to 5°, however, offers a good compromise between T1 bias reduction (the maximum residue bias is 3% for a true fat-fraction of 0.5, i.e., 0.50 ± 0.015) and reasonable SNR performance in the fat-fraction measurement. We refer to this method as the “small flip angle approach.”

Dual Flip Angle Method

Despite the effectiveness of the small flip angle approach to reduce the T1 bias, the low SNR of the small flip angle method raise some concerns for the noise performance of the resulting fat-fraction image. In addition, we wish to find a definitive approach to completely remove T1 bias, which the small flip angle method cannot achieve. Inspired by the “DESPOT” (Driven-equilibrium single-pulse observation of T1) techniques described by Deoni et al. (35) for rapid estimation of T1 maps, we propose a second approach by performing two consecutive imaging acquisitions at two different flip angles, which is referred to as the “dual flip angle” method.

IDEAL-SPGR imaging is performed at two different flip angles, followed by reconstruction into separated fat and water images. With the measured signal amplitudes (S1w, S2w for water and S1f, S2f for fat) and flip angles (α1, α2), Eqs. [4] and [5] can be rewritten as Eqs. [9] and [10], to give T1-corrected water (fat) signal, and therefore η.

equation image(9)
equation image(10)

An analytical solution for choosing the optimum flip angles was described by Deoni et al. (35), where an optimal flip angle pair that provides the best possible noise performance based on a single value of T1 can be determined. Using Deoni's approach and assuming T1w = 586 ms and T1f = 343 ms, the two flip angles are 4.4° and 25.0° for water, and 5.8° and 32.3° for fat. This results in different optimal flip angle pairs because of unequal T1 values. As a preliminary approach, averaged values of 5° and 29° will be used as a pair. Further optimization of flip angles will be thoroughly considered in future work.

A known limitation of DESPOT is its sensitivity to RF (B1) inhomogeneities, which cause inaccuracy in the expected flip angles and leads to errors in the estimation of proton densities and T1. However, the fat-fraction will be insensitive to B1 variation. Figure 4 illustrates the contour plots of the resulting error (percentage of the true fat-fraction, 0.5) for fat quantification in the presence of B1 inhomogeneities. Less than a 2.5% error over a wide range of B1 variation is demonstrated. This is due to the fact that errors in the estimation of water and fat compensate for one another, particularly if we assume that relative errors of the flip angles are the same. Since the flip angle is proportional to the B1 amplitude, there will be almost no error in the estimation of fat-fraction if the relative B1 error is the same at each flip angle (a reasonable assumption), as indicated by the dashed line in Fig. 4.

Figure 4.

Effects of B1 inhomogeneities on dual flip angle T1 correction methods. Contour plots of the simulated error (percentage of the true fat-fraction, 0.5 for this simulation) in fat-fraction using the dual flip angle method under the influence of B1 inhomogeneities. Less than a 2.5% error over a wide range of B1 variation is predicted. If we assume that the relative error in the flip angle is the same for α1 and α2 (dashed line), the errors in the estimation of water and fat exactly compensate for one another and there is no error in the estimation of fat-fraction, even with large B1 inhomogeneities.

Although the dual flip angle method is an attractive approach in the case of unknown T1, a major restriction of this algorithm is the impact of the noise. If either of separated water or fat signals is low (e.g., true fat-fraction = 0), the estimation of the true water and fat signals (Eqs. [9], [10]) become highly erratic. This occurs because the fat (water) signal in the images acquired at the two flip angles is extremely low and only contains noise. Mathematically, this could arise from a very long, nonphysiological T1, or from a very low fat (water) signal (which is actually the case); it is difficult to resolve the two scenarios mathematically. In the presence of noise, the calculation of T1 corrected fat (water) signal using Eqs. [9] and [10] becomes highly unstable. Figure 5a illustrates this effect in a Monte Carlo simulation (3000 trials, SNR = 10), where estimates of fat-fraction becomes highly erratic at low and high fat-fractions.

Figure 5.

a: Simulated fat-fraction in the presence of noise (SNR = 10), with dual flip angle correction method. Highly erratic estimates of fat-fraction are seen for low and high fat-fraction, due the unstable estimates of T1. Use of the T1-constrained method greatly improved estimation of fat-fraction (b).

In this situation, we must rely on additional information. Specifically, we must constrain the possible values of T1 to those that reflect physiologically possible relaxation parameters. In particular, we require that T1 must be as follows: 1) real, 2) greater than zero, and 3) less than some physiologic upper bound. In this way, we use a priori information to determine the true fat-fraction for very low (high) fat-fractions. Simulations with these assumptions are shown in Fig. 5b, where T1 is constrained to be real and in the range of 1 < T1 < 2000 ms for both water and fat. T1w and T1f are derived from Eqs. [9] and [10], and compared to the limits. For example, if T1w exceeds the upper bound, 2000 ms is used in Eq. [9] to obtain a corrected value for emath image, which is then applied to calculate the proton density Mw. The calculation of fat-fraction is considerably more stable with this approach, even with mild T1 constraints.

The small flip angle approach does not suffer from the instability of the unconstrained dual flip angle method, because it does not require any mathematical transformation (e.g., Eqs. [9] and [10]) to determine the fat-fraction. As shown in Fig. 3a, the noise performance of the small angle approach does suffer at very small flip angles, however, the calculation of fat-fraction with the small flip angle method is inherently stable, since there is no ambiguity: the low fat (water) signal arises because there is simply little fat (water) in that voxel, reflecting the physics of the SPGR acquisition. The major disadvantage of the small flip angle method compared to the dual flip angle method is the residual bias (Fig. 3b).

In comparison to the small flip angle method, the dual flip angle approach eliminates T1 bias. Figure 6a plots the absolute difference between the calculated and true fat-fractions (T1 bias) using a 5° flip angle. The bias for dual flip angle method is zero because the dual flip angle method is an exact analytical solution. Figure 6b plots a Monte Carlo simulation of the noise performance (SD) of the estimated fat-fraction (3000 trials, with TR = 10 ms, T1w = 586 ms, and T1f = 343 ms) using both the small flip angle (5°) with two averages and the dual flip angle method with T1 constraint. The scan time was the same for both methods in order to compare SNR performance, although it is important to note that the minimum possible scan time for the small flip angle is half that of the dual flip angle method. As for the simulations in Fig. 3a, the noise variance for the simulations in Fig. 6b is based on an SNR value of 10 for water at its Ernst angle (TR = 10 ms, T1 = 586 ms). The noise performance of the small flip angle method for the same scan time is very similar, or slightly inferior to the dual flip angle method using mild T1 constraints (1 < T1 < 2000 ms).

Figure 6.

a: Absolute difference between the calculated and true fat-fractions (T1 bias) using 5° flip angle. The bias for the dual flip angle method is zero. b: Noise performance (SD) of the fat-fraction estimation obtained with a Monte Carlo simulation (3000 trials, SNR = 10, with TR = 10 ms, T1w = 586ms, and T1f = 343 ms) using both 5° flip angle with two averages and dual flip angle methods with T1 constraint limits of 1 < T1 < 2000 ms.

Bias Created by Image Noise

For most clinical anatomical imaging applications, evaluation of fat-fraction is performed using the magnitude-separated water and fat images. The noise in complex MR images is Gaussian with zero mean (36), and after performing the magnitude operation, areas with high signal will have unaffected noise statistics. However, in regions of low signal, the noise distribution becomes skewed (Rician) and has a biased, nonzero mean (37). Figure 7a and b compare the noise level when complex and magnitude images are displayed. The signal intensities of the decomposed fat images with low fat content and water images with low water content will be artifactually increased by the noise. Hence, a bias in the fat-fraction with very low and very high fat content regions would be introduced. This effect is demonstrated with a simulation in Fig. 7c, where complex zero-mean Gaussian noise was added to signals (SNR = 10, ignoring T1 effects). In this example, the magnitude operation makes the noise nonzero mean, causing a positive bias of nearly 8% for very low fat-fractions. This effect would be clinically significant for low fat-fractions and could lead to false-positive diagnoses of mild steatosis.

Figure 7.

Noise behavior using SNR = 10 and 3000 trials in a Monte Carlo simulation. Regions of low signal in complex images (a) have Gaussian, zero-mean noise. In magnitude images, however, these regions have skewed noise distributions with nonzero, biased noise (b), which will lead to biased estimates of low fat-fractions (c). Noise bias corrected reconstruction using either the magnitude discrimination or phase-constrained method removes this bias (d).

This bias can also be understood from the definition of fat-fraction. In general, Sw and Sf in Eqs. [4] and [5] are complex and have a different phase. The fat-fraction based on Eq. [2] can be rewritten explicitly with the water and fat signals at different initial phase ϕw and ϕf, respectively,

equation image(11)

However, if ϕw ≠ ϕf and both are unknown, the magnitude estimates must be used, i.e.,

equation image(12)

When the fat or water signal is low, this leads to a significant bias in ηs′ because the nonzero averaged noise exaggerates the signal amplitude. Such bias has been reported by Hussain et al. (19) (Fig. 4), where 5% overestimation of the apparent fat content in pure water was observed in their phantom studies. We believe that the noise-related effect described above may be the source of this bias.

We first propose a “magnitude discrimination” method to eliminate the noise bias. This method applies if we can assume that the signal from fat and/or water is sufficiently high that noise remains zero-mean. The first step is to estimate water and fat with the conventional IDEAL algorithm. Next, the IDEAL signal model is modified slightly to estimate the sum of fat and water signals,

equation image(13)

where tn is echo time, Δf is the chemical shift frequency, and ψ is the local field inhomogeneity. Estimation of |Sw + Sf| provides an estimate of the denominator without noise bias. Next, the signals from water and fat are compared to determine which is the dominant component (i.e., water is dominant if Sw > Sf, and vice versa). If fat is the dominant component, the fat-fraction is calculated as ηs = |Sf|/|Sf + Sw|; otherwise, ηs = 1 – (|Sw|/|Sf + Sw|) if water dominates. Here we have exploited the fact that the sum of the fat-fraction (Sf/(Sf + Sw)) and the “water fraction” (Sw/(Sf + Sw)) must equal 1. By choosing the larger component, we avoid noise bias in the numerator. It is worth noting that any method that acquires an in-phase image (14, 15), the magnitude in-phase image will have no noise bias and can be used as the denominator of the fat-fraction calculation. However, the magnitude discrimination for the numerator must be performed in the same way.

However, if low SNR exists in both fat and water images, a “phase-constrained” method can be used. A phase-constrained approach has been implemented by Yu et al. (38) as part of a one-point water-fat separation method for dynamic contrast enhanced imaging. This method assumes that the phase of water and fat within a voxel are equal at TE = 0. This is a very reasonable assumption, which directly reflects the physics of SPGR pulse sequences, where the phases of water and fat are equal at TE = 0. In fact, most other water-fat separation methods (12–15) make this assumption, i.e., ϕw = ϕf ≡ ϕ. Unlike these methods, IDEAL does not require that the phase of water and fat be equal at TE = 0, which provides increased flexibility for other pulse sequences such as balanced steady state free precession (SSFP). This flexibility is not required for SPGR imaging, however. Using this assumption, Eq. [11] becomes,

equation image(14)

The decomposed fat/water images are real quantities (not complex) and the resulting fat-fraction will have nonbiased zero-mean noise. Using this model, we avoid taking the magnitude of a complex signal to estimate the fat-fraction. Figure 7d shows the reduced bias from the image noise using both approaches.

MATERIALS AND METHODS

A phantom designed to create a continuum of fat-fractions was constructed as shown in Fig. 8. This phantom consisted of two trapezoids filled with equal volumes of olive oil and water doped with CuSO4 (2.3 mM/liter). The oil-water interface of the trapezoids is shifted to each side to create a 100% water region, linearly varying oil/water ratio region, and a 100% oil region. To reduce surface tension and create a flat, smooth interface between water and fat, a small amount (∼0.5 ml) of surfactant (Merpol A surfactant; Sigma-Aldrich, St. Louis, MO, USA) was added to the water. Without the surfactant, a significant meniscus occurred between the acrylic, water, and oil interface because of the phantom geometry and different water-oil surface tension.

Figure 8.

Photograph (axial view) of the fat/water phantom with oil floating on top of water in the Plexiglas cavity. The arrow (y) denotes the long axis of the phantom. This configuration provides a true volume fat-fraction ranging linearly from 0% to 100%.

Experiments were performed on 1.5T clinical scanners (TwinSpeed EXCITE; GE Healthcare, Waukesha, WI, USA) using a transmit-receive single channel quadrature head coil for most of the studies. To measure the bias due to image noise, low SNR data were collected using the body coil.

Phantom Calibration

We measured the T1 values of the oil and water in the phantom to validate the T1 correction algorithm and calculate the two flip angles used in the dual flip angle method. In general, T1 mapping is not considered as routine process in vivo for fat quantification, however, we wished to characterize our phantom. T1 measurements were carried out using an inversion-recovery fast spin echo (IR-FSE) sequence with a variable inversion time (TI) and T2 values were determined using a spin echo (SE) sequence at various TEs. Axial images from the lateral view of the phantom (shown in Fig. 7) were acquired.

To spatially register the percentage of oil along the long axis of the phantom, we performed a calibration scan using a 2D IDEAL-SPGR sequence prescribed in the axial plane as described in the T1 measurements. Imaging parameters included TR = 11.3 ms, TE = 4.4, 6.0, and 7.5 ms, corresponding to optimized IDEAL echo shifts at 1.5T (16), slice = 50 mm, FOV = 14 cm, Nx = Ny = 256, bandwidth (BW) = ± 31.25 kHz, and α = 45°. A continuum of fat-fractions was linearly scaled between 0% and 100%. This fat-fraction was based on an assumption of equivalent fat and water proton densities at each position and could be considered as volume fat-fraction. Throughout the following sections, this was also named “true fat-fraction” for simplification.

Calibration was necessary to account for slight imperfections (meniscus) in the phantom. Differences in proton density were removed as part of this calibration, in order to determine the true fat-fraction for comparison. Removal of proton density differences does not complicate the T1 and noise bias compensation methods and no such calibrations will be necessary for in vivo applications. A single coronal slab parallel to the floor of the phantom was acquired. To avoid chemical shift artifacts, the phase encoding direction was oriented along the long axis of the phantom. Water or fat signal amplitude was calculated at each location along this axis. The protocol presented in the previous study was used with proton density weighting (TR = 4 s, TE = 4.4, 6.0, and 7.5 ms, α = 90°). The curve of the resultant fat signal fraction was calibrated with the volume fat-fraction. This permitted the examination of T1 and noise bias without the complication of proton density differences and minimal residual menisci in the phantom.

T1 Correction

To examine the flip angle dependence of the fat-fraction, the acquisition scheme presented in the previous calibration study was used and a 2D IDEAL-SPGR sequence (TR = 11.3 ms, TE = 4.4, 6.0, and 7.5 ms) was applied with flip angles ranging from 5° to 45°. Both T1 bias and the SNR performance were evaluated for decreasing flip angles.

To validate the proposed dual flip angle method, we first calculated two pairs of optimum flip angles from the measured T1 values for water and fat respectively using Deoni et al.'s (35) approach. Phantom images were acquired using the final averaged two flip angles. Imaging parameters were the same as in the flip angle studies.

Noise Bias Correction

Finally, we investigated the bias created by image noise by performing low SNR measurements using the body coil and the same imaging parameters as the T1 correction studies. In particular, we used a bottle phantom containing only water to ensure that the fat-fraction was truly zero. Images with six different SNR values were acquired by changing the number of averages (1, 4, 10, 20, 40, and 80) and α = 5° to reduce T1 bias. Image reconstruction was performed offline using programs written in Matlab (Mathworks, Natick, MA, USA). The fat-fractions calculated with both magnitude discrimination and phase-constrained approaches were compared to those estimated using the regular magnitude data method.

RESULTS

T1 and T2 values obtained from the phantom at 1.5T were 628 ± 8 ms and 520 ± 10 ms for water, and 175 ± 3 ms and 90 ± 10 ms for fat, respectively. The measured T2 values were relatively long compared to the TE used in the imaging protocol of SPGR sequence for fat quantification. Hence, T2* effects were ignored.

Examples of the 2D IDEAL-SPGR fat-water separated images are shown in Fig. 9. The axial images (Fig. 9a and b) provided the reference for pixel location and its corresponding true fat-fraction. The coronal slab images (Fig. 9c and d), which covered a continuous transition from mostly water pixels to mostly oil pixels, were used in the fat signal fraction calculations as described in the MRI algorithm.

Figure 9.

2D IDEAL-SPGR fat-water separated images. a,b: Axial images through the phantom. These images provided reference for pixel location and its corresponding true fat-fraction. c,d: Coronal slab images that consisted of a continuous transition from pure water (left side of image) to pure oil (right side of image).

In Fig. 10a, the behavior of the fat signal fractions (calculated oil content) agrees well with the simulation (Fig. 1b), and demonstrates the utility of the small flip angle method, in which fat-fraction bias is reduced as flip angle is decreased. A maximum error of 40.5% was observed with α = 30° data and 7.5% error with α = 5° data assuming a true fat-fraction of 0.5 (Fig. 10b). Although the small flip angle results correlated well with true values, the SNR of the fat image acquired with α = 5° was 38.5% lower than that acquired with α = 30° (Fig. 10c). SNR was evaluated with signals drawn from pure oil and pure water regions in the separated fat and water images. Because of its long T1 value, water SNR was lower than that of fat as predicted in Fig. 1a.

Figure 10.

a: Calculated oil content measured at different flip angles, which agree with the confounding T1 effects predicted by theory. b: Bias of fat signal fractions vs. flip angles. Results were calculated from (a) at a fat-fraction of 0.5. c: SNR performance of fat and water at different flip angles. Signals were measured from pure water and pure oil regions. Because of its longer T1 value, water SNR was lower than that of fat. These measurements were consistent with the simulations shown in Fig. 1, and provide experimental confirmation of the small flip angle approach for reducing T1-related bias.

To validate the dual flip angle method in fat quantification, we first calculated the optimum flip angles according to the analytic solution given by Deoni et al. (35) using T1 values of water and fat measured in the phantom. flip angles of 4° and 24° were derived theoretically for water, with 8° and 44° for fat. Hence, we used the averaged values 6° and 34° as a pair of flip angles for both water and fat images. Figure 11a demonstrates the feasibility of this approach. The estimated fat-fraction agrees well with the expected values, indicating the effectiveness of this method. Improved estimation of fat-fraction was seen after T1-constrained (Fig. 11b). For this phantom studies, T1 was constrained to be real, and in the range of 1 < T1 < 2000 ms for both water and fat to avoid erroneous values of T1 as indicated by the spikes at 15% and 95% fat-fractions. Figure 11b and the 5° curve in Fig. 10a also allow quantitative performance comparison between the two techniques for T1 correction. The mean absolute differences between the calculated and true fat-fractions are 1.9% and 3.0% for the dual flip angle and small flip angle method, respectively. Depending on the severity of steatosis, theses results provide references for choice of the techniques for quantification of hepatic fat content with considerations including the SNR, scan time, and T1 bias.

Figure 11.

Fat-fraction estimated with dual flip angle correction method. a: The estimated fat-fraction agrees well with the expected values. b: Improved estimation, without spurious fat-fractions are achieved using the T1-constrained approach.

Figure 12 shows in vitro results of the bias created by image noise in fat quantification acquired using the body coil, plotted against the SNR of the water images. The bias is the difference between the calculated fat-fraction and its true value, which is zero in the water phantom. The skewed, nonzero mean image noise resulted in a 4% to 15% bias in calculated fat-fraction when using the most obvious approach (magnitude data). This bias was reduced to below 1% using either magnitude discrimination or phase-constrained IDEAL.

Figure 12.

Bias created by image noise in fat quantification measured in the water-only phantom, plotted as a function of the SNR of the water images. The skewed, nonzero mean image noise resulted in a 4% to 15% bias in calculated fat-fraction when using the most obvious approach (magnitude data). This bias was reduced to below 1% using either magnitude discrimination or phase-constrained IDEAL.

DISCUSSION

A highly accurate means of quantifying hepatic steatosis would be extremely beneficial for the diagnosis, treatment, and early intervention of NAFLD, as well as for clinical trials developing new treatments for NAFLD. Although MRI is capable of separating water signal from fat, the quantitative measurement of the fat content of the liver using MRI is technically challenging. True fat quantification should be independent of imaging sequences and protocols. However, naive calculation of the signal fraction will be confounded by the effects of T1 and T2*, with potentially large, pulse sequence–dependent bias. To accurately quantify the fat-fraction with rapid volumetric gradient echo methods, two dominant sources of bias should be addressed: differences in water and fat relaxation times, and image noise. We have demonstrated the feasibility of small angle and dual-flip angle approaches to reduce T1 effects. By using magnitude discrimination or phase-constrained methods, true fat-fraction can be estimated without noise bias.

The effects of T2* are negligible in normal livers, and are generally ignored for short-TE gradient echo imaging. In the presence of iron deposition, however, T2* is shortened due to increased signal dephasing. The signal decays more rapidly, corrupting the water-fat decomposition and disrupting the calculation of true fat-fraction. The relationship between iron content and measurements of T2* using the T2*-corrected IDEAL method (21) will be explored in future studies, and is beyond the scope of this work. Furthermore, both the T1 and noise bias corrections described in this study can be incorporated into the T2*-corrected IDEAL to address the clinical utility of this method. This may provide insight into the presence of iron in patients with chronic liver disease and be helpful in the development of noninvasive methods for quantification of hepatic iron overload.

The noise performance of the dual flip angle method was similar, or perhaps slightly improved, compared to the small flip angle method (with α = 5°). In addition, the dual flip angle method entirely eliminates bias. Unfortunately, this approach requires the sequential acquisition of two images, which may be challenging for breathhold applications such as liver imaging. For applications in which scan time is a limitation and a small amount of bias may be tolerable, the small flip angle approach may be the preferred method. As an example, consider a true fat-fraction of 0.15. From Fig. 6a, we see that there will be a small bias of approximately 0.8% (i.e., 0.15 ± 0.0012) using the small flip angle method. The dual flip angle method, however, requires twice the minimum scan time compared to the small flip angle approach, but will have an SNR improvement of approximately 24% for this fat-fraction, for the same scan time (Fig. 6b).

Our proposed dual angle method removes the bias from T1 effects, even though flip angle pairs were not optimized. Although the precise selection of optimized flip angles is not necessary to obtain fat-fraction images free from T1 bias, the optimal choice of flip angles would improve the noise performance of the fat-fraction estimates. The prior optimization by Deoni et al. (35) cannot be extrapolated because of the estimation of a range of T1 values. The noise performance of fat-fraction estimation should be investigated through calculation of the Cramér-Rao bound (CRB) (39) to determine the optimal choice of flip angles. The CRB represents the theoretically best noise performance that can be achieved by a signal estimation method; any estimator that matches the CRB is said to be “efficient.” The optimal choice of flip angles will be computed as a weighted average across the variances over the range of biologically reasonable T1 values for water and fat. The CRB will help predict the best possible combination of flip angles that optimizes the noise performance of the fat-fraction estimation. When using the dual flip angle approach, it is important to constrain T1 to reasonable values in order to avoid erroneous estimates of fat-fraction.

Although the small flip angle approach is simpler and does not require special image reconstruction, there is a residual flip angle-dependent T1 bias introduced into the estimated fat-fraction (Fig. 6a). However, the noise performance of the small flip angle approach is similar to the dual flip angle method when using the same total scan time (Fig. 6b), even with considerable T1 constraint. Further improvement in the noise performance of the dual flip angle method will be possible with optimization of the flip angles for this approach, as well as through refinement of T1 constraint methods. The major disadvantage of the dual flip angle method is the doubling of scan time, which may be alleviated through the use of phased array coils and parallel imaging (25). The choice of T1 correction method will likely depend on the specific application: applications that are scan time limited but can tolerate a small amount of residual bias may prefer the small flip angle method. Conversely, applications that are not limited by scan time may prefer the dual flip angle method to achieve the lowest possible T1 bias.

CONCLUSIONS

We have validated the IDEAL-SPGR method for quantification of fat-fraction in a phantom, reducing or removing the effects of T1 bias, and removing the effects of noise bias. Small-flip angle or dual-flip angle approaches are two alternatives to minimize the T1 bias. Magnitude discrimination and phase-constrained methods can effectively remove noise bias. Finally, clinical validation will be needed for complete validation of this method for the accurate quantification of hepatic steatosis.

Acknowledgements

We thank Ernest Madsen and Gary Frank for their assistance in the oil/water phantom construction. SBR is the recipient of an Afga Laboratories Radiological Society of North America Research Scholar Grant.

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