Fat/water separation in single acquisition steady-state free precession using multiple echo radial trajectories


  • Aiming Lu,

    1. Department of Biomedical Engineering, University of Wisconsin, Madison, WI, USA
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  • Thomas M. Grist,

    1. Department of Biomedical Engineering, University of Wisconsin, Madison, WI, USA
    2. Department of Radiology, University of Wisconsin, Madison, WI, USA
    3. Department of Medical Physics, University of Wisconsin, Madison, WI, USA
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  • Walter F. Block

    Corresponding author
    1. Department of Biomedical Engineering, University of Wisconsin, Madison, WI, USA
    2. Department of Medical Physics, University of Wisconsin, Madison, WI, USA
    • Department of Biomedical Engineering, University of Wisconsin–Madison, E3/311 Clinical Science Center, 600 Highland Avenue, Madison, WI 53792-3252, USA
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  • Part of this article was presented at the 12th ISMRM meeting, Kyoto, 2004.


Phase detection in fully refocused SSFP imaging has recently allowed fat/water separation without preparing the magnetization or using multiple acquisitions. Instead, it exploits the phase difference between fat and water at an echo time at the midpoint of the TR. To minimize the TR for improved robustness to B0 inhomogeneity, a 3D projection acquisition collecting two half echoes at the beginning and end of each excitation was previously implemented. Since echoes are not formed at the midpoint of the TR, this method still requires two passes of k-space for fat/water separation. A new method is presented to linearly combine the half echoes to separate fat and water in a single acquisition. Separation using phase detection provides superior contrast between fat and water voxels. Results from high resolution angiography and musculoskeletal studies with improved robustness to inhomogeneity and a 50% scan time reduction compared to the two pass method are presented. Magn Reson Med, 2005. © 2005 Wiley-Liss, Inc.

Fully refocused steady-state free precession techniques (1, 2) (SSFP, also known as true-FISP, FIESTA, and balanced FFE) are capable of generating images with clinically useful contrast and high signal-to-noise ratio (SNR) and have thus found wide applications for cardiac imaging. However, lipid signal appears bright in balanced SSFP images because of its high T2/T1 ratio and consequently complicates the interpretation of water signals that are of interest in abdominal and musculoskeletal imaging. Therefore, fat suppression is usually needed to reduce or remove fat signal.

Several fat suppression techniques have recently been proposed, which generally can be grouped into four categories: 1) Multiple k-space acquisition methods, including fluctuating-equilibrium MR (FEMR) (3), suppression of lipids by RF-modulated FIESTA (4), linear combination steady-state free precession MRI (LCSSFP) (5), and various types of multiple point Dixon techniques that belong to this category (6). A major limitation of the multiple k-space acquisition technique is the increased acquisition time as compared to a standard SSFP scan. 2) Selective water excitation (7), where a frequency-selective RF pulse is performed every repetition, which increases the repetition time (TR) and scan time, and results in greater sensitivity to magnetic field inhomogeneity. 3) Magnetization preparation for fat suppression, where fat suppression pulses are performed periodically while the magnetization is stored on the longitudinal axis. This scheme only slightly increases the acquisition time but may result in image artifacts due to transients in the transverse signal as it returns to the steady-state (8). 4) Fat/Water separation by phase detection (9, 10), which exploits the fact that fat and water spins exhibit a phase difference of π at an echo time (TE) of TR/2 when the TR is properly chosen. No increase in acquisition time is required; however, a TE of approximately TR/2 is essential in this approach.

Meanwhile, SSFP sequences that acquire multiple echoes have been implemented to increase the acquisition efficiency (11, 12). Projection-based multiple echo techniques have demonstrated inherent fat suppression through direct echo combination. Fat suppression is possible providing that the fat spins are nearly π out of phase in each pair of echoes (13, 14), while water spins are on resonance and therefore in phase in all echoes. The resultant image quality highly depends on acquisition parameters, such as the echo times and TRs. Data acquisition efficiency may be compromised if TEs are to be optimized to achieve better fat suppression since this usually means a longer TR. These techniques often suffer unwanted signal dropouts.

We have implemented a true 3D multiple-half-echo projection reconstruction technique (15), which is capable of acquiring a large field of view (FOV) with isotropic resolution while being robust to motion. Very short TRs have been achieved in a dual-half-echo implementation, which significantly reduces artifacts due to susceptibility. The LCSSFP method has been applied to this sequence to separate fat and water signals, and volumetric fat suppressed images with good spatial resolution, coverage, and SNR have been obtained. However, fat and water spins develop different relative phases in these two echoes due to their off-resonance behavior. As a result, signals from both echoes are not aligned after the combination, which compromises the SNR gain from the dual-echo acquisition depending on the relative phases of the signals.

In this work, we present a method to linearly combine the echoes acquired at the beginning and the end of the TR in the dual-half-echo VIPR sequence to suppress either fat or water in a single acquisition. This combination also achieves a better alignment of the signals and, therefore, improves the SNR. By exploiting the phase information of the resultant signal, further fat suppression can be achieved with a phase mask technique. Non-Contrast enhanced angiography and musculoskeletal applications demonstrate good fat/water separation and insensitivity to field inhomogeneity.


Balanced SSFP Magnetization

SSFP signal with an off-resonance frequency f accumulates a phase of β = 2πf * TR over each TR interval. With a constant-phase RF pulse (applied along the positive x-axis), a flip angle of α, and ignoring relaxation effects, the signal at an echo time TE, where the net phase accrual of static tissue due to gradients is zero, can be written as a modification to an expression shown in (5):

equation image(1)

where a = E2(E11)sinα, b = (1 − E1)sinα, c = E2(E11)(1 + cosα), d = (1 − E1 cosα) − (E1 − cosα)Emath image, E1 = emath image, and E2 = emath image. Usually TR ≪ T1, T2, and thus E1 ≈ 1 −TR/T1, E2 ≈ 1 −TR/T2, equation image and equation image. The phase of the signal with respect to the positive y-axis is then (the denominator is real and thus doesn't affect the phase):

equation image(2)

Assume the TR is short and thus the off-resonance frequencies of the spins of interest are within the range of equation image (e.g., −200Hz < f < 200Hz when TR = 2.5 ms). Consider only spins with off-resonance frequencies equation image, and thus (1 − eiβ) is not 0 and | 1 − eiβ |≫TR/T2. Now Eq. [2] simplifies to:

equation image(3)

Let τ = TETR/2(− TR/2 < τ < TR/2). The phase can be rewritten as:

equation image(4)

Therefore, all these isochromats cross either the positive or negative x-axis at an echo time of TR/2 (τ = 0), depending on their resonant frequencies.

Dual-Half-Echo VIPR Sequence

The dual-half-echo implementation of the VIPR sequence, as shown in Fig. 1, acquires data immediately after the refocusing gradient for slab excitation. An algorithm evenly distributes the radial lines by sampling the spherical surface of k-space with a spiral trajectory over the upper hemisphere, with the conditions of constant path velocity and surface area coverage, and then mirroring them in the lower hemisphere (16). Each repetition samples two adjacent radial lines in k-space in a form similar to a half “bowtie.” A small blip gradient creates a rotation between the first and second radial lines, but only requires 50–100 μs, as the rotation is quite small. Sampling at two different projection angles in each TR is beneficial since it helps to reduce the undersampling artifacts in the point-spread-function (PSF) of the sequence. Two half-echoes are collected immediately after RF excitation (echo time 1 or TE1) and near the end of the TR (echo time 2 or TE2) to achieve high acquisition efficiency. This sequence has several aspects that favor a short TR. No phase encoding gradients and phase rewinders, where each would require at least 0.7 ms for 1 mm resolution using our gradient system, are necessary. The thick slab excitation in VIPR also minimizes its refocusing gradient. In addition, sampling during gradient ramps further shortens TR. While the radial sequence is ideal for creating a short TR with two echoes for balanced SSFP imaging, a Cartesian dual echo implementation would likely increase the TR.

Figure 1.

(a) Pulse sequence and k-space trajectories for the dual-half-echo sequence. (b) A k-space trajectory for four TRs is shown.

Fat/Water Separation by Linearly Combining Echoes

On-Resonance spins have near zero signal in SSFP images with a constant RF phase. Although alternating RF phase is usually employed instead to shift the spectral response of SSFP to achieve high signal for on-resonance spins, an alternative approach is adopted here where the center frequency is placed halfway between the fat and water resonance frequencies (∼110 Hz lower than the water resonance frequency at 1.5T). In this study, all design parameters and examples are based on 1.5T and, thus, both fat (∼−110 Hz) and water (∼110 Hz) spins present high signals. With the dual-half-echo VIPR sequence, a very short TR (typically ∼2.4 ms) can be achieved and, therefore, the relative precession angle between fat and water over a repetition internal is approximately π. Eq. [4] can thus be used to describe the phase behaviors of fat and water spins.

The magnetization behavior during a repetition of the dual-half-echo sequence with τ1,2 = ±1.1 ms(τ1,2 = TE1,2TR/2) is illustrated in Fig. 2, showing two species with off-resonance frequencies of −110 Hz (fat) and 110 Hz (water), respectively. Water spins have a phase angle of π/4 at TE1 and 3π/4 at TE2, whereas the fat spins have a phase angle of −π/4 at TE1 and −3π/4 at TE2, giving a phase difference of π/2 between these two isochromats at both echo times. These phase offsets are used for illustration; in practice, there can be different phase offsets. As illustrated in Fig. 2b, linear combination of these two echoes can generate either fat or water only signal. Although Fig. 2 can be understood if both echoes acquire the same projection angle, it also applies to the case where different projection angles are acquired in each repetition in regions where k-space is oversampled. Since these two radial lines are adjacent in k-space, neighboring low frequency signals from both echoes will be interpolated onto the same Cartesian points and combined to create fat or water suppressed points on a Cartesian grid during reconstruction. Further description of signal combination in undersampled regions of k-space is provided in the Discussion section.

Figure 2.

Schematic illustration of combining signals at different echo times to create fat or water suppression. (a) Magnetization vectors for fat and water at different time points during a repetition. (b) Magnetization vectors showing the resulting signals from the echo combination.

This observation can, therefore, lead to a fat/water separation strategy for SSFP sequences that acquire echoes at different echo times. The feasibility of this strategy for more general cases where echo times cannot be optimally placed so that the fat and water signals are π/2 out of phase is demonstrated in Fig. 3. Here a typical set of parameters for the dual-half-echo VIPR sequence is used for a simulation considering oxygenated blood (TE1/TE2/TR = 0.3 ms/1.9 ms/2.6 ms and T1/T2/flip angle = 1000 ms / 200 ms / 30°). In Fig. 3a, the spectral response of the first echo, second echo, and the following echo combinations: echo1 + i*echo2 and echo1 − i*echo2 are shown from the top to the bottom, respectively. The left and right “*” marks in the plots correspond to the ideal off-resonance frequencies of fat and water spins, respectively. As can be seen from the plots, by linearly combining these two echoes, either fat (echo1 + i*echo2) or water (echo1 − i*echo2) can be suppressed. The passbands in the resultant spectral responses are as broad as conventional SSFP, although it is significant that fat and water can't be centered in the passband. A signal level nearly double that of the single half echo is achieved in the passband, demonstrating that the signal is utilized effectively.

Figure 3.

Spectral and phase responses of SSFP signals of different echoes or echo combinations. Left and right * symbols in each plot refer to the ideal fat and water frequency, respectively. From top to bottom, plots in each row correspond to the spectral (a) and phase (b) responses for first echo, second echo, echo1 + i*echo2, and echo1 − i*echo2, respectively.

Phase Masking

The phase responses of the spins at different echo times are governed by Eq. [4] and are also shown in Fig. 3. The combinations flatten the phase response of the combined signal, and make it resemble a rectangular wave. The phases of the passband and stopband are clearly differentiable, as shown in the corresponding plots. Although the bandwidth applicable for phase masking is narrower than the magnitude passband, its width is only slightly narrower than 1/2TR, the width available in FEMR or LCSSFP. Therefore, further fat/water suppression can be achieved by applying threshold techniques to display only those pixels whose phases fall outside of the suppressed band, which we term phase masking. In this way, purely water or fat images can be created. Instead of zeroing the fat pixels, it is also possible to provide variable suppression of the fat signal by scaling its amplitude with a factor less than unity. The phase responses of the combined signals become an ideal square wave when these two echo times are at equal distances from the middle point of the repetition, so it is possible to optimize this response by adjusting the echo times.

Non-Contrast-Enhanced MRA

The T2-like contrast of balanced SSFP results in high contrast between blood and background tissues, since arterial blood has relatively longer T2 than that of the muscle, venous blood, and connective tissues. Thus, by suppressing the lipid signal, visualization of the blood vessels via a maximum intensity projection (MIP) becomes feasible. Several groups have demonstrated this possibility using different fat suppression techniques (3, 5, 8, 13, 17, 18). Since the VIPR sequence employs a large volumetric excitation and, thus, flowing spins can stay in the excited region and remain in the steady-state for a longer period, it is advantageous for non-contrast enhanced MRA.

Experimental Parameters

The studies were conducted on a 1.5 T GE CVi scanner (GE Healthcare, Milwaukee, Wisconsin), with a 33 mT/m maximum peak gradient amplitude and a 120 mT/m/s maximum slew rate. A bandwidth of ±125 kHz was used for all studies to achieve a short TR. A maximum k-space excursion equivalent to 128 evenly spaced Cartesian points was used for each radial line, giving an equivalent image matrix size of 256*256*256. Minimal TEs and TRs are used in all experiments to achieve higher acquisition efficiency and, therefore, these are not optimized for the best fat/water separation performance, as mentioned above. Typical scan parameters include TR/TE1/TE2 = 2.6 ms/0.3 ms/1.9 ms. For musculoskeletal studies, the acquisition time was 150 s, and the total number of repetitions was about 58,000; while for angiography the scan time was 75 s and, therefore, there were approximately 29,000 repetitions. The flip angle used for musculoskeletal studies was 15°, and it was 30° for MR angiography studies. The projections were regridded to a Cartesian cube using either a separable triangle function or a Kaiser–Bessel function, and then an inverse FFT was used to reconstruct the images.


Fat/Water Separated Musculoskeletal Imaging

Fat suppression is desirable in knee imaging since otherwise lipid, which has a strong signal, can obstruct the visualization of objects of interest, such as cartilage. Using only the echo combination approach, fairly good fat or water suppression was achieved, as shown in Figs. 4a and b. However, the lipid signal level is still comparable with that of the muscle and cartilage after fat suppression. The phase image corresponding to Fig. 4b is shown in Fig. 4c. As predicted in Fig. 3b, these phase values can clearly be classified into two groups, with an apparent discontinuity between them: the group with lower phase values corresponds to the fat pixels and the group with higher phase values corresponds to water pixels. By simply setting the magnitudes of the pixels whose phases fall into the lipid group to zero, a pure water image can be obtained, as shown in Fig. 4d. With a spherical FOV of 18 cm, the cartilage is shown in great detail with 0.7 mm isotropic resolution. The femoral artery is also apparent (arrowhead), and some vessels in the subcutaneous tissue are more apparent in Fig. 4d than in Fig. 4b (arrows).

Figure 4.

Fat and water separation through different echo combinations and phase masking. (a) Water suppressed and (b) fat suppressed images obtained with only echo combination. Fairly good fat or water suppression is achieved. (c) Phase image corresponding to (b). (d) Water only image after applying phase masking to (b) to remove pixels whose phases fall into the fat band. Excellent depiction of the cartilage (arrow), muscle, femoral vasculature, and vasculature embedded in lipid (small arrow) is shown with 0.7 mm isotropic resolution and a scan time of 150 s.

The feasibility of using phase masking to further suppress fat is again demonstrated in the ankle images in Fig. 5, where a 20 cm spherical FOV is acquired with 0.8 mm isotropic resolution. The images are shown as the summation of three sagittal slice reformats to improve SNR, providing 0.8 mm*0.8 mm in-plane resolution and a slice thickness of 2.4 mm. After the removal of the fat component from Fig. 5a, better depiction of the cartilage contour is shown in Fig. 5b.

Figure 5.

Reformatted sagittal ankle images show the feasibility of using phase masking to further suppress fat. (a) Fat suppressed images using echo combination. (b) Resultant image after phase masking shows better contrast between the cartilage and bone (short arrow) and improved fat suppression, especially in the distal tibia (arrow).

Non-Contrast-Enhanced MR Angiography

The applicability of the proposed techniques to non-contrast enhanced MRA is demonstrated in our volunteer studies in Fig. 6. A 24 cm spherical FOV is imaged in these two studies, with 0.94 cm isotropic resolution. As shown in Figs. 6a and b, excellent depiction of the external and internal carotid artery was shown in the sagittal and oblique targeted MIP images. Fat suppression with only echo combination was sufficient in this case. In Figs. 6c and d, the peripheral MIP images acquired using an extremity coil depict the popliteal artery in great detail. Here fat suppression is achieved with both echo combination and phase masking. Fat signal is removed in the water volume and, thus, does not contaminate the water MIP. The contrast between the arteries and the veins is well demonstrated. The isotropic resolution provided by this sequence makes it possible to visualize the volume at any angle and, thus, the obstruction of the bright fluid signal is alleviated.

Figure 6.

Non-contrast-enhanced carotid artery imaging (a, b) and peripheral angiography (c, d) using the dual-half-echo VIPR sequence with fat suppression in 75 s. (a) sagittal and (b) oblique reformats of the carotid arteries. (c) and (d) show the knee vasculature at different angles. The inherent isotropic resolution allows visualization of the volume at any angle and facilitates volume rendering. Good contrast between the artery and vein is shown due to the difference in T2/T1 of arterial and venous blood.


We have demonstrated that very good fat and water separation can be achieved by exploiting phase properties to mask out an unwanted spectral component in SSFP imaging. Unlike many other fat suppression techniques, only a single acquisition is needed in this approach and there are no extra preparation pulses. Fat/Water separation is achieved purely by post-processing. Relative to a single pass conventional SSFP acquisition of a similar FOV, the dual-half-echo VIPR SSFP sequence requires π/2 more excitations to fully sample k-space. While Cartesian imaging also allows time savings with anisotropic imaging volumes, the ability to moderately undersample VIPR SSFP and its reduced TR may offset this Cartesian advantage.

As compared to the previous implemented LCSSFP technique, the fat suppression effect of the new method with only echo combination (without phase masking) is not as good as that of LCSSFP. The fat stopband has a higher amplitude that is more similar to the stopband in FEMR (3). However, the spectral response of the proposed technique has a much wider passband as compared to that of the LCSSFP method with similar parameters, which helps to reduce the banding artifacts due to susceptibility for positive off-resonance frequency shifts. While the phase masking method creates very high contrast between water and fat voxels, the masking eliminates the small remaining amount of water signal, which may be seen as a deleterious effect by some physicians.

B0 field inhomogeneity can effectively shift some fat/water frequencies to the incorrect passband or stopband. Similarly to LCSSFP or FEMR, the fat/water separation performance of the proposed method thus depends on the available chemical shift. In these situations, robust fat/water separation has been demonstrated with the 3-point Dixon IDEAL method through correctly measuring and compensating for off-resonance phase shifts (19). Though its scan time is longer, enhancements in the technique are mitigating this increase (20). In SSFP imaging, however, the longest of the three echo times, 4.8 ms, can create banding artifacts for which IDEAL can't compensate.

As demonstrated in the head images in Fig. 7, both images show very good fat suppression. There is no signal dropout near the sinus cavities in Fig. 7b using echo combination, while dropout is seen in the LCSSFP water image in Fig. 7a. This benefit is enjoyed independent of phase masking.

Figure 7.

Axial head reformats from whole brain study reconstructed using LCSSFP (a) and the new method (b) show good fat suppression. Scan time is reduced from 150 s in (a) to 75 s in (b) because the new method uses only half of the data as LC SSFP. Signal dropout in areas of susceptibility difference in (a) is not seen in (b) (arrows).

Fat and water separation with the presented method is achieved only over a portion of the center k-space, where the data from both echoes contribute evenly to the Cartesian grid points. The radius of this well-combined region mainly depends on the number of the radial lines (Np) and is approximately equation image, with Nr being the equivalent readout resolution for a k-space diameter and kmax the radius of the sampled k-space sphere. k-space outside of this region may contain an uneven amount of information from the two echoes (or only information from one echo) and, thus, have mixed fat and water signals. After post-processing, data in the center region of k-space results in effective signal combination, where the phase difference of the desired components is near zero and the undesired components is approximately π. However, since image contrast is determined primarily by the low frequency signal where significant lipid energy is present, the effects of this limited suppression is mitigated. For partial volume voxels containing both fat and water, echo combination will work to suppress the undesired species as described. However, the concept of phase masking is limited as in (9) and, thus, this method works best in high resolution imaging.

A phase evolution occurs between the outgoing and incoming radial lines and, therefore, a growing phase oscillation exists over an outer shell of k-space after the π/2 phase shift is applied to the second of the dual echoes. The phase oscillation is moderate, however, and, thus, benefits from reducing undersampling by acquiring different angles during the return to the k-space origin are achieved. Due to the limits of peripheral nerve stimulation, receiver bandwidth, and gradient strength, approximately 80 percent of the readout period is spent along gradient ramps. Because the outer k-space samples are covered during gradient ramps where k-space velocity is slowing, the worst phase errors are beneficially compressed to a smaller outer shell of k-space than would occur with gradients with an infinite slew rate. The optimal implementation would thus acquire as much of the first echo as possible immediately after the RF pulse, acquire the second half echo as close as possible to the next RF pulse, and acquire less data near TR/2. We are working to eliminate deadtimes before and after the RF pulse to fully achieve this with our scanner manufacturer. Using the most recent software release, phase errors would be limited to approximately 0.6 radians within the inner 2/3 of k-space and to 1.0 radian at the edge of k-space.

Unlike contrast-enhanced or phase contrast MRA, where high contrast and relatively few objects allow large undersampling factors, the larger number of signal producing objects with SSFP do not allow significant undersampling factors in the applications shown in this study. For this reason, these artifacts have little impact on the phase-masking operation.

The proposed method may apply at other field strengths, such as 0.5 T and 3T, where the chemical shift between fat/water is approximately 70 Hz and 440 Hz, respectively. The optimal TR would correspondingly increase by a factor of 3 at 0.5T and decrease by a factor of 2 at 3T. The increase in TR at 0.5T would not cause decreased robustness to B0 inhomogeneity relative to 1.5T for the same magnitude of off-resonance as measured in Hz, but similar performance for similar off-resonance in ppm. Decreasing the TR to approximately 1.2 ms while achieving reasonable resolution is impractical at 3T. Skipping a passband may be possible, however, by using a 3.3 ms TR where data acquisition occurs over the first and last millisecond. Offsetting the center frequency to higher frequencies in the water passband while using similar TR and TEs as used in this study may also be possible at 3T.


The new fat/water suppression technique exploits the off-resonance phase accrual at different echo times within each excitation to achieve excellent fat and water separation in a single acquisition. It is also very robust to field inhomogeneity. Our volunteer studies demonstrate that this technique provides a promising approach for MR angiography and musculoskeletal imaging, and additional clinical studies are warranted.