Balanced SSFP (TrueFISP, FIESTA, b-FFE, bSSFP) shows high SNR at short repetition times (1, 2) and is frequently used in applications that require high temporal resolution, such as in cardiac imaging or perfusion studies. The T2/T1-weighted contrast of bSSFP generates a bright fat signal (T2/T1∼0.3) comparable to the signal intensity of liquids or fluids. A separation or suppression of fat signals is thus essential for, e.g., coronary artery imaging (3) or cartilage imaging (4), or in general, to separate different resonances or metabolites.
Several methods have been proposed to generate frequency selective bSSFP images. A simple and robust approach is FS-SSFP (spectral or fat saturated SSFP) (5), where magnetization is longitudinally stored after an α/2 flipback pulse, thereby offering an interruption of the steady state and making the insertion of a spectral selective saturation pulse possible. A different method is FEMR (fluctuating equilibrium MR) (6), which is based on a modification of the frequency response function of bSSFP generated by modified phase cycling schemes. Two resonances, such as fat and water images, can be acquired simultaneously in an interleaved manner. In LC-SSFP (linear combination SSFP) (7, 8), several images with different frequency responses are combined to generate a shaped frequency sensitivity. A similar approach is based on binominal excitation patterns (9) or on the direct synthesis of shaped frequency response function (10). A further possibility is to use the phase difference of the fat and water spins for separation, either by direct phase detection (11) or Dixon-type post processing (12–15).
An intrinsic drawback of FEMR, LC-SSFP, binominal excitation patterns (9), and similar variants (16) is the large increase (∼100%) in total acquisition time to generate the required frequency response function, as well as a restriction of possible repetition times TR. FS-SSFP shows an increase in total imaging time of about 30%, depending on the number of steady state interruptions during which a spectral selective saturation pulse is played out, and is not restricted in TR. FS-SSFP is regarded to be the most robust fat suppressing SSFP method (4, 5); however, only a single resonance can be detected.
The method introduced here is based on the new concept of using two different and apparently independent repetition times, TR1 and TR2, and a tailored RF phase cycling (17). The specific sequence parameters, such as TR2/TR1 ratio and phase cycling scheme, are derived from a general approach designed to produce a shaped steady state frequency response profile with broad stop- and passband. The cyclic variation of repetition times offers a further mechanism not only to shape, but also a new parameter to control the periodicity of the frequency response profile.
The conventional bSSFP sequence consists of a train of RF-pulses with flip angle α equidistantly spaced by TR. The phase of the RF-pulse is incremented by 180° from pulse to pulse. Imaging gradients are applied on the x-, y-, and z-axis with vanishing zeroth moment within one repetition period. In the steady state, the magnetization vector immediately after RF excitation consists of the three components Mx = M0(E1 − 1)E2sinαsinθ/D, My = M0(1 − E1)sinα(1 + E2cosθ)/D, and Mz = M0(1 − E1)[E2(E2 + cosθ) + (1 + E2cosθ)cosα]/D, with E1 = exp(−TR/T1), E2 = exp(−TR/T2), and D = (1 − E1cosα)(1 + E2cosθ) − E2(E1 − cosα)(E2 + cosθ) (from (18), including RF phase increment of 180°). θ is the dephasing during TR due to chemical shift or local B0 field variations. For TR ≪ T2, the signal for on-resonance spins (θ = 0°) is maximized at α = arccos([T1/T2 − 1]/[T1/T2 + 1]) (19), and the resulting signal magnitude is proportional to (T2/T1)1/2.
The dependency of the magnitude of the transversal magnetization component on θ (Fig. 1, dashed line) is 1/TR-periodic and shows up experimentally as the banding artifact. According to this frequency response function (FRF), an isochromat with θ = 180° or odd integer multiples thereof is largely suppressed and appears dark in the image. In practice, this stopband is too narrow to give a robust spectral selection or suppression technique.
Balanced SSFP with Alternating TR
A novel approach to broaden the stopband of the FRF is based on alternating TR (ATR) and modified RF-pulse phases (Fig. 2) (17). In general, alternating repetition times TR1 and TR2 (TR1≥TR2) with τ = TR2/TR1 produces an FRF that is no longer 2π periodic as in bSSFP, but has a periodicity of 2π/τ (if 1/τ is an integer value), for which an integer multiple of 2π dephasing occurs both within TR1 and TR2. The resulting ATR steady state signal can be calculated as follows: without loss of generality, the phase ϕ1 of the first RF-pulse can be set to zero, as a constant phase added to each RF-pulse does not change the magnitude of the FRF, and TR2 ≤ TR1. The steady state magnetization after pulse RF1 is
and equivalently after pulse RF2
Combination of Eq.  and Eq.  yields the steady state magnetization
with the matrix D1 representing relaxation and dephasing by θ during TR1, with E21 = exp(−TR1/T2), and E11 = exp(−TR1/T1)
and matrix D2 representing relaxation and dephasing τθ during TR2, with τ = TR2/TR1 ≤ 1, E22 = exp(−TR2/T2), and E12 = exp(−TR2/T1).
The RF-pulse matrices R1,2 include the influence of RF excitation (exemplarily shown for α = 90° and arbitrary phase ϕ2 of second RF-pulse):
With these rotation and relaxation matrices, the steady state after RF1 of the sequence can be computed. A similar calculation starting with Eq.  and Eq.  gives the steady state after RF2 in dependence of R1, R2, D1, D2, M0, E11, and E12. As will be shown later, TR2 is in general too short to switch imaging gradients after RF2; only the steady state after RF1 is analyzed. In that case, TR1 takes over the role of TR in bSSFP, while RF2 and TR2 are only means to change the shape of the FRF.
ATR gives a dual steady state and can introduce a new mechanism for generating stopbands. In conventional bSSFP, the stopband emerges because of a nearly completely saturated spin-system at certain off-resonance angles. For alternating TR, however, one steady state configuration is composed mainly of longitudinal magnetization (producing a transverse stopband); the other steady state configuration is a mixture of longitudinal and transverse magnetization (passband), as depicted in Fig. 3, where the 3D location of the steady state magnetization, i.e., the tip of the magnetization vector, of bSSFP, FEMR, and ATR is plotted for a range of off-resonance angles θ from 0° to 1080° (corresponding to the periodicity of the simulated ATR sequence).
RF Phase Cycling for Balanced SSFP with Alternating TR
In the following, conditions for the free parameters τ = TR1/TR2 and phase ϕ2 of the second RF-pulse RF2 will be deduced to produce a broad stopband generated by longitudinal magnetization at a certain dephasing θstop. If longitudinal magnetization = (0 0 1) is one possible steady state solution, is an eigenvector of the composite matrix R1D2R2D1 (neglecting relaxation, E11 = E12 = E21 = E22 = 1) with eigenvalue 1. Solving R1D2R2D1= leads to the condition
which connects the position of the stopband, θstop, with the phase ϕ2 of RF2. To make the stopband robust against local field inhomogeneities, it should be as broad as possible with a symmetric shape around θstop. This symmetry condition in combination with Eq.  leads to the second constraint for ϕ2 given by
for the location of the stopband. Then, due to symmetry, there is a passband with its center located at θpass = −θstop = ϕ2 (the pulse phase ϕ2 is always negative, see Eq. ).
The resulting steady state of the transversal magnetization Mxy is shown in Fig. 4 for a range of 1/25 ≤ τ ≤ 1. For ATR, the position of the stop- and passbands depends on τ (see Eqs.  and ). Therefore, in order to position the passband at on-resonance frequency, the entire FRF has to be shifted accordingly, which means the passbands shall be at θpass = 0 and no longer at θpass = ϕ2. This results in a shift of the FRF by δθ = −θpass = θstop = −ϕ2 and places the stopband finally at θstop = −2ϕ2 = 360°/(τ + 1). This shift of the FRF can be produced by adding a phase cycle with alternating increment ϕinc, which is for the two RF-pulses RF1 and RF2 given by
The ATR frequency responses depicted in Fig. 4 are calculated using the conditions given in Eqs.  and , and with a shift of the passband to θ = 0° using Eq.  as described.
Examples of different sequences and their appropriate parameter setting that can be derived from the general ATR concept are:
1Conventional bSSFP with TR2 = TR1 = TR and ϕ2 = 180°.
2FEMR (6) with TR2 = TR1 = TR and ϕ2 = 90°. Shift of the passband according to Eq.  gives 0° 180° 180° 0° phase cycle, and θstop = 180°. This method is designed to acquire water and fat images simultaneously in a k-space-interleaved manner. As the FRF alternates between even and odd sequence cycles, each phase encoding gradient is played out twice and assigned to the water or fat k-space. FEMR requires a certain TR to ensure θ = 180° for fat spins during TR, i.e., TR = 2.3 ms or TR = 6.9 ms with a chemical shift of Δf = 217 Hz at 1.5T.
3Wideband SSFP (20), which consists of alternated TR with phase cycle of 0° 180° 0° 180°, and aims to broaden the passband.
Balanced SSFP with Alternated TR Applied to Fat Suppression (FS-ATR)
Based on the described concept of ATR, a variant FS-ATR (fat suppressing ATR) can be designed with the following parameters and features: choosing TR1 = 3TR2, i.e., τ = 1/3, it follows from Eq.  that ϕ2 = −135° (ϕ1 = 0°), and from Eq.  θstop = 135°. To center the passband at θ = 0°, the FRF is shifted by 135° along the θ-axis using ϕinc = −135° for pulse RF2 and ϕinc = −45° for pulse RF1, respectively, according to Eq. . This leads to an RF phase cycle over all RF-pulses of 0° (pulse RF1) − 270° (pulse RF2) − 180° (pulse RF1) − 450° (pulse RF2) − 360° (pulse RF1), which is equivalent to a 0° 90° 180° 270° 0° cycle, i.e., a constant phase increment for each RF-pulse regardless of the difference in TR1 and TR2. Then, the stopband minimum is located at θstop = 270°, which is practicable as it requires TR1 = 3.46 and TR2 = 3.46/3 ms = 1.15 ms for fat to dephase by 270° during TR1. In principle, also, shorter τ values than 1/3 are possible, resulting in a slightly increased stopband broadness. However, for fat suppression at 1.5 T the restriction
must be fulfilled. Eq.  is derived by combining θfat = TR1 · Δf · 360° (the off-resonance angle that fat acquires during TR1) and θstop = 360°/(τ + 1) (the stopband minimum of an FRF shifted in order to place a maximum on θ = 0°). The latter is the result of combining Eqs.  and  and carrying out a shift according to Eq. . Then, setting θfat = θstop will lead to Eq. .
Therefore, smaller τ can only be reached with a shorter TR2, which requires shorter RF-pulses as the length of the slice selection gradient (including ramps) determines the shortest possible TR2. Thus, shorter τ deteriorates the slice profile or increases SAR.
The fat-suppression ability of FS-ATR is visualized in Figs. 1 and 3, in comparison to conventional bSSFP and FEMR. For bSSFP, the minima or stopbands of the FRF are created by saturation; both the longitudinal and transverse part of the steady state magnetization is nearly zero at a stopband. As described in detail by Freeman and Hill (18), the density of steady states within a certain dephasing interval Δθ is not constant but varies with θ. It exhibits a small density around θ = 180° (giving a narrow stopband) and high density around θ = 0° (broad passband), as indicated by the density of the dots in Fig. 3. For FEMR and ATR, the density of steady states and thus the broadness of stop- and passbands as a function of dephasing θ is totally different. A high density of states composed of large longitudinal but almost vanishing transverse components is located for FS-ATR around θ = 270° (FEMR: θ = 180°), which generates the broad stopband. RF2 partially transfers this distribution into transverse magnetization to produce a broad passband before it is again transferred back into the longitudinal configuration by the next RF excitation RF1. If TR2 is sufficiently long to switch imaging gradients, two different steady states can be recorded as in FEMR, one during TR1 and one during TR2, i.e., the steady state alternates between two configurations. If TR2 is short as in FS-ATR, only the FRF during TR1 can be observed.
Optimal Flip Angle for FS-ATR
A practical issue is the increased power deposition of FS-ATR per unit time in comparison to bSSFP. Therefore, the maximal reachable flip angle within the SAR limit is lower. However, FS-ATR has maximal signal amplitude at flip angles lower than αopt(bSSFP), as demonstrated in Fig. 5. This can be explained by the fact that for on-resonance spins, FS-ATR becomes identical to bSSFP with an RF phase increment of 90°, if the small difference in relaxation during TR1 and TR2 is neglected. This RF phase increment shifts the FRF of bSSFP by −90°. In order to keep the maximum of the FRF at θ = 0° the excitation angle has to be lowered accordingly, as the maximum amplitude of the FRF for bSSFP is constant for varying α within the limit α < αopt, but is located at different positions on the θ-axis (18, 21); see Fig. 5c.
TR1 Insensitivity of FS-ATR
Eq.  offers the possibility to reach a stopband in ATR under variation of TR1→TR while keeping TR2 and RF-pulse phases constant. According to Eq. , the minimum moves to θstop = (180° + ϕ2)/τ′, with τ′ = TR2/TR1′, and thus linearly depends on TR1′. As a result, the fat resonance stays within the stopband even if TR1 is changed. However, the symmetry condition Eq.  is broken, which slightly decreases the broadness of the stopband. The effect of varying TR1 on the FRF of FS-ATR is demonstrated in Fig. 6. FS-ATR can be regarded to be largely TR1 insensitive, as long as the stopband does not coincide with the narrow gaps at θ = 135° and θ = 405° (see Figs. 1 and 6), i.e., for the range of about 2.5 ms < TR1 < 4.5 ms.
Initial FS-ATR Preparation
ATR shows signal oscillations during the transition into the steady state, which can lead to image artifacts. In analogy to the bSSFP − α/2 preparation (22), the on-resonance magnetization vector can be aligned to its steady state position before the sequence starts. The preparation pulse for FS-ATR is played out at time tprep = TR2 before the first TR1 interval. To determine the flip angle and phase of the preparation pulse, the steady state after the RF-pulse RF2 with phase of 270° was simulated and the vector representing on-resonance spins was determined. The alignment of this vector and the alignment of the magnetization for on-resonance spins after the preparation pulse must be equal. The simulation gives a flip angle of 2α/3 and a phase of 225° for the preparation pulse. The signal evolution of FS-ATR with and without a preparation pulse is plotted in Fig. 7. For water spins (with relaxation times of blood), which are on-resonance, there are severe signal oscillations in the simulation at the beginning of the sequence without preparation. These oscillations are removed by the preparation pulse. Some slight oscillations remain; however, they are not expected to have significant influence on image quality.
IMPLEMENTATION AND EXPERIMENTS
The diagram of the implemented FS-ATR sequence is shown in Fig. 8. Due to the very short TR2 of 1.15 ms and RF-pulse duration of about 600 to 1000 μs, the polarity of the slice selection gradient is alternated from RF-pulse to RF-pulse in order to save time during TR2. Otherwise, unipolar slice selection gradients would require additional rephasing and dephasing gradient lobes as in conventional bSSFP, which will need too much time to be switchable during a short TR2 of 1.15 ms.
Experiments to evaluate signal intensities, frequency response profiles, and image quality of bSSFP, FEMR, and FS-ATR were performed on phantoms and healthy volunteers on a 1.5 T scanner (Sonata, Siemens Medical Solutions, Erlangen, Germany). All phantom experiments were performed with a receiving CP head coil. For the in vivo experiments, a CP spine array coil was used for receiving in combination with a CP body array coil for the abdominal images; knee images were performed with a CP flexible coil.
The FRF of bSSFP, FEMR, and FS-ATR were measured (Fig. 9) in a 2D acquisition with voxel size of 0.9 mm × 0.9 mm × 10 mm on a bottle phantom (T1 = T2 = 300 ms). A shim gradient of 0.34 mT/m was applied along the readout direction to create a range of off-resonance frequencies (17° per voxel). Parameters are corresponding to the simulations shown in Fig. 1: bSSFP: TR = 3.47 ms, α = 63°; FEMR: TR = 3.47 ms, α = 49°; FS-ATR: TR1 = 3.47 ms, TR2 = 1.15 ms, α = 50°.
Signal intensity versus excitation flip angle (Fig. 5) was experimentally verified for two different phantoms by evaluating an ROI in the fifth slice out of a 12-slices 3D image set. The relaxation times of the phantom used for Fig. 5a was T1 = T2 = 300 ms. A second phantom with T1 = 520 ms and T2 = 90 ms was examined to show the flip angle dependency of the signal with a T2/T1 ratio smaller than one (Fig. 5b). Practically, relaxation times of fluid/blood are of interest, but in this case flow effects have to be considered to assess the flip angle dependency of the signal in vivo.
The fat suppression performance of FS-ATR and FEMR was compared on phantoms and volunteers. Figure 10 a shows an image of two bottles (diameter 12 cm) of Gd-doped water (T1 = T2 = 300 ms) with a small bottle (diameter 7.5 cm) with vegetable oil on top acquired with conventional bSSFP. Depicted are 2D acquisitions with 256 × 256 matrix size and in-plane resolution of 1.2 mm × 1.2 mm and α = 60°. Fig. 10b has been acquired with FS-ATR using TR1 = 3.47 ms and TR2 = 1.15 ms, and Fig. 10c with FEMR and TR = 6.58 ms. The average signal of two ROIs (water and fat) was evaluated for each experiment. Abdominal 3D breath-hold images (Figs. 11–13) have been acquired with bSSFP, FEMR, and ATR using comparable acquisition parameters as for the phantom experiments. To demonstrate TR1 insensitivity of FS-ATR, 3D high resolution images (Fig. 14, 0.8 mm × 0.8 mm) of the knee have been measured with the shortest possible but increased TR1 of 4.29 ms (TR2 = 1.14 ms).
Figure 9 shows a clearly broadened stopband for ATR in comparison to FEMR and bSSFP. The overall signal maximum of FS-ATR is not at θ = 0° but at θ = 810° for the given set of T1, T2, and α. Therefore, the images shown in Fig. 9 correspond well with the simulations in Fig. 1.
Phantom fat-water images presented in Fig. 10 show a similar fat suppression for ATR and FEMR. In both cases a sufficient field homogeneity within the phantom could be achieved to produce sharp resonances of both fat and water that are located precisely within the stop- and passband, respectively. According to the simulations and measurements shown in Fig. 5, FEMR gives a higher signal for both fat and water for an excitation flip angle of 60°. However, the signal ratio of water/fat is higher for FS-ATR. Experiments show the optimal flip angle for FS-ATR being smaller than the optimal flip angle for balanced SSFP (Fig. 5, α = 80° and α = 90°; could not be measured for FS-ATR due to SAR limitations).
The in vivo fat suppression ability of FS-ATR and FEMR is demonstrated in Fig. 11 on volunteer #1 in coronal and transversal images. FS-ATR shows improved fat suppression compared to FEMR, and several artifacts are visible in the coronal FEMR image. In general, the fat suppression works better for the intraabdominal fat tissue; the suppression of the subcutaneous (s.c.) fat is not homogenous, most probably due to frequency variations induced by the imperfect shim. The homogeneity of fat suppression in FS-ATR is demonstrated in Fig. 12 on volunteer #2, where a maximum intensity projection through a transversal 3D block is shown. The same behavior is demonstrated in the coronal abdominal images of volunteer #3 in Fig. 13. In Fig. 14, the robustness of FS-ATR against variations of TR1 is demonstrated; TR1 was increased from 3.46 ms to 4.29 ms, while keeping RF-pulse phase cycling constant and TR2 at 1.15 ms. Depicted is a slice with thickness of 3 mm, taken out of a 3D data set.
The method of alternating TR introduces a novel and general mechanism for the modification of the FRF of bSSFP-type sequences. By appropriate adjustment of the RF-pulse phases, at certain off-resonance frequencies the magnetization oscillates between longitudinal orientation and orientation with transverse part resulting in a broad stop- and passband. Signal is acquired during the long TR1 (3.46 ms) whereas the short TR2 (1.15 ms) is only used to modify the FRF. With this setup a broader stopband compared to FEMR can be achieved, which makes ATR less sensitive to field inhomogeneities. The maximal signal at the passband of ATR is identical to conventional bSSFP, but is achieved at a reduced flip angle compared to the optimal flip angle of bSSFP.
For FS-ATR with τ = 1/3, the frequency separation Δf of the stop- and passband can be controlled within a certain range by changing TR1 and TR2 on condition that TR1 + TR2 = 1/Δf (Eq. ), with RF phase cycle remaining unchanged. In general, any frequency separation Δf can be achieved with the appropriate choice of τ and corresponding RF phase cycling, as given by Eqs. –(11). This makes ATR also promising for chemical shift imaging of metabolites of nuclei different from protons (23). An important advantage of FS-ATR over other methods is its insensitivity to variations in TR1 within a certain range given in Fig. 6. This can be used either to speed up acquisition by lowering TR1, or to take account for the need of stronger gradients when increasing resolution by lengthening TR.
The scan time of FS-ATR is about 33% longer than for bSSFP, resulting in a loss of scan efficiency (SNR divided by total scan time). FEMR requires a longer and fixed TR of 6.6 ms to 6.8 ms (depending on the fat-water separation) and acquires each k-space line twice to produce both water and fat images. The increased TR of FEMR in combination with its higher steady state amplitude gives an increased scan efficiency compared to FS-ATR. However, if only a single resonance is of interest, FEMR is less efficient compared to FS-ATR. Especially in applications that require short total acquisition time, e.g., scans during breath hold (3), total scan time becomes more important than scan efficiency, as long as SNR is sufficiently high. However, in cases where both the water and fat image is of interest, FEMR or the binominal approach of Hardy and Dixon (9) would be the method of choice. FS-bSSFP requires a scan time comparable to FS-ATR, depending on the number of steady state interruptions (5). The general drawback of FS-bSSFP and other non-steady state techniques (24) is the sensitivity to off-resonance effects in terms of signal oscillations generated after each steady state interruption that can lead to artifacts. In contrast, FS-ATR and FEMR are continuous steady state techniques that show no artifacts due to signal oscillations.
The direct applicability of FS-ATR at 3 T is problematic since Eq.  requires very short repetition times of TR1 + TR2 = 1/Δf(3T) = 2.3 ms. However, the FRF of ATR consists of three passbands (Fig. 1), allowing for a shift of on-resonance spins to the second passband located at θ = 810°. With this trick, possible parameters for FS-ATR at 3T become TR1 = 3.46 ms, TR2 = 1.15 ms, and RF phase cycle 0° 180° 180° 0°. This version produces an FRF with high on-resonance signal and stopband at θ = 540°, which is equal to the off-resonance angle of fat (Δf = 434 Hz) at 3.46 ms at 3T.
The limiting factor of FS-ATR is the sensitivity to local field variations, which will dislocate the fat off-resonance frequency in the FRF and lead to visible fat (or vice versa, invisible water). However, these problems occur in any fat-suppressed bSSFP method. Due to the alternating polarity of the slice gradient, the first moment is not zero at the time of RF excitation. This might increase flow sensitivity; however, no severe flow artifacts have been observed for the abdominal acquisitions performed in this study.
We have presented a novel and easy to implement method to achieve fat suppressed bSSFP images. FS-ATR relies on the intrinsic behavior of off-resonance spins; it can tolerate shim variations over a practically useful range and does not require a certain repetition time, which makes it easy to change image parameters, e.g., increasing resolution. Total scan time is increased about 30% in comparison with bSSFP; thus, the method is promising for fast imaging during breath hold.