a: The period of a multiple-TR sequence consists of N different RF excitations (with flip angles, α_n) and repetition times (with durations, TR_n). We can compute the periodic spectral response for an echo acquired at TE_j (during TR_j) by solving the discrete time system governing the magnetization change from one period to the next, taking this echo as the starting point. b: Once the echo at TE_j is assumed to be the initial point, the RF excitations and the repetition times will be reordered. This specific ordering of the multiple-TR period determines the aforementioned discrete time system and the resulting spectral response.

a: The two echoes in the subsequent data acquisition intervals, TR₁ and TR₂, of the 2-2-1-1 sequence have substantially equivalent magnitude profiles. However, the corresponding phase profiles (the solid line for TR₁ and the dotted line for TR₂) are different even after the 180° offset due to phase cycling is removed from the second echo, yielding a nonlinear phase difference increasing with off-resonance. While this difference is relatively bounded within the pass-band (marked with the light gray rectangle), it becomes significant in the stop-band. Furthermore, the difference assumes two mean values (marked with the dashed black lines) for separate frequency ranges within the stop-band. b: As shown in Combinations 1 and 2, the two echoes can be linearly combined to improve the stop-band suppression in either of the two stop-band frequency ranges. The mIP of these linear combinations achieves this improvement over the whole stop-band, at the expense of slightly reduced pass-band signal. We can compensate for this loss by thresholding the phase difference of the two echoes and magnitude-summing the pass-band data while performing the projection only within the stop-band.

To demonstrate the effect of the TR-durations in multiple-TR bSSFP (N = 4, TR₁ = TR₂, TR₃ = TR₄), we can keep either TR₁ (a) or the total TR (2*[TR₁+TR₃]) constant (b), and vary τ = TR₃/TR₁. In the first case, TR₃ and the total TR are shortened by decreasing τ because TR₁ is fixed. However, the pass-band width has a very weak dependence on τ for fixed TR₁, if it is defined as the full width at half maximum. In contrast, TR₁ is lengthened for smaller τ and a fixed total TR, effectively shrinking the pass-band. In both a and b, τ = 0.5 (marked with the ticks on the vertical axis) creates a stop-band (marked with the dashed white line) that has 1.67 times the width of the corresponding pass-band (marked with the dashed black line). Finally, τ = 1 produces a regular bSSFP response as expected.

The contour plots show the average blood-to-fat signal ratio computed over a band of [−80 80] Hz around the water and fat resonances. The magnetization profiles for blood (T₁/T₂ = 1000/200 ms) and fat (T₁/T₂ = 270/85 ms) were simulated for a practically useful range of parameters: TR₁ ∈ [2.5 4.5] ms, τ = TR₃/TR₁ ∈ [0.2 1], and three different flip angles: 30°, 45°, and 60°. The boundary conditions for the simulations were TR₁ = TR₂ and TR₃ = TR₄. The near-optimal values for the suppression ratio are achieved when τ is in the [0.4 0.65] range. The level of suppression improves at higher flip angles. Finally, the highest level of suppression is attained around TR₁ ≈ 3.4 ms for α = 60°.

Phantom images were acquired to demonstrate the created magnetization profiles, where the precession frequency was vertically varied with a linear field gradient in that direction. The ATR-SSFP, 3-1-1, and 2-2-1-1 images are shown in order from left to right. Water and fat resonances at 1.5 T are marked with the dashed black and white lines respectively. The multiple-TR sequences have significantly more uniform pass-bands than ATR. Meanwhile, the 2-2-1-1 sequence has the broadest stop-band and the highest level of suppression. The suppression in separate segments of the stop-band can be independently improved with linear combinations as shown in Comb. 1 and 2. Finally, a mIP of these combinations yields enhanced suppression over the whole stop-band.

3 T results. The thin-slab (a) and whole-volume (b) MIPs of ATR and multiple-TR acquisitions are shown. The broad multiple-TR stop-band successfully reduces the fat signal in regions where ATR-SSFP fails. Poor fat suppression deteriorates the vessel depiction with ATR-SSFP as seen in a. Furthermore, improperly suppressed bone-marrow signal in the fibula with ATR-SSFP confounds the thin-slab MIPs. These regions are shown with arrows in a. The ATR-SSFP image in b has very bright fat signal in the peripheral regions. This indicates that the stop-band width of ATR-SSFP becomes insufficient with the increased field inhomogeneity at 3 T. In contrast, the multiple-TR image has adequate suppression over the whole volume.

a: Examples of multiple-TR sequences are shown: bSSFP (N = 1), ATR-SSFP (N = 2), 3-1-1 (N = 3), 2-2-1-1 (N = 4). All RF pulses have the same flip angle (α); however, the phase cycling pattern may vary: (0-90-180-270)° for ATR-SSFP, and (0-180)° for the rest. Data is acquired only during the labeled intervals, which are usually in the longer TRs. b: The corresponding transverse magnetization profiles for the bSSFP, ATR-SSFP, 3-1-1, and 2-2-1-1 sequences are shown. ATR-SSFP creates a stop-band around the fat resonance (−220 Hz at 1.5 T); however, its pass-band is non-uniform. In contrast, both multiple-TR sequences (3-1-1 and 2-2-1-1) have a flatter pass-band. The 2-2-1-1 profile has a broader stop-band compared to the other techniques.

a: The signal at the water resonance (on-resonance) was simulated as a function of the flip angle for the bSSFP, ATR-SSFP, and multiple-TR sequences. b: The differences between the bSSFP signal and the signals generated by ATR-SSFP and multiple-TR SSFP. T₂/T₁ (r) values were increased from 0.1 to 1 in 0.1 steps, assuming TR ≪ T₁,T₂ and RF-tip duration ≪ TR. Since no phase is accrued during the TRs at on-resonance, the relative TR-durations mainly affect the on-resonant signal through relaxation effects. The echoes during longer TRs, usually used for data acquisition, yield smaller signal. If we neglect the small relaxation difference between the separate TRs within the multiple-TR period, bSSFP and multiple-TR sequences produce very similar contrast at the water resonance with identical phase-cycling (0-180-0-180)°. On the other hand, fat-suppressing ATR-SSFP is roughly equivalent to a (0-90-180-270)° phase-cycled bSSFP sequence. Therefore, the ATR-SSFP contrast is actually different due to the inhomogeneity of the bSSFP pass-band.

The transient signal in the 2-2-1-1 pass- (phase offset in the ±3π/4 range) and stop-bands is shown as a function of the number of excitations with a: no preparation, b: a single-tip preparation, and c: a reduction of the magnitude of the magnetization vector followed by the single-tip preparation. Assuming α = 60° and T₁/T₂ = 1000/200 ms for the 2-2-1-1 sequence, the single-tip preparation was a −30° pulse applied TR₄/2 prior to the first RF pulse (with zero phase), and a single 64° pulse was used to reduce the magnitude of the magnetization vector to its steady-state value at on-resonance. Without any preparation, there are significant signal oscillations, and the initial signal level is much higher than the steady-state level. The oscillations are substantially reduced over the pass-band with a single-tip preparation. Finally, the magnitude reduction instantly decreases the signal level to its steady-state value at on-resonance. This also reduces the signal oscillations in the stop-band. It is important to note that the flatness of the multiple-TR pass-band improves the efficacy of the single-tip preparation.

The ATR-SSFP and 2-2-1-1 profiles were simulated for a range of flip angles. The 2-2-1-1 stop-band was further improved with a linear combination. a: To determine the signal efficiency, the average blood signal (T₁/T₂ = 1000/200 ms) over a [−80 80] Hz band was normalized by the square-root of the total TR. The flatter pass-band of the 2-2-1-1 sequence yields higher signal efficiency compared with ATR. Although the linear combination (Combination 1 in Fig. 3.b) slightly reduces the pass-band signal, it still has comparable efficiency to ATR. b: The water-to-fat suppression ratio was computed assuming T₁/T₂ = 270/85 ms and a [−300 −140] Hz band for fat. The 2-2-1-1 sequence achieves better suppression than ATR at higher flip angles. In addition, the linear combination significantly improves the 2-2-1-1 stop-band, and the suppression ratio is maximized around 60°.

1.5 T results. Axial (a) and coronal slices (b) from ATR and multiple-TR acquisitions are displayed along with the corresponding whole-volume MIPs (c). Multiple-TR bSSFP has a broader stop-band with a higher level of suppression compared to ATR-SSFP. This improved suppression results in more detailed depiction of the underlying vasculature. Arrows point to the vessels that are lost within the surrounding fat tissue in ATR-SSFP, while these vessels are accurately visualized with multiple-TR bSSFP.