Analysis of multiple-acquisition SSFP



Refocused steady-state free precession (SSFP) is limited by its high sensitivity to local field variation, particularly at high field strengths or the long repetition times (TRs) necessary for high resolution. Several methods have been proposed to reduce SSFP banding artifact by combining multiple phase-cycled SSFP acquisitions, each differing in how individual signal magnitudes and phases are combined. These include maximum-intensity SSFP (MI-SSFP) and complex-sum SSFP (CS-SSFP). The reduction in SSFP banding is accompanied by a loss in signal-to-noise ratio (SNR) efficiency. In this work a general framework for analyzing banding artifact reduction, contrast, and SNR of any multiple-acquisition SSFP combination method is presented. A new sum-of-squares method is proposed, and a comparison is performed between each of the combination schemes. The sum-of-squares SSFP technique (SOS-SSFP) delivers both robust banding artifact reduction and higher SNR efficiency than other multiple-acquisition techniques, while preserving SSFP contrast. Magn Reson Med 51:1038–1047, 2004. © 2004 Wiley-Liss, Inc.

Refocused steady-state free precession (SSFP, TrueFISP, or FIESTA) imaging yields high signal in short scan times, but is limited by its high sensitivity to local field variation (1–11). Characteristic banding artifacts may appear where local field variations are large, due to the strong dependence of signal strength on local resonant frequency. At certain off-resonant frequencies, signal nulls are observed, leading to bands of signal loss in the reconstructed image.

Field inhomogeneity can scale with main magnetic field strength B0, leading to more pronounced banding artifact at higher field strengths. Likewise, as the sequence repetition time (TR) is increased, any off-resonance banding artifact will become more pronounced due to the increased off-resonance precession per TR. To eliminate off-resonance banding from an image, the resonant frequency across the field of view (FOV) must be confined to a range of frequencies with width no larger than about 2/(3TR) (12). Even with a very good shim, this requirement can be difficult to meet at higher field strengths, or in situations where a longer TR is required for higher resolution or due to specific absorption rate (SAR) constraints.

A method for reducing or eliminating off-resonance banding in SSFP at higher field strengths and longer TRs would clearly be useful. Many applications could benefit from the contrast and fast scan times of SSFP, coupled with the enhanced signal of higher B0 and increased flexibility in choice of TR to increase resolution or reduce SAR. Several such methods have been proposed that reduce the banding artifact by combining multiple SSFP acquisitions, each with a different RF phase increment from excitation to excitation (3, 6, 7, 10, 13). These methods include maximum-intensity (e.g., PC-FIESTA or CISS) (6, 14), complex-sum (10), and magnitude-sum (13) combinations.

Gauging the performance of each of these methods poses some interesting problems, which we divide into three groups:

  • 1Banding artifact reduction: With each combination method, some residual banding artifact remains. How effective is each method at removing off-resonance banding? How does this effectiveness vary with scan parameters, such as flip angle and the relevant tissue parameters? Which technique most effectively removes banding for a given application?
  • 2Signal-to-noise ratio (SNR): After a multiple-acquisition technique is used to form an image, the SNR is a function of local resonant frequency. How can the SNR of a multiple-acquisition SSFP image be consistently defined and predicted? How do each of the techniques compare in terms of SNR efficiency?
  • 3Contrast: What effect (if any) do the various combination techniques have on image contrast? Do they preserve SSFP contrast, and if not, how is the contrast modified?

In this work, we describe the maximum-intensity and complex-sum SSFP combination techniques mentioned above, and introduce a sum-of-squares combination method. We provide a general framework for analyzing banding artifact reduction, SNR, and contrast of any multiple-acquisition technique, and apply it to the techniques considered. We then verify our results experimentally, comparing the actual banding reduction and SNR to that predicted by theory. Finally, we present theoretical comparisons of each technique across a range of sequence and tissue parameters.


Summary of Multiple-Acquisition Techniques

Figure 1 shows a series of SSFP off-resonance spectra for several tissue parameters and flip angles. As shown in the figure, the signal level is a strong function of free precession per TR (denoted by β), and a sharp signal null periodic in β is observed. This signal null is the main source of off-resonance banding artifact. Furthermore, the shape of the off-resonance spectrum varies significantly with T1, T2, and flip angle α. One typically tries to limit β across the FOV to a flat region in the off-resonance spectrum, thus avoiding any signal nulls. This flat region in general is no wider than approximately 4π/3 radians (Fig. 1c), and for certain tissue and sequence parameters it can be even thinner (Fig. 1a).

Figure 1.

SSFP off-resonance signal profiles for several tissues. The magnitude and shape of SSFP spectral profiles are a strong function of T1/T2 and flip angle α. The shape of a profile varies little with TR, provided that TR is small compared to T2. All graphs shown employed TR/TE = 10/5 ms. For each tissue, profiles are computed for α = 30°, 60°, and 90°. Notice the variations in signal homogeneity and passband width with T1/T2 and flip angle.

The spectra shown in Fig. 1 employ identical RF phase ϕ from excitation to excitation. If the phase is instead incremented by a constant value Δϕ from excitation to excitation, the off-resonance profile is shifted by Δϕ along the β axis, as illustrated by the spectra in the shaded boxes in Fig. 2 (3). This shift in the off-resonance spectra with RF phase increment is what makes multiple-acquisition SSFP possible.

Figure 2.

The magnitudes of the spectral profiles for single-acquisition phase-cycled SSFP and the resultant combined profiles are shown in a for Δϕ = 0 and equation imageN = 2 case), and in b for Δϕ = 0, equation image π, and equation image (N = 4 case). Notice the shifting of the profile by Δϕ in each case. When phase-cycled images are combined, more homogeneous spectral profiles are obtained. The spectral profiles shown were computed for TR/TE = 3.6/1.8 ms, α = 30°, and T1/T2 = 600/100 ms.

All of the multiple-acquisition combination methods analyzed in this work employ identical data-acquisition techniques, and differ only in reconstruction. A series of N SSFP acquisitions are obtained (N ≥ 2), and each acquisition employs a fixed RF phase increment Δϕ = 2πn/N radians from excitation to excitation, where n ranges from 1 to N. Thus a set of N individual SSFP data sets is acquired, each with a shifted spectral profile as illustrated in Fig. 2a for the N = 2 case and Fig. 2b for N = 4. Each of the methods considered is differentiated by the manner in which the individual acquisitions are combined to form the reconstructed image.

Maximum-Intensity SSFP (MI-SSFP)

Each of the N acquisitions is independently reconstructed. The final image is formed by assigning each pixel the maximum magnitude of the corresponding pixels across the N acquired images. The flatness of the resultant off-resonance profile, and hence the method's effectiveness at removing banding, is clearly a function of both N and the shape of the component off-resonance spectra. This is true for each of the combination methods considered. For some tissue and sequence parameters, the maximum-intensity combination performs quite well, even for N = 2. The resultant profiles for N = 2 and N = 4, T1 = 600 ms, T2 = 100 ms, α = 30°, and TR/TE = 3.6/1.8 ms are shown in Fig. 2.

Complex-Sum SSFP (CS-SSFP)

In this technique, the complex k-space data from each of the N acquisitions are summed and reconstructed, and the magnitude is taken to yield the final image (or, equivalently, each acquisition is reconstructed and the resulting complex images are summed, followed by a magnitude operation). Again, the flatness of the resultant off-resonance profile depends strongly on N and the shape of the off-resonance spectrum of an individual acquisition, which depends in turn on T1, T2, α, and (to a much smaller degree) TR. Sample profiles for the N = 2 and N = 4 cases are shown in Fig. 2. As N becomes large, the spectral profile of CS-SSFP converges to that of gradient-spoiled sequences. CS-SSFP is also sensitive to the choice of TE, requiring TE = TR/2 for best performance.

Magnitude-Sum SSFP (MS-SSFP)

If each of the individual acquisitions is reconstructed, and the final image is formed by summing the magnitude of each individual image, better SNR is expected because there is no signal loss from phase differences across the constituent images. However, calculations of the resulting off-resonance profile show that this method is significantly less effective at reducing banding artifact (Fig. 2). The sum-of-squares technique presented below yields similar SNR to MS-SSFP, but is much more effective at eliminating banding artifact. For this reason, we omit MS-SSFP from further consideration in this work.

Sum-of-Squares SSFP (SOS-SSFP)

An SOS reconstruction is performed by individually reconstructing each of the N acquisitions. Each image is then squared, the results are summed, and the final image is formed by taking the square root. A similar method is often employed when component images are combined from phased-array coils (15). A heuristic justification for this technique is presented in the Discussion. Again, the resultant profiles for N = 2 and N = 4 are shown in Fig. 2.

Statistical Analysis of Multiple-Acquisition SSFP

In this section, we present a framework for the statistical analysis of multiple-acquisition SSFP that can be applied to all of the techniques considered.

The signal in an SSFP acquisition is proportional to the steady-state transverse magnetization MXY at the TE, which has both a magnitude and phase that vary with β (1, 2, 16). This is indicated in Fig. 1.

Consider a reconstructed pixel from a single SSFP acquisition (before the image magnitude is taken for display). The pixel contains both magnitude and phase information, and is therefore complex valued. To a good approximation, this signal can be modeled as a bivariate Gaussian random variable X with complex mean μX and standard deviation (SD) σX. That is:

equation image(1)

where N(μ, σ2) represents the Gaussian (or normal) distribution with mean μ and variance σ2.

If N phase-cycled SSFP acquisitions are performed, a set of N sample points is acquired for each voxel to be reconstructed. We represent these samples by bivariate Gaussian random variables X1,…,XN, and denote their respective means by μ1,…,μN. We expect each Xn to have the same SD, which we denote by σ0, since the noise is a property of the system and scan parameters and will not vary with n. Now suppose that the voxel on which we are performing our analysis undergoes an off-resonance free precession of β0 radians over one TR. The complex mean of the nth sample is then given by:

equation image(2)

where MXY,n(β) is the off-resonance profile of a single SSFP acquisition with phase-cycle increment Δϕ = 2πn/N.

When the observations Xn are combined to yield a final reconstructed voxel, the statistical distribution of the reconstructed voxel may be described by a new random variable Y, which is some function of the Xn. That is,

equation image(3)

The above analysis permits the determination of the statistical distribution of Y for any value of the free-precession angle β. We can then find both μY(β) and σY(β). Note that μY(β) represents the expected signal at any value of β, and is simply the resulting off-resonance spectrum (or magnetization profile) of the multiple-acquisition technique.

To apply the above framework to predict μY(β) and σY(β), we need to know σ0 in addition to the tissue and scan parameters. Let SNRSSFP denote the SNR we would get from a single SSFP acquisition perfectly shimmed to the center of the passband. SNRSSFP is related to σ0 as:

equation image(4)

where MXY,equation image is the off-resonance spectrum with phase-cycling Δϕ = π. Note that a phase-cycling value of Δϕ = π centers the passband around β = 0, as shown in Fig. 2. If needed, we can empirically determine SNRSSFP from a single SSFP acquisition in a region close to the center of the passband (as determined by the band structure of the image). As a practical matter, we are more interested in applying the above analysis to gauge the performance of each multiple-acquisition technique across a range of possible values of SNRSSFP. We can then evaluate the trade-offs in scan time, residual banding, contrast, and SNR between the ideal case of a single center-passband SSFP acquisition and each multiple-acquisition technique. It is therefore more convenient to use SNRSSFP as an input into our analysis than σ0.

Using our framework, we represent the statistics of a reconstructed voxel in each of the multiple-acquisition techniques as follows:

equation image(5)
equation image(6)
equation image(7)

Solving for these distributions determines μY(β) and σY(β) for each technique, which in turn can be applied to analyze residual banding, SNR, and contrast, as outlined below.

Residual Banding and Contrast

We can quantify the residual banding of an SSFP combination scheme by examining the signal variations across a period of the spectrum. Let Smax, Smin, and 〈S〉 denote the maximum, minimum, and mean, respectively, of the spectral profile μY(β). That is,

equation image(8)
equation image(9)
equation image(10)

as illustrated in Fig. 3. Note that we assume that all combination techniques include a magnitude operation to form the final image, so that μY(β) is real-valued and positive. The integral defining 〈S〉 runs from 0 to 4π since SSFP off-resonance profiles have a periodicity in β of 4π, and any combined profiles will therefore share at least this periodicity. We use angled brackets throughout to denote any such average across β.

Figure 3.

None of the combination methods produces a perfectly homogeneous spectral profile. The residual ripple can be predicted by examining the variations in the expected signal profile with free-precession angle β. Likewise, the average expected signal (where the average is across β) can be used to predict the contrast resulting from a given combination technique.

We now define the percent ripple across the profile as:

equation image(11)

The percent ripple as defined provides a good measure of the ability of an SSFP combination technique to reduce off-resonance banding artifact. Note that the percent ripple will vary considerably with T1, T2, and α. Any comparison of multiple-acquisition techniques should examine a range of T1 and T2 value pairs expected to be present in the region to be scanned, and should perform the calculations at the appropriate flip angles. We graph the theoretical performance across a range of tissue parameters for α = 30° and 60° in the Results section of this work.

The determination of the mean signal 〈S〉 for any tissue allows us to address our earlier question: do each of the multiple-acquisition combination schemes preserve SSFP contrast? That is, for a given flip angle and TR, will an image resulting from the combination of N individual phase-cycled SSFP acquisitions exhibit the same (or similar) T2/T1 contrast as a center-passband SSFP image with the same imaging parameters? As a measure of this “fundamental” image contrast, we compare the distribution of normalized mean tissue signals for each method across a range of tissue T1 and T2. Differences in mean signal distribution across a range of tissues correspond to changes in fundamental image contrast. Such a comparison is presented below in Results.

We should point out that obtaining the mean tissue signal by averaging across β implicitly assumes that the variations in β across the region of interest (ROI) are evenly distributed across a full period of the spectrum. This is not entirely accurate, but is a convention we adopt in order to concisely define contrast and SNR in multiple-acquisition SSFP. The error associated with this definition of average signal decreases as the banding artifact is more effectively removed (leading to less signal variation, or ripple, with variations in β).

SNR and SNR Efficiency

The SNR of a reconstructed voxel with free-precession frequency β is given by

equation image(12)

where μY and σY denote the mean and SD of Y, respectively. However, variations in β across an ROI are generally not known a priori. It is therefore useful to consider the average of SNRY(β) across one period in β. The off-resonance profile of an individual phase-cycled SSFP acquisition has a period in β of 4π, so SNRY(β) will share at least this periodicity. Thus,

equation image(13)

Again, our definition of 〈SNRY〉 implicitly assumes an even distribution of β across a full period over the ROI.

Perhaps a more useful metric for comparing scanning techniques of different lengths is the SNR efficiency, which we denote by η. SNR efficiency is a measure of the SNR normalized by the square root of the total scan time. In our case, we define an average SNR efficiency across β as

equation image(14)

The use of SNR efficiency allows a fair SNR comparison between single-acquisition SSFP and multiple-acquisition techniques with N times the total scan time.

Measurements of SNR from actual images generally estimate signal noise from the background noise measured in a region of no signal. However, the measured background noise variance can be different than the actual signal noise variance. Magnitude and other operations performed during the combination of constituent phase-cycled images must be taken into consideration to accurately determine the signal noise variance from the measured background noise variance. This becomes important when one validates the theory by comparing the theoretically predicted SNR to that measured from actual images.


Implementation of Framework

A Matlab (The MathWorks, Inc., Natick, MA) function was written to compute the transverse magnetization profile across one period in β as a function of T1, T2, proton density ρ, flip angle α, TR, TE, and the phase cycle increment Δϕ. This function provided the phase-cycled spectra MXY,1(β),…,MXY,N(β) needed to perform our statistical analysis.

A full analytical analysis would quickly become intractable, so further Matlab functions were written to numerically perform the statistical analysis outlined in the Theory section. For each combination scheme, a function computes the probability density function (PDF) for a reconstructed voxel as a function of tissue parameters, sequence parameters, SNRSSFP, and β. The mean μ(β) and the SD σ(β) were in each case determined from the PDF.

Further Matlab functions computed residual banding and average SNR from μ(β) and σ(β). Correction factors relating the signal noise variance to the measured background noise variance were also computed for each method, enabling accurate SNR measurement from actual images. The correction factor for normal SSFP and CS-SSFP images is the standard Rayleigh correction factor 0.6551 arising from the single magnitude operation in reconstruction. The correction factors for MI- and SOS-SSFP are tissue and scan parameter dependent. The mean correction factor for MI-SSFP images across the range of tissue and sequence parameters considered was 0.6561, with an SD of 0.0480. That for SOS- SSFP was 0.7056, with an SD of 0.0181.

We partially verified the theory (and our implementation of the statistical computations) by generating simulated SSFP images. Each image contains three tissues (T1/T2 = 300/150 ms, 300/90 ms, and 900/90 ms). Signal levels were computed from the theoretical spectral profiles for each tissue with TR/TE = 10/5 ms and α = 60°. Figure 4a shows a center-passband SSFP image (that is, tissue signal levels are taken from the center of the spectral passband). Bivariate Gaussian noise was added to the images such that SNRSSFP of the brightest (top) tissue was 15.0. Figure 4b shows a series of four phase-cycled SSFP images, where a variation in β is applied in the horizontal direction across the images to yield banding. These images were then combined with each combination method.

Figure 4.

a: Simulated center-passband SSFP phantom with three tissues (T1/T2 = 300/150, 300/90, and 900/90 ms, α = 60°, and TR/TE = 10/5 ms). Bivariate Gaussian noise was added to the complex image data such that SNRSSFP = 15.0 for the top tissue. b: A series of four such simulated phantoms, with a variation in β assumed across each phantom to simulate field inhomogeneity (causing the visible banding). Each phantom was generated with a different value of Δϕ (phase cycling), resulting in the horizontal displacement of the bands from image to image. c–e: Images resulting from the combination of four phase-cycled images. In each case, our model was used to predict the expected theoretical average SNR. The tables compare the theoretical values with those measured from each image.

We obtained theoretical predictions using our framework for average SNR and measurement correction factor for each method. Measurements of average SNR were then made on the combined images, and compared with theory. In each case, the measured values of average SNR were corrected by the theoretically predicted measurement correction factor. The theoretical and measured values are compared in the tables in Fig. 4c–e, and are in excellent agreement.

It should be noted that this experiment only validates the theory inasmuch as the simulated phantom images correspond to actual phase-cycled SSFP images. In practice, a detailed and accurate empirical verification of the theory is difficult to perform using actual MR images. Accurate values of T1, T2, and the flip angle are needed to determine the theoretical signal level and spectral profile for a tissue. While T1 and T2 may be known quite accurately, the flip angle can vary significantly across a slice due to an imperfect slice profile. Furthermore, intravoxel dephasing can cause undesired signal loss, leading the measured signal levels to fall short of theory. Finally, an accurate empirical determination of SNRSSFP from actual images can be difficult to obtain. Off-resonance variations often make the measurement of a suitable sample of center-passband voxels challenging.

That said, measurements and relative comparisons of SNR across different combination schemes are easily performed. We can also perform a simple comparison of average SNR for a tissue of known characteristics, and verify that measurements of average SNR are roughly consistent with those predicted by theory. Figure 5 shows one such comparison. In Fig. 5a, we see a single SSFP acquisition exhibiting banding artifact. A measurement of SNR was performed across a region of muscle deemed to be roughly at center-passband. This value was used for SNRSSFP in a subsequent prediction of muscle SNR using each method for N = 4. Phase-cycled images were then combined with each method, and measurements of muscle SNR were taken. The theoretical and measured values are compared below each image, and are in reasonably good agreement. Interestingly, the measured and theoretical values are in much better agreement if the predictions are performed assuming a flip angle of 22° rather than the nominal 25°. This is likely the result of B1 inhomogeneity across the slice.

Figure 5.

a: Single SSFP acquisition exhibiting banding artifact (arrows), TR/TE = 10/5 ms, FOV = 28 cm, α = 25°. A measurement was performed in the center-passband region to determine SNRSSFP of muscle. b–d: The resultant images when four SSFP acquisitions were combined with each technique (N = 4). Predictions of average muscle SNR were in each case performed using muscle T1/T2 = 870/47 ms and α = 25°. Measurements of average muscle SNR were then performed. The results are shown below each image and are in reasonably good agreement, although the CS and SOS predictions are somewhat lower than those measured. This is likely due to the actual flip angle across the slice varying slightly from the nominal flip angle of 25°. The measured results are in much better agreement with a prediction based on α = 22°.

Data Generation

To get a better sense of the overall performance of each combination method, we applied our model across a range of tissue and sequence parameters that typically arise in practice.

The performance of each technique will clearly depend on the shape of the magnetization profile, which will in turn depend heavily on α and T1/T2. It is therefore important to generate data for a variety of values of α, T1, and T2. We would also like to know how the performance varies with SNRSSFP and N. To this end, data were generated for the parameter ranges shown in Table 1. For each combination of parameters, the residual banding (percent ripple), average SNR (〈SNR〉), average signal (〈S〉), and measurement correction factor (CF) were calculated.

Table 1. Parameter Ranges Used for Data Generation
N2, 4, 8
α30°, 60°, 90°
SNRSSFP5, 10, 15, 20, 25
T1300–2300 ms (200 ms increments)
T230–230 ms (20 ms increments)

All simulations employed TR/TE = 10/5 ms. To make our data analysis tractable, we did not consider variations in TR. This is justified for TR less than approximately T2/4, where the shape of the off-resonance profile changes very little with changes in TR.

The calculations for each parameter combination were repeated for MI-SSFP, CS-SSFP, and SOS-SSFP. The residual banding and average SNR results allow the banding artifact reduction and SNR performance of the various techniques to be compared across a broad range of parameters. The average signal results were used to ascertain whether SSFP contrast is preserved with each method. Finally, the average correction factors enable comparison with SNR measurements on actual magnitude images. The salient results are summarized below.


To make the interpretation of the large resultant data set tractable, we looked for trends that could be generalized across the entire data set.

First, we observed that average signal and residual banding do not depend heavily on SNRSSFP. In fact, in the CS case there is virtually no dependence. The dependence is stronger at low SNR for the MI-SSFP case. However, in the range considered here (SNRSSFP ≥ 5), the variations are negligible. Therefore, we need not consider variations in SNRSSFP when discussing band reduction. SNRSSFP does, however, enter into play when the average SNR is predicted.

A second trend observed is that (SNR) for the different combination techniques is linear to an excellent approximation in SNRSSFP for SNRSSFP ≥ 5. This is illustrated for one set of sequence and tissue parameters in Fig. 6. For very low values of SNRSSFP, the linearity in the MI-SSFP and SOS-SSFP cases will break down, as each line must pass through the origin. The slope of the SOS-SSFP line was also uniformly larger than that in the other two methods. These observations are important because they enable us to summarize 〈SNR〉 at a single value of SNRSSFP, and to expect that the results will roughly scale with SNRSSFP.

Figure 6.

Graph of average SNR vs. SNRSSFP for each combination method. The average SNR is linear to a very good approximation in SNRSSFP. Although the results for only one tissue and set of sequence parameters are shown, the linear relationship is very accurate across a broad range of T1, T2, N, and α.


Figure 7 shows residual banding for the N = 4 case as a function of T1 and T2 for each combination method. Results are shown for flip angles of 30° and 60°, with SNRSSFP = 15 and TR/TE = 10/5 ms. Notice that the banding artifact reduction improves significantly with increasing flip angle for all of the methods. This is due to the change in shape of the off-resonance spectra as flip angle is increased, as illustrated in Fig. 1. At low flip angles, tissues with small T1/T2 are characterized by large “humps” at the edges of the passband. As flip angle is increased, this bimodal shape tends to smooth out into a single hump. The latter shape is much more easily smoothed through combination techniques than the bimodal shape.

Figure 7.

Comparison of residual banding as a function of T1 and T2. Part a shows the residual banding at N = 4 and α = 30°, while b shows the effect of increasing the flip angle to 60°. Notice that the banding can be very pronounced for tissues with small T1/T2 at a low flip angle. While CS is the most robust at removing residual banding, in practice the banding reduction achieved with SOS-SSFP at N = 4 and α ≥ 30° is adequate for most tissues.

The graph shown in Figure 7a (α = 30°) shows quite severe banding (almost 30% in the SOS-SSFP case) for some T1, T2 combinations (more precisely, for small T1/T2). In vivo, the residual banding of SOS-SSFP at N = 4 is often almost imperceptible, even at α = 30°. Most real tissue T1/T2 values lie in the low ripple region. This is illustrated in Fig. 8a. Axial head images at α = 30° are shown for both normal fluid-suppressed SSFP (17, 18) (left) and N = 4 SOS-SSFP (also fluid-suppressed) (right). Signal averaging of four acquisitions was used to form the left image, so as to normalize scan time for the two images. Residual banding can be detected in the SOS-SSFP image, but it is not severe.

Figure 8.

a: Axial fluid-suppressed SSFP acquisition of brain (left) and N = 4 SOS combination (right) at α = 30°. The SOS image exhibits approximately 30% and 38% higher white-matter SNR, respectively, than the corresponding MI and CS images (not shown). b: The same acquisition, with flip angle increased to 70°. The SOS image again achieved considerably higher white-matter SNR (approximately 50% and 35%, respectively) than the corresponding MI and CS images (not shown). Signal averaging of four single-acquisition SSFP images was used to produce each of the images on the left, to normalize scan time for all images. TR/TE = 8.0/4.0 ms, TI = 2.0 s, FOV = 24 cm, 256 × 192 matrix, 5-mm slice thickness.

At higher flip angles (α ≥ 60°), SOS-SSFP is very good at removing banding (Fig. 7b), and actually outperforms MI-SSFP for most T1, T2 combinations. Figure 8b illustrates the SOS method at α = 70° (right). Residual banding is virtually imperceptible. The degree of gray/white matter contrast is also increased at this higher flip angle.

High-resolution SSFP imaging often requires the use of relatively long TRs due to gradient amplitude, slew rate, and heating limitations, as well as long readout times. These scans often necessitate the averaging of multiple acquisitions to achieve adequate SNR, and are therefore ideal candidates for multiple-acquisition SSFP. Figure 9 illustrates the use of SOS-SSFP to eliminate banding and increase SNR in a high-resolution 2D SSFP phantom scan. A TR of 35 ms was employed to achieve an in-plane resolution of 78 μm, with a custom-made 1-inch surface coil.

Figure 9.

a: High-resolution 2D SSFP phantom image (in-plane resolution of 78 μm) exhibiting banding artifact (arrows), b:N = 4 SOS-SSFP acquisition: TR/TE = 35/17.5 ms, α = 60°, FOV = 4 cm, 512 × 512 matrix, 2-mm slice thickness. The total scan times were 1 m 28 s and 5 m 52 s, respectively.

To visualize early changes in cartilage degeneration, very high resolution is required (19). Again, because of the long TR needed to achieve high resolution with SSFP, techniques such as SOS may be helpful in removing banding from high-resolution cartilage images. A high-resolution axial patellofemoral joint scan is shown in Fig. 10, which employs the relatively long TR (for SSFP) of 16 ms. We achieved an in-plane resolution of 235 μm using a 3-inch surface coil. The banding is effectively removed in the SOS image.

Figure 10.

a: High-resolution 2D SSFP axial image of the patellofemoral joint (in-plane resolution of 235 μm) exhibiting severe banding artifact (arrow). b:N = 4 SOS-SSFP acquisition. TR/TE = 16/8 ms, α = 35°, FOV = 12 cm, 512 × 512 matrix, 2-mm slice thickness. The total scan times were 49 s and 3 m 16 s, respectively.

All images shown were obtained on a 1.5 T GE Signa scanner with a maximum gradient amplitude of 40 mT/m and a maximum gradient slew rate of 150 mT/m/ms.

SNR Efficiency

Figure 11 shows a comparison of average SNR efficiency (η) as a function of T1 and T2 for the N = 4 case, at flip angles of 30° and 60°, SNRSSFP = 15, and TR/TE = 10/5 ms. In both cases, the average SNR efficiency obtained with SOS-SSFP is significantly higher than in the other two cases (often more than 30% higher). In fact, SOS-SSFP outperformed the other two methods in SNR efficiency in virtually every one of our test cases (at N = 2, 4, and 8, at α = 30°, 60°, and 90°, and for the full range of values of SNRSSFP considered).

Figure 11.

Comparison of average SNR efficiency as a function of T1 and T2, relative to the SNR efficiency of center-passband SSFP (ηSSFP). a: The average SNR efficiency for each combination method at N = 4 and α = 30°. b: The effect on average SNR efficiency of increasing the flip angle to 60°. In both cases, the average SNR efficiency obtained with the SOS method is significantly higher than that obtained with the other two cases. This result holds across virtually all of the test cases considered.

The SNR performance of MI-SSFP and CS-SSFP at N = 4 is similar. For N = 2, we found that MI performed slightly better than CS. The opposite was true at N = 8, where CS outperformed MI by a slightly better margin. These results are consistent across the range of α and SNRSSFP considered.

Verification of SSFP Contrast

To visualize fundamental contrast variations, we plotted the mean signal as a function of T1 and T2. Signal levels were normalized for each technique such that a value of 1.0 corresponded to the largest mean signal for that technique. These normalized signals were then plotted as grayscale, with no signal indicated by black, and the largest normalized signal (1.0) indicated by white. Graphs of this type for each method (center-passband, MI-, CS-, and SOS-SSFP) are shown in Fig. 12 at N = 4 for flip angles of 30° and 60°.

Figure 12.

Part a shows the mean tissue signal as a function of T1 and T2 for N = 4 and α = 30°, while b shows the same mean tissue signal at N = 4 and α = 60°. In all cases, the mean signals were normalized such that the maximum signal present on any graph is 1.0. The graphs illustrate that each of the multiple-acquisition techniques yields fundamental contrast that is very SSFP-like. Each simulation employed TR/TE = 10/5 ms and SNRSSFP = 15.

We found very little variation in the distribution of tissue signal mean values between each method. All of the multiple-acquisition methods are very similar, and only slight distribution changes from that of center-passband SSFP can be ascertained. The very slight variations observed will likely not have a significant effect on image appearance. There were likewise only very slight variations at N = 2 and N = 8. We can therefore conclude that each of the multiple-acquisition techniques preserve SSFP contrast to a good approximation.

The slight variation in fundamental contrast for small T1/T2 values can be understood by looking at the shape of the off-resonance spectra. For small T1/T2, the off-resonance spectrum exhibits more pronounced “humps” at the edges of the passband, as discussed in the Banding subsection. Variations in the magnitude of these humps are much more pronounced with changes in T1/T2 than the center-passband signal. While center-passband SSFP samples only the center-passband signal, the multiple-acquisition techniques derive information from a full period of the off-resonance spectrum.


Our results indicate that SOS-SSFP yields significantly higher SNR efficiency than either of the other two methods. A simple intuitive argument can help us understand why this is true. In each method, we have N signal observations for any given pixel. Although each of the N observations measures the same tissue, the phase-cycling varies from observation to observation. Hence each observation will give a different signal level, depending on where that observation falls on the off-resonance spectrum. If one of the observations falls near the off-resonance null, we expect very low signal. An observation in the pass-band should give relatively high signal.

Despite the signal variations, we expect the same error in each of the N observations. Observations with higher signal will therefore have a higher SNR than observations with lower signal, and should be weighted more if we wish to maximize SNR in our reconstructed image. By what, then, should we weight each observation? Since noise is constant across observations, a higher observed signal should correspond to a higher weighting in our sum. We simply weight each observation with its observed signal, or square the constituent acquisitions, thereby giving higher weight to observations with higher SNR. The square root operation at the end is needed to normalize contrast.

For certain applications, one could perhaps devise a more sophisticated combination technique whereby individual observations are more optimally weighted based on information about the local resonant frequency and tissue characteristics.

Several other useful observations and generalizations follow from our analysis and results. First, total scan time is clearly an issue when multiple-acquisition techniques are used. While the SNR efficiency of the SOS method may approach that of center-passband SSFP, the minimum scan time possible is always N times that of single-acquisition SSFP. The choice of N is therefore constrained by the total scan time limits.

If scan time constraints only allow the use of two phase-cycled acquisitions, MI-SSFP is the most effective at removing SSFP banding. However, for tissues with small T1/T2 values or at low flip angles, the percent residual ripple can still exceed 30%. At N = 8, all of the techniques are quite robust at removing SSFP banding, but scan times can be prohibitively long.

If time allows, we believe the N = 4 SOS case to be a good choice. SSFP banding artifact reduction at N = 4 with SOS is quite robust in practice, and the SNR efficiency is significantly higher than that obtained with the other two combination methods. Relatively quick scan times can still be achieved for many applications. If slightly better band elimination is required, CS-SSFP can be used, albeit with an accompanying SNR penalty.


Many applications could benefit from the contrast and high SNR efficiency of SSFP, but are limited by its high sensitivity to local field variations (seen as bands of signal loss in an image). This sensitivity places an upper limit on the sequence TR, which can be difficult to comply with at high fields or resolutions, or when longer excitation and gradient pulses are required.

Multiple phase-cycled SSFP acquisitions can be combined in various ways to eliminate SSFP banding artifact. These include performing a MI, CS, or SOS combination of the constituent acquisitions. If N phase-cycled acquisitions are acquired, the penalty for band elimination is a loss in SNR efficiency and an N-fold increase in total scan time over a single SSFP acquisition. A straightforward statistical analysis can be applied to examine the banding artifact reduction, SNR efficiency, and contrast of each method.

Each of the combination methods has a negligible effect on fundamental image contrast, but they vary in performance with respect to banding artifact suppression and SNR efficiency. Although MI- and CS-SSFP generally yield better band reduction than SOS-SSFP, the SOS method yields approximately 30% higher SNR efficiency while still achieving good SSFP band removal, particularly at higher flip angles. The combination of four phase-cycled acquisitions with any of these techniques is sufficient for robust band removal in many applications.