Signal-to-noise ratio behavior of steady-state free precession

NIH Public Access Author Manuscript Magn Reson Med. Author manuscript; available in PMC 2008 May 26. NIH-PA Author Manuscript Published in final edited form as: Magn Reson Med. 2004 July ; 52(1): 123–130. Signal-to-Noise Ratio Behavior of Steady-State Free Precession Scott B. Reeder1,*, Daniel A. Herzka2,3, and Elliot R. McVeigh3,2 1Department of Radiology, Stanford University Medical Center, Stanford, California. 2Department of Biomedical Engineering, Johns Hopkins University School of Medicine, Baltimore, Maryland. 3Laboratory of Cardiac Energetics, NHLBI, National Institutes of Health, DHHS, Bethesda, Maryland. Abstract NIH-PA Author Manuscript Steady-state free precession (SSFP) is a rapid gradient-echo imaging technique that has recently gained popularity and is used in a variety of applications, including cardiac and real-time imaging, because of its high signal and favorable contrast between blood and myocardium. The purpose of this work was to examine the signal-to-noise ratio (SNR) behavior of images acquired with SSFP, and the dependence of SNR on imaging parameters such as TR, bandwidth, and image resolution, and the use of multi-echo sequences. In this work it is shown that the SNR of SSFP sequences is dependent only on pulse sequence efficiency, voxel dimensions, and relaxation parameters (T1 and T2). Notably, SNR is insensitive to bandwidth unless increases in bandwidth significantly decrease efficiency. Finally, we examined the relationship between pulse sequence performance (TR and efficiency) and gradient performance (maximum gradient strength and slew rate) for several imaging scenarios, including multi-echo sequences, to determine the optimum matching of maximum gradient strength and slew rate for gradient hardware designs. For standard modern gradient hardware (40 mT/m and 150 mT/m/ms), we found that the maximum gradient strength is more than adequate for the imaging resolution that is commonly encountered with rapid scouting (3 mm × 4 mm × 10 mm voxel). It is well matched for typical CINE and real-time cardiac imaging applications (1.5 mm × 2 mm × 6 mm voxel), and is inadequate for optimal matching with slew rate for high-resolution applications such as musculoskeletal imaging (0.5 × 0.8 × 3 mm voxel). For the lower-resolution methods, efficiency could be improved with higher slew rates; this provokes interest in designing methods for limiting dB/dt peripherally while achieving high switching rates in the imaging field of view. The use of multi-echo SSFP acquisitions leads to substantial improvements in sequence performance (i.e., increased efficiency and shorter TR). NIH-PA Author Manuscript Keywords SSFP; SNR; cardiac MRI; gradients; efficiency; fast imaging; real-time imaging Steady-state free precession (SSFP) is a rapid gradient-echo imaging technique that has received renewed interest in recent years, owing to the widespread availability of high-speed gradient systems. It has notably improved the signal-to-noise ratio (SNR) over other gradientecho techniques, and has excellent contrast behavior with mixed dependence on both T1 and T2 (1,2). SSFP is commonly known as fast imaging with steady precession (trueFISP), fast imaging employing steady-state acquisition (FIESTA), or balanced fast field echo (BFFE) (on Siemens, GE, and Philips platforms, respectively). *Correspondence to: Scott B. Reeder, M.D., Ph.D., Department of Radiology, Stanford University Medical Center, Rm. H1307, 300 Pasteur Ave., Stanford, CA 94304. E-mail: [email protected] Reeder et al. Page 2 NIH-PA Author Manuscript SSFP has been applied successfully to many areas, including neuroradiology (3), musculoskeletal imaging (4-6), abdominal imaging (7), and cardiac imaging (8-13). SSFP is particularly advantageous for cardiac imaging because of its fast performance, excellent contrast between blood and myocardium, and good image quality with high SNR. Specific cardiac SSFP applications (apart from CINE imaging (8)) include real-time imaging (11), myocardial tagging (14), and coronary angiography (9). In previous work, we described the dependence of SNR on imaging parameters such as TR, bandwidth (BW), and image resolution for spoiled gradient-echo (SPGR) and gradient-recalled (GRE) imaging (15). In addition, we analyzed the relationship between gradient performance (slew rate and maximum gradient strength) and SNR in order to optimize gradient hardware design. The purpose of this work was to conduct a similar SNR analysis for SSFP in the context of cardiac CINE and real-time imaging applications. Equations that describe SSFP signal behavior were derived, and the relationship between SNR and imaging parameters was explored in depth. Finally, an analysis of gradient hardware performance and its effect on SNR was performed for both single and multi-echo SSFP sequences. THEORY NIH-PA Author Manuscript The mathematics of steady-state behavior of magnetization for SSFP has been well described in the literature (1,2,16,17). The maximum SSFP signal can be shown to be [1] when the optimal flip angle, [2] is used for alternating polarity RF pulses. For short TR acquisitions where TR ≪ T2, T1, Eqs. [1] and [2] reduce to [3] and NIH-PA Author Manuscript [4] This explicitly shows that the maximum signal and optimum imaging tip angle are independent of TR, and depend only on the proton density (Mo) and ratio of T2 to T1. This behavior has been described previously (1). SNR and SSFP The SNR of a generic pulse sequence can be written as (18) [5] where ΔV is the voxel volume, Ts = TR NSA Ny Nz is the total scan time, NSA is the number of signal averages, Ny and Nz are the number of phase- and depth-encoding steps (for 3D imaging), and η is the sequence efficiency, previously defined as (15,19) Magn Reson Med. Author manuscript; available in PMC 2008 May 26. Reeder et al. Page 3 [6] NIH-PA Author Manuscript where NxT is the duration of a readout window, and ETL is the echo train length for multi-echo acquisitions, such that ETL · NxT is the total sampling time during one TR. The voxel bandwidth equals (NxT)−1. Efficiency is determined by the duration of “dead time,” where no signal is sampled. Such dead time includes the RF pulse, slice-selection gradients, readout gradient prephaser, and rewinders, as well as periods between readout plateaus in multi-echo acquisitions. The length of the RF pulse often meets a lower bound based on specific absorption ratio (SAR) limits, while other periods of dead time are determined by the gradient hardware performance. Combining Eqs. [4]-[6] gives [7] NIH-PA Author Manuscript where Ts′ is the total sampling time, defined as the product of the total scan time (Ts) and efficiency (η), and represents the total amount of sampling time during the acquisition of an image. Equation [7] shows that the SNR for an SSFP acquisition depends only on the voxel size, T1 and T2, and the cumulative sampling time, Ts′. For constant scan time (Ts), SNR is independent of bandwidth and TR, which implies that an SSFP pulse sequence can be run as fast as possible at high bandwidth with minimal SNR penalty unless decreases in TR achieved through increases in bandwidth become detrimental to sequence efficiency. In addition, multiecho SSFP acquisitions are advantageous through their increases in sequence efficiency only, and do not benefit SNR from increased T1 recovery during the longer TR of a multi-echo sequence, a phenomenon exploited with SPGR imaging (20-22). MATERIALS AND METHODS Scanner and Pulse Sequence All images were acquired on a Siemens 1.5T Magnetom Sonata scanner (Siemens Medical Solutions, Erlangen, Germany) with a high-performance gradient system (40 mT/m amplitude, 200 mT/m/ms slew rate). The product “trueFISP” pulse sequence (RF pulse duration = 600 μs) was used for all experiments (8). Standard product autoshim routines with five secondorder shims were used for all of the experiments. Phantom Studies NIH-PA Author Manuscript Three phantoms made from agarose and CuSO4 were made to emulate the relaxation characteristics of myocardium, blood, and a long T2 species (23). The “myocardium” phantom contained 10.0 g of agar and 50 mg CuSO4 in 500 ml of deionized water, and the T1 and T2 values were measured as 990 ± 2 ms and 62 ± 2 ms, respectively. The “blood” phantom contained 3.0 g of agar and 50 mg CuSO4 in 500 ml of deionized water, and the T1 and T2 values were measured as 1210 ± 2 ms and 191 ± 2 ms, respectively. In addition, a long T2 phantom was made from 2.0 g of agar and 50 mg CuSO4 in 500 ml of deionized water, and the T1 and T2 values were measured as 1295 ± 2 ms and 269 ± 2 ms, respectively. Based on Eq. [7], the optimal flip angles for the myocardium, blood, and long T2 phantoms were 28°, 43°, and 49°, respectively. For each phantom, we performed SNR measurements at different TRs by adjusting the voxel bandwidth from 1500 to 100 Hz/pixel, which increased TR from 2.6 ms to 11.6 ms. Other imaging parameters were as follows: rectangular FOV = 36 × 27 cm; slice thickness = 6 mm, Nx = 256, Ny = 192, and slew rate = 200 mT/m/ms. TE was always one-half of TR. To ensure that the SSFP sequence reached steady state, 30 sequential images of each phantom at each bandwidth were acquired. No additional prescanning was performed between each scan, to Magn Reson Med. Author manuscript; available in PMC 2008 May 26. Reeder et al. Page 4 NIH-PA Author Manuscript ensure that gain settings were the same for all phantom measurements. Signal and noise mean and standard deviations (SDs) were measured via identical regions of interest (ROIs). SNR and normalized SNR quantities were reported as the mean ± SD of the SNR measured from the last 10 images collected. Human Studies The relationship between SNR and Ts (Eq. [5]) was investigated in three healthy human volunteers. Our institutional review board approved the study, and all of the volunteers provided informed consent. A standard phased-array cardiac coil was used, and the imaging parameters included FOV = 36 × 27 cm, slice = 6 mm, 256 point full-echo readout, 195–207 phase-encoding steps, and segmentation factor = 5–9. A 30° flip angle was used to maximize myocardial signal, calculated from Eq. [4], assuming T1 = 800 ms and T2 = 60 ms (23). Shortaxis images were acquired with bandwidth varied from 130 to 1502 Hz/pixel. SNR was measured as the ratio of signal in the inferior or anterior left ventricular walls and noise from a region outside the subject, in all images that were not compromised by flow artifact. Gradient Performance Simulations NIH-PA Author Manuscript All simulations were written with the use of MATLAB 6.5 (The Mathworks, Natick, MA). We employed an algorithm based on the SSFP sequence used for the experiments to examine the relationship between pulse sequence efficiency and gradient hardware performance (maximum gradient slew rate and maximum gradient strength). We used three imaging scenarios for both single- and multi-echo sequences to examine this relationship under different imaging conditions, as described in Table 1. RESULTS NIH-PA Author Manuscript The image quality of all of the phantom images was excellent, with only very minimal banding artifact at the very periphery of the phantom in the sequences with longest TR. Figure 1a plots the efficiency of the pulse sequence calculated from Eq. [6] as a function of both voxel bandwidth and TR. Figure 1b plots the SNR normalized by the square root of scan time, which demonstrates the effect of efficiency on SNR for a constant scan time. In the short-TR regime, SNR was most sensitive to decreases in TR obtained through increases in bandwidth, where small drops in TR were obtained through large increases in bandwidth, resulting in degradation of sequence efficiency. Figure 1c plots the SNR normalized by the square root of total sampling time (= total scan time × efficiency), demonstrating that SNR is constant when total sampling time is fixed. The slope of the three lines normalized by the intercept were fit to 0.35% ± 0.1%, 0.36% ± 0.09%, and 0.45% ± 0.06% for the three T1/T2 combinations, 1295/269, 1210/191, and 990/62, respectively, verifying the behavior predicted from Eq. [7]. Figure 2a plots representative sequence efficiency and SNR measurements from the anterior wall of the left ventricle of one volunteer, averaged over all end-diastolic short-axis images and normalized by the square root of scan time. The normalized SNR was relatively insensitive to TR except at very high bandwidths, when efficiency dropped significantly. The box suggests a possible operating point that balances speed performance with SNR performance. Increasing the bandwidth from 930 to 1502 Hz/pixel yields a minimal decrease in TR (3.1 to 3.0 ms) with a substantial drop in SNR, caused by a 36% drop in sequence efficiency. Interestingly, the readout plateau was 1074 μs at 930 Hz/pixel, and decreased by 409 μs to 665 μs when bandwidth is dropped to 930 Hz/pixel. This implies that nearly all gains in TR made by increasing bandwidth were offset by the additional dead time needed to slew the gradients to the higher gradient amplitude. Figure 2b-d shows representative images from one volunteer at different bandwidths. Results from two additional volunteers showed very similar behavior. Magn Reson Med. Author manuscript; available in PMC 2008 May 26. Reeder et al. Page 5 NIH-PA Author Manuscript Figures 3 and 4 are contour plots of TR and efficiency as functions of maximum gradient strength and efficiency for the six imaging scenarios listed in Table 1. The dashed lines connect the “corner” points of each isocontour, and determine the optimal performance relationship between maximum gradient strength and gradient slew rate. For a fixed slew rate, the corner point is determined when further increases in maximum gradient strength yield no further improvements in TR or efficiency. In this way, the corner point reflects an optimal pairing of gradient strength and slew rate that minimizes the maximum slew rate, which may be limited by FDA limits for nerve stimulation (24,25). Along the dashed lines that connect the corner points, the gradient performance parameters (maximum strength and slew rate) are well “matched” for that specific imaging scenario. The small square drawn in all graphs in Figs. 3 and 4 denotes the operating point of most modern scanners (40 mT/m, 150 mT/m/ms). DISCUSSION NIH-PA Author Manuscript Our analysis of the signal behavior in SSFP imaging shows that the maximum achievable signal and optimum flip angle are independent of TR so long as TR ≪ T2, T1. From this analysis, we conclude that for a constant scan time, SNR depends only on the voxel volume, T1 and T2, and the pulse sequence efficiency, and is independent of bandwidth unless increases in bandwidth significantly decrease efficiency. Therefore, SSFP sequences can be run as fast as possible with high bandwidths so long as sequence efficiency is not degraded. Gradient hardware performance and RF pulse width (through limits on the SAR) are the primary determinants of the maximum achievable efficiency. For typical imaging parameters, the duration of the phaseencoding pulse and readout prephaser is longer than that of the slice rewinding pulse, and increases in RF pulse duration do not increase dead time by increases in the length of the slice rewinder. The theoretical predictions outlined above were verified in three phantoms and in images of the heart of a healthy volunteer. Excellent agreement was seen between the theoretical predictions and experimental data. Multi-echo SSFP sequences improve SNR performance further through improved efficiency, so long as increases in the ETL do not degrade image quality due to banding artifacts resulting from increased TR. Losses from T2* decay will be small in most circumstances, because the maximum TR used in multi-echo SSFP sequences will be short compared to the T2* of most tissues. The SNR behavior of SSFP differs from that of SPGR, in which increases in TR due to additional dead time result in increased signal from T1 recovery. The SNR of SPGR sequences (15) can be written in a form similar to Eq. [7]: NIH-PA Author Manuscript [8] demonstrating that the SNR of SPGR sequences depends on efficiency and TR for constant scan time. Unlike multi-echo SSFP, which benefits only from improvements in efficiency, multi-echo SPGR sequences benefit from both improved efficiency and a longer TR that allows increased T1 recovery. Interestingly, when the bandwidth is fixed, it can be shown that Eq. [8] is independent of TR, and that single-echo SPGR sequences should be run at low bandwidths while maintaining adequate speed performance and restricting chemical shift artifact to an acceptable level (15). This reflects the fact that the addition of dead time to an SPGR sequence to increase T1 recovery is exactly offset by a loss of averaging, unless additional slices or echoes can be acquired during that time. SSFP benefits from the improved efficiency realized in multiecho sequences, but it can be run at a higher bandwidth so long as increases in bandwidth do not significantly decrease efficiency. Magn Reson Med. Author manuscript; available in PMC 2008 May 26. Reeder et al. Page 6 NIH-PA Author Manuscript There were several limitations to the theoretical and experimental analyses conducted in this study. First, we performed the analyses at steady state, and did not consider signal optimization during that period. Traditional segmented k-space cardiac acquisitions (26) use prospective cardiac gating and acquire multiple images through the cardiac cycle, during the transition of magnetization toward steady state. However, more modern segmented k-space approaches acquire data continuously through the cardiac cycle, relying on retrospective gating (27), and are effectively at steady state. Second, the effects of slice profile on SNR were ignored, although the experimental data agree closely with the overall behavior predicted by Eqs. [4] and [7]. Third, the effects of field heterogeneities on signal behavior were ignored. Banding artifacts did not corrupt the experimental data, and the field was relatively homogeneous across the sample. This is not the case in vivo, where susceptibility and the presence of fat will create substantial phase shifts during TR. Although the analysis predicts that the maximum achievable SSFP signal is independent of the field map, one still must have knowledge of the field map or chemical shift in order to calculate the optimum flip angle that will give the maximum signal. When alternating flip angles are used (α, −α, α, …), however, the SSFP signal is relatively constant over most phase shifts caused by field heterogeneities and chemical shift. This is not true near band artifacts; however, this may be less important since the signal at these locations is already degraded. NIH-PA Author Manuscript The optimization of gradient performance, and its effect on sequence efficiency have a direct impact on the SNR performance of pulse sequences. In addition, it is important to understand the effects of slew rate and maximum gradient strength when designing gradient hardware, since slew rate and maximum gradient strength should be coupled (15). Consequently, we conducted an analysis of the TR and efficiency performance of a fast SSFP pulse sequence and the dependence on gradient hardware parameters (maximum gradient strength (mT/m) and slew rate (mT/m/ms)) for several imaging scenarios. For all low-resolution imaging scenarios, including one-, three-, and five-echo acquisitions, the maximum available gradient amplitude and slew rate of most modern scanners (40 mT/m and 150 mT/m/ms, respectively) far exceed those required to maximize efficiency and TR. For example, for a slew rate of 150 mT/m/ms, maximum gradient strengths greater than ∼25 mT/m do little to improve TR and efficiency for the low-resolution imaging scenarios that are commonly encountered with ultrafast real-time imaging applications. Increases in slew rate, however, would provide substantial increases in efficiency and decreases in TR. Unlike the SNR performance of SPGR imaging, which benefits only from decreases in bandwidth, SSFP SNR performance benefits significantly from improvements in efficiency achieved by increases in slew rate, even if bandwidth is held constant. NIH-PA Author Manuscript Hardware optimized trapezoid (HOT) gradient pulses (28), as implemented by Derbyshire and McVeigh (29), can be used to further optimize pulse sequence efficiency for imaging in oblique planes. For a given pulse sequence, HOT pulses are the best way to improve efficiency, and can be advantageous in particular oblique coordinates where substantial gains in efficiency can be realized. One can achieve substantial increases in efficiency and time per echo (TR/ETL) by acquiring additional echoes while maintaining TR < 5 ms, above which image quality degrades. For example, at 40 mT/m and 150 mT/m/s, efficiency increases from 17% to 30% when moving from a one-echo to a three-echo acquisition, and increases further to 36% with a five-echo acquisition. Therefore, one would expect a five-echo sequence to have a 46% increase in SNR performance over the comparable single-echo sequence. All SSFP multi-echo acquisitions have odd numbers of echoes because the readout waveform must be refocused to maintain the steady-state condition, and even numbered echo trains are difficult to balance while maintaining efficiency (10). Magn Reson Med. Author manuscript; available in PMC 2008 May 26. Reeder et al. Page 7 NIH-PA Author Manuscript The contour plots of TR and efficiency for the normal-resolution scenario that is commonly used with cardiac CINE and real-time applications demonstrate that modern gradient hardware performance (40 mT/m and 150 mT/m/ms) is well matched for imaging parameters commonly encountered with standard and real-time cardiac CINE imaging. The optimum performance curve that indicates good matching for maximum gradient strength and slew rate lies just below the operating point of our gradient hardware. In addition, substantial gains in efficiency (from 38% to 60%) are achieved at the typical operating point for a three-echo acquisition and normalresolution imaging parameters, representing a 26% increase in SNR performance. The TR and efficiency plots for the high-resolution scenario indicate that the gradient performance substantially limits the efficiency and TR performance of the sequence. An optimal performance curve cannot be drawn on the plot with the scale shown, indicating that increases in both maximum gradient strength and slew rate would tremendously benefit imaging applications with these imaging parameters. The corner points where optimal gradient performance matching occurs require maximum gradient strengths of 70–80 mT/m (not shown). Indeed, the readout gradient strength required to attain FOV = 16 cm and BW = ±120 kHz is 36 mT/m, which is just under the maximum gradient strength of most modern scanners (40 mT/m). NIH-PA Author Manuscript In summary, the simulations show that current gradient performance is well matched for the image resolution that is commonly used in cardiac CINE and real-time applications. No appreciable increase in efficiency or SNR is possible within current peripheral stimulation limits or without the development of gradient hardware concepts for reduced stimulation. Current FDA guidelines limit the maximum changes in magnetic field (dB/dt) to 20 T/s over a pulse of 120μs duration (30). Switching rates may exceed this limit only after it has been demonstrated in volunteer studies that no painful stimulation occurs, and typical maximum specified slew rates for commercial scanners with modern gradients are 150–200 mT/m/ms (30). Future improvements in SSFP pulse sequence efficiency (and therefore SNR efficiency) must come from either an easing of the current peripheral stimulation restrictions or the design and development of new gradient hardware for reduced stimulation (24). CONCLUSIONS NIH-PA Author Manuscript The SNR of SSFP depends on the square root of the efficiency of the pulse sequence, and, unlike SPGR, it is independent of bandwidth. Therefore, SSFP sequences can be run as fast as possible with high bandwidths as long as sequence efficiency is not overly compromised by large increases in bandwidth. This implies that the maximum possible slew rates should be used, along with matched increases in the maximum gradient strength. Improvements in the SNR performance of SSFP imaging are made through improvements in efficiency, even when bandwidth is held constant. This differs from SPGR imaging, which should be run with as low a bandwidth as possible while maintaining adequate speed performance and restricting chemical shift artifact to an acceptable level. ACKNOWLEDGMENTS The authors thank Richard B. Thompson, Ph.D., for assistance with the Siemens pulse sequence operation, and J. Andrew Derbyshire, Ph.D., for his HOT pulse design algorithms. REFERENCES 1. Oppelt A. FISP. A new fast MRI sequence. Electromedia 1986;3:15–18. 2. Sekihara K. Steady-state magnetizations in rapid NMR imaging using small flip angles and short repetition intervals. IEEE Trans Med Imaging 1987;6:157–164. [PubMed: 18230442] Magn Reson Med. Author manuscript; available in PMC 2008 May 26. Reeder et al. 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Simple linear formulation for magnetostimulation specific to MRI gradient coils. Magn Reson Med 2001;45:916–919. [PubMed: 11323819] 26. Atkinson DJ, Edelman RR. Cineangiography of the heart in a single breath hold with a segmented turboFLASH sequence. Radiology 1991;178:357–360. [PubMed: 1987592] 27. Feinstein JA, Epstein FH, Arai AE, Foo TK, Hartley MR, Balaban RS, Wolff SD. Using cardiac phase to order reconstruction (CAPTOR): a method to improve diastolic images. J Magn Reson Imaging 1997;7:794–798. [PubMed: 9307903] 28. Atalar E, McVeigh ER. Minimization of dead-periods in MRI pulse sequences for imaging oblique planes. Magn Reson Med 1994;32:773–777. [PubMed: 7869900] 29. Derbyshire, J.; McVeigh, E. Gromit: a SSFP imaging sequence employing hardware optimized gradients and just-in-time waveform synthesis; Proceedings of the 10th Annual Meeting of ISMRM; Honolulu. 2002. p. 2359 30. Zaremba, L. Guidance for the submission of premarket notifications for magnetic resonance diagnostic devices. U.S. Department of Health and Human Services, Food and Drug Administration, Center for Devices and Radiological Health, Radiological Devices Branch, Division of Reproductive, Abdominal, Ear, Nose and Throat, and Radiological Devices, Office of Device Evaluation; Rockville, MD: 1998. NIH-PA Author Manuscript NIH-PA Author Manuscript Magn Reson Med. Author manuscript; available in PMC 2008 May 26. Reeder et al. Page 10 NIH-PA Author Manuscript NIH-PA Author Manuscript NIH-PA Author Manuscript FIG. 1. a: Efficiency as a function of TR, increased through decreases in receiver bandwidth. b: SNR normalized by the root scan time is relatively insensitive to TR and bandwidth, except when efficiency drops off sharply at shorter TR. c: SNR normalized per root sampling time demonstrates close agreement with the SNR behavior of SSFP predicted in Eq. [7]. Magn Reson Med. Author manuscript; available in PMC 2008 May 26. Reeder et al. Page 11 NIH-PA Author Manuscript NIH-PA Author Manuscript FIG. 2. a: SNR normalized per root scan time obtained from the anterior wall of the left ventricle from end-diastolic short-axis images from one healthy volunteer, and the sequence efficiency plotted against TR. The ROI used for the measurements was positioned to avoid flow artifact. Normalized scan time is relatively insensitive to TR except at very high bandwidths, when efficiency drops significantly. The box is an operating point that balances speed performance with SNR performance. b–d: Example short-axis end-diastolic images at selected TRs (5.1 ms, 4.0 ms, and 3.0 ms). NIH-PA Author Manuscript Magn Reson Med. Author manuscript; available in PMC 2008 May 26. Reeder et al. Page 12 NIH-PA Author Manuscript NIH-PA Author Manuscript FIG. 3. NIH-PA Author Manuscript Contour plots of TR (a, c, and e) and efficiency (b, d, and f) as functions of maximum gradient strength and slew rate, for single-echo SSFP imaging and low-resolution (a and b), normalresolution (c and d), and high-resolution (e and f) scenarios. The dashed line in each case is the “optimum” operating point, which we calculated for a given slew rate by determining the maximum gradient strength at which further increases in gradient strength no longer improved speed performance or efficiency. The small square drawn in each graph indicates the operating point of most modern scanners (40 mT/m, 150 mT/m/ms). Magn Reson Med. Author manuscript; available in PMC 2008 May 26. Reeder et al. Page 13 NIH-PA Author Manuscript NIH-PA Author Manuscript NIH-PA Author Manuscript FIG. 4. Contour plots of TR (a, c, and e) and efficiency (b, d, and f) for multi-echo SSFP imaging, plotted as functions of maximum gradient strength and slew rate, for the three-echo normalresolution (a and b), three-echo low-resolution (c and d), and five-echo low-resolution (e and f) scenarios. The dashed line in each case is the “optimum” operating point, which we calculated for a given slew rate by determining the maximum gradient strength at which further increases in gradient strength no longer improved speed performance or efficiency. The small square drawn in each graph indicates the operating point of most modern scanners (40 mT/m, 150 mT/m/ms). Magn Reson Med. Author manuscript; available in PMC 2008 May 26. Reeder et al. Page 14 Table 1 Typical Imaging Scenarios Used With Single and Multi-echo SSFP Imaging Scenario NIH-PA Author Manuscript Single echo Low resolution Single echo Normal resolution Single echo High resolution Three echo Normal resolution Three echo Low resolution Five echo Low resolution Resolution parameters FOV = 40 cm ST = 10 mm 128 × 90 matrix FOV = 36 cm ST = 6 mm 256 × 192 matrix FOV = 16 cm ST = 3 mm 512 × 256 matrix FOV = 36 cm ST = 6 mm 256 × 192 matrix FOV = 40 cm ST = 10 mm 128 × 90 matrix FOV = 40 cm ST = 10 mm 128 × 90 matrix Bandwidth (± kHz) Potential use 200 Rapid scout 120 General CINE/real-time cardiac imaging 120 Musculoskeletal imaging 120 General CINE/real-time cardiac imaging 200 Rapid scout 200 Rapid scout ST, slice thickness; FOV, field of view. NIH-PA Author Manuscript NIH-PA Author Manuscript Magn Reson Med. Author manuscript; available in PMC 2008 May 26.