Subject-specific water-selective imaging using parallel transmission


  • In equations 1&2, vectors are written using an arrow over the character (in these equations, x and k are written in this way), whereas in the text the same characters are written using bold lowercase. It was not possible to use bold in our equation typesetting software, but the equations should be written using bold rather than arrow notation.


Spectral-spatial excitation pulses are an efficient means of achieving water- or fat-only imaging and can be used in conjunction with a variety of pulse sequences. However, the approach lacks reliability since its performance is dependent on the homogeneity of the static magnetic field. Sensitivity to static magnetic field variation can be reduced by designing pulses with wider frequency stop bands, but these require longer pulse durations. In the proposed method, spectral-spatial pulses are optimized on a subject-dependent basis to take into account measured subject-specific static magnetic field variation. Extra control of the radiofrequency (RF) field from multichannel transmission is used to achieve this without increasing the length of the pulses. The method characterizes RF pulses using relatively few parameters and has been applied to abdominal imaging at 3 T with an eight-channel system. In a comparison of standard and subject-specific pulses on five healthy volunteers, the latter improved fat suppression in all subjects, with a reduction in RF power of 13% ± 6%. A forward model suggests that the mean flip angle in fat was reduced from 0.72° ± 0.55° to 0.12° ± 0.04° for a 20° excitation; uniformity of water excitation also improved, with the standard deviation divided by mean reduced from 0.26 ± 0.05 to 0.16 ± 0.05. Magn Reson Med, 2010. © 2010 Wiley-Liss, Inc.

Achieving uniform fat suppression is an important diagnostic requirement for body and musculoskeletal MR examinations. The most commonly used approaches distinguish water from fat based on differences in frequency, T1, or both. T1-based methods (1) use an inversion pulse followed by a short delay so that fat, which has a short T1, is suppressed. Such approaches are robust with respect to static magnetic field (B0) inhomogeneity and radiofrequency (RF) field (B1) inhomogeneity if adiabatic pulses are used but tend to be slow and inefficient in terms of signal-to-noise ratio due to the inversion pulses. A number of different frequency-based methods exist, which rely on the chemical shift between water and fat resonances (Δf ≈ 435 Hz at 3 T). Methods include frequency-selective saturation of the fat signal (2), water-selective imaging using spectral-spatial (spsp) pulses (3), and signal-phase-based water-fat separation (4, 5). Methods that rely on selective excitation can be efficient and flexible but require a homogenous B0 field to work well, which is hard to achieve for large fields of view. The phase-based methods can be more robust to B0 field variation but generally require extra data, with information from multiple images acquired at offset echo times being combined to determine and correct for local frequency offsets.

Spsp RF pulses are commonly used to excite only protons from water or fat within a spatially local region, typically a slice or slab. Slice-selective spsp pulses consist of trains of slice selective subpulses with different amplitudes; a commonly used example is the binomial excitation pulse (6), where the relative amplitudes are given by binomial coefficients. Pulses of this type can be described straightforwardly using the small tip angle approximation (3, 7), which establishes a Fourier relationship between the resulting transverse magnetization (m(x)) and the applied RF pulse (b(t)):

equation image(1)

In this formalism x = (x,y,z,ω) and so m(x) is the resulting transverse magnetization as a function of space and (angular) frequency. The transmit sensitivity of the RF coil and static field inhomogeneity are represented by S(x) and B0(x), respectively, and γ is the gyromagnetic ratio. Fourier transform variable k(t) = (kx,ky,kz,kω) has components corresponding to both spatial and temporal frequencies; the spatial components are given by integrals of the applied magnetic field gradients equation image where, for example, Gx is the x gradient strength and the temporal term is given by kω(t) = tT where T is the total pulse duration. Simultaneous slice and frequency selection (i.e., selection in z-ω) are achieved by applying RF energy while traversing a trajectory in kz-kω (3). For the slice-selective spsp pulses used, the k-space trajectory is such that the spatial and spectral responses are independent to first approximation as the subpulse duration is much shorter than the interval between them. In this case, spatial selection is determined from the individual subpulses while spectral selectivity comes from the pattern of amplitude and phase variation of the pulse train (8, 9). A binomial pulse train with N subpulses separated in time by period τ has frequency response equation image giving strong fat suppression if τ = 1/(2Δf) = 1.15 ms at 3 T. Use of higher N provides broader stop bands at the expense of longer RF pulse durations. Inhomogeneity of the static magnetic field causes the water and fat resonant frequencies to vary in space so that they may move out of the frequency bands defined by the RF pulse's structure. The result can be poor fat suppression or even fat selection with water suppressed in regions where the effect is severe. Pulses with a broader stop band are less vulnerable to this effect, and for this reason at 3 T the N = 4 binomial sequence (1-3-3-1) is commonly used; however, failure of fat suppression is still often seen. This clinically used N = 4 binomial pulse has been used as an exemplar in this work.

The recent advent of parallel transmission has provided more direct control of the RF field in space, as well as time; we can describe these extra degrees of freedom by modifying Eq. 1 (10):

equation image(2)

where Sc and bc(t) are the spatial transmit sensitivity and RF pulse waveform, respectively, of coil c and Nc is the number of coils. Much interest has been placed on using these degrees of freedom to improve spatial homogeneity of excitation, particularly at high field strengths (11, 12). RF shimming (13) is a straightforward method of achieving this by adjusting the relative amplitudes and phases of each channel such that the overall RF field is more uniform. Alternatively, the entire waveform and k-space trajectory can be redesigned to gain more control. In this vein, there is a body of work exploring use of composite RF pulses (referred to as “fast kz” or “spokes” (14, 15)) in which subpulses played out along a kz trajectory are offset in kx-ky in order to achieve modulation of in-plane excitation. Recently, it has been recognized that spectral properties of these pulses can be optimized to improve wideband uniformity (16–18). There is thus a close link with conventional water-selective binomial pulses in which each subpulse can be seen as a spoke at (kx,ky) = 0. In this work, we explored the potential for using extra degrees of freedom available from parallel transmission to improve performance of binomial-style pulses by correcting for B0 inhomogeneity. Fat-suppressed images of the pelvis acquired in healthy volunteers are presented, demonstrating the application of this method to a large field of view.


RF Pulse Design

Subject-specific tailoring of the spectral response is achieved by computing the relative magnitude and phase of each of the N subpulses in the spsp pulse. We have used the image domain small tip angle formalism for multiple transmitter systems proposed in Grissom et al. (10), in which Eq. 2 is discretized in space and time and written in matrix form m(x) = A b(k). The x and k variables include the spectral response, as outlined in the introduction, and system matrix A incorporates B1 sensitivity profiles modulated by the phase effects arising from B0 and k-space traversal. The k-space trajectory consists of N points k = (0,0,0,kω) where kω = (nN)τ with n = [1,N] and the solution b(k) contains the N complex values for each of the Nc coils. These were calculated using magnitude least squares optimization (19, 20), which performs the minimization b = argb min{‖|Ab| − mmath image + λ‖b2}, where m is a real valued target magnetization, W represents relative weights as a function of space/frequency, and λ is a regularization parameter that can be used to control total RF power. Ignoring the phase of the target allows more degrees of freedom for improving the fidelity of the magnitude response. The implementation used follows the local variable exchange method in Kassakian (19), initialized using a random target phase; no phase smoothness constraints (as in Setsompop et al. (20)) were used. Total RF power is represented by ‖b2, which is proportional to the specific absorption rate (SAR) for single channel transmission. It should be noted that for parallel transmission, this is not strictly true since the effect on the electric field of changing phase relationships between channels is not accounted for.

The nature of the solution depends on the way in which the problem is posed. Since we are attempting to correct the binomial excitation for off-resonance effects, we might choose to define the target excitation as the binomial frequency response with no off-resonance effect. This has a known analytic form and is symmetric about ω = 0; however, neither of these properties is necessary for good fat suppression, and as an optimization target they are overly restrictive. For water-selective imaging, only the responses at the water and fat frequencies are important. In keeping with this, the target was defined only within narrow frequency bands centered on 0 Hz (“water band”) and −435 Hz (“fat band”), with the goals of uniform flip angle in the water band and zero in the fat band for all spatial locations. The width of these bands was selected to be 40 Hz to accommodate the expected local line widths of the water and fat resonances. Optimal pulse weightings were calculated in a single-voxel small tip angle model using this target, with no off-resonance effect. The resulting normalized pulse amplitudes and phase offsets are given in Table 1. For N ≤ 4, the solutions reproduced binomial weightings. This implies that for the N = 4 pulses presented in this paper, it is reasonable to use the 1-3-3-1 sequence as an unoptimized comparison.

Table 1. Optimized Pulses From Single-Voxel Model*
NBinomial amplitudesOptimized pulses
Relative pulse amplitudeRelative phase (degrees)Relative Power
  • *

    Relative pulse amplitude and phase computed from single-voxel optimization with no off-resonance compared with equivalent binomial pulses. Relative power of optimized pulses is given, normalized to the relative power of the same-order binomial pulse.

21 11.0 1.00 01.0
31 2 11.0 2.0 1.00 0 01.0
41 3 3 11.0 3.0 3.0 1.00 0 0 01.0
51 4 6 4 11.0 10.3 22.4 10.3 1.0179 0 0 0 −1791.6
61 5 10 10 5 11.0 1.6 9.8 9.8 1.6 1.0179 0 0 0 0 −1791.9

Frequencies outside the water and fat bands are left unconstrained by excluding them from x; the same approach is taken for spatial locations outside the object. The two optimization goals, flip angle uniformity for water and zero fat excitation, compete with one another. Since small failures in fat suppression are diagnostically more significant than small deviations of water flip angle, we set the requirement for fat suppression to be stronger than that of water signal uniformity. This was achieved by reducing the relative weight of the water band in W. Experience gained from pilot data suggested that a relative weighting of w = 10−3 for the water band gives an effective balance between the two goals, and this value was used for all of the presented in vivo experiments. The effect of this parameter was retrospectively investigated using forward simulations from the calibration data obtained for this study; the optimization was carried out for different values of w, with the predicted excitations and required RF power evaluated.

All experiments used λ = 16, which was found to yield an effective tradeoff between RF power and excitation fidelity in phantom tests. The effect of λ on the optimization was investigated retrospectively using calibration data obtained for the study. Computation grid resolutions were 8 mm in space and 20 Hz in frequency, with optimization performed using Matlab R2008a (Mathworks, Natick, MA) on an IBM x3755 system (four dual-core processors, 32-GB random access memory) linked via Ethernet connection to the scanner console.

In Vivo Experiments

Experiments were performed using a 3-T Achieva MRI system (Philips Healthcare, Best, The Netherlands) equipped with an eight-channel body coil capable of parallel transmission (21). The coil consists of strip elements arranged around the bore of the magnet, giving maximum variation in transmit sensitivity in the axial plane. When simulating a single body coil, the elements are driven with a fixed precalibrated amplitude and phase relationship designed to give quadrature excitation for a wide field of view (referred to as “quadrature mode”). A six-element phased-array surface coil was used for signal reception. Research ethics committee approval was obtained for the study, and all participants gave written informed consent prior to enrollment. In total, five healthy volunteers (two male, three female) underwent fat-suppressed pelvic imaging.

A slab-selective spsp pulse with N = 4 subpulses and slab thickness 200 mm was used for all experiments. Fly-back gradients were used between subpulses in order to avoid side lobes occurring at the gradient oscillation frequency from appearing inside the intended stop band (8, 22). Gradient waveforms were designed with maximum slew rate 30 T/m/sec, enough to achieve the desired slab thickness/flip angle for this study but not a fundamental limit; the system maximum slew rate is 200 T/m/sec. The sinc subpulses had a time-bandwidth-product of 8, and time between them was set to τ = 1/(2Δf) = 1.15 ms, as is generally used in clinical imaging. Experiments compared optimized pulses using parallel transmission with a 1-3-3-1 binomial sequence using the same trajectory but with the coil driven in quadrature mode. Optimized pulses were designed to give a target flip angle of θw = 20° in water and θf = 0° in fat; binomial pulse amplitudes were set using the scanner's standard power optimization method.

Imaging was performed using a standard abdominal protocol, three-dimensional Fourier-encoded RF spoiled gradient echo sequence (T1FFE) with flip angle 20°, pulse repetition time (TR) = 30 ms, and echo time (TE) = 4.6 ms. Acquired images were in axial orientation, with a 400 mm field of view and resolution 2 × 2 × 5 mm3. Standard first-order B0 shimming was performed using scanner preparation phases; the same shim settings and center frequency were used for all experiments on a given subject.

The scanner software estimated the SAR load of the sequence incorporating the 1-3-3-1 pulse to be ∼6% of the local torso limit (10 W/kg), depending on patient weight. Scanner SAR estimates are based on mean square RF drive amplitudes, which, as mentioned above, determine RF power but not necessarily the local SAR for parallel transmission. As a conservative safety margin, the operating procedure adopted was to ensure that the local SAR estimate produced by the scanner did not exceed 10% of the local torso limit. Time-resolved B1 field estimates were also produced by combining RF pulse waveforms with the B1 maps, and peak/mean square values were computed by integrating these through space and time.

Calibration Data

Although imaging was performed over a 200 mm slab, optimization was only performed for a single slice at the center of this slab. The effect of the optimization outside the slice of interest was evaluated. B1 mapping was performed using the actual flip angle imaging sequence (23) with a slice selective pulse, implemented with modifications proposed in (24) using the “all but one” array mapping method from Nehrke and Boenert (25). Actual flip angle imaging used TR1 = 30 ms, TR2 = 150 ms, TE = 4.6 ms (in phase), nominal flip angle 80° with resolution 4 × 4 × 10 mm3, and field of view varying, depending on the size of the subject; acquisition time was approximately 1 min 50 sec for all eight channels. B0 mapping was performed using a multiecho gradient echo sequence with all echoes in phase (three echoes, first echo time = 2.3 ms, ΔTE = 2.3 ms) to avoid interference between water and fat; TR = 30 ms, flip angle 20°. Fly-back gradients were used to minimize errors from eddy currents. Resolution and field-of-view settings were the same as the B1 maps, acquisition time was approximately 35 sec (16 signal averages). The relatively large interecho spacing leads to phase aliasing in the acquired B0 map; this was corrected in postprocessing using spatial unwrapping.


Figure 1 contains images from all five volunteers, comparing the standard binomial and optimized excitations. The images from binomial pulse excitation show varying degrees of fat suppression failure, depending on the quality of the original shim. The optimized pulses produced universal improvement of fat-suppression quality. Although optimization was performed only for a single 10 mm slice, it was observed that fat suppression uniformity improved throughout the 200 mm imaged volume in all volunteers. Figure 2 shows exemplary slices from one subject (volunteer number 5) over range ± 50 mm out of the central slice. The uniformity of fat suppression is improved for all of these slices; importantly, overall image quality is not worsened in other slices by the optimization.

Figure 1.

Central slice of axial three-dimensional pelvis examination shown for all five volunteers, comparing binomial and optimized water-selective excitations. Window and level settings are the same for all images. The difference images show the optimized image subtracted from the binomial one; positive differences in fat indicate improved fat suppression. The improvements are more obvious in larger volunteers (numbers 2, 3, and 5), but in all cases fat-suppression quality is improved. Large differences can be seen in the center of the images from volunteers 3 and 4 since images were acquired approximately 15 min apart, during which motion due to bowel peristalsis occurred.

Figure 2.

Slices from volunteer number 5 with distance from central slice indicated. Optimization was performed for the central slice (z = 0 mm). The best image quality is obtained in the central slice after optimization; however, there is an improvement in fat-suppression quality in all slices. For z = −50 mm, the off-resonance effect is severe and so the optimized pulse offers only a partial correction but is better than the binomial pulse.

More quantitative comparisons can be made by considering the predicted excitation properties from the small tip angle model in each case. For a target flip angle of 20° in water, the mean flip angle in fat as predicted from the model for the binomial pulse was 0.72° ± 0.55° (mean and standard deviation calculated across the volunteer group). This fell to 0.12° ± 0.04° for subject-specific pulses, indicating a 6-fold improvement in fat suppression. The dynamic range of flip angles in the water band was quantified by taking the standard deviation divided by the mean flip angle and fell from 0.26 ± 0.05 before optimization to 0.16 ± 0.05 afterward.

The mean square RF drive amplitude (often taken as a surrogate measure for the SAR) was reduced by 13% ± 6% across the volunteer group, while peak drive amplitude on a single channel increased by 36% ± 9%. The B1 map-based RF field model predicts that mean square B1 was reduced by 17% ± 9% across the volunteers, with the peak value (in space and time) showing no significant change (change of −5% ± 10%).

The optimized RF subpulse amplitudes and phases for volunteer 5 are plotted in Fig. 3. The amplitudes of the middle two subpulses are higher than the others for all channels but do not follow the 1-3-3-1 pattern. For most channels, the phase changes monotonically in time, suggesting a frequency offset. Figure 4 shows the predicted B1 field at the middle of each subpulse. The total field amplitudes more closely follow a 1-3-3-1 pattern, but there is spatial variation. Figure 5 shows the predicted frequency responses from the standard and optimized pulses in a voxel on the anterior left-hand side of volunteer 5, where there is a failure of fat suppression with the binomial pulse visible on Figs. 1 and 2. The target excitation is only defined in narrow bands, and the optimized excitation is not constrained outside these. As expected, there is a frequency shift in the response; however, it also has a different shape to the binomial version, losing the symmetry that the latter possesses.

Figure 3.

Optimized pulse amplitudes and phases compared to standard binomial pulse for volunteer number 5. The traces for the different channels are color coded, with the approximate position of the corresponding RF coil with respect to the magnet bore indicated on the diagram. For this volunteer, the mean square RF drive of the optimized pulse was 22% less than that of the binomial pulse; the peak RF drive amplitude was 34% higher.

Figure 4.

Instantaneous RF field at the center of each subpulse for volunteer number 5, calculated using measured B1 maps and optimized pulses (Fig. 3). The overall amplitude of the RF field approximately follows the 1-3-3-1 ratio between subpulses but with spatial variation. The phase of the RF field changes through the subpulses, with similar spatial variation to the measured off-resonance map.

Figure 5.

Predicted frequency responses for binomial and optimized pulses in the anterior left-hand side of volunteer number 5, where there is a strong off-resonance effect (see Fig. 1). The target excitation is only defined in narrow bands of frequencies, as depicted here. The optimized excitation results in reduced flip angle in fat (∼−440 Hz; from 5° to <1°) and increased flip angle in water (0 Hz; from 7° to 14°). As well as being shifted with respect to the binomial frequency response, the response of the optimized pulse also has a different shape.

Relative Weighting of Water Versus Fat

Figure 6a shows the predicted excitations in water and fat using calibration data from volunteer number 1 for different values of w and Fig. 6b-d shows plots that summarize results for all five volunteers. Using w < 10−5 leads to the trivial solution of no excitation in water or fat, satisfying the optimization goal for the fat frequency but not for water. Increasing this weighting improves the properties of the water excitation but at the same time increases the mean flip angle in fat to the point where w = 1 results in a mean fat flip angle that for some volunteers is greater than that from the unoptimized binomial pulse. While there is some variability between the volunteers, the overall trends are the same and the choice of w = 10−3 gave both a large improvement in fat suppression and reduced dynamic range of flip angles in water.

Figure 6.

a: Simulated water and fat excitations in subject number 1 for binomial (1-3-3-1) pulse and optimized pulses using different w. The same window settings are used for all water images and all fat images. b-d: Plots summarize results of forward simulations for data from all volunteers; all values are normalized to the corresponding values from a 1-3-3-1 binomial pulse and averaged across the volunteer group, with error bars depicting variability within the group. b: Mean square RF drive amplitude. c: Mean flip angle in water band (θw) and fat band (θf). d: Dynamic range (standard deviation divided by mean).


Figure 7a shows the relative RF power (mean square RF drive relative to 1-3-3-1 pulse) for pulses optimized using a range of values of λ; a weighting of w = 10−3 was used in all cases. Optimization was carried out using calibration data from all volunteers, and the plots show average values for the volunteer group. For comparison, pulses were also optimized for flip-angle homogeneity in the water band only, ignoring the excitation in the fat band. Both optimizations behave similarly for large λ, with relative RF power slowly falling as expected. However, the water-only optimization experiences dramatic increases in RF power as λ→0; this does not occur for the dual-band water-selective optimization, which maintains a lower RF power than the binomial sequence, even if λ = 0. Figure 7b displays the relative error achieved by the optimizations; in both cases the error increases smoothly with λ.

Figure 7.

Effect on optimization of varying values of λ; pulse calculation was repeated using data for all volunteers, and the error bars reflect variation within the volunteer group. For comparison with the “dual band” fat-suppressing excitation, optimization was also performed considering only homogeneity of water excitation (“water only”). a: Relative power is calculated as mean square RF drive normalized to the 1331 binomial pulse. b: Normalized root mean square error (NRMSE) quantifies the residual difference between the optimization result and target excitation (magnitude only).


In this work, we have optimized commonly used spsp RF pulses for use with parallel transmission and have demonstrated improved fat suppression quality at 3 T over a large field of view. An improvement in image quality was obtained in all subjects (Fig. 1) and is corroborated by predictions from the small tip angle model.

The optimization used a relative weighting of water with respect to fat of w = 10−3, and simulations (Fig. 6) confirmed that this was a reasonable choice for this study and that results were similar for all of the volunteers. In general, it is likely that the optimal choice of this parameter would be different, depending on the geometry of the object and the coil. The fact that the optimal choice is stable for the fixed geometry used here, with a range of volunteer sizes, suggests that clinical use of this method could perhaps proceed using predetermined optimal values for given examinations.

A fixed value for the regularization parameter (λ = 16) was used for all studies. Figure 7 suggests that while smaller values lead to lower residual error in the excitation, the RF power does not rapidly increase, even if λ = 0. If, however, we only optimize for flip angle uniformity in water without regard for the excitation in fat, then small λ leads to very high RF power. The implication is that the dual band problem is more inherently constrained, making choice of λ less important. Setting the weighting parameter w to a very high value would move the situation toward water-only shimming, and as a protection against this eventuality a small but nonzero value for λ should be used to constrain RF power.

The pulse design algorithm was tailored to maximize the effeciveness of the available degrees of freedom for fat suppression. At a given location in space, the frequency response of an spsp pulse with N subpulses is determined by the instantaneous RF field at the center of each subpulse. This in general can be any spectral shape determined by N parameters. By only defining the target excitation in narrow frequency bands around the water and fat resonances, we implicitly state that the symmetry produced by a binomial pulse is not required. In the absence of field imperfections, single-voxel optimization (Table 1) shows that for N ≤ 4 the binomial sequence is still optimal. For N ≥ 5, the methods diverge because higher orders of the binomial sequence give a wider stop band but a narrower pass band; the solutions found by the presented approach instead aim to generate pass and stop bands with flat regions of 40 Hz. These solutions have a higher relative power (Table 1) than the equivalent binomial since some subpulses have opposite phase; use of higher λ leads to lower-power solutions more similar to binomial excitations. The pulses are still, however, symmetric in time (and in frequency). Moving to the more demanding problem of optimization over spatially varying fields with the relatively small set of parameters (N × Nc) results in this symmetry disappearing, as the example response in Fig. 5 demonstrates.

Links to Frequency Correction

It has been proposed that the extra degrees of freedom afforded by parallel transmission may be used to improve performance by individually tuning the center frequency of each element to match the local resonance frequency (26). This on its own, however, does not take into account interactions between the coil elements; neglecting this aspect results in unpredictable performance that can compromise image quality severely. The proposed method results in a spatially varying RF phase profile, which progresses through time (Fig. 4); in the limit that the subpulses have zero duration, a linear phase progression is equivalent to a spatially varying RF frequency distribution. As Fig. 4 shows, this phase progression is correlated with the strength and sign of the off-resonance field but it does not follow a strict linear form, demonstrating that correction applied is more complex than localized frequency correction alone.

Limitations and Further Degrees of Freedom

In this study, a 200 mm three-dimensional slab was imaged with a 20° excitation, chosen to reflect a typical pelvic examination. This does not represent the minimum slice thickness possible, whose value depends on the peak B1, flip angle, and gradient strength/slew rate. A slice thickness of approximately 10 mm can be achieved using the maximum gradient slew rate of 200 T/m/sec, and thinner slices are possible if smaller time-bandwidth product subpulses are employed. Pulses were designed using the small tip angle approximation, which is valid up to at least 30° (10); performance at higher flip angles has not yet been investigated.

The design of the RF body coil used gives maximum sensitivity variation in the axial plane used for pelvic imaging, with slow variation through slice. Images for a single volunteer at different slice locations (Fig. 2) demonstrate that for this configuration, the optimization results in better fat suppression also outside the optimized slice. Less favorable coil and/or slice geometries may require optimization to be performed through multiple slices; however, extra B0/B1 maps would be required to achieve this at the cost of increased calibration time. Acquisition times for calibration data used in this study (35 sec for B0 map, 1 min 50 sec for B1 maps) could further be reduced by employing parallel imaging and more signal-to-noise ratio efficient methods for array coil calibration (27); a total calibration time of 1 min per slice is a reasonable goal with current capabilities. While this still represents a significant overhead for clinical imaging, new, rapid B1 mapping strategies are the subject of significant effort in the community (28–30) and this time is expected to be further reduced.

In this work, we focused on the extra control afforded by parallel transmission. Where there are highly local or large B0 offsets, this may fail; an example of this can be seen in the images from volunteers 2 and 3 (Fig. 2), where fat-suppression failure in the right-hand side of the subject has been reduced but not completely eradicated. Peripheral regions such as the ankle or shoulder often demonstrate rapid variation in B0 and may suffer similar problems. A potential solution is to use local transmit coils and/or arrays with larger numbers of smaller coils since these will have more rapidly varying B1 fields, offering increased spatial control; this is the subject of current investigation. In addition, the close connection between slice-selective spsp pulses and the more general spokes method indicates that in order to tackle more difficult situations, moving to a solution where the k-space trajectory can explore the kx-ky plane could also be beneficial. Preliminary work suggests that this is also the case for single channel transmission. If optimizing the k-space trajectory, then the timing of the subpulses could also be considered. In general, we use the minimum τ required to resolve frequency difference Δf; τ = 1/2Δf since this minimizes pulse duration. Alternatively, shorter pulses can be achieved by using τ < 1/2Δf, which results in aliasing that can be shifted using phase modulation (31, 32) at the expense of reducing the efficiency of water excitation.

B0 and B1 homogeneity are usually controlled using different subsystems, B0 using the gradients and dedicated shim coils and B1 more recently using parallel RF transmitters. In this work, a standard linear B0 shimming approach was used. The quality of the B0 shim might have been improved in some cases by using a different algorithm to calculate the required offsets or by using higher-order shimming; this would then impact on the fat-suppression quality achieved using the binomial pulse. We have demonstrated that the RF system can be used in a complementary manner that is true regardless of the starting point. The ability to create a spatially varying RF phase progression to counteract off resonance comes directly from extra degrees of freedom offered by parallel transmission. A still more integrated approach would be to optimize B0 shim settings and the RF pulse simultaneously, allowing full advantage to be taken from all degrees of freedom.


The ability of parallel transmission to create a spatially and temporally varying RF field leads to concerns over the nature of the electric fields involved and their impact on RF power deposition. All experiments led to a reduced mean square RF drive amplitude (mean reduction 13%), which suggests a reduction of the overall power deposition. The peak drive amplitude, however, increased in all cases (mean increase 36%). The peak B1 field (in space and time) estimated from the calibration data did not, however, increase by this amount, suggesting that cancellation of fields occurs. In this work, the RF power is controlled by the scalar parameter λ, which penalizes solutions with high mean square RF drive. If required, this could be replaced by a diagonal matrix containing independent regularization parameters for each of the RF subpulses/coils (as suggested in Grissom et al. (10)), which can be used to avoid large peak amplitudes for coils with low sensitivity in the region of interest. As demonstrated by Fig. 6b, there is also a tradeoff between water excitation fidelity and mean square RF drive mediated by choice of w; for example, using w = 10−2 rather than 10−3 as used in this work would result in better water flip-angle homogeneity but also higher RF power. If electric field data were available, for example, derived from relevant simulations, then this could be incorporated into the pulse design process in order to explicitly control the SAR (33, 34).


Using the extra degrees of freedom available from an eight-channel parallel transmission system, we demonstrate improved fat-suppression quality over a large field of view at 3 T. Results from a pelvis imaging study with five healthy volunteers showed an improvement in image quality in all cases. Spsp RF pulses were designed online, with necessary B0 and B1 field data acquired within 3 min and pulse calculation taking approx 15 sec, making the approach suitable for future adoption in a clinical setting when parallel transmit technology becomes more widely available.


We thank Philips Medical Systems for their development of the multichannel transmit system.