Design of parallel transmission pulses for simultaneous multislice with explicit control for peak power and local specific absorption rate
2014; Wiley; Volume: 73; Issue: 5 Linguagem: Inglês
10.1002/mrm.25325
ISSN1522-2594
AutoresBastien Guérin, Kawin Setsompop, Huihui Ye, Benedikt A. Poser, Andrew Stenger, Lawrence L. Wald,
Tópico(s)Electron Spin Resonance Studies
ResumoMagnetic Resonance in MedicineVolume 73, Issue 5 p. 1946-1953 NoteFree Access Design of parallel transmission pulses for simultaneous multislice with explicit control for peak power and local specific absorption rate Bastien Guérin, Corresponding Author Bastien Guérin Department of Radiology, Martinos Center for Biomedical Imaging, Massachusetts General Hospital, Charlestown, Massachusetts, USACorrespondence to: Bastien Guérin, 149 Thirteenth Street, Suite 2301, Charlestown, MA 02129. E-mail: guerin@nmr.mgh.harvard.eduSearch for more papers by this authorKawin Setsompop, Kawin Setsompop Department of Radiology, Martinos Center for Biomedical Imaging, Massachusetts General Hospital, Charlestown, Massachusetts, USASearch for more papers by this authorHuihui Ye, Huihui Ye Department of Radiology, Martinos Center for Biomedical Imaging, Massachusetts General Hospital, Charlestown, Massachusetts, USA Department of Biomedical Engineering, Zhejiang University, Hangzhou, ChinaSearch for more papers by this authorBenedikt A. Poser, Benedikt A. Poser Maastricht Brain Imaging Centre, Department of Cognitive Neuroscience, Maastricht University, Maastricht, Netherlands John A. Burns School of Medicine, University of Hawaii, Honolulu, Hawaii, USASearch for more papers by this authorAndrew V. Stenger, Andrew V. Stenger John A. Burns School of Medicine, University of Hawaii, Honolulu, Hawaii, USASearch for more papers by this authorLawrence L. Wald, Lawrence L. Wald Department of Radiology, Martinos Center for Biomedical Imaging, Massachusetts General Hospital, Charlestown, Massachusetts, USA Harvard-MIT Division of Health Sciences Technology, Cambridge, Massachusetts, USASearch for more papers by this author Bastien Guérin, Corresponding Author Bastien Guérin Department of Radiology, Martinos Center for Biomedical Imaging, Massachusetts General Hospital, Charlestown, Massachusetts, USACorrespondence to: Bastien Guérin, 149 Thirteenth Street, Suite 2301, Charlestown, MA 02129. E-mail: guerin@nmr.mgh.harvard.eduSearch for more papers by this authorKawin Setsompop, Kawin Setsompop Department of Radiology, Martinos Center for Biomedical Imaging, Massachusetts General Hospital, Charlestown, Massachusetts, USASearch for more papers by this authorHuihui Ye, Huihui Ye Department of Radiology, Martinos Center for Biomedical Imaging, Massachusetts General Hospital, Charlestown, Massachusetts, USA Department of Biomedical Engineering, Zhejiang University, Hangzhou, ChinaSearch for more papers by this authorBenedikt A. Poser, Benedikt A. Poser Maastricht Brain Imaging Centre, Department of Cognitive Neuroscience, Maastricht University, Maastricht, Netherlands John A. Burns School of Medicine, University of Hawaii, Honolulu, Hawaii, USASearch for more papers by this authorAndrew V. Stenger, Andrew V. Stenger John A. Burns School of Medicine, University of Hawaii, Honolulu, Hawaii, USASearch for more papers by this authorLawrence L. Wald, Lawrence L. Wald Department of Radiology, Martinos Center for Biomedical Imaging, Massachusetts General Hospital, Charlestown, Massachusetts, USA Harvard-MIT Division of Health Sciences Technology, Cambridge, Massachusetts, USASearch for more papers by this author First published: 17 June 2014 https://doi.org/10.1002/mrm.25325Citations: 42AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Abstract Purpose To design parallel transmit (pTx) simultaneous multislice (SMS) spokes pulses with explicit control for peak power and local and global specific absorption rate (SAR). Methods We design SMS pTx least-squares and magnitude least squares spokes pulses while constraining local SAR using the virtual observation points (VOPs) compression of SAR matrices. We evaluate our approach in simulations of a head (7T) and a body (3T) coil with eight channels arranged in two z-rows. Results For many of our simulations, control of average power by Tikhonov regularization of the SMS pTx spokes pulse design yielded pulses that violated hardware and SAR safety limits. On the other hand, control of peak power alone yielded pulses that violated local SAR limits. Pulses optimized with control of both local SAR and peak power satisfied all constraints and therefore had the best excitation performance under limited power and SAR constraints. These results extend our previous results for single slice pTx excitations but are more pronounced because of the large power demands and SAR of SMS pulses. Conclusions Explicit control of local SAR and peak power is required to generate optimal SMS pTx excitations satisfying both the system's hardware limits and regulatory safety limits. Magn Reson Med 73:1946–1953, 2015. © 2014 Wiley Periodicals, Inc. INTRODUCTION Simultaneous multislices (SMS) techniques accelerate the acquisition of volume MRI data by exciting several slices at once 1-5 and then unalias the collapsed data using parallel imaging methods 6-8. SMS methods are compatible with fast echo-planar trajectories, which make them useful for a wide range of applications, including functional and diffusion MRI 3, 5. A drawback of multiplexed SMS pulses is their large SAR and peak power demands. To reduce peak power, Wong 9 optimized the phases of the individual slice excitations so as to minimize the peak voltage of the total SMS pulse and showed that this approach yields SMS pulses with peak power scaling with the number of multiband (MB) slices as opposed to MB2 as usual. Another strategy to reduce the SMS peak power consists of shifting the individual slice excitation by different time delays 10. Although these techniques significantly reduce peak voltage of the total SMS pulse, they do not reduce total radiofrequency (RF) power or SAR. Indeed, at low flip angles, the Fourier relationship between transverse magnetization and the RF pulse 11 implies that total RF power is equal to the integral of the slice profile (squared) along the slice direction (Parseval theorem). Therefore, if the slices excited simultaneously are well separated spatially, the total RF power of the SMS pulse equals the sum of the total RF power of the individual slice excitations. SAR can be reduced, albeit at the cost of a degradation of off-isocenter slice profiles, by reducing the peak power of the individual slice excitations using the VERSE algorithm 12-15. This reduction may not be sufficient for high MB factors and spin echo pulses at high fields, however. Power independent of number of slices (PINS) pulses have been proposed as another solution to this problem. PINS pulses approximate slice-selective RF profiles using trains of rectangular subpulses and excite many slices at once by undersampling transmit (Tx) k-space in the slice direction 16. They provide significant peak power and SAR reduction at high MB factors and for demanding acquisition such as diffusion imaging 17 and turbo spin echo 18; however, they are long and, therefore, like VERSE pulses, sensitive to off-resonance effects. Recently, SMS techniques have been combined with parallel transmission (pTx) in order to yield uniform excitations of multiple slices or slabs at ultra-high fields; which was first demonstrated by Katscher et al. 19. In a study by Wu et al. 20, SMS RF-shimming pTx pulses were designed by optimization of RF-shimming coefficients for the different slices excitations while constraining the average power of the total SMS pulse (Tikhonov regularization). This led to excitations that were more uniform and with smaller average power than SMS excitations designed by using the same set of RF-shimming coefficients for all slices. In another study, Poser et al. 21 used an eight-channel pTx coil with two rows in the z-direction (four channels per row) and showed that such a coil is beneficial for SMS RF shimming because it creates slice excitations that are largely contained in the two distinct rows, thus reducing total power and SAR. Finally, in a recent abstract, PINS and kT points pulses 22 were combined by adding small rectangular kx-ky excitations between the PINS rectangular subpulses to improve the homogeneity of the slice excitations 23. This approaches yields pulses that are even longer than traditional PINS pulses however. These early combinations of pTx and SMS focused on flip-angle uniformization and reduction of peak power using RF-shimming strategies and did not consider SAR explicitly in the pulse design process. Control of RF power and SAR are not equivalent in pTx, and explicit control of both SAR (local and global) and RF power is required to yield pulses of the highest quality that are both safe and playable on the scanner 24. In this study, we extend the SMS pTx design strategies of Wu et al. 20 and Poser et al. 21 beyond RF shimming to the design of magnitude least-squares pTx SMS pulses with multiple spokes. As in "standard" pTx (i.e., without SMS), we show that local SAR can be constrained explicitly in the design of spokes SMS pTx pulses along with global SAR and peak power. This strategy allows generation of the best possible SMS pulses compatible with all safety and system limits, which is not possible using Tikhonov-regularized approaches that typically handle a single constraint. METHODS Parallel Transmission Pulse Design We design low flip-angle multiplexed SMS pTx spokes pulses with explicit control for local SAR using a compression of the SAR matrices called the virtual observation points (VOPs) 24, 25. Global SAR and peak power are also constrained, as shown in the following equation: (1)where n (varies from 1 to N), c, and i are the time, channel, and VOP indices, respectively. As explained by Wu et al. 20, the SMS system matrix A is the block-diagonal of the system matrices associated with each individual slice's excitations 26 and b is the vertical concatenation of the target magnetization of all slices. Additionally, x is the vertical concatenation of the spokes amplitudes of all simultaneously excited slices, and xSMS(t) is the total SMS RF pulse, which is the sum of the individual excitations, at time t. To achieve the best possible flip-angle uniformity, we used a magnitude least-squares (MLS) objective in Equation 1, which can be simply implemented as a series of least-squares constrained optimizations with phase adaptation 24, 27. Constraints a), b), and c) constrain local SAR at all VOPs, global SAR, and peak power, respectively. Z0 is the reference impedance [see Guérin et al. 24 for an explanation of the factor of 8 in constraint c)], 〈Q〉 is the global SAR matrix, and VOPi is the VOP matrix number i (all SAR matrices are C × C, where C is the number of channels). Note that these constraints depend on the total SMS pulse. In regular spokes pTx pulses with no SMS acceleration, the maximum peak power occurs at the maximum of the subpulses. This is not necessarily the case in SMS pulses; therefore, we apply the peak power constraint at all time points, which increases computation time. We solved the constrained optimization problem of Equation 1 using the fmincon optimizer of MATLAB 8 (MathWorks, Natick, Massachusetts, USA). Specific Absorption Rate of Simultaneous Multislice Pulses It is instructive to expand a quadratic SAR constraint of Equation 1 in the case of an SMS2 pulse (we note "SMSX" is an SMS pulse exciting X slices simultaneously). In this case, we have xSMS (t) = x1(t) + x2(t) = A1su(t) + A2su(t) , where A1s contains the complex amplitudes played on all channels for spoke s (we note S the total number of spokes) for the first slice excitation and u(t) is the slice-select subpulse shape, and , where γ is the gyromagnetic ratio, z is the distance between the two slices, Gz is the slice-selection gradient, and T is the pulse duration. Assuming that RF is played during constant gradient only, this formula reduces to φSMS(t) = ωSMS(T − t) with ωSMS = 2πγzGz. Using these notations, a generic SAR term in Equation 1 becomes: (2) Where Ns is the number of time samples in the subpulse shape u. A first observation is that the final SAR expression only involves sums of quadratic forms over the number of spokes instead of the number of time samples, which considerably reduces computation time of the constraints and their derivatives 24. The first and second terms of the last equality in Equation 2 are the SAR associated with the excitation of slices #1 and #2 if they were played independently (i.e., one after the other), and the last term contains the destructive and constructive SAR interferences between them. We note that this term is proportional to the discrete Fourier transform (DFT) of |u(t)|2 evaluated at the frequency ωSMS. By replacing the discrete DFT by a continuous Fourier integral and using the sinc subpulse u(t) = sinc(ωt), where ω = 2πγΔzGz (where Δz is the slice thickness), this Fourier term becomes the triangle function Tri(ωSMS/ω) = Tri(z/Δz), which is zero for z ≥ Δz. In other words, for an idealized slice selection, the SAR cross term in Equation 2 is exactly zero if and only if the slices excited simultaneously are not overlapping. In practice, the slice-selection and low-flip angle approximation are not perfect, and this SAR cross term is not exactly zero; however, as long as the excited slices are well separated, the SAR of the SMS pulse is, to an excellent approximation, the sum of the SAR of the individual slice excitations (Fig. 1a and e). This result generalizes to pTx the observation, mentioned in the Introduction, that the RF power of a single-channel SMS pulse is equal to the sum of the total RF power of the individual slice excitations (Parseval theorem). Figure 1Open in figure viewerPowerPoint a: Simulated 3T parallel transmission (pTx) body array (two z-rows of four channels per row). b: Simulated 7T pTx head array (also two z-rows). c-e: Detailed data for a magnitude least-squares SMS2 two-spoke pulse designed with constraints for local SAR, global SAR, and peak RF power. The target Ernst flip angle was 16°, TR was 30 ms, duty cycle was 10%, and interslice distance was 5.4 cm. Local SAR, global SAR, and peak power were constrained to 10 W/kg, 3 W/kg, and 1000 W/channel (equivalent to 632 V/channel), respectively, for the total SMS pulse. c: RF waveforms of the individual slice excitations and the total SMS pulse. d: Flip angle maps created by the SMS2 pulse at the two slice locations (Bloch simulation). The three numbers at the bottom of each map are the mean (in degrees), standard deviation (in degrees) and root mean square error of the flip angle excitations (in percent of the target flip angle). e: SAR maximum intensity projection maps of the SMS2 pulse and its individual slice excitations (1 g average, the numbers below each SAR map are the local SAR/global SAR in W/kg). For these well-separated slices, the SAR of the SMS pulse is equal (to an excellent approximation) to the sum of the SAR of the individual slice excitations (see Methods). However, since the local SAR hotspots of slice excitations #1 and #2 (white arrows) do not occur at the same locations, the local SAR of the SMS pulse is smaller than the sum of the local SAR of the individual slice excitations. If only global SAR and/or average RF power were constrained in Equation 1, the observation of the previous paragraph implies that it would be equivalent to design the slice excitations of the SMS pulse jointly (as in Eq. 1) or separately. However, when constraining local SAR, these approaches are not equivalent because the maximum of the sum of two SAR maps is not necessarily equal to the sum of the maximum of these maps (this only occurs if the SAR hotspots of the individual slice excitations occur at the same location [see Fig. 1a and e]). Therefore, the joint design strategy of Equation 1 is expected to yield pulses achieving better trade-offs between flip-angle uniformity and local SAR than an independent design strategy consisting in optimizing independently the individual slice excitations with respect to local SAR and flip angle (from this point of view, the joint design of Equation 1 is similar to "SAR hopping" approaches, also referred to as "time-multiplexed" or "time-averaging" SAR methods, described in references 28–31). Evaluation in Electromagnetic Simulations We evaluated the SMS design strategy of Equation 1 in electromagnetic simulations of an eight-channel 7T head coil and an eight-channel 3T body coil (Fig. 1a.). Both coils were composed of two staggered z-rows, each containing four Tx channels, a design that has been shown to be beneficial for SMS 21. The coils were loaded with the male Ansys body model (33 tissue types). The fields generated by these coils were simulated using a cosimulation strategy based on the field simulator HFSS (Ansys, Canonsburg, Pennsylvania, USA) and the circuit simulator ADS (Agilent, Santa Clara, California, USA) 24, 32, 33. Matching and decoupling between any two channels were better than −30 dB and −15 dB, respectively. SAR matrices obtained from the electric fields were averaged over 1 g and 10 g in the head and body simulations, respectively, and were compressed into a smaller set of virtual observation points (VOPs) 24, 25. We designed SMS2 and SMS8 RF shimming and two-spoke pTx pulses based on a Hanning-filtered seven lobes sinc subpulse profile. When using two spokes, the first spoke was placed at the center of Tx k-space and the second was placed at [2; 2; 0] and [3; 3; 0] in unit of m−1 for the body and head simulations, respectively. The second spoke position was chosen so that it laid at a distance approximately equal to 1/FOV of the flip angle excitation, where FOV is equal to 30 cm for the torso (1/0.3 = 3.3 m−1) and 20 cm for the head (1/0.2 = 5 m−1). All pulses were designed to achieve a uniform flip angle of 16°. The repetition time (TR) was fixed to 30 ms for all pulses so that the duty cycle varied depending on the pulse duration (Figs. 2-5). Peak power was limited to 1000 W and 5000 W in the head and torso simulations, respectively. In the head simulation, the interslice distance was 5.6 cm and 1 cm for SMS2 and SMS8, respectively. In the torso simulation, the interslice distance was 20 cm and 2.5 cm for SMS2 and SMS8, respectively. We compared our local SAR-constrained and peak power–constrained pulse design strategy to the Tikhonov-regularized SMS pTx design approach of Wu et al.: (3) Figure 2Open in figure viewerPowerPoint Trade-offs between local SAR, peak power, and excitation fidelity for SMS2 RF shimming (a) and two-spokes (b) pulses in the head at 7T. The flip angle maps on the right are the best excitations that could be obtained with each design method (L, G, P, and A) while satisfying both the power and SAR limits. Pulses were designed using a least-squares objective with a uniform 16° Ernst flip angle target profile and a target phase profile obtained from a magnitude least-squares design (the same target phase was used for all RF shimming pulses, but the RF shimming and two-spoke target phases were different). The interslice distance was 5.6 cm. Blue and red L-curves were obtained by varying the local SAR land global SAR limits, respectively, while simultaneously constraining peak power to 1000 W/channel. The purple L-curves were obtained by varying the peak power limit (no SAR limits). The green L-curves were obtained by varying the total average power by variation of the Tikhonov regularization free parameter as in reference 20 (no SAR limits). The three numbers below flip angle maps indicate the mean (in degrees), standard deviation (in degrees), and root mean square error of the flip angle excitation of all slices (in percent of the target flip angle). Where λ is a free parameter 20. RESULTS The VOP algorithm yielded 2209 and 304 VOPs in the head (5% SAR overestimation) and body (1% SAR overestimation) simulations, respectively. These VOP compression parameters are typical and were chosen because they yielded a reasonable number of VOPs in both the head and the body and led to only minor overestimations of SAR (For a discussion on the relationship between the number of VOPs and the SAR overestimation factor, see references 25 and 34). The average computation times (MATLAB 8 code parallelized on 8 Intel Xeon 2.27 GHz CPUs) for the peak power and local and global SAR constrained two-spoke pulse design in the torso were 8.9 min and 22.5 min for SMS2 and SMS8, respectively. Average computation times in the head were 7.6 min and 7.3 min for SMS2 and SMS8, respectively. Note that the computation times depend on the number of channels, the number of pixels in the optimization mask, the number of VOPs, and the convergence rate, which can vary dramatically depending on the number of binding constraints. In previous study 24, we found that power- and SAR-constrained single slice pTx excitations could be designed in less than 10 s using a dedicated primal-dual algorithm implemented in C++, which is ∼15 times faster than using the fmincon function of MATLAB parallelized on eight CPUs. Therefore, we expect that MLS SMS8 pulse design with two spokes can be performed in <2 min using a C++ implementation similar to that described by Guérin et al. 24. Fig. 1. shows detailed data for a two-spoke MLS pTx pulse designed at 7T and exciting two slices separated by 5.6 cm. The peak voltage (632 V), local SAR (8.19 W/kg), and global SAR (1.93 W/kg) of the total SMS pulse are all within their prescribed limits of 632 V, 10 W/kg, and 3 W/kg, respectively. As expected for these well-separated slices (see Methods), the SAR map of the SMS pulse of Fig. 1 is equal, to a very good approximation, to the sum of the SAR maps of the two-slice excitations. Moreover, because the SAR hotspots of the two-slice excitations occur at different locations, the local SAR of the SMS pulse is smaller than the sum of the local SAR of pulses #1 and #2 ("SAR hopping" between excitations #1 and #2). Figs. 2-5 show L-curves obtained by varying individual constraints of the pulse design of Equation 1. The SMS2 pulses of Fig. 2 are not significantly power-limited and/or SAR-limited, therefore there is no great difference between our SAR-constrained and peak power–constrained approach and the Tikhonov-regularized pulse design strategy of Wu et al. 20. For brain imaging at 7T using the two z-rows eight-channel system shown in Fig. 1. constraining both SAR and peak power is necessary to yield SMS8 pulses that satisfy both the hardware limits and the US Food and Drug Administration (FDA) regulatory SAR limits (Fig. 3). For both SMS2 and SMS8 pulses, there seems to be little difference between control of local SAR and global SAR in the head at 7T. Figure 3Open in figure viewerPowerPoint Trade-offs between local SAR, peak power, and excitation fidelity for SMS8 RF shimming (a) and two-spokes (b) pulses in the head at 7T. The flip angle maps on the right are the best excitations that could be obtained with each design method (L, G, P, and A) while satisfying both the hardware and SAR limits. Pulses were designed using a least-squares objective with a uniform 16° Ernst flip angle target profile and a target phase profile obtained from a magnitude least-squares design (the same target phase was used for all RF shimming pulses, but the RF shimming and two-spoke target phases were different). The interslice distance was 1 cm. The three numbers below flip angle maps indicate the mean (in degrees), standard deviation (in degrees), and root mean square error of the flip angle excitation of all slices (in percent of the target flip angle). In the body at 3T, local SAR and global SAR are not as correlated as in the head, which is a phenomenon that we have described previously 24. Therefore, constraining global SAR does a poorer job at keeping local SAR under control than controlling local SAR explicitly (the blue and red L-curves of Figs. 4 and 5 are significantly different). In the body at 3T, controlling peak power does not allow any control of local SAR: This strategy yields pulses within hardware capabilities but that can clearly violate the FDA local SAR limit of 8 W/kg (Figs. 4 and 5). This phenomenon is much more pronounced for SMS8 pulses (Fig. 5) than for SMS2 pulses (Fig. 4). Therefore, both local SAR and peak power control are needed for high MB factors in the body at 3T. Figure 4Open in figure viewerPowerPoint Trade-offs between local SAR, peak power, and excitation fidelity for SMS2 RF shimming (a) and two-spokes (b) pulses in the body at 3T. The flip angle maps on the right are the best excitations that could be obtained with each design method (L, G, P, and A) while satisfying both the hardware and SAR limits. Pulses were designed using a least-squares objective with a uniform 16° Ernst flip angle target profile and a target phase profile obtained from a magnitude least-squares design (the same target phase was used for all RF shimming pulses, but the RF shimming and two-spoke target phases were different). The interslice distance was 20 cm. The three numbers below flip angle maps indicate the mean (in degrees), standard deviation (in degrees), and root mean square error of the flip angle excitation of all slices (in percent of the target flip angle). Figure 5Open in figure viewerPowerPoint Trade-offs between local SAR, peak power, and excitation fidelity for SMS8 RF shimming (a) and two-spokes (b) pulses in the body at 3T. The flip angle maps on the right are the best excitations that could be obtained with each design method (L, G, P, and A) while satisfying both the hardware and SAR limits. Pulses were designed using a least-squares objective with a uniform 16° Ernst flip angle target profile and a target phase profile obtained from a magnitude least-squares design (the same target phase was used for all RF shimming pulses, but the RF shimming and two-spoke target phases were different). The interslice distance was 2.5 cm. The three numbers below flip angle maps indicate the mean (in degrees), standard deviation (in degrees), and root mean square error of the flip angle excitation of all slices (in percent of the target flip angle). Both in the head at 7T and the body at 3T, control of average power of the total SMS pulse using a Tikhonov regularization (Eq. 3) does a poor job at controlling both SAR and peak power at high MB factors. For the pulses of Figs. 3-5, enforcing the peak power (and to a smaller extend the local SAR limit) with this approach required heavy overregularization of the pulse design problem which, in turn, yielded poor flip angle excitations compared with our joint pTx SMS design with local SAR and peak power constraints. DISCUSSION We described an MLS pTx SMS spokes pulse design strategy with simultaneous control of local SAR, global SAR, and peak power. We showed in electromagnetic simulation of a 3T body coil and a 7T head coil that, even for a relatively small flip angle of 16°, SMS pulses are often SAR-limited and peak power–limited, especially at high MB factors and large duty cycles (for the sinc subpulses and duty cycles studied in this work, only the RF shimming and two-spoke SMS2 pulses in the head at 7T were neither SAR-limited nor peak power–limited). This indicates that pTx SMS pulses should be designed not only using flip angle uniformity metrics but also local SAR and peak power metrics. In this study, simply controlling average RF power 20 yielded pulses with peak power demands that exceeded the hardware capability. This strategy also created local SAR hotspots exceeding the local SAR limit; however, this violation was less pronounced than the peak power violation. Because of the suboptimality of the Tikhonov regularization design strategy with respect to the peak power metric, enforcing the peak power constraint using this strategy required overregularization of the pulse design process, thus yielding poor flip angle excitation profiles that did not achieve the target flip angle. In contrast, explicitly enforcing the peak power and local SAR limits in the pulse design process allowed getting the most out of the hardware system in a way that did not violate the FDA SAR limits. Therefore, this strategy yielded the best flip angle maps under limited local SAR and peak power. These results are in accordance with our findings for non-SMS pTx pulses 24 and extend them to SMS. However, because of the large power demands and SAR of SMS pulses, the benefit of explicitly controlling these quantities in the pulse design process compared with the simpler Tikhonov power regularization approach is greater for SMS than single slice excitations. Because of the quadratic dependence of SAR with RF voltage, one would intuitively expect the SAR of an SMS pulse to be greater than the sum of the SAR created by the individual slice excitations. We have shown that this is not the case, however: When the slices excited simultaneously are well separated, the SAR cross terms between slice excitations are null (Fig. 1.). Therefore, a possible way of controlling SAR in pTx SMS could consist of designing individual slice excitations with some form of SAR control (i.e., without SMS). Such a technique would allow control of the local SAR of the SMS pulse by controlling the local SAR of the individual pulses. It would not be optimal, however, because it would not take into account possible reductions of local SAR obtained by moving the SAR hotspots of the individual slice excitations to different locations ("SAR hopping", see Fig. 1.). The joint pulse design strategy proposed in this study explicitly constrains the SAR of the total SMS pulse and therefore uses "SAR hopping" to reduce the total local SAR. In this sense, this design algorithm is similar to the "SAR hopping" local SAR reduction strategy that we proposed previously for rapid sequential multislice imaging 31. To cope with the high peak power and SAR of multiplexed pTx SMS pulses, one can increase the duration of the RF excitation by applying VERSE to the subpulse sinc profile 12-15. This strategy can be combined with our proposed pulse design approach in order to yield pTx SMS pulse with even lower peak power demands and smaller local SAR hotspots. However, increasing the length of the excitation pulse usually degrades the slice profile quality for off-isocenter slices 35 so that this process should be limited. REFERENCES 1 Larkman DJ, Hajnal JV, Herlihy AH, Coutts GA, Young IR, Ehnholm G. Use of multicoil arrays for separation of signal from multiple slices simultaneously excited. J Magn Reson Imaging 2001; 13: 313– 317. Wiley Online LibraryCASPubMedWeb of Science®Google Scholar 2 Breuer FA, Blaimer M, Heidemann RM, Mueller MF, Griswold MA, Jakob PM. Controlled aliasing in parallel imaging results in higher acceleration (CAIPIRINHA) for multi-slice imaging. Magn Reson Med 2005; 53: 684– 691. Wiley Online LibraryPubMedWeb of Science®Google Scholar 3 Feinberg DA, Moeller S, Smith SM, Auerbach E, Ramanna S, Glasser MF, Miller KL, Ugurbil K, Yacoub E. Multiplexed echo planar imaging for sub-second whole brain FMRI and fast diffusion imaging. PLoS One 2010; 5: e15710. CrossrefCASPubMedWeb of Science®Google Scholar 4 Moeller S, Yacoub E, Olman CA, Auerbach E, Strupp J, Harel N, Uğurbil K. Multiband multislice GE-EPI at 7 Tesla, with 16-fold acceleration using partial parallel imaging with application to high spatial and temporal whole-brain fMRI. Magn Reson Med 2010; 63: 1144– 1153. Wiley Online LibraryCASPubMedWeb of Science®Google Scholar 5 Setsompop K, Gagoski BA, Polimeni JR, Witzel T, Wedeen VJ, Wald LL. Blipped-controlled aliasing in parallel imaging for simultaneous multislice echo planar imaging with reduced g-factor penalty. Magn Reson Med 2012; 67: 1210– 1224. Wiley Online LibraryCASPubMedWeb of Science®Google Scholar 6 Pruessmann KP, Weiger M, Scheidegger MB, Boesiger P. SENSE: sensitivity encoding for fast MRI. Magn Reson Med 1999; 42: 952– 962. Wiley Online LibraryCASPubMedWeb of Science®Google Scholar 7 Griswold MA, Jakob PM, Heidemann RM, Nittka M, Jellus V, Wang J, Kiefer B, Haase A. Generalized autocalibrating partially parallel acquisitions (GRAPPA). Magn Reson Med 2002; 47: 1202– 1210. Wiley Online LibraryPubMedWeb of Science®Google Scholar 8 Sodickson DK, Manning WJ. Simultaneous acquisition of spatial harmonics (SMASH): fast imaging with radiofrequency coil arrays. Magn Reson Med 1997; 38: 591– 603. Wiley Online LibraryCASPubMedWeb of Science®Google Scholar 9 Wong E. optimized phase schedules for minimizing peak RF power in simultaneous multi-slice RF excitation pulses. In Proceedings of the 20th Annual Meeting of ISMRM, Melbourne, Australia, 2012. p. 2209. Google Scholar 10 Auerbach EJ, Xu J, Yacoub E, Moeller S, Uğurbil K. Multiband accelerated spin-echo echo planar imaging with reduced peak RF power using time-shifted RF pulses. Magn Reson Med 2013; 69: 1261– 1267. Wiley Online LibraryPubMedWeb of Science®Google Scholar 11 Pauly J, Nishimura D, Macovski A. A k-space analysis of small-tip-angle excitation. J Magn Reson 1989; 81: 43– 56. CrossrefWeb of Science®Google Scholar 12 Conolly S, Nishimura D, Macovski A, Glover G. Variable-rate selective excitation. J Magn Reson 1988; 78: 440– 458. CrossrefWeb of Science®Google Scholar 13 Hargreaves BA, Cunningham CH, Nishimura DG, Conolly SM. Variable-rate selective excitation for rapid MRI sequences. Magnetic resonance in medicine 2004; 52: 590– 597. Wiley Online LibraryPubMedWeb of Science®Google Scholar 14 Xu D, King KF, Liang ZP. Variable slew-rate spiral design: theory and application to peak B1 amplitude reduction in 2D RF pulse design. Magn Reson Med 2007; 58: 835– 842. Wiley Online LibraryCASPubMedWeb of Science®Google Scholar 15 Lee D, Grissom WA, Lustig M, Kerr AB, Stang PP, Pauly JM. VERSE-guided numerical RF pulse design: a fast method for peak RF power control. Magn Reson Med 2012; 67: 353– 362. Wiley Online LibraryCASPubMedWeb of Science®Google Scholar 16 Norris DG, Koopmans PJ, Boyacioğlu R, Barth M. Power independent of number of slices (PINS) radiofrequency pulses for low-power simultaneous multislice excitation. Magn Reson Med 2011; 66: 1234– 1240. Wiley Online LibraryPubMedWeb of Science®Google Scholar 17 Eichner C, Setsompop K, Koopmans PJ, Lützkendorf R, Norris DG, Turner R, Wald LL, Heidemann RM. Slice accelerated diffusion-weighted imaging at ultra-high field strength. Magn Reson Med 2013; 71: 1518– 1525. Wiley Online LibraryPubMedWeb of Science®Google Scholar 18 Norris DG, Boyacioğlu R, Schulz J, Barth M, Koopmans PJ. Application of PINS radiofrequency pulses to reduce power deposition in RARE/turbo spin echo imaging of the human head. Magn Reson Med 2014; 71: 44– 49. Wiley Online LibraryPubMedWeb of Science®Google Scholar 19 Katscher U, Eggers H, Graesslin I, Mens G, Börnert P. 3D RF Shimming uSing Multi-frequency Excitation. In Proceedings of the 16th Annual Meeting of ISMRM, Toronto, Canada, 2008. p. 1311. Google Scholar 20 Wu X, Schmitter S, Auerbach EJ, Moeller S, Uğurbil K, de Moortele V. Simultaneous multislice multiband parallel radiofrequency excitation with independent slice-specific transmit B1 homogenization. Magn Reson Med 2013; 70: 630– 638. Wiley Online LibraryPubMedWeb of Science®Google Scholar 21 Poser BA, Anderson RJ, Guérin B, Setsompop K, Deng W, Mareyam A, Serano P, Wald LL, Stenger A. Simultaneous multi-slice excitation by parallel transmission. Magn Reson Imaging 2013; 71: 1416– 1427. Web of Science®Google Scholar 22 Cloos M, Boulant N, Luong M, Ferrand G, Giacomini E, Le Bihan D, Amadon A. kT-points: short three-dimensional tailored RF pulses for flip-angle homogenization over an extended volume. Magn Reson Med 2011; 67: 72– 80. Wiley Online LibraryPubMedWeb of Science®Google Scholar 23 Sharma A, Holdsworth S, O'Halloran R, Aboussouan E, Van AT, Maclaren J, Aksoy M, Stenger VA, Bammer R, Grissom WA. kT-PINS RF pulses for low-power field inhomogeneity-compensated multislice excitation. In Proceedings of the 21st Annual Meeting of ISMRM, Salt Lake City, Utah, USA, 2013. p. 73. Google Scholar 24 Guérin B, Gebhardt M, Cauley S, Adalsteinsson E, Wald LL. Local specific absorption rate (SAR), global SAR, transmitter power, and excitation accuracy trade-offs in low flip-angle parallel transmit pulse design. Magn Reson Med 2014; 71: 1446– 1457. Wiley Online LibraryPubMedWeb of Science®Google Scholar 25 Eichfelder G, Gebhardt M. Local specific absorption rate control for parallel transmission by virtual observation points. Magn Reson Med 2011; 66: 1468– 1476. Wiley Online LibraryPubMedWeb of Science®Google Scholar 26 Grissom W, Yip C, Zhang Z, Stenger VA, Fessler JA, Noll DC. Spatial domain method for the design of RF pulses in multicoil parallel excitation. Magn Reson Med 2006; 56: 620– 629. Wiley Online LibraryCASPubMedWeb of Science®Google Scholar 27 Setsompop K, Wald L, Alagappan V, Gagoski B, Adalsteinsson E. Magnitude least squares optimization for parallel radio frequency excitation design demonstrated at 7 Tesla with eight channels. Magn Reson Med 2008; 59: 908– 915. Wiley Online LibraryCASPubMedWeb of Science®Google Scholar 28 Zelinski A. Improvements in magnetic resonance imaging excitation pulse design. Cambridge, MA: Massachusetts Institute of Technology; 2008. Google Scholar 29 Homann H, Graesslin I, Nehrke K, Findeklee C, Dössel O, Börnert P. Specific absorption rate reduction in parallel transmission by k-space adaptive radiofrequency pulse design. Magn Reson Med 2010; 65: 350– 357. Wiley Online LibraryPubMedWeb of Science®Google Scholar 30 Graesslin I, Steiding C, Annighoefer B, Weller J, Biederer S, Brunner D, Homann H, Schweser F, Katscher U, Pruessmann K. Local SAR constrained hotspot reduction by temporal averaging. In Proceedings of the 19th Annual Meeting of ISMRM, Stockholm, Sweden, 2010. p. 4932. Google Scholar 31 Guerin B, Adalsteinsson E, Wald L. local SAR reduction in multi-slice pTx via "SAR hopping" between excitations. In Proceedings of the 20th Annual Meeting of ISMRM, Melbourne, Australia, 2012. p. 642. Google Scholar 32 Lemdiasov RA, Obi AA, Ludwig R. A numerical postprocessing procedure for analyzing radio frequency MRI coils. Concepts Magn Reson Part A Bridg Educ Res 2011; 38A: 133– 147. Wiley Online LibraryWeb of Science®Google Scholar 33 Kozlov M, Turner R. Fast MRI coil analysis based on 3-D electromagnetic and RF circuit co-simulation. J Magn Reson 2009; 200: 147– 152. CrossrefCASPubMedWeb of Science®Google Scholar 34 Lee J, Gebhardt M, Wald LL, Adalsteinsson E. Local SAR in parallel transmission pulse design. Magn Reson Med 2012; 67: 1566– 1578. Wiley Online LibraryCASPubMedWeb of Science®Google Scholar 35 Setsompop K, Cohen-Adad J, Gagoski B, Raij T, Yendiki A, Keil B, Wedeen VJ, Wald LL. Improving diffusion MRI using simultaneous multi-slice echo planar imaging. Neuroimage 2012; 63: 569– 580. CrossrefCASPubMedWeb of Science®Google Scholar Citing Literature Volume73, Issue5May 2015Pages 1946-1953 FiguresReferencesRelatedInformation
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