Velocity selective spin labeling using parallel transmission

Ultra‐high field (UHF) provides improved SNR which greatly benefits SNR starved imaging techniques such as perfusion imaging. However, transmit field (B1+) inhomogeneities commonly observed at UHF hinders the excitation uniformity. Here we show how replacing standard excitation pulses with parallel transmit pulses can improve efficiency of velocity selective labeling.


INTRODUCTION
MRI is intrinsically sensitive to motion, which can be a curse or a blessing. 1Blood flow, for example, can lead to flow artifacts along the phase encoding direction of the image, 2 but it can also be leveraged to create flow-based contrast.In its most rudimentary form, inflow can be used to visualize vascular system.Using a large flip angle (FA) in a slab-selective fast spoiled gradient echo sequence the magnetization of stationary spins is saturated.Blood flowing into the imaging slab, carrying fresh magnetization with it, produces a bright signal contrasted against a dark background.A more advanced strategy is velocity selective labeling (VSL), which uses a combination of RF and gradient pulses to exclusively excite the magnetization of flowing spins. 3SL modules are particularly sensitive to inhomogeneities in the transmit RF (B 1 + ) field.VSL consists of a 90 • tip-down and a 90 • tip-up RF pulse, separated by a bi-polar gradient pair.The bipolar gradients have no effect on the stationary spins.Therefore, the latter pulse reverts the magnetization back to equilibrium.Magnetization flowing at cutoff velocity (V c ) in the direction of the gradients, accumulate a 180 • phase between the two RF pulses.Hence, the second pulse continues to rotate the magnetization down to 180 • instead of returning it back to equilibrium.Consequently, any deviation of the tip-down and tip-up pulses from 90 • due to B 1 + inhomogeneities lead to reduced inversion efficiency.At ultra-high field (UHF) strengths large B 1 + inhomogeneities are commonly observed, even in the human brain, due to the short RF wavelength. 4 Therefore, at 7T, VSL based sequences often produce contrast artifacts and/or quantification errors in peripheral regions of the brain where the B 1 + is low.
Many have sought to mitigate B 1 + inhomogeneities in MRI, such as RF shimming to reshape B 1 + . 5Although these approaches can provide local improvements, it remains challenging to achieve a uniform B 1 + across the whole brain.Instead of addressing the B 1 + field inhomogeneity directly, RF pulses can be designed to create uniform excitations even when B 1 + is not.A classic example of such a pulse is the adiabatic pulse, such as the hyperbolic-secant 6 and more recently frequency offset corrected inversion (FOCI) pulses. 7However, these pulses have long durations and a high specific absorption rate (SAR), limiting their applicability at UHF.Other pulses exploit transmit k-space to create a desired transverse magnetization. 8By visiting a subset of low spatial frequencies in k-space it is possible to create pulses that produce a uniform magnetization.For example, Fast-kz pulses (commonly known as spokes) are capable in exciting a slice along the kz direction while mitigating in-plane B 1 + inhomogeneities. 9However, even with sparsity-enforced Fast-kz pulses, prohibitively long pulse trains are required to create uniform excitations for UHF MRI. 10 Inspired by ideas pioneered in parallel imaging [11][12][13] ; parallel transmission (pTx) was introduced to accelerate in transmit k-space. 14,15Using pTx, it becomes possible to design low SAR pulses with short durations that can produce arbitrary magnetization patterns for an arbitrary B 1 + distribution.Using an eight-channel pTx system, as little as two spokes is needed to create uniform slice-selective excitations in the brain at 7T. 16 Similarly, a sparse distribution of short rectangular pulses at discrete k-space locations (known as k T -points) can be used to create uniform non-selective excitations. 17Although pTx is now gradually finding its way into standard imaging sequences such as gradient recalled echo (GRE)-EPI, 18 MPRAGE, 19 and SPACE, 20 integration into advanced contrast preparation modules such as VSL has yet to be demonstrated.
Although applications utilizing VSL stand to benefit from the increased SNR and parallel imaging performance offered by UHF MRI systems, 21 routine application remains challenging.The high SAR of current B 1 + insensitive methods, utilizing full adiabatic pulse combinations, are impractical when short scan times are required.In this work, we demonstrate the implementation of low SAR B 1 + non-uniformity mitigated VSL using k T -points in an eight-channel pTx setup at 7T.

Velocity selective labeling
The VSL module (Figure 1) implemented used 1.5 ms bi-polar flow-encoding gradients with a 28 ms separation.
To mitigate ΔB 0 effects, refocusing pulses were placed between the tip-down and tip-up pulses. 3The VSL module was then followed with an imaging module consisting of a slice-selective excitation (from here on referred to as the "readout excitation") and 2D EPI readout.Three VSL module configurations were tested: (1) 1.66 ms rectangular tip-down/tip-up pulses using the circularly polarized transmit mode (CP-mode) of the coil (VSL-RECT), (2) 5.12 ms FOCI pulses for the 90 • tip-down/tip-up pulses using the CP-mode of the coil (VSL-FOCI), and (3) using k T -points 17 for the 90 • tip-down/tip-up (VSL-PTX).Following the VSL-RECT preparation, a 3.072 ms sinc was used for readout excitation.Additionally, all module configurations VSL-RECT, VSL-FOCI and VSL-PTX were tested with pTx spokes 9 readout excitations.In all cases adiabatic FOCI pulses (pulse duration = 10.24 ms, CP-mode) were used to refocus the magnetization.

Pulse design
All pTx pulses (k T -points and spokes) were calculated based on the small-tip-angle approximation 8,22 using the spatial domain method 23 with a magnitude least squares optimization approach. 16Tikhonov regularization was used to control total RF power. 23Using the pTx B 1 + maps acquired in the calibration process, both k T -points and spokes pulses were designed with a 1 • FA and linearly scaled to the desired FA.A predefined k-space trajectory targeting low frequency locations in transmit k-space were chosen given the slow varying B 1 + profile. 17on-selective k T -points pulses with a total duration of 2.62 ms (sub-pulse duration = 0.24 ms, eight sub-pulses, gradient blip duration = 0.1 ms) were designed for the tip-down and tip-up 90 • RF pulses in the VSL-PTX module.Two versions of the tip-up pulse were designed and tested.The first approach applied a phase inversion (180 • phase shift) to the tip-down pulse designed.For the second approach, in addition to phase inversion, the tip-down design was time reversed by playing the sub-pulses in reverse order (Figure 1B), ensuring that the tip-up pulse train traverses k-space in a reverse order to the tip-down pulse.For the slice-selective pTx readout excitation at the start of the EPI module, a two-spokes pTx solution (sub-pulse duration = 2 ms, TBWP = 3) was designed.Accuracy of the pulse designs were evaluated using Bloch simulations.

Experimental setup
All experiments were conducted using a 7T whole-body research system (Siemens Healthcare, Erlangen, Germany) equipped with an 8 × 2 kW parallel transmit system, and an 8Tx/32Rx head coil (Nova Medical, Wilmington, MA, USA).All phantom experiments were performed using a custom flow phantom (Figure 2).Refer to Supporting Information Text S1 for construction details.

PTx-calibration
The same set of calibration protocols were used in phantom and in vivo experiments.First, the reference voltage was calibrated to achieve a 90 • FA excitation with CP-mode in the center of the phantom or brain.Subsequently, pTx calibration measurements were acquired.The SA2RAGE 24 (TR = 2400 ms, TE = 0.95 ms, TD1,2 = 5 ms,1705 ms, 4 × 4 × 4 mm 3 , GRAPPA = 2) was used to measure the B 1 + field using all eight transmit channels in the CP-mode.In combination, a 2D interleaved GRE sequence (TR = 300 ms, TE = 3 ms, 4 × 4 × 4 mm 3 , GRAPPA = 3) that acquires relative sensitivity maps for each transmit channel was used to generate a full set of absolute B 1 + maps.In addition, GRE images with two different TEs were collected for B 0 mapping (TR = 1420 ms, TE = 11/12 ms, 2 × 2 × 2 mm 3 , GRAPPA = 3).Total calibration acquisition time was approximately 6 min.

Flow profile mapping
A phase-contrast GRE 25 sequence (TR = 28.55 ms, TE = 10.8 ms, 0.5 × 0.5 × 4 mm 3 , VENC = 5 cm/s, GRAPPA = 3) was used to measure the through-plane flow profile in the tubes.The flowrate in the phantom was set to a mean rate of approximately 2.4 cm/s.The corresponding flow profile measurement was used in the Bloch simulations described in Section 2.6.

Simulations
Bloch simulations were performed to evaluate different pulse configurations in the VSL module.The effect of flow was incorporated by dynamically updating the spatial coordinates of each isochromat for every time step in the simulation (time step = 10 us, 100 isochromat per voxel).This allowed modeling of displacements less than one voxel.Off-resonance sensitivity of the VSL configurations were evaluated over a physiologically representative flow range of +/−6 cm/s with V c = 2 cm/s.Simulations were run using the B 1 + , B 0 and flow velocity maps measured in the physical flow phantom.Longitudinal and transverse magnetization response was recorded for each pulse configuration.As a gold standard, the magnetization map was also simulated using ideal B 1 + .The normalized RMS error (NRMSE) across multiple slices including both flow and static regions was calculated between the expected transverse magnetization (S) and the gold standard magnetization (T) maps based on the following formula: In addition, a sweep of varying flow encoding gradients (axial direction, 0 to 40 ms*mT/m, increments of 2 ms*mT/m) was used to profile the encoding behavior of each VSL module.
The average transverse magnetization in each tube was calculated.

Phantom experiments
For all velocity selective measurements, the flowrate in the flow phantom was fixed to a constant mean rate of approximately 2.4 cm/s.The VSL module behavior was verified by taking multiple measurements with varying flow encoding gradients (axial direction, 0 to 40 ms*mT/m, increments of 2 ms*mT/m).The following sequence parameters were used: TR = 10s, TE = 23 ms, 1 × 1 × 5 mm 3 , GRAPPA = 3.Additionally, a reference scan was acquired in each configuration with flow encoding gradient amplitude set to zero.Eight repeated measurements were averaged and normalized using the reference scans for each configuration.Due to phantom geometry, some turbulence is expected from the 90 • bends at both ends of the phantom.Further upstream, a laminar flow profile is expected to form (Figure 2C).Therefore, when quantifying the labeling efficiency, signals were averaged across each tube.

In vivo experiments
To evaluate the fidelity of the four combinations under in vivo conditions, the brain of a healthy volunteer was scanned at 7T. Prior to the scan, the subject provided written informed consent of the project ethics which was approved by the local human research ethics committee in accordance with national guidelines.To mimic the effect of flow throughout the brain a 180 • phase shift is applied to the second RF pulse, effectively setting V c to zero.For brevity we will refer to this as the tip-down-tip-down (DD) configuration, whereas the standard configuration will be referred to as the tip-down-tip-up (DU).Comparing DU and DD configurations without vascular crushing or background suppression elements in the sequence allowed the assessment of pulse performance throughout the whole brain, instead of isolated regions of major vessels.Slices were collected in axial, sagittal and coronal orientation.All other sequence parameters were the same as those used for in vitro (TR = 10s, TE = 23 ms, 1 × 1 × 5 mm 3 , GRAPPA = 3).

RESULTS
Figure 3 shows the simulated VSL performance, in terms of longitudinal magnetization, as a function of off-resonance.The long pulse duration of tip-down/up in VSL-FOCI led to severe off-resonance sensitivity observed as tilted inversion bands as a function of B0, indicating the labeling is shifted away from the intended V c .Phase inverted and time reversed pTx solutions were relatively insensitive to B0 variations up to +/-150 Hz where this inverted range remained relatively vertical.Above 150 Hz, the lines blur and curve, indicating significant deviations from the target flowrate V c .Enhanced B0 robustness was obtained using shorter pTx pulses with reduced gradient blip-durations.
Figure 4A shows the estimated FA distribution generated by the VSL preparation when V c was matched to the measured mean flowrate.The B 1 + non-uniformities in the tip-down and tip-up pulses significantly impacts the VS fidelity in CP-mode (NRMSE FA = 0.763).By replacing the hard pulses with adiabatic pulses an improvement in magnetization in the peripheral tubes was observed (NRMSE FA = 0.163).Our pTx solution mitigated majority of the B 1 + artifacts within the flow regions.Simulations indicated that simple phase inversion to implement the tip-up pulse was an improvement compared to CP-mode.However, substantial residual magnetization (NRMSE FA = 0.485) remained, particularly in the static spin region because of non-commutative pTx pulses at higher FA.Therefore, as might be expected based on the time symmetry of the design problem, the time reversed pTx pulse solution reduced the NRMSE FA significantly to 0.061.Predicted signal maps are shown in Figure 4B.A distinct B 1 + artifact was observed using VSL-RECT with CP sinc readout excitation, with central brightening and signal drop around the peripheral regions (NRMSE |Mxy| = 0.489).The VSL-RECT with spokes readout improves signal uniformity within the static spin region.However, reduced labeling fidelity is still observed in the outer tubes with a NRMSE |Mxy| of 0.473.The VSL-FOCI with pTx spokes readout excitation improved signal uniformity notably (NRMSE |Mxy| = 0.073).Using the pTx pulse combination improves the inversion in all flowing spin regions.However, the effects of the residual magnetization produced by the phase inverted tip-up pTx pulse degrades the overall contrast uniformity (NRMSE |Mxy| = 0.176).Significantly improved signal and contrast uniformity across the slice was demonstrated using the time reversed pTx pulse (NRMSE |Mxy| = 0.047).Additionally, signal uniformity was maintained across multiple slices (slab NRMSE |Mxy| = 0.051).A comparison of measured signal maps of a single axial slice is shown in Figure 4C.
Figure 4D,E shows the signal intensity as a function of flow encoding gradient moment in each of the four tubes.It is expected that the flow encoding when maximum inversion occurs (approximately 18 ms* mT/m) should correspond to the average flow rate (approximately 2.4 cm/s) measured in the phantom (Figure 2C).In both simulation and experiment, the profile of the center tube (red) produces the expected sinc response, 26 because the reference voltage was calibrated in the center of the phantom.However, the VSL-RECT configuration fails to invert the flowing spins in the outer three tubes (blue, green, yellow) where B 1 + is low.Comparing the first and second panel in Figure 4E, exciting the slice using pTx spokes pulses did not improve labeling efficiency, highlighting that the observed contrast artifacts were caused by the tip-down/up pulses in the VSL module (as expected).The use of adiabatic FOCI pulses as tip-down/tip-up mitigated the B 1 + artifacts in the peripheral tubes, however at the cost of 40% higher RF power output (averaged over the full protocol duration) compared to VSL-RECT.On the other hand, our VSL-PTX solution achieved inversion in all tubes with only 10% higher time averaged RF power output compared to the VSL-RECT configuration (21% lower than VSL-FOCI).
Figure 5A shows images obtained with the DU and DD pulses.VSL-RECT DD shows reduced inversion uniformity in peripheral regions with insufficient B 1 + .Whereas signal lost in the periphery was recovered using VSL-FOCI and VSL-PTX.This can be seen with the improved uniformity in the ratio maps (Figure 5C).However, VSL-FOCI showed high sensitivity to off-resonance effects observed as dark bands as opposed to VSL-PTX.In addition, VSL-PTX achieved uniform VSL excitation with 44% lower RF power output.

DISCUSSION
In this paper, we evaluated pTx based tip-down and tip-up pulses in a VSL module.Our tailored pTx pulses exhibited high robustness against B 1 + , ΔB0 and flow effects.Using pTx pulses in the VSL module improved fidelity and labeling efficiency across the whole ROI, provided that the tip-up pulse is phase-and time-reversed.Phase inversion alone fails to return the static spin magnetization uniformly back to equilibrium (Figure 4A).Within the small-tip-angle regime where longitudinal magnetization is assumed to be constant, rotations generated by composite pulses are commutative.For large tip angles, the individual sub-pulses are no longer commutable.As a result, time-reversed k T -point pulses were implemented to satisfy the time symmetry of rotational Bloch operations. 27A significant reduction in residual transverse magnetization was achieved.Furthermore, we evaluated the flow-rate selective specificity.The signal amplitude in each of the tubes was recorded using varying amounts of gradient encoding.Using VSL-RECT in combination with a spokes-based readout excitation only improved the SNR in areas of low B 1 + , but did not improve the inversion fidelity.This highlights the importance of optimized RF solutions for use in VSL modules.Nevertheless, the occurrence of the first full inversion point varied slightly among tubes, even when using the VSL-FOCI and VSL-PTX implementations.This may be attributed to small differences in the effective flowrate between tubes due to turbulence formed by the right-angle bends in the phantom.Flow maps measured using phase-contrast GRE confirmed the presence of turbulent flow in the center and right tube (Figure 3C).
Looking beyond velocity selectivity, we observed that a combination of both k T -points and spoke pulses produce a magnetization map with higher uniformity throughout the slice across multiple slices (Figure 4C).This was also observed in vivo (Figure 5) where we compared VSL modules with a DU and DD pulse configuration to evaluate the effective inversion fidelity.Similar to the phantom experiments, both VSL-FOCI and VSL-PTX achieved a higher degree of signal and contrast fidelity in areas where the CP-mode produces a low B 1 + .Given the effective V c is zero, the DU and DD should produce identical images except for a 180 • phase difference.Therefore, we note that the subtraction of DU and DD images is not expected to produce a perfusion map.
The advantage of VSL-PTX over VSL-FOCI becomes clear when considering the pulse durations and their relative SAR contribution.As seen in vivo (Figure 5A,C), VSL-FOCI falls short in producing a uniform inversion, particularly above the nasal cavity and lower cerebellum region.Additionally, the longer adiabatic pulses (5.12 ms) were more sensitive to off-resonance effects.To improve uniformity across the whole brain would require higher amplitude and frequency modulation to satisfy adiabatic conditions.Even with the current pulse configuration the SAR for the adiabatic solution is already 24% higher than the pTx solution.Making the adiabatic pulses shorter would increase the SAR further, making fast imaging even more difficult.On the other hand, the much shorter 2.62 ms k T -points pulses provide reduced sensitivity to off-resonance effects, especially because it allows for a significant reduction in the total duration of the VSL module.Interestingly, total duration of the k T -points solution could be reduced even further, without SAR increase, by reducing the gradient blip-durations from 0.1 to 0.05 ms with a total reduction of 0.35 ms while the gradient pulses (max slew rate = 156mT/m/ms, and max gradient = 3.13mT/m) stay within the gradient coil limits.If desired, the trajectory and number of points in k-space may also be further optimized.Further SAR efficiency improvement can be expected by incorporating SAR penalties by means of virtual observation points 28 into the pulse design, implementing SAR "hopping", 29 and replacing the pair of refocusing pulses with a dedicated pTx solution.
The current implementation used a 2D EPI readout, which requires tailored designs for each slice.To accelerate the offline pulse design workflow and acquisition a 3D EPI readout [30][31][32] may be a viable alternative as the same non-selective pTx pulse design can be utilized for both the VSL module tip-down/up pulses and readout excitations.It is also noted, to generate perfusion maps, the pulses must be built into a comprehensive ASL sequence.This requires implementation of additional sequence elements such as vascular crushing and background suppression. 26n addition, timings and gradient moments must be tuned in consideration of physiological flow behaviors.These are all necessary future work to evaluate pTx based VSL solutions in ASL applications.
Sequence diagram of the VSL preparation module and imaging module for four combinations including VSL-RECT (CP readout excitation), VSL-RECT (Spokes readout excitation), VSL-FOCI, and VSL-PTX."RO" stands for readout.Double refocusing adiabatic pulses in all configurations are applied in CP-mode.(B) Example k T -point pulse solution for one of eight RF transmit channels and the three gradient axes.RF sub-pulse train and gradient blips designed for two versions of the tip-up pulse: phase inverted RF pulse and phase inverted RF pulse plus time reversal where the sub-pulse train and k-space trajectory are reversed.Gradient blips are color-coded (matching Figure 1C) to show the corresponding segment of the trajectory.(C) The pre-defined trajectory used to move between points in transmit k-space.
A) Custom made flow phantom positioned in the head coil (Nova Medical).Arrows indicate the flow direction in the tubes.(B) The water tank and pump control system are set up in the MR console room.Inflow and outflow tubes are fed via the waveguide.(C) Measured flow map of corresponding slice used in simulations acquired with phase contrast GRE.Water in left and bottom tubes flow in +z direction, whereas flow in center and right tubes flow in -z direction.Cross-sectional flow profile of all tubes.

F I G U R E 3
Simulated performance of the VSL module configurations to off-resonance effects ranging from +250 to −250 Hz with nominal B 1 + = 1.Longitudinal magnetization response shown for varying flowrates.The first VSL-PTX subplot uses a 2.62 ms duration k T -point pulse for tip-down/up excitation whereas the second uses 1.79 ms k T -point pulses within the VSL module.Note that laminar flow effects were not considered in these simulations.

F I G U R E 4
Comparisons of expected magnetization and measured signal maps between different VS pulse configurations including VSL-RECT, VSL-FOCI, VSL-PTX (phase inverted tip-up), and VSL-PTX (phase inverted and time reversed tip-up).All magnetization maps were simulated with the measured flow profile where (A) shows estimated FA map of VSL prep module only and (B) shows estimated signal map of the VS prep module followed by the readout excitation (RO exc.).(C) The reconstructed image of the phantom showing same slice with matched gradient encoding to the mean flow rate set in the phantom.Note that, in contrast to the simulations, the measured images have the receive sensitivity bias superimposed.The plots show the normalized signal response of the four tubes for varying levels of gradient encoding in four configurations: (1) VSL-RECT with CP sinc pulse readout excitation and (2) VSL-RECT with spokes readout excitation; (3) VSL-FOCI and (4) VSL-PTX time reversed.(D) Predicted signal response modeled with the measured flow profile.(E) Normalized average signal across each tube corresponding to the colored mask regions shown in (C) over eight repeated measurements conducted on the flow phantom.

F
Measurement showing the fidelity of four VSL module configurations in vivo.Each row shows images collected using the same non-selective VSL pulse design.Columns labeled DU show the tip-down-tip-up configuration.Columns labeled DD show the tip-down-tip-down configuration.The DD implementation mimics the 180 • phase shift to induce inversion.(B) Axial phase images showing the 180 • phase difference between DU and DD configurations.(C) The ratio of the DD/DU images.