Near real-time parallel-transmit pulse design
Emre Kopanoglu1

1School of Psychology / CUBRIC, Cardiff University, Cardiff, United Kingdom


With many MRI scans lasting several minutes, patient motion is a common problem, especially with uncooperative subjects such as paediatric patients or patients with dementia or Parkinson’s. Realizing the finer-resolution that higher field strengths offer through the availability of increased SNR necessitates even longer scans, exacerbating this problem. While prospective motion correction techniques can compensate for motion at lower field strengths, such techniques are not directly applicable at higher field strengths, when more complicated parallel-transmit pulses are used. This study proposes a pulse design technique that can design multi-spoke and simultaneous multi-slice parallel-transmit pulses in less than one second, while adhering to peak-voltage limits, local and global SAR.


This study proposes a parallel-transmit pulse-design method that can design pulses in near real-time, with the long term goal of prospective motion correction at UHF. Initial results show three-spoke three-slice SMS pulses can be designed in 0.7 seconds.

Many imaging protocols, specifically at ultra-high-field (UHF) suffer from long acquisition times with individual protocols exceeding 20min1. Patient motion might become unavoidable especially with longer scans or less cooperative patients, which makes sedation common practice in paediatric imaging2-5, or for patients with Parkinson’s6 or dementia7. However, sedation is invasive and can cause adverse effects2-4. While prospective motion correction techniques8,9 can be used to compensate for motion at lower fields, such calculations may not be directly applied at UHF with parallel-transmit pulses. To compensate for the inhomogeneity artifacts caused by the shorter wavelength at higher fields, parallel-transmit (pTx) pulses have been used for single-10-15 and simultaneous-multi-slice excitation16-22, with local SAR16 and temperature constraints18,21. However, the complexity of parallel-transmit pulse-design increases computation times to beyond feasible for prospective motion correction. This study aims to reduce pulse-design computation times to near real-time to allow prospective motion correction.


With slice-/slab-selection being the most common type of excitation, and fast pulse-design being the main goal, small-tip-angle spoke-trajectories were prescribed as they allow separation of spoke-selection and slice-selection. This reduces the size of the computation domain for the former, and the latter can be precomputed.

  • Slice-selection: A library of unit flip-angle slice-selection pulse envelopes and gradients were precomputed23. By i) temporally stretching pulses, or ii) using variable-rate-selective-excitation (VERSE24), the library was populated for a range of peak-voltage and energy values.
  • Spoke-selection: Spokes were selected and pulse-weights were designed by adapting the Matching-Pursuit-guided-Conjugate-Gradient25 (MPgCG) algorithm to pTx. While selecting the nth-spoke, pulse-weights were optimized via CG for the previously selected spokes and the candidate spoke. After selecting a new spoke, pulse-weights were re-optimized for all spokes with CG, where the phase of the target profile was relaxed to improve results. Figure 1 and Ref25 outline the algorithm.
  • System and safety limits: To reduce computational cost, Virtual Observation Points were used26. When the same envelopes are used for each channel on any spoke, SAR calculation reduces to i) finding the self- and cross-terms of pulse-weights across channels at each VoP for that spoke, ii) multiplying with spoke envelope energy, iii) repeating (and summing SAR) over spokes. After local and global SAR and peak-voltages were calculated for each spoke, the envelopes and gradients were replaced (as necessary) using the library to satisfy limits i) simultaneously, or ii) sequentially (first: system limits, second: safety limits; may yield different envelopes for each spoke).

Simulations were made in Matlab (Mathworks Inc. Natick, MA, USA) on a quad-core PC with Intel i7-6700 CPU and 32GB RAM, using 8-channel B1-maps for the abdomen (resolution:83x58), SAR VoPs (local and global) and system characteristics published by the ISMRM for the RF pulse-design challenge22,27. Pulses were designed for different number of i) spokes, ii) slices (single-, 3-, 5-, 7-slices), iii) transmit-coils, iv) candidate spokes (default: 11x11) and v) VoPs. Also, computation times for different SAR-management approaches summarized above were compared.

Results and Discussion

All pulse-design times reported in this section include selecting spokes, optimizing channel pulse-weights, replacing envelopes to satisfy local and global SAR and peak-voltage limits, and writing the outputs to a scanner-recognized file; and were averaged over 100 pulses designed with the same parameters.

With the proposed method, pulse-design times are 0.02 seconds for a single-spoke, 0.24 seconds for three-spokes (Figure 2a) and slightly below a second for a 6-spoke pulse (Figure 2b). Pulse-design times vary quadratically with the number of spokes and linearly with the number of simultaneously excited slices, coils, candidate spokes, and (weakly with) VoPs (Figure 2b-f). As a lookup table is used, computations times are not affected significantly by which approach the system and safety limits are satisfied (Figure 2a).

Figure 3 shows a single-slice 3-spoke pulse, which was designed in 0.26 seconds, and its simulated excitation profile. Figure 4 shows a 3-slice 3-spoke SMS-pulse, which was designed in 0.7 seconds. Figure 5 shows the method can efficiently design pulses for arbitrarily defined target profiles as well. No difference in root-mean-squared-error was observed for Figures 3-5 when more candidate spokes were used.

In practice, the time that passes after acquiring B1maps and before applying the next sequence would also include a one-off B1-map processing and computing the candidate spokes, which took 0.41 and 0.17 seconds, respectively (100runs).


A method was proposed that can design SMS pTx pulses in less than a second. Future work includes incorporating B0 off-resonance, real-time field measurements from a field-camera and motion-tracking information for prospective motion correction with real-time pulse redesign.


The author would like to thank Arcan Erturk and the ISMRM for making the simulation data available online.


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Figure 1: The pulse-design algorithm of MPgCG-pTx. In run-time, spoke locations are selected and the channel pulse-weights are optimized. Then, peak-voltages and SAR are compared with system and safety limits (simultaneous mode shown here). A library of pulses with varying peak-voltage and SAR levels are pre-computed before pulse-design as these do not depend on spoke locations or pulse-weights. The envelopes of each spoke are replaced with entries from the library as needed, and all outputs are written to a file recognized by the scanner.

Figure 2: Pulse-design times (mean and standard deviation across 100 runs per case) are reported. (a) The pulse-design times are independent of if VERSE or temporal stretching is used, and whether peak-voltages and SAR are investigated sequentially (seq.) or simultaneously (sim.). (b-f) Pulse-design times increase quadratically with number of spokes (b), linearly with the number of simultaneously excited slices (c), the number of coils used for excitation (d), number of candidate spokes evaluated (e). Pulse-design times also have a weak linear dependence on the number of SAR VoPs evaluated (f). Defaults: 3-spokes, single-slice, 8-coils, 121-candidate spokes, 47 VoPs.

Figure 3: Single-slice excitation pulse-design for the abdomen. (a) Designed three-spoke pulse has 6.8ms duration and yields an RMSE of 1.2%. The quadrature mode pulse is 2.8ms long and yields an RMSE of 19.9%. (b) The pulse was designed, adjusted to satisfy safety and system limits (reported values are ratios with respect to the limits) and written to a file recognized by the scanner in 0.26 seconds. (c) Pulse envelopes were first replaced as necessary (with envelopes from the library) to satisfy maximum voltage limit, and then all were replaced to satisfy SAR limits. Hence, the third spoke has different Gz and duration.

Figure 4: Simultaneous-multi-slice excitation pulse-design for the abdomen. (a) Designed three-spoke pulse reduces maximum RMSE across slices to 1.25%, compared to 22.8% of the quadrature excitation pulse (duration: 4.9ms) (b) Three-spoke pulses was designed, adjusted to satisfy safety and system limits (reported values: ratios w.r.t. the limits) and written to a file recognized by the scanner in 0.7 seconds. (c) All envelopes were replaced simultaneously to satisfy safety and system limits, leading to the pulse shape and duration being the same across spokes. VERSE’d pulses were used to reduce SAR.

Figure 5: An SMS pTx pulse was designed for dissimilar and non-smooth target profiles across slices. (a) Target excitation profile and simulated excitation profile of the designed pulse. (b) 5-spoke 4-slice SMS pTx pulse.

Proc. Intl. Soc. Mag. Reson. Med. 26 (2018)