1 INTRODUCTION

Parallel transmission (pTx) of RF pulses through independently controlled channels can help to overcome B1 nonuniformity seen in the head at 7 T,1, 2 particularly when tailored pulses are used.3 Tailored pulse design incorporates the measured transmit sensitivities () of each pTx channel, achieving a homogeneous flip angle across specified slices or regions. For optimal tailored pulse performance, the measured distributions must match those present at the time of pulse playout. However, channels’ electromagnetic fields (including ) and their interference patterns depend critically upon the object being imaged (i.e., the coil load), including its position, geometry, and composition.4-6

Geometrical and compositional differences between human subjects are partly addressed in alternative, nontailored approaches such as universal pulses (UPs),7, 8 SmartPulse,9 and fast online-customized pTx pulses.10 Intersubject robustness is achieved by designing a UP (offline) to minimize error across a small database of representative subjects. An underlying assumption is that the range in head geometry and composition across human subjects is relatively constrained, implying that distributions are similarly constrained. The designed pulse (a minimum error solution for excitation over multiple distributions) is therefore assumed to work fairly well for any individual subject without the need for mapping. Plug-and-play usability of UPs in pTx has led to the method’s growing popularity.

However, the intersubject robustness of UPs comes at a cost to flip-angle uniformity. Tailored pulses typically yield lower normalized RMS error (nRMSE) of flip angle compared with UPs (7% vs 11% in Gras et al7). Additionally, the database approach is problematic in cases in which an individual is an outlier with respect to anatomies represented in the database. Moreover, these methods do not address the dependence of on load position, leading to unpredictable pulse performance in cases of different initial subject positioning11 and/or within-scan head motion.12-14 The former is often overlooked, whereas the latter is commonly reported.15 Large head movements (exceeding 20 mm/degree) often occur among certain clinical populations,16, 17 elderly,18 and pediatric19, 20 subjects. Because flip angle (and therefore the acquired signal) depends on , displacements of approximately 5° have been found to cause an excitation error of 12%–19% (percent of target flip angle) when using pTx at 7 T,12 with larger movements causing larger flip angle–related artifacts.

A few approaches have been proposed to correct motion-related RF field changes. Faraji-Dana et al partially overcame motion-related effects on the (receive) B1 field by simply reorienting coils’ measured sensitivity maps using a Euclidean transformation.21 Similarly, Wallace et al used radial basis functions to extrapolate channel sensitivities to voxel locations outside of the head, providing sensitivity information for all voxels in the FOV, regardless of head position.22 Extrapolated maps were used for retrospective correction. Neither approach considered dynamic motion-related field changes (e.g., changes in coil loading, shifting susceptibility gradients in tissue), as their effects were deemed minimal at 3 T. However, interactions between channels’ highly nonuniform transmit fields at 7 T,23 especially with pTx, indicate that dynamic motion-induced field changes cannot be overlooked. In contrast with these approaches, data-driven approaches inherently incorporate these changes.

Motion artifacts are often addressed through retrospective correction22, 24-27; however, this is problematic for several reasons. First, the issues described previously cannot be corrected retrospectively without motion-resolved maps, which are not available. Second, channels’ electric fields depend on the same factors, including load position. Specific absorption rate (SAR) distribution and associated tissue heating are therefore also sensitive to motion, and are especially so in pTx due to constructive interference between channels’ electric fields.28-30 Peak local SAR can exceed safety limits when head motion occurs in pTx simulations29—a critical issue that cannot be addressed retrospectively. Conservatively bounded SAR estimates may be used, but this can prevent optimal imaging performance by limiting the RF power.2, 11, 31 In this study, the effect of motion on flip angle is the primary focus.

It is therefore desirable to overcome the motion dependence of tailored pTx pulse performance, and to do so using prospective techniques. Real-time pTx pulse design has been proposed as a solution, in which channels’ complex coefficients are continuously updated to counteract motion-induced sensitivity changes. Multispoke pTx pulses can be designed in less than 0.5 seconds,32 whereas 2D spatially selective spiral pulses can be estimated in about 9 ms using deep neural networks.33 With motion detection (e.g., Refs 22, 25, 34, and 35), channel updates could be determined by instantaneous head position, retaining flip-angle uniformity in cases of arbitrary and/or extreme motion. However, the required updates to channel coefficients depend on the motion-related field changes. Because real-time (i.e., motion-resolved) maps are not measurable, this requires that the relationship between head position and distribution to be characterized.

Deep convolutional neural networks have previously been used to estimate (non-pTx) distributions. In Wu et al,36 high-quality maps were predicted from reconstructed T1-weighted images, removing the need for mapping, while still allowing retrospective correction of related artifacts in quantitative MRI. This approach was limited to postprocessing; prediction quality deteriorated when was predicted directly from undersampled images. Abbasi-Rad et al used a convolutional neural network to reconstruct from a localizer scan for the purpose of SAR reduction through pulse scaling based on slice-wise magnitude; however, prediction quality was dependent on head position.37

In this work, we train a system of conditional generative adversarial networks38 to predict pTx distributions (referred to as B1 maps) following simulated head motion, given the initial B1 maps at the centered position as input. If used in conjunction with motion detection, this would constitute motion-resolved B1-map estimation, and therefore permit real-time tailored pulse design. B1-map prediction quality is assessed by comparison with ground-truth (simulation output) B1 maps following motion. Furthermore, flip-angle distributions of multispoke pTx pulses designed using network-predicted B1 maps are compared with those produced by tailored pulses designed using the initial subject-specific B1 maps alone. Finally, we also observe peak 10-g averaged local SAR for both pulses following motion.

2 METHODS 2.1 Simulations and data

Dizzy, Billie, Duke, and Ella (Figure 1A–D) of the Virtual Population39 (IT’IS, Zurich, Switzerland) were simulated with a generic 8-channel pTx coil in Sim4Life (ZMT, Zurich, Switzerland). Each model was simulated at one central, and 32 off-center, positions. Off-center positions included rightward 2, 4, 5, 10, and 20 mm, posterior 2, 4, 5, and 10 mm, and all possible combinations thereof. These 29 positions are hereafter referred to as the R-P grid (Figure 1E). In addition, yaw 5°, 10°, and 15° positions were also simulated (Figure 1F). The Duke model was scaled to 90% of the original size, as the body and coil models intersected at some positions when the model was full-sized. To ensure consistent voxelization (and therefore consistent partial volume effects) in the body model across all simulated positions, the coil array was displaced rather than the body model. Simulations included the head, neck and shoulders,40 and were run at 295 MHz following coil tuning to this frequency. Simulation results were normalized to an accepted power of 1 W per channel beyond the input port to the coil elements, to override imperfections in coil matching and any positional dependencies. The simulations were manually checked for input impedance and reflection coefficient as well as field smoothness across positions.

Simulation model setup. (A–D) The four body models used in Sim4Life simulations. Ella and Duke (C, D) were used to generate training data for networks, Billie (B) was used for network validation and testing, and Dizzy (A) was used for testing only. Testing (including pulse design) was conducted at the six indicated slice locations. Validation slices were offset by about 4 mm from these, but within the same axial range. Slices in orange were also used for specific absorption rate (SAR) evaluations. All axial slices within the dashed slab were used for training. (E) Positions simulated for the R-P grid. The origin of the central position is indicated with a red circle, whereas all other positions’ origins are indicated with black dots. Axial displacements were all possible combinations of rightward (R) 0, 2, 4, 5, 10, and 20 mm and posterior (P) 0, 2, 4, 5, and 10 mm. (F) Yaw rotations were 5°, 10°, and 15°. The head at the central position (gray isosurface) and most extreme displaced position (yellow isosurface) are shown

Channels’ 3D B1, electric field, current density, and SAR distributions were masked to exclude background (air) voxels and exported to MATLAB (The MathWorks, Natick, MA). To incorporate interactions between channels for local SAR evaluations, 10g-averaged Q-matrices were calculated.28, 41, 42 Elements of the 8 × 8 Q-matrices were (1)where is the tissue mass density (kg/m3) in voxel ; is the complex current density (A/m2); is the complex electric field (V/m); , and are the three Cartesian axes; and are transmit channel indices; and denotes Hermitian transpose.

B1 maps from 51 slices spanning a mid-axial slab with a thickness of 9 cm from the Duke and Ella body models (Figure 1C,D) were prepared for network training by interpolating to 256 × 256 in-plane resolution. The same preprocessing was applied to the Billie and Dizzy data, but at only six slice locations (Figure 1A,B). Magnitude and phase data were separated and normalized between 0 and 1, where 1 corresponds to the maximum magnitude across all channels, slices, and body models, and to 2π for phase. Random offsets were applied to phase maps so that the phase wrap boundary did not occur at the same location across slices. B1 maps were input to networks as individual axial slices with size 256 × 256 × 8, where the third dimension is channels. Corresponding B1-map slices before (input) and after (ground truth) a given displacement formed the networks’ input-target pairs. Note that inputs are not necessarily at the centered position (explained later in Section 2.2).

2.2 Neural networks and network training

Models were implemented in TensorFlow 2.343 using Python 3.7. Network architecture is summarized in Figure 2. Except where specified, network hyperparameters were the same as those used in the Pix2Pix conditional generative adversarial network.44 The generators were U-Net45 models with eight convolutional (encoding) and eight deconvolutional (decoding) layers linking the input and output (predicted) B1 maps, each followed by rectified linear unit activation layers. Filters were 4 × 4 for magnitude and 8 × 8 for phase. Although comprehensive hyperparameter optimization was beyond the scope of this project, during initial testing it was found that phase networks benefited from the large receptive field of 8 × 8 filters. Conversely, magnitude networks generated smoother maps when more filters were used. To avoid increasing the number of trainable parameters, filters were smaller for magnitude. The number of filters (initially 128 for magnitude, and 64 for phase) increased to a maximum of 1024 (512 for phase) for the middle layers, and stride size was 2. Filters were split into eight groups to facilitate simultaneous processing of all pTx channels. For phase, batch normalization was applied at all layers except the first convolution layer. For magnitude, removing batch normalization resulted in a smoother training curve and higher-quality estimated maps. Skip connections joined each convolution layer to the symmetric deconvolution layer for network stability. The network was regularized through dropout layers following each of the first three deconvolution layers (rate = 0.5).

Conditional generative adversarial network (cGAN) architecture. Generators were U-Nets with eight convolution and eight deconvolution layers, each with rectified linear unit (ReLU) activation. Discriminators consisted of five convolutional layers with ReLU activation. Square matrix size and number of filters (initially 64 for phase networks) are indicated beneath the layers. Convolution stride was 2 except where specified. Skip connections are shown with arrows. Dropout was applied at indicated layers (dark blue). Batch normalization (red) was used for phase networks, but not for magnitude networks. Filters for phase networks were 8 × 8. Magnitude networks used double the number of filters, with filter size = 4 × 4

In contrast to encoder–decoder models that typically rely on minimizing L1 loss between predicted and target images, generative adversarial networks include an additional loss term, which helps to reduce blurring often seen with L1 loss alone.44 This is provided through a second convolutional neural network—the discriminator—which is trained to distinguish between generator-predicted and ground-truth distributions. The input B1 maps, concatenated with either ground-truth or generator-predicted B1 maps, served as input to the discriminators, which consisted of five convolution layers. The discriminators used leaky rectified linear unit activation layers (ɑ = 0.3) as recommended in Radford et al.46 Filter size was the same as that for the generators, and convolution stride was 2 except for the final two layers, where it was 1. A single 2D distribution of probability (entropy) values was output.

The overall conditional generative adversarial network loss function can be expressed as (2)where denotes the generator; is the discriminator; and (set to 100) is a scaling parameter acting on the L1-norm between generator-predicted and ground-truth maps. The first term can be further described as (3)where B1gt are the ground-truth displaced B1 maps; B1predicted are the generator-predicted displaced B1-maps; and B1initial are the pre-displacement B1 maps (network input).

The effect of head motion on B1 depends on the displacement type (i.e., direction, magnitude).12, 13 Because data-driven approaches assume that all input-target pairs share a common underlying mapping, separate networks were trained for different displacement types (e.g., rightward vs posterior). Head motion was discretized into large (5 mm) and small (2 mm) displacements in rightward (R) and posterior (P) directions to cover the R-P grid. Additional networks were trained for 5° yaw rotation. Separate networks were trained for magnitude and phase, yielding a total of 10 networks.

The Duke and Ella data were used for training. All available relative displacements were included. For example, to train the R5 mm network, such as (input)–(target) pairs included (R0, P0 mm)–(R5, P0 mm); (R5, P0 mm)–(R10, P0 mm); (R5, P2 mm)–(R10, P2 mm). This yielded a training data set of 1020 unique slices for rightward and leftward networks, and 1224 for each posterior network. The yaw network training database was smaller (306 slices).

The Adam47 optimizer was used to train models for 60 epochs. Learning rate was critical during initial testing, so learning rates within the range 5e−5 to 1e−3 were tested. The default value of 2e−4 converged most effectively and was therefore used for all networks. Network weights were saved at the epoch, which yielded the lowest total error across the validation data set (the Billie data) as a form of early stopping to help prevent network overfitting. Networks took approximately 16 hours to train with a batch size of 1 using a standard PC with NVIDIA GeForce GTX 1050 Ti.

2.3 Network evaluation and cascading

Networks were tested using the Billie and Dizzy data at six slice locations (Figure 1A). For Billie, different slices were used compared with those used for early stopping (Dizzy was not involved in the training process at all). Like training, testing was conducted for all available examples of each displacement, yielding test data sets of between 6 and 72 slices. In addition to the positions listed in section 2.1, Billie and Dizzy models were simulated at three combined yaw-rightward positions to test performance for motion involving both rotation and translation. Because networks were only trained for five displacements but evaluated at 35 positions, networks were cascaded where necessary. Starting with the center position’s B1 maps as input, generators were run sequentially, with the output of one generator used as input to the next, until the desired evaluation position was reached. For example, R5 mm, R5 mm, and P2 mm networks were cascaded for evaluation at the (R10, P2 mm) position. Finally, the Billie model was also simulated at inferior 5, 10, and 15 mm to investigate error for through-plane motion.

Predicted B1 maps were exported to MATLAB. Voxels with < 1% of the maximum magnitude were smoothed with a Gaussian kernel. Corresponding magnitude and phase network outputs were subsequently combined to form complex predicted maps (B1predicted).

The B1predicted quality was assessed through voxel-wise correlation (using MATLAB’s corrcoef function) and prediction error between predicted and ground-truth maps at each position. These values were compared with error and correlation following head motion (i.e., between the two simulated maps). Calculations were performed on the tissue-masked region, with the outermost two voxels excluded to avoid artificial amplification of error due to partially filled voxels. Prediction error for magnitude and phase distributions were assessed through nRMSE and L1 norm, respectively, as follows: (4) (5)where is ; and is the number of voxels in a slice, indexed by . Motion-induced error was calculated analogously, but substituting B1initial for B1predicted in Equations 4 and 5. 2.4 Pulse design and analysis

Outputs from the R-P grid positions were further processed to assess whether predicted maps were of sufficient quality to be used for tailored pTx pulse design. Five-spoke excitation pulses were designed using a small tip-angle spatial domain method,3, 48, 49 and two approaches were compared in terms of their performance following motion within the R-P grid. A schematic of the process is shown in Figure 3. First, a conventional tailored pulse (pulseinitial) was designed using the subject-specific B1 maps at the initial position (B1initial). A uniform magnitude target excitation profile (target flip angle = 70°) was specified for pulseinitial. Pulse coefficients were optimized iteratively to minimize magnitude error, whereas the profile’s phase was relaxed.50 The resultant complex profile was used as the target profile for a second pulse (pulsere-designed), which was designed without phase relaxation (because magnitude and phase distributions need to be consistent across positions to ensure data consistency for motion occurring mid-acquisition). Pulsere-designed was designed using the network-output B1predicted (the proposed approach).

Outline of the testing workflow. Simulated maps from the center position are input to the first trained generator. Generators were trained for small displacements but can be run sequentially (cascaded) until the desired off-central (displaced) position is reached in evaluations. Prediction quality is assessed by normalized RMS error (nRMSE) and voxel-wise correlation with respect to the ground-truth (simulation output) displaced map. In addition, pulses designed using the initial map are compared with those designed using predicted maps, in terms of their excitation profiles following head motion Both pulses (pulseinitial and pulsere-designed) were subsequently evaluated using the ground-truth B1 maps at the displaced position (B1gt) to quantify motion-induced effects on the conventional approach, and improvement provided by the proposed method. Their flip-angle distributions were compared with that of pulseinitial without motion in terms of nRMSE, expressed as percent target flip angle as follows: (6)where is flip angle without motion; is that following motion (with either pulseinitial or pulsere-designed); and is the target flip angle. The nRMSE for pulseinitial without motion (i.e., the “gold standard”) was also calculated by substituting for in Equation 6.

Peak local SAR (psSAR) of both pulses was also evaluated using the 10-g averaged Q-matrices at each position. Because psSAR sensitivity to motion has been reported to exhibit no slice dependence,29 SAR was evaluated at four target imaging slices (out of the six used for pulse design) (Figure 1A).

3 RESULTS 3.1 B1 prediction quality

B1 maps were predicted by networks in about 14 ms using the same PC as used for training. Example B1 maps, motion-induced error, and prediction error are shown for a 5 mm displacement in Figure 4. Motion-induced error (averaged across channels) for this example was 15.1% (magnitude) and 4.9° (phase), whereas mean prediction error was 3.2% (magnitude) and 3.5° (phase).

Example magnitude and phase maps and error following a rightward displacement of 5 mm (slice location = 2). Motion-induced (M-I) error shows difference between simulation-output B1 at the centered and displaced positions (B1initial and B1gt, respectively). Prediction (P) error shows the difference between simulation-output B1gt and generator-predicted B1 (B1predicted). Motion-induced error (averaged across channels) for this example was 15.1% (magnitude) and 4.9° (phase), whereas mean prediction error was 3.2% (magnitude) and 3.5° (phase). Abbreviation: pTx, parallel transmission

Figure 5 shows a summary of error and correlation coefficient for magnitude and phase at each evaluated displacement (averaged across Dizzy and Billie models, slices, channels, and initial positions). Position dependence of prediction quality was minimal compared with motion-related error, as seen by the reduced gradient with respect to displacement norm in all cases. Dizzy and Billie models yielded very similar prediction quality (Supporting Information Figure S1).

Error (nRMSE for magnitude, L1 norm for phase) and correlation coefficient (ρ) shown for magnitude and phase, averaged over Dizzy and Billie body models, channels, slices, and initial positions for each evaluated displacement. Translational displacements (the R-P grid) are shown in the large panels, while rotations (yaw) and combined rotation-translations (yaw plus a 4-mm translation) are shown in the smaller panels below (for the purpose of the x-axis, the amount of yaw rotation is treated as magnitude displacement; for example, yaw 5° plus 4-mm translation is shown at x = 6). The effects of motion are shown in purple, while network-related prediction error is shown in yellow. The SD is shown as shaded regions for magnitude but is omitted for phase for clarity, as values were similar

Mean motion-induced magnitude error scaled linearly with displacement magnitude at about 3% per millimeter (or 3.2% per degree of rotation), compared with 0.36% per millimeter (0.27% per degree) for prediction error. Prediction error was lower than motion-related error in 99.8% of translation, and 90% of rotation evaluations. Figure 6A shows B1 magnitude nRMSE for magnitude for all slices and channels for 10 example displacements. Motion caused a worst-case magnitude error of 117% following a displacement of R20, P10 mm, whereas maximum prediction error was 33% (at the y15°, R4 mm position). Worst-case prediction error from the R-P grid was lower (20% at the R20, P10 mm position).

B1 error (nRMSE for magnitude [A], L1 norm for phase [B]) for all evaluations with the Billie model following 10 example displacements. Motion-related error is shown in purple, while error for predicted maps is in yellow. Asterisks indicate the number of network cascades required for evaluation. The blue-shaded region shows the maximum observed prediction error across all 35 displacements for the Billie model (consistent across panels)

Example magnitude correlations are shown in Figure 7A. The lowest observed correlation coefficient between B1initial and B1gt magnitudes was 0.79 following a y15°, R4 mm displacement. Correlation between B1predicted and B1gt did not fall below 0.96.

Example voxel-wise correlations between B1initial and B1gt (left) and B1predicted and B1gt (right) for nine example displacements. The pTx channels are indicated by color. The x and y axes range between 0 and 3 µT for magnitude (A), and 0 and 2π for phase (B)

Motion-induced error and correlation were observed to be slice-dependent and channel-dependent (i.e., the error depended on the displacement relative to each channel’s location, as expected). The B1predicted quality was similar across channels, as demonstrated by the strong correlation across all channels in Figure 7A. However, prediction error was somewhat slice-dependent, with the most inferior slice locations yielding the highest prediction errors (slice information not shown).

Phase error for 10 example displacements are shown in Figure 6B. For phase, maximum observed prediction error (57°) was similar to maximum motion-related error (55°). These worst cases arose in the Dizzy model; for the Billie model, maximum prediction error (29.4°) was lower than that caused by motion (44.2°). Furthermore, prediction error was lower than motion-induced error for phase in 68% and 66% of translation and rotation evaluations, respectively (including both models).

Yaw rotation caused substantially higher error than axial translations; for the R-P grid, maximum prediction-related and motion-related errors were 19.8° and 34.7°, respectively. Mean phase prediction error was less position-dependent than motion-related error, with axial translations causing error of approximately 0.9° per millimeter displacement, compared with 0.4° per millimeter in predicted maps. For displacements including rotation, analogous gradients were 2° and 0.2° per degree of yaw, respectively.

Mean phase correlation coefficient between predicted and ground-truth maps was higher than (or very similar to) that between initial and ground-truth maps for all displacements. Phase correlation examples are shown in Figure 7B. Correlation coefficient between B1predicted and B1gt exceeded that between B1predicted and B1initial in 69% of cases.

3.2 Parallel-transmit pulse performance

Subsequent analyses were conducted using the Billie model with the R-P grid data only. Five-spokes pTx pulses designed using B1initial (pulseinitial) yielded uniform flip-angle profiles (mean nRMSE ~1%) without motion. However as expected, uniformity was lost following axial translation. Pulses were about 7.7 ms long.

Figure 8 shows that flip-angle nRMSE for pulseinitial was strongly position-dependent, reaching a maximum of 76% following a displacement of R20, P5 mm. Conversely, pulses redesigned using B1predicted (pulseredesigned) produced much improved flip-angle profiles when evaluated at the displaced position, yielding nRMSE of 14% for the same displacement. Maximum pulseredesigned nRMSE was 17% (at the R2, P10 mm position), whereas this error value was exceeded by pulseinitial (i.e., without any correction) after displacements of just ≥ 5 mm. The largest errors occurred in inferior slice locations for both pulses (slice information not shown). Maximum motion-related error in the excitation profile’s phase (110.4°) was reduced by 7.8° when using pulseredesigned.

Excitation profile results for five-spoke pTx pulses following head motion. (A) Mean flip-angle nRMSE (above) and phase RMSE (below) for excitation profiles, averaged over slices and initial positions for each evaluated displacement. Excitation pulses were five-spoke pTx pulses designed using either the initial position (pulseinitial) or predicted (pulseredesigned) B1 maps. The SD is shown as shaded regions for magnitude but is omitted for phase for clarity, as values were similar. (B) Example flip-angle profiles produced by pulseinitial at the initial position, by pulseinitial at the displaced position, and by pulseredesigned at the displaced position

Figure 8B shows flip-angle profiles for both pulses following several example displacements. Supporting Information Figure S2A also shows flip-angle nRMSE for nine example displacements. It should be noted that flip-angle uniformity for pulseredesigned could be further improved by including phase relaxation in the design (as was done for pulseinitial); however, this would permit excitation phase to vary throughout the scan, causing reconstruction inconsistencies.

3.3 Cascading

The B1predicted quality remained high when networks were cascaded multiple times; however, there was a weak linear relationship between prediction error and motion magnitude. To investigate the impact of cascading on prediction quality, we ran secondary analyses for displacements of R0, P10 mm, R-2, P10 mm, and R-5, P10 mm using only the P2 mm network for the posterior component. Running the 2 mm network five times (i.e., four cascades) led to approximate average increases in magnitude and phase error of 1.2% and 1.2°, respectively, compared with running the 5 mm network twice (one cascade). There was also reduced flip-angle uniformity compared with using the 5 mm network. Nevertheless, Figure 9 shows that motion-induced error was appreciably reduced using either approach.

Effect of cascading the P2 mm network four times compared with cascading the P5 mm network once for evaluation at the R5, P10 mm position (along with the R5 mm network for the rightward component). (A) Example motion-induced (M-I) error and prediction (P) error for both cascade approaches for magnitude (left) and phase (right). Error shown below maps is nRMSE (%) for magnitude and L1 norm (°) for phase, both averaged over channels. (B) Comparison of flip-angle profiles and nRMSE for pulses designed using initial (left) and predicted maps using both cascade regimes (center and middle). Target flip angle is 70°

3.4 Specific absorption rate

In addition to flip angle, SAR was also evaluated for the R-P grid positions. Following motion, psSAR produced by pulseredesigned was lower than that of pulse