Replication of the bSTAR sequence and open‐source implementation

The reproducibility of scientific reports is crucial to advancing human knowledge. This paper is a summary of our experience in replicating a balanced SSFP half‐radial dual‐echo imaging technique (bSTAR) using open‐source frameworks as a response to the 2023 ISMRM “repeat it with me” Challenge.


INTRODUCTION
The reproducibility of scientific reports is crucial to advancing human knowledge.Due to its growing importance in computational research, the ISMRM has hosted two past reproducible research challenges (organized by the Reproducible Research Study Group in 2019 1 and 2020 2 ) and has a current 2023 ISMRM Challenge titled "Repeat it With Me: Reproducibility Team Challenge." 3his paper is a summary of our experience in replicating bSTAR imaging 4,5 using open-source frameworks as a response to the 2023 ISMRM Challenge.
The bSTAR technique has been proposed for non-electrocardiogram (ECG)-triggered breath-held 4 and free-breathing 5 thoracic imaging with an extremely short TR at 1.5T and has been recently demonstrated at 0.55T. 6he bSTAR sequence consists of a 3D half-radial dual-echo balanced SSFP (bSSFP) readout in combination with a non-selective hard RF pulse to achieve minimal TR.To minimize eddy currents caused by large jumps in k-space, the bSTAR technique employs smooth k-space trajectories including an Archimedean spiral pattern, 4,7,8 a wobbling Archimedean spiral pole (WASP) pattern, 5 and an adapted spiral phyllotaxis (SP) pattern. 5,9,10he bSTAR technique is suitable for various applications at low field strengths.For example, it is especially attractive for lung parenchyma imaging at low field due to prolonged transverse relaxation times. 11The half-radial bSSFP readout provides an advantage over a full-radial bSSFP readout in reducing concomitant fields, which are inversely proportional to field strength (B 0 ) and scale quadratically with gradient amplitude.For a trapezoid lobe designed with a fixed maximum gradient amplitude, the accumulated concomitant field phase is proportional to the duration of a trapezoid lobe 12 ; thus, a shorter readout that achieves the same spatial resolution is advantageous at low field.This versatility of the bSTAR technique provides a strong motivation to USC group (N.G.L. and K.S.N.) to initiate this replication study.
In this work, we replicate breath-held bSTAR and self-gated free-breathing bSTAR for thoracic imaging at 0.55T using vendor neutral open-source frameworks to enable code sharing across different institutions, vendors, and scanner software versions.We used the Pulseq framework 13 for pulse sequence implementation, and Berkeley Advanced Reconstruction Toolbox (BART) for image reconstruction. 14We demonstrate our implementation of the bSTAR sequence on a Siemens hardware platform (Numaris4 VE11S) and interested readers can adapt this implementation to different vendors or platforms.The open-source implementation of bSTAR imaging using Pulseq and BART, denoted open-source bSTAR, is compared to the original author's bSTAR imaging, denoted original bSTAR.6][17][18] We believe this is the best way to describe details to researchers who are less familiar with pulse sequence programming.Since readers may be new to the Pulseq framework, essential basics of Pulseq are introduced as well.

Pulse sequence
The bSTAR sequence consists of a non-selective hard RF pulse, one bipolar gradient on each gradient axis, one analog-to-digital converter (ADC) window, and hardware time delays.A detailed pulse sequence diagram implemented in the Pulseq framework is illustrated in Figure 1.Implementation details are in Appendix A.
A free-running non-ECG-triggered bSTAR sequence was implemented with three different sampling patterns that provide interleaved smooth k-space trajectories: an Archimedean spiral pattern, 4 a WASP pattern, 5 and an SP pattern. 5Each 3D trajectory in a sampling pattern is parameterized by a pair of azimuthal angle () and polar angle () in the spherical coordinate system.
The phase encoding, readout, and slice directions (denoted PE, RO, and SL, respectively) define the three axes of a right-handed logical coordinate system.The polar angle is measured from the RO direction to the PE-SL plane and the azimuthal angle is measured from the SL direction to the PE-RO plane.Rotating a gradient along the RO direction into any arbitrary direction is achieved by multiplying two right-handed rotation matrices sequentially: (1) apply a rotation matrix that rotates a vector about the PE direction by  (polar angle), and (2) apply a rotation matrix that rotates a vector about the RO direction by  (azimuthal angle).A graphical illustration of two steps and the definitions of right-handed rotation matrices are shown in Figure 2.
Pulseq provides a Cartesian coordinate system, referred to as Pulseq logical x, y, and z axes.We interpret Pulseq logical axes ("x," "y," "z") as vendor's logical axes (RO, PE, SL) using the "old/compat" option in the "Ori-entationMapping" parameter of a Pulseq interpreter to comply with the vendor's coordinate transformation from the logical coordinate system (PE, RO, SL) to the physical coordinate system (X, Y, Z).

Imaging system
All imaging experiments were performed on a whole-body 0.55T scanner (prototype MAGNETOM Aera; Siemens Detailed pulse sequence diagram for bSTAR imaging implemented in the open-source Pulseq framework.The bSTAR sequence consists of two sequence blocks (each comprising different events): Block 1 (rf, and delayTE) and Block 2 (adc, gx_bipolar, gy_bipolar, gz_bipolar, and delayTR).User-defined parameters are rf_length, base_resolution, bandwidth, and gradient_factor.The duration of an ADC window (adc_duration) is calculated based on the dwell time with oversampling (real_dwell_time).The shorted ramp time to reach the system's maximum gradient strength using the system's maximum slew rate is rounded to (i.e., to the nearest number greater than or equal to) a multiple of gradRasterTime (10 μs) and is set to the ramp time of a trapezoid lobe (ramp_time).The maximum gradient amplitude is controlled by gradient_factor (e.g., a gradient factor of 1 uses the system's maximum gradient strength).The duration of an ADC window is divided by 2, rounded to a multiple of gradRasterTime (10 μs), and set to the duration of a trapezoid lobe (total_time).A single, base bipolar gradient event is created by combining a positive trapezoid event with a negative trapezoid event.An ADC event (adc) requires a hardware time delay, adcDeadTime, at the beginning and at the end of the event.adcDeadTime is inserted at the beginning and at the end of a bipolar gradient event since the duration of a bipolar gradient event is greater than or equal to the duration of an ADC window (adc_duration).Half the time difference between the duration of a bipolar gradient shape and adc_duration is rounded to a multiple of 1 μs (shift_adc) and is set to the delay field of a bipolar gradient event to place an ADC window symmetric around the center of a bipolar gradient shape.ADC sample points are in the centers of time raster steps, where edges of time raster steps are indicated as short bars in ADC.An RF pulse event (rf) requires two (system-specific) hardware time delays: rfDeadTime and rfRingdownTime.
Healthineers, Erlangen, Germany) with gradients capable of 45 mT/m amplitude and 200 T/m/s slew rate.A six-element body coil (anterior) and six elements from an 18-element spine coil (posterior) were used for signal reception.

Trajectory measurements
K-space trajectories along the +X, −X, +Y, −Y, +Z, and −Z physical axes were measured with Duyn's method 19 for original bSTAR (implemented in Siemens's IDEA programming language) and with a recently proposed method by Zhao et al. 20 for open-source bSTAR using a 14-cm diameter spherical ball phantom placed at gradient isocenter.Assuming that the measured k-space trajectory scales linearly with the peak gradient amplitude, arbitrarily oriented 3D radial half-spokes were synthesized by a linear combination of the measured k-space trajectories on three physical axes. 4,21The measurement and correction of B 0 eddy currents 22 were not performed in this study.Note that we used a different trajectory measurement technique for open-source bSTAR, explained in Appendix B.

Imaging parameters for the bSTAR sequence
For both phantom and human experiments, the default vendor-calibrated shim setting (i.e., tune-up mode) Illustration of rotating a vector in the readout (RO) direction into an arbitrary orientation in a right-handed logical coordinate system (PE, RO, SL).All rotation matrices are right-handed.An arbitrary orientation is parameterized by a pair of azimuthal angle () and polar angle ().A starting vector is always placed on the readout direction.The first step is to apply a rotation matrix that rotates a vector about the PE direction (first direction) by .The second step is to apply a rotation matrix that rotates a vector about the RO direction (second direction) by .
was used with the following imaging parameters: FOV = 34 × 34 × 34 cm, twofold readout oversampling, TE1/TE2/TR = 0.13/1.17/1.38 ms, 200 μs hard RF pulse, flip angle = 25 • , bandwidth= 1929 Hz/pixel, 1.61 mm nominal isotropic resolution based on the diameter of k-space coverage, and 288 samples (576 with oversampling) per half-radial (dual-echo) projection.The (α/2-TR/2) preparation 23 followed by a train of 100 dummy TRs with a constant flip angle was used prior to the data acquisition to accelerate the transition into the steady-state.The ramp time and duration of a trapezoid lobe, the duration of an ADC window, and spatial resolution were 140/520/1036.8/1.61, which were perfectly matched with the values displayed in the original bSTAR pulse sequence.The time delay between the end of an RF pulse shape and the beginning of a bipolar gradient shape was 30 μs, which was identical to the time delay Δt 1 (=30 μs) reported in Ref. 5. The time delay between the end of a bipolar gradient shape and the beginning of the next RF pulse shape was 110 μs, which was identical to the time delay Δt 2 (=110 μs) reported in Ref. 5 and identical to the value shown in the original bSTAR pulse sequence (TR_ delay).The following parameters were selected in the Siemens Pulseq interpreter: Imaging plane at isocenter, sagittal orientation (A ≫ P) to place the RO direction along the SI direction, 2D mode, and "old/compat" option under "OrientationMapping."

Phantom experiments
An accredited American College of Radiology (ACR) structural phantom 24 was scanned with WASP and SP patterns to reproduce Figure 3

Human experiments
Three healthy volunteers (one male and two females) were scanned under a protocol approved by our institutional review board after providing written informed consent.Both breath-held original bSTAR and open-source bSTAR imaging during end-expiration were performed in a back-to-back manner for two volunteers and in a

Image reconstruction
Raw data were converted from vendor proprietary format to the ISMRMRD format 25 and read in MATLAB R2022b (MathWorks, Natick, MA).BART commands were called within MATLAB on a laptop PC equipped with one 2.30 GHz eight-core Intel i7-11800H processor and 128 GB of random-access memory.
Image reconstruction was performed with parallel imaging and compressed sensing with  1 -wavelet regularization using the pics command of the BART toolbox.Density compensation factors were computed with Ref. 27.We utilized the parameterized fast iterative shrinkage thresholding algorithm (Para-FISTA) 28 which reduces the oscillatory behavior of the fast iterative shrinkage thresholding algorithm (FISTA) 29 during the convergence.This was implemented with modifications to the BART source code.Each echo dataset was reconstructed separately, and complex images from two echoes were added to result in echo combined images.The reconstruction took ∼60 min for 30 Para-FISTA iterations with a fixed regularization parameter of 1e-4.
A parameter called recon_interp_factor was defined to control reconstruction resolution.This was achieved by scaling normalized k-space trajectories ([−0.5, 0.5] * size of each dimension) by traj_scale_factor: traj_scale_factor = ceil(recon_ matrix_size/recon_interp_factor); All datasets were reconstructed with recon_matrix_ size = [360 360 360] and recon_interp_ factor = 1.06, resulting in an interpolated reconstruction resolution of 1.52 mm from a nominal resolution of 1.61 mm. Figure 4 replicates Figure 4 of Ref. 5 using an ACR phantom.Echo combined images are shown.WASP patterns with 88 and 89 interleaves did not create noticeable eddy current artifacts, demonstrating its flexibility in the design of 3D radial trajectory patterns.The SP pattern with the number of interleaves equal to one of the Fibonacci sequence (e.g., 89) provides good image quality as expected.However, when a non-Fibonacci number of interleaves is selected (e.g., 88), the SP pattern becomes non-smooth and severely degrades image quality due to eddy currents caused by large jumps in k-space.The image artifacts due to eddy currents at this scanner (0.55T prototype MAGNETOM Aera, Siemens Healthineers) are not identical to those shown in Ref. 5 (1.5T MAGNETOM Avanto-Fit, Siemens Healthineers).The eddy current artifacts at this scanner rather resemble a geometric distortion caused by trajectory errors.

RESULTS
Figure 5 and Video S1 show the exemplary bSTAR images of volunteer 1 acquired during a single 50-s end-expiratory breath-hold.Images generated using data from the first echo and second echo as well as echo combined images are shown.Images reconstructed from the second echo show noticeable artifacts along the AP direction (i.e., Y physical axis), which could be attributed to B 0 eddy currents generated during the acquisition of the first echo.Banding artifacts are not visible within the FOV of interest (thoracic area).Echo combined images show improved SNR with reduced geometric distortion.
Figure 6 and Video S2 compare echo combined images of volunteer 1 acquired on day 1 with open-source bSTAR against images of volunteer 1 acquired on day 2 with original bSTAR.Each technique acquired data separately with its own pulse sequence (Pulseq vs. IDEA) and performed image reconstruction with different methods for selecting a regularization parameter (fixed regularization vs. data-driven Bayesian shrinkage).Density compensation factors were estimated by Ref. 30 for open-source bSTAR and by the Voronoi method 31 for original bSTAR.A CSM estimation strategy could be different as well.Note that images are not perfectly registered because each dataset was acquired on a different day.Different slices showing similar pulmonary vasculature were selected.Despite the differences in methodology, open-source bSTAR provides adequate SNR, spatial resolution, level of artifacts, and conspicuity of pulmonary vessels comparable to original bSTAR.

DISCUSSION
We have successfully replicated bSTAR lung imaging at 0.55T using two open-source frameworks: (1) Pulseq for a pulse sequence and (2) the BART toolbox for image reconstruction.Full replication of a research method solely relying on information described in research papers is unfortunately rare in research, but our success gives greater confidence that a research methodology can be indeed replicated as described.
An immediate question that one may ask is "would it have been possible without direct interaction/collaboration with original authors?".In an ideal world, the answer would be yes, and all publications would include enough detail to enable "arms-length" replication.However, in this study, we found that there are some important details that require interaction for full replication, such as the specific image filtering method, and the respiratory signal estimation method for self-gated free-breathing bSTAR using the WASP pattern.Even if full details are provided, the replicating group must have sufficient expertise in pulse sequence design and image reconstruction to faithfully reproduce the advertised methodology.Interaction with the original authors is of course necessary when making head-to-head comparisons with the original authors implementation.

F I G U R E 6
Head-to-head comparison between open-source bSTAR and original bSTAR.Coronal (A and C) and axial (B and D) views are shown for open-source bSTAR (left column) and original bSTAR (right column).Note that images are not registered because a dataset for each technique was acquired on a different day from the same volunteer (volunteer 1, 39/M).Each technique acquired a dataset using its own pulse sequence (Pulseq vs. IDEA) and performed image reconstruction with its own reconstruction pipeline.Despite the differences in methodology, open-source bSTAR provides image quality comparable to original bSTAR.No spatial filtering was applied on images from both techniques.A movie that pans through only coronal slices is provided in Video S2.
We found Pulseq to be an excellent open-source framework for fast prototyping a pulse sequence.However, it is important to realize that images acquired with pulse sequences written in Pulseq are not identical to those acquired with vendor product pulse sequences or those written in a vendor provided programming environment.They become close to each other (not 100% identical considering subtle differences in image reconstruction) only when all details in pulse sequence design are perfectly matched.For bSTAR imaging, it was very fortunate that the bSSFP kernel was very simple to implement.One limitation of Pulseq is that Pulseq does not provide full capabilities that vendor proprietary programming languages can provide.For example, adding an additional user-selectable box to locate an inversion pulse is not possible without modifying the Pulseq interpreter source code substantially, which is beyond the capability of normal Pulseq users.
The BART toolbox provides a rich set of MRI reconstruction algorithms.We greatly benefit from BART's FISTA implementation when modifying FISTA to Para-FISTA.Without BART, developing a reconstruction algorithm from scratch in a middle-level language (e.g., C/C++) would have been a daunting task.It is important to note that having basic knowledge of C/C++ to comprehend the BART source code and mathematical skills (e.g., convex optimization) are essential when implementing new algorithms in BART.Although the BART toolbox is a great open-source framework for fast prototyping new reconstruction algorithms, the pics command currently supports only single GPU (version 8.0.0).Its limited multi-GPU support may limit widespread use of BART among researchers handling multi-dimensional non-Cartesian datasets.
There are several limitations of this work: (1) both acquisition and image reconstruction were implemented in open-source frameworks, but open-source bSTAR to date has only been tested at one center; and (2) open-source bSTAR has been demonstrated only with limited sample size.We plan to address these limitations in future studies.

CONCLUSIONS
We have successfully replicated the bSTAR technique using open-source frameworks, and replicated figures shown in the published literature 4,5 with comparable quality.This study also demonstrates the power of open-source frameworks, especially Pulseq, because designing a pulse sequence in a vendor proprietary environment requires expertise and tremendous effort.
start and end only at time points that are multiples of blockDurationRaster (e.g., 10 μs for Siemens).
Hardware time delays are imposed on RF and ADC events.For RF events, two hardware time delays are required.The one imposed at the beginning of an RF event is known as rfDeadTime, and the other imposed at the end of an RF event is known as rfRingdownTime.For ADC events, a hardware time delay, known as adcDeadTime, is imposed on both ends of the ADC event.These delays are vendor and hardware platform dependent.Specifically, a non-zero value of adcDeadTime is required for Siemens (e.g., 10 μs), and for other vendors the sequence designer might need to use different dead times before and after the ADC event.Note that the required hardware time delays only apply to RF and ADC events.Events of different type can be played during the period of a required hardware time delay.

A.2.5. Block 2: Base bipolar gradient (g_bipolar)
Only arbitrary gradient events and trapezoid gradient events are supported in the current version (1.4.1) of a file specification.Thus, a bipolar trapezoid gradient event should be designed as an arbitrary gradient event.In this subsection, we focus on creating the gradient shape of a bipolar gradient event along the readout direction.
A simple way to design a bipolar gradient event using the mr toolbox is described as follows.where type indicates the type of a gradient event ("trap" for trapezoid gradients or "grad" for arbitrary gradients), channel indicates the designated gradient axis ("x," "y," or "z"), amplitude is the amplitude of a gradient event in Hz/m, area and flatArea are the entire area and plateau area of a trapezoid gradient in Hz/m⋅sec, respectively, and delay is the delay before starting the gradient event in seconds.Second, a negative trapezoid event (g_negative) is created by scaling g_positive with −1 using the scaleGrad.mfunction and setting its delay to the duration of a positive trapezoid event: g_negative = mr.scaleGrad(g_positive,-1); Duyn's method at 0.55T, a substantial amount of a concomitant field-induced phase could be created at off-center slices when a large gradient amplitude is played along the slice-selection direction.These spatially varying phase errors cause bias in the estimation of measured k-space trajectories.We used the method developed by Zhao et al. 20 because it is more robust to concomitant fields.Specifically, (1) a slice at isocenter is used so that concomitant fields are minimized; and (2) a linear phase slope in the excited slice is estimated with global least-squares fitting using all spatially resolved voxels that are affected by a different amount of concomitant fields.This weighted fitting reduces bias in the estimation of k-space trajectories.After comparing image quality of the second echo images obtained with Duyn's method and Zhao's method (not shown), Zhao's method was chosen because it reduced artifacts along the AP direction.

F I G U R E 3
Replication of Figure 3 of Ref. 4 using an ACR phantom.Coronal (A and D), sagittal (B and E), and axial (C and F) views are shown for the first echo (top row) and the second echo (bottom row).The spiral phyllotaxis pattern using 31 150 half-radial projections with 89 interleaves was used to minimize eddy currents.The images reconstructed from the second echo show subtle, but enhanced artifacts (e.g., smearing artifacts near the boundaries) compared to those reconstructed from the first echo (orange arrows).F I G U R E 4 Replication of Figure 4 of Ref. 5 using an ACR phantom.A comparison between bSSFP images acquired with bSTAR with WASP patterns and bSTAR with SP patterns.Coronal (A, C, E, G) and sagittal (B, D, F, H) views of echo combined images are shown.Both WASP patterns with 89 and 88 interleaves did not create noticeable eddy current artifacts.Since a SP pattern with a non-Fibonacci number of interleaves is known to create non-smooth trajectories which consequently cause large eddy currents, images reconstructed from the SP pattern with 88 interleaves contain image artifacts as expected.The eddy current artifacts resemble a geometric distortion caused by trajectory errors.

F
I G U R E 5Exemplary open-source bSTAR images of volunteer 1 (39/M) acquired during one 50-s end-expiratory breath-hold.Sagittal (A), coronal (D), and axial (G) views of images reconstructed from the first echo (Echo 1).Sagittal (B), coronal (E), and axial (H) views of images reconstructed from the second echo (Echo 2).Sagittal (C), coronal (F), and axial (I) views of echo combined images (Combined).Images reconstructed from the second echo show noticeable artifacts (red arrows), which could be attributed to eddy currents created during the acquisition of the first echo.Banding artifacts (blue arrows) are located far away from the FOV of interest (thoracic area).Echo combined images show improved SNR with less noticeable geometric distortion contributed by the second echo.A movie that pans through all slices is provided in Video S1. different day for one volunteer.Different trajectory patterns were used: (1) volunteer 1 (39/M) and volunteer 2 (27/F): breath-hold duration = 23.5 s and WASP pattern with 17 000 half-radial projections with 4 interleaves, (2) volunteer 3 (26/F): breath-hold duration = 20.3s and WASP pattern with 15 000 half-radial projections with 4 interleaves.For volunteer 1, 50-s breath-held open-source bSTAR imaging during end-expiration was additionally performed with the SP pattern using 39 961 half-radial projections with 89 interleaves to assess the image quality of bSTAR without radial undersampling artifacts.A direct comparison between open-source bSTAR and original bSTAR was demonstrated only on volunteer 1 because original bSTAR has applied spatial filtering on reconstructed images except volunteer 1.

Figure 3 replicates
Figure 3 replicates Figure 3 of Ref. 4 using an ACR phantom.The SP pattern using 31 150 half-radial projections with 89 interleaves was used as opposed to an Archimedean spiral pattern using 18 000 half-radial projections (unclear about the number of interleaves) used in Ref. 4. Both echo images obtained from open-source bSTAR contain no visible artifacts such as off-resonance or banding artifacts and show identical spatial resolution and image quality to those shown in Ref. 4. Note that geometric distortions are not matched due to the use of different gradient sets and image shading is different due to the use of different receive coils.A close inspection of the images reconstructed from the second echo reveals smearing artifacts near the boundaries of the ACR phantom, indicating residual trajectory inaccuracies.Figure4replicates Figure4of Ref. 5 using an ACR phantom.Echo combined images are shown.WASP patterns with 88 and 89 interleaves did not create noticeable eddy current artifacts, demonstrating its flexibility in the design of 3D radial trajectory patterns.The SP pattern with the number of interleaves equal to one of the Fibonacci sequence (e.g., 89) provides good image quality as expected.However, when a non-Fibonacci number of interleaves is selected (e.g., 88), the SP pattern becomes non-smooth and severely degrades image quality due to eddy currents caused by large jumps in k-space.The image artifacts due to eddy currents at this scanner (0.55T prototype MAGNETOM Aera, Siemens Healthineers) are not identical to those shown in Ref.5 (1.5T MAGNETOM Avanto-Fit, Siemens Healthineers).The eddy current artifacts at this scanner rather resemble a geometric distortion caused by trajectory errors.Figure5and Video S1 show the exemplary bSTAR images of volunteer 1 acquired during a single 50-s end-expiratory breath-hold.Images generated using data from the first echo and second echo as well as echo combined images are shown.Images reconstructed from where signal contains RF samples in Hertz, t contains time samples in seconds, shape_dur is the duration of an RF pulse shape in seconds, freqOffset is the frequency offset of an RF pulse in Hertz, phaseOffset is the phase offset of an RF pulse in radians, deadTime is the hardware time delay required at the beginning of an RF pulse in seconds, ringdownTime is the hardware time delay required after the end of an RF pulse in seconds, and delay is the delay before starting the RF pulse shape in seconds, which is greater than or equal to deadTime.and is referred to as the required hardware time delay Δt 1 between RF and ADC in Ref.4, 5.Note that the dwell time is rounded down to a multiple of 100 ns, which is the minimum ADC raster time (sys.adcRasterTime).The number of ADC samples and the duration of an ADC window are calculated as.
delayTE = round((rf.deadTime+ rf_length / 2 + TE1 -sys.adcDeadTime)/ sys.gradRasterTime) * sys.gradRasterTime;Note that sys.gradRasterTime is identical to sys.blockDurationRaster.The sum of sys.rfRingdownTime and sys.adcDeadTime dictates the minimum TE1 First, a positive trapezoid event (g_positive) is created by calling the makeTrapezoid.m function:where ramp_time is the rise time and fall time of a trapezoid gradient in seconds, total_time is the sum of the rise time, plateau time, and fall time of a trapezoid gradient in seconds, and amplitude is the amplitude of a trapezoid gradient in mT/m.The unit of the amplitude field is Hz/T and thus the amplitude variable is scaled by sys.gamma, which is in Hz/T.The data structure g_positive contains the following fields: