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RF Pulse design and parallel transmission (pTx)

7 Tesla Ultra-High Field MR Imaging (UHF-MRI) offers various advantages such as a higher signal-to-noise ratio (SNR), higher spectral resolutions, or in many cases a stronger contrast. At the same time, UHF-MRI introduces various problems, which are mostly due to the higher frequency of the electromagnetic (EM) radiofrequency (RF) pulses. The inhomogeneous transverse magnetic RF field, i.e. B1+ (see also section "RF fields and safety in body UHF imaging"), that is responsible for spin excitation leads to spatially varying flip angles and, thus, to inhomogeneous image contrast. In unfavorable cases, particularly in MRI body imaging, local voids of the signal may occur (cf. Figure 3, left).

Such and other issues can be addressed successfully using static or dynamic parallel transmission (pTx) techniques that make use of (local) multi-channel transmit (Tx) coils of for example 8, 16 or 32 Tx elements (cf. Fig. 1a). Each coil element has a different complex B1+ field distribution (indicated by colors in Fig. 1a) and the resulting superposed complex B1+ field interacts with the spins and determines the flip angle (FA). This resulting B1+ field be modified by changing the amplitude and the phase of the individual driving RF pulses, which then scales or phase-shifts the individual B1+ field. The vector of N phases and N amplitudes for an N-Tx-channel coil are often termed the B1+ shim setting. In static pTx this shim setting is kept constant throughout the RF pulse while in dynamic pTx this shim setting varies as a function of time during the RF pulse. In practice, dynamic pTx is more hardware-demanding, as it requires in most cases N independent RF waveform generators and amplifiers for N independent Tx channels. The aim is to optimize the resulting B1+ field or the FA distribution such that it matches a predefined spatial pattern (e.g. spatially homogeneus B1+ or FA), In order to optimize the B1+ field or the resulting FA, the individual B1+ fields need to be measured. So far, however, the lack of 3D human B1+ maps of the human body at 7 Tesla hindered the development of 3D pTx methods. Therefore, our lab focusses on both, the mapping of the fields (see section "RF fields and safety in body UHF imaging") and the development of 3D imaging methods in the body using pTx.

Fig. 1: a) Setup for body imaging at 7T using a local 8-channel body coil. Each individual Tx element generates an individual B1+ field that differs from neighboring elements. By complex superposition a resulting B1+ field is generated that is responsible for spin excitation. b) Schematic view of static pTx. Here the 8 RF pulses are characterized by a common RF pulse shape that are multiplied by a channel-specific complex (phase and ampliutde) factor. This can be realized by splitting a single RF pulse into 8 identical RF pulses that are subsequently phase shifted and scaled prior to amplification. c) Schematic view of dynamic pTx. Here the 8 RF pulses are independent of each other. This setup requires 8 independent waveform generators.

Recently, the lab developed and proposed a new method to compute respiration-resolved 3D B1+ maps for multi-channel Tx coils applied to the human body [1] that were used intensively to address the problem of spatial heterogeneities of the B1+ fields by means of pTx [2,7,8].

The lab focusses on the following pulse design topics:

  • Subject-specific static and dynamic RF pulse design
  • Calibration-free, subject-independent dynamic RF pulse design
  • Respiration-insensitive subject-specific RF pulse design
  • Deep learning in RF pulse design
  • Parallel transmission in Simultaneous Multi-Slice (SMS) imaging

Subject-specific, static RF pulse design in the human body [2]

In static pTx, often also termed B1+ shimming, the desired excitation pattern is created by superimposing the B1+ fields of several independent Tx elements in order to generate the desired superposed spatial B1+ field. This pTx approach is often applied to perform a subject-specific homogenization of the resulting superposed spatial B1+ pattern in a region of interest. In static subject-specific pTx, the independent Tx elements are controlled by superimposing the individual fields with different phase and magnitude scaling such that the resulting B1+ pattern in the desired ROI is as homogeneous as possible or that the achieved B1+ field is maximized.

Fig. 2: An example of static B1+ shimming of the human heart over three slices. The plots illustrate a 3D view of the nominal flip angle maps of the complex sum of estimated B1+ maps with the non-optimized default phase setting (default - top row) and the optimized static phase setting (static shim - bottom row) of one subject. After shimming the resulting B1+ and thus the flip angle shows increased homogeneity that will lead to more homogeneous image contrast [2].

Fig. 3: Cardiac gradient echo cine images obtained at 7 Tesla before (left) and after (right) B1+ shimming.

Subject specific, dynamic RF pulse design

Subject-specific dynamic RF pulses can be used to homogenize the resulting FA in larger regions such as the whole 3D heart volume as shown in Fig. 4 or to achieve a more homogeneous slice selective excitation.

Fig 4: Pulse diagram showing the RF pulses (magnitude and phase) and three-dimensional gradient blips of the subject-specific 4 kT-points pulse and the 3D view of the nominal FA maps (color-coded) of the complex sum of estimated B1+ maps [2].

Calibration-free, subject-independent RF pulse design [7]

Calibration-free universal kT-point pulses were proposed by the group to achieve a subject independent, homogeneous flip-angle within the human heart at 7T. The universal pulses were computed offline based on channel-wise 3D B1+-maps acquired in 22 subjects with varying BMI and age. The optimized universal pulses were successfully applied to nine unseen test subjects and yielded robustly a homogeneous FA pattern in the 3D heart ROI as outlined in Figure 3.

Fig 5: FA prediction of one sagittal slice of the 3D heart volume using the default setting and the universal subject-independent 4kT-points pulse for nine test-cases (4M/5F, 25-56 years, 19.5-35.3 kg/m2).

Experimental data at 7T validate the B1+ predictions and demonstrate successful plug-and-play 3D pTx of the human heart. One of the nine subjects is shown in Figure 4. Compared to the tailored case, the universal pulse saves roughly 10-15 minutes of precious scan time per subject and generates comparable signal in the 3D heart volume.

Fig 6: Respiration corrected 3D GRE images during shallow breathing with default shim, optimized tailored pTx pulse and precomputed universal pulse of one unseen test case. The 3D images are free of breathing artifacts and both, tailored and universal pulse result in comparable signal of the 3D heart volume. The universal pulses can greatly mitigate the RF field inhomogeneity problem without lengthy adjustments (yellow arrows). The remaining signal changes in the AP direction of the acquired images are a result of receive (B1-) variations [7].

Respiration-insensitive subject-specific RF pulse design [2,8]

Imaging the human heart at ultra-high fields is highly challenging due to spatially heterogeneous B1+ profiles but also due to respiratory motion, that may affect the resulting RF pulse performance. RF pulses are typically designed based on a single respiratory state (e.g. exhale - Fig. 7 top, left) and such respiration-specific pulses may result in poor image quality for respiratory states other than used during optimization (e.g. inhale - Fig. 7 top, right). Respiration-robust pulses instead are calculated based on respiration-resolved 2D or 3D B1+ maps of multiple respiratory states, and therefore they result in homogeneous 2D or 3D flip angles across all respiratory states. The benefits of using respiration robust pulses is shown in 2D experiments in Figure 7 and for the 3D case in Figures 8+9.

Figure 7: respiration-robust pulses in cine imaging.

Fig 8: Evaluation of four different pulses optimized for a 3D heart ROI on exhale, intermediate, inhale and optimized on all respiration states (respiration robust) for deep breathing of a representative subject. Depicted are the overall coefficient of variation (CV) and the flip angle (FA) spread of all respiration states. The respiration robust pulse performs best across all respiration states [8].

Fig 9: Side-by-side comparison of reconstructed 3D GRE images with the 4 kT-points pTx pulses optimized for inhale and respiration robust of the subject shown in Figure 8. The arrows point to signal drop-out regions in using the inhale pulse which are corrected by the respiration robust pulse [8].

Deep learning in RF pulse design

For certain applications the RF pulse calculation times pose a challenge, in particular when high flip angles are regarded. Therefore, the group is interested in deep learning-based methods for fast design of RF pulses and to investigate potential limitations.

Design of slice-selective RF pulses using deep learning [9]

We proposed a residual neural network for the design of slice-selective (small and large flip angle) RF and gradient trajectories. The network was trained with 300k SLR RF pulses and predicts the RF pulse and the gradient for a desired magnetization profile. The aim is to evaluate the feasibility and dependence on different parameter variations of this new approach. These insights serve as a basis for more general and complex pulses for future neural network design.

Figure 10: Example of a slice-selective SLR RF pulse and gradient learned by the residual neural network. In (e), (f), (g) the output is compared to the ground truth. The prediction is used for a second Bloch simulation to analyze the difference between the desired and the predicted magnetization in (a), (b), (c), (d). The predicted result is in good agreement with the ground truth for this example.

Design of 2D RF pulses using deep learning [10]

Further work is performed in a collaboration with Mads Vinding (University of Aarhus, Denmark). The proposed convolutional neural network-based pulse design method predicts 2D RF pulses with an excellent excitation pattern and compensated B1+ and B0 variations at 7 T [10]. The same convolutional neural network was also tested for brain slice 2DRF excitations (single-channel) at 7 T with a uniform FA profile [10]. The rapid 2DRF pulse prediction (9 ms), which is more than 1000 times faster than the optimal control, enables subject-specific high-quality 2DRF pulses without the need to run lengthy optimizations.

Figure 11: The DeepControl convolutional neural network. The input on the left-hand side consists of three 64x64 matrices: 1) the target pattern being the shape of the brain in a particular slice given a nominal FA of 30o; 2) the B0 map; and 3) the B1+ map. The output on the right-hand side, is the 1400-length array, consisting of the RFx (real) and RFy (imaginary) pulse waveforms yielding the 2DRF pulse together with the gradient waveform [10,11].

Figure 12: FA maps and corresponding B1+/B0 maps. First row: the DeepControl result. Second row: the corresponding OC result. The printed numbers in white are normalized root-mean-square errors. Row three to five, between the two dashed line, are intended to recap what missing field information results in with respect to FA maps [11].

Parallel transmission in Simultaneous Multi-Slice (SMS) imaging [11-14]

MRI of the human body and particularly the human heart often requires fast and time-efficient acquisition techniques in order to avoid artefacts due to cardiac and respiratory motion. Simultaneous Multi-Slice (SMS) imaging is such a time-efficient acquisition technique as it allows to image multiple slices at the same time in contrast to conventional methods that acquire each slice serially. Thereby, the imaging process can be accelerated by a factor that approximately matches the number of simultaneously acquired slices. While a conventional image reconstruction would return collapsed images of multiple slices (e.g. 3 slices, see Figure 13, left column) the technique makes use of multiple receiver coils to separate the individual slices. SMS is investigated by the group for various applications.

Figure 13: Cardiac gradient echo images obtained at 7 Tesla with SMS factor of 3. While the left image contains the combined signal of all three excited slices, the right image shows the three separated slices after reconstruction.


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