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Accelerated 2D Cartesian MRI with an 8-channel local B0 coil array combined with parallel imaging
Rui Tian1, Martin Uecker2,3,4,5, Mathias Davids6,7, Axel Thielscher8,9, Kai Buckenmaier1, Oliver Holder1, Theodor Steffen1, and Klaus Scheffler1,10
1High-Field MR Center, Max Planck Institute for Biological Cybernetics, Tübingen, Germany, 2Institute of Biomedical Imaging, Graz University of Technology, Graz, Austria, 3Institute for Diagnostic and Interventional Radiology, University Medical Center Göttingen, Göttingen, Germany, 4German Centre for Cardiovascular Research (DZHK), Partner Site Göttingen, Göttingen, Germany, 5BioTechMed-Graz, Graz, Austria, 6A. A. Martinos Center for Biomedical Imaging, Department of Radiology, Massachusetts General Hospital, Charlestown, MA, United States, 7Harvard Medical School, Boston, MA, United States, 8Department of Health Technology, Technical University of Denmark, Kongens Lyngby, Denmark, 9Danish Research Centre for Magnetic Resonance, Centre for Functional and Diagnostic Imaging and Research, Copenhagen University Hospital Amager and Hvidovre, Hvidovre, Denmark, 10Department for Biomedical Magnetic Resonance, University of Tübingen, Tübingen, Germany

Synopsis

Keywords: YIA, Hybrid & Novel Systems Technology, Physics & Engineering, Acquisition & Reconstruction, New Trajectories & Spatial Encoding Methods, Acquisition Methods, nonlinear gradient

Motivation: The inherently slow MRI scans can be accelerated through rapid modulation of nonlinear gradient fields; however, its fundamental mechanisms and limits remain incompletely understood and validated.

Goal(s): We investigate accelerated MRI with flexible modulations of nonlinear B0 fields using a custom-built local B0 array.

Approach: The sampling theory is extended to rigorously compare nonlinear field modulation schemes in a quantitative k-space. A novel field calibration technique is proposed to enhance reconstruction. With safety evaluations, we perform in-vivo accelerated scans.

Results: Our in-vivo 2D FLASH scans make significant steps to speed up MRI with local B0 array, achieving eight-fold joint acceleration with parallel imaging.

Impact: For the first time, the sampling efficiency of nonlinear gradients in the entire k-space is quantitatively visualized, allowing rigorous comparison of distinct B0 modulations. Furthermore, the field estimation technique enables fast and robust in-vivo scans accelerated by flexible nonlinear fields.

Introduction

Despite significant advancements1–11 over recent decades, MRI remains inherently slow due to sequential data acquisitions. While methods using multiple RF receivers12,6–8 and rapid switching of linear gradient13,14 became well explained15, fast MRI techniques leveraging nonlinear gradient fields16–20 appeared much less investigated and understood. To unlock further acceleration potentials, we developed an 8-channel local B0 coil array, adapted from multi-coil shim design21 and accommodates a 16-transceive-32-receive RF array22, to explore rapid and flexible modulation of nonlinear B0 fields for fast 2D Cartesian MRI.
As a more general technique23 than wave-CAIPI13 and FRONSAC19, we employ eight small B0 loops (i.e., 10cm x 10cm) driven by independent current waveforms (here, sinusoidal) during the signal readout of multi-slice FLASH1 scans (see Figure 1). This approach imposes additional localized spin phase evolution on objects, rather than global13,19, to disentangle mixed pixels in accelerated scans7. Moreover, it can generate various nonlinear gradient fields24 to identify the optimal modulation schemes.
To rigorously compare the k-space encoding efficiency across distinct modulation schemes in arbitrary acquisition time durations, we extend a mathematical framework for parallel imaging25 based on reproducing kernel Hilbert space (RKHS) to incorporate nonlinear B0 field encoding23. Additionally, a novel field calibration technique utilizing amplifier current monitors and the ESPIRiT algorithm15 is proposed to calibrate our setup and enhance reconstruction. Safety evaluations are performed26,27, and ex-vivo and in-vivo brain scans validate the feasibility of MRI acceleration using local B0 modulations28.

Methods

With RKHS, image reconstruction can be seen as interpolating the continuous k-space signal representations of the objects from discrete MRI samples acquired using arbitrary “spatial encoders”. The norm of interpolation weights (i.e., cardinal function) represents time-domain noise amplification of sampling operators. According to Equation (14-16)28, relative to fully sampled k-space, the time-domain encoding efficiency incorporating linear, nonlinear gradient fields and RF receivers’ sensitivity can be computed from the signal encoding matrix:
$$E_{\bar{t},j}E_{t,i}^\ast U=E_{\bar{t},j}E_{\dot{t},k}^\ast$$
$$P^{\dot{t},k}\ =\ \sqrt{\left(\ E_{\dot{t},k}E_{\dot{t},k}^\ast\ -\ \ {U^\ast E}_{t,i}E_{\dot{t},k}^\ast\right)_{diag}}$$
where $$$E_{t,i},E_{\bar{t},j}$$$ are both the tested encoding matrix including all “spatial encoders”, and $$$E_{\dot{t},k}$$$ is a reference encoding matrix (e.g., DFT matrix), $$$U$$$ is the matrix to be solve for cardinal function, $$$P^{\dot{t},k}$$$ is the power function representing approximation errors. The noise amplification factor is obtained by vertically summing $$$U$$$. The asterisk $$$\ast$$$ denotes the conjugate transpose operation.
Only one field calibration scan is required for all distinct modulation experiments (see Figure 2). Essentially, low-resolution field mapping scans with a current blip in each local coil are input to the ESPIRiT algorithm15 to extrapolate phase maps in high-resolution grid with robustness. The current monitors are exploited to resolve phase offset maps by unit current in a local B0 coil, which are later combined with monitored modulation currents for forward model reconstruction13.
A comprehensive safety evaluation of our local B0 array is performed with respect to PNS stimulation and acoustic noise (see Figure 3). Ex-vivo and in-vivo brain scans in a 9.4T human scanner (Siemens Healthineers, Germany) are tested with various B0 modulation schemes, including distinct nonlinear field shapes, and time shifts of current waveforms between consecutive phase encoded steps similar to aliasing control9.

Results

Utilizing the RKHS framework, we visualized the quantitative k-space sampling efficiency (see Figure 4), identifying a nearly linear gradient along the phase encoding dimension as the optimal modulation field for 2D Cartesian MRI, similar to bunched phase encoding10. The usefulness of readout aliasing control is demonstrated only in limited scenarios (e.g., 5kHz, scheme of “45 deg”). Facilitated by the field calibration technique, the brain scans with local B0 coils modulation are successfully reconstructed, reaching threefold and eightfold acceleration without and with SENSE7, respectively, and free of apparent artifacts (see Figure 5).

Discussion & Conclusion

Our study highlights the extended RKHS framework as a novel mathematical foundation for pulse sequence design involving nonlinear gradient fields, potentially benefiting other nonconventional spatial encoding29–34 as well. Beyond the local k-space20 and the G-map7, this framework provides insights showing how the k-space efficiency maps computed based on a time segment (e.g., a single TR in this paper) can decouple the entire acquisition duration, and quantify individual contributions of nonlinear gradients encoding within smaller temporal periods to the full k-space.
Eventually, our local B0 array substantially accelerate 2D Cartesian ex-vivo and in-vivo scans, validating the feasibility of this emerging technology in practice. Although the optimized local B0 coils converges to a linear gradient35 for accelerated 2D FLASH scans, our study doesn’t eliminate all possibility for potential advantages of more flexible nonlinear field modulation in spatial-temporal domain, especially in 3D Cartesian and other non-Cartesian acquisitions for future study.

Acknowledgements

This study is supported by the ERC Advanced Grant (No.834940). The ex vivo brain phantom was with courtesy of the Institute of Clinical Anatomy and Cell Analysis, Department of Anatomy, Eberhard Karls University of Tübingen. The first author thanks Dr. Thomas Shiozawa (Institute of Clinical Anatomy and Cell Analysis) for assistance with sample preparation, and Dr. Gisela Hagberg for assistance in scanning this phantom. M.D. receives research support from Siemens Healthineers. A.T. was supported by the Lundbeck foundation (grant R313-2019-622).

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Figures

Figure 1 A. Illustration of system Integration for the custom-built 8-channel local B0 coil array in a 9.4T human scanner. B. The setup for in-vivo accelerated scans. C. The local B0 coil in production. D1. The magnetic field map produced by 1A in a local coil in transverse plane. D2. The magnetic field distribution along the central horizontal line of D1. D3. The magnetic field distribution along z direction, at the pixel with the maximum field strength in D1.

Figure 2 A. Sequence diagram for 9.4T scans with local B0 coil array. A small current blip or sinusoidal currents are sent in one or all local coils, after RF excitation or during readout, respectively B. Procedure to utilize ESPIRiT to extrapolate phase maps in high-resolution grid, combined with monitored currents to produce high-accuracy encoding matrix for reconstruction. C. Accuracy with different current monitoring rates. D1-D3: Reconstruction quality with different current monitoring rates.

Figure 3 A1-A5. Simulation and measurements of the B-field produced by our setup. A6. Cross-validation through field camera measurements. A7. The nerve stimulation function for scanner gradients and local coils for conservative access of safety margin. B1-B2. The PNS threshold curve based on realistic human model and calculated E-field. C1-C3. The E-field computed in SimNIBs for cross-validation, with minor scaling potentially by different tissue conductivities. D. Acoustic measurements, far below the critical limit of 140 dB(Z).

Figure 4 Column A. Various field shapes produced by local coils with distinct phase offsets of sinusoidal modulation currents. Column B. Corresponding B0 field shapes, with gradient indicated by arrows. Column C. Reconstruction of ex-vivo scans with 3x retrospective undersampling along one phase encoding dimension. Column D. G-map illustrating image-space noise amplification. E-G. k-space efficiency maps in one or all TR for 3x accelerated scans.

Figure 5 In-vivo 2D FLASH scans utilizing local B0 modulation (7kHz, 0&π, R22.5°), with retrospective undersampling ranging from 6x to 12x. A reference of 6x accelerated parallel imaging scan without local B0 modulation is also included for comparison. The G-maps representing theoretical image-space noise amplification are shown.

Proc. Intl. Soc. Mag. Reson. Med. 32 (2024)
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DOI: https://doi.org/10.58530/2024/0008