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Tušar K, Serša I. Use of nonlinear pulsed magnetic fields for spatial encoding in magnetic resonance imaging. Sci Rep 2024; 14:7521. [PMID: 38553559 PMCID: PMC10980706 DOI: 10.1038/s41598-024-58229-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/29/2023] [Accepted: 03/26/2024] [Indexed: 04/02/2024] Open
Abstract
This study examines the use of nonlinear magnetic field coils for spatial encoding in magnetic resonance imaging. Existing theories on imaging with such coils share a complex reconstruction process that originates from a suboptimal signal interpretation in the spatial-frequency domain (k-space). In this study, a new solution to this problem is proposed, namely a two-step reconstruction process, in which in the first step, the image signal is converted into a frequency spectrum, and in the second step, the spectrum, which represents the distorted image, is geometrically and intensity corrected to obtain an undistorted image. This theory has been verified by numerical simulations and experimentally using a straight wire as a coil model for an extremely nonlinear magnetic field. The results of this study facilitate the use of simple encoding coil designs that can feature low inductance, allowing for much faster switching times and higher magnetic field gradients.
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Affiliation(s)
- Kaja Tušar
- Jožef Stefan International Postgraduate School, Jamova 39, 1000, Ljubljana, Slovenia
| | - Igor Serša
- Jožef Stefan Institute, Jamova 39, 1000, Ljubljana, Slovenia.
- Faculty of Medicine, University of Ljubljana, Vrazov trg 2, 1000, Ljubljana, Slovenia.
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Selvaganesan K, Ha Y, Sun H, Zhang Z, Sun C, Samardzija A, Galiana G, Constable RT. Encoding scheme design for gradient-free, nonlinear projection imaging using Bloch-Siegert RF spatial encoding in a low-field, open MRI system. Sci Rep 2024; 14:3307. [PMID: 38332252 PMCID: PMC10853509 DOI: 10.1038/s41598-024-53703-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/10/2023] [Accepted: 02/03/2024] [Indexed: 02/10/2024] Open
Abstract
Eliminating conventional pulsed B0-gradient coils for magnetic resonance imaging (MRI) can significantly reduce the cost of and increase access to these devices. Phase shifts induced by the Bloch-Siegert shift effect have been proposed as a means for gradient-free, RF spatial encoding for low-field MR imaging. However, nonlinear phasor patterns like those generated from loop coils have not been systematically studied in the context of 2D spatial encoding. This work presents an optimization algorithm to select an efficient encoding trajectory among the nonlinear patterns achievable with a given hardware setup. Performance of encoding trajectories or projections was evaluated through simulated and experimental image reconstructions. Results show that the encodings schemes designed by this algorithm provide more efficient spatial encoding than comparison encoding sets, and the method produces images with the predicted spatial resolution and minimal artifacts. Overall, the work demonstrates the feasibility of performing 2D gradient-free, low-field imaging using the Bloch-Siegert shift which is an important step towards creating low-cost, point-of-care MR systems.
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Affiliation(s)
| | - Yonghyun Ha
- Department of Radiology and Biomedical Imaging, Yale School of Medicine, New Haven, CT, USA
| | - Heng Sun
- Department of Biomedical Engineering, Yale University, New Haven, CT, USA
| | - Zhehong Zhang
- Department of Biomedical Engineering, Yale University, New Haven, CT, USA
| | - Chenhao Sun
- Department of Radiology and Biomedical Imaging, Yale School of Medicine, New Haven, CT, USA
| | - Anja Samardzija
- Department of Biomedical Engineering, Yale University, New Haven, CT, USA
| | - Gigi Galiana
- Department of Biomedical Engineering, Yale University, New Haven, CT, USA
- Department of Radiology and Biomedical Imaging, Yale School of Medicine, New Haven, CT, USA
| | - R Todd Constable
- Department of Biomedical Engineering, Yale University, New Haven, CT, USA.
- Department of Radiology and Biomedical Imaging, Yale School of Medicine, New Haven, CT, USA.
- Yale University School of Medicine, Magnetic Resonance Research Center, 300 Cedar Street, New Haven, CT, 06520, USA.
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Tian R, Uecker M, Davids M, Thielscher A, Buckenmaier K, Holder O, Steffen T, Scheffler K. Accelerated 2D Cartesian MRI with an 8-channel local B 0 coil array combined with parallel imaging. Magn Reson Med 2024; 91:443-465. [PMID: 37867407 DOI: 10.1002/mrm.29799] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/10/2023] [Revised: 06/26/2023] [Accepted: 06/30/2023] [Indexed: 10/24/2023]
Abstract
PURPOSE In MRI, the magnetization of nuclear spins is spatially encoded with linear gradients and radiofrequency receivers sensitivity profiles to produce images, which inherently leads to a long scan time. Cartesian MRI, as widely adopted for clinical scans, can be accelerated with parallel imaging and rapid magnetic field modulation during signal readout. Here, by using an 8-channel localB 0 $$ {\mathrm{B}}_0 $$ coil array, the modulation scheme optimized for sampling efficiency is investigated to speed up 2D Cartesian scans. THEORY AND METHODS An 8-channel localB 0 $$ {\mathrm{B}}_0 $$ coil array is made to carry sinusoidal currents during signal readout to accelerate 2D Cartesian scans. An MRI sampling theory based on reproducing kernel Hilbert space is exploited to visualize the efficiency of nonlinear encoding in arbitrary sampling duration. A field calibration method using current monitors for localB 0 $$ {\mathrm{B}}_0 $$ coils and the ESPIRiT algorithm is proposed to facilitate image reconstruction. Image acceleration with various modulation field shapes, aliasing control, and distinct modulation frequencies are scrutinized to find an optimized modulation scheme. A safety evaluation is conducted. In vivo 2D Cartesian scans are accelerated by the localB 0 $$ {\mathrm{B}}_0 $$ coils. RESULTS For 2D Cartesian MRI, the optimal modulation field by this localB 0 $$ {\mathrm{B}}_0 $$ array converges to a nearly linear gradient field. With the field calibration technique, it accelerates the in vivo scans (i.e., proved safe) by threefold and eightfold free of visible artifacts, without and with SENSE, respectively. CONCLUSION The nonlinear encoding analysis tool, the field calibration method, the safety evaluation procedures, and the in vivo reconstructed scans make significant steps to push MRI speed further with the localB 0 $$ {\mathrm{B}}_0 $$ coil array.
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Affiliation(s)
- Rui Tian
- High-Field MR center, Max Planck Institute for Biological Cybernetics, Tübingen, Germany
| | - Martin Uecker
- Institute of Biomedical Imaging, Graz University of Technology, Graz, Austria
- Institute for Diagnostic and Interventional Radiology, University Medical Center Göttingen, Göttingen, Germany
- German Centre for Cardiovascular Research (DZHK), Partner Site Göttingen, Göttingen, Germany
- BioTechMed-Graz, Graz, Austria
| | - Mathias Davids
- A. A. Martinos Center for Biomedical Imaging, Department of Radiology, Massachusetts General Hospital, Charlestown, Massachusetts, USA
- Harvard Medical School, Boston, Massachusetts, USA
| | - Axel Thielscher
- Department of Health Technology, Technical University of Denmark, Kongens Lyngby, Denmark
- Danish Research Centre for Magnetic Resonance, Centre for Functional and Diagnostic Imaging and Research, Copenhagen University Hospital Amager and Hvidovre, Hvidovre, Denmark
| | - Kai Buckenmaier
- High-Field MR center, Max Planck Institute for Biological Cybernetics, Tübingen, Germany
| | - Oliver Holder
- High-Field MR center, Max Planck Institute for Biological Cybernetics, Tübingen, Germany
| | - Theodor Steffen
- High-Field MR center, Max Planck Institute for Biological Cybernetics, Tübingen, Germany
| | - Klaus Scheffler
- High-Field MR center, Max Planck Institute for Biological Cybernetics, Tübingen, Germany
- Department for Biomedical Magnetic Resonance, University of Tübingen, Tübingen, Germany
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Cooley CZ, Haskell MW, Cauley SF, Sappo C, Lapierre CD, Ha CG, Stockmann JP, Wald LL. Design of sparse Halbach magnet arrays for portable MRI using a genetic algorithm. IEEE TRANSACTIONS ON MAGNETICS 2018; 54:5100112. [PMID: 29749974 PMCID: PMC5937527 DOI: 10.1109/tmag.2017.2751001] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
Permanent magnet arrays offer several attributes attractive for the development of a low-cost portable MRI scanner for brain imaging. They offer the potential for a relatively lightweight, low to mid-field system with no cryogenics, a small fringe field, and no electrical power requirements or heat dissipation needs. The cylindrical Halbach array, however, requires external shimming or mechanical adjustments to produce B0 fields with standard MRI homogeneity levels (e.g., 0.1 ppm over FOV), particularly when constrained or truncated geometries are needed, such as a head-only magnet where the magnet length is constrained by the shoulders. For portable scanners using rotation of the magnet for spatial encoding with generalized projections, the spatial pattern of the field is important since it acts as the encoding field. In either a static or rotating magnet, it will be important to be able to optimize the field pattern of cylindrical Halbach arrays in a way that retains construction simplicity. To achieve this, we present a method for designing an optimized cylindrical Halbach magnet using the genetic algorithm to achieve either homogeneity (for standard MRI applications) or a favorable spatial encoding field pattern (for rotational spatial encoding applications). We compare the chosen designs against a standard, fully populated sparse Halbach design, and evaluate optimized spatial encoding fields using point-spread-function and image simulations. We validate the calculations by comparing to the measured field of a constructed magnet. The experimentally implemented design produced fields in good agreement with the predicted fields, and the genetic algorithm was successful in improving the chosen metrics. For the uniform target field, an order of magnitude homogeneity improvement was achieved compared to the un-optimized, fully populated design. For the rotational encoding design the resolution uniformity is improved by 95% compared to a uniformly populated design.
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Affiliation(s)
- Clarissa Zimmerman Cooley
- Athinoula A. Martinos Center for Biomedical Imaging, Department of Radiology, Massachusetts General Hospital, Charlestown, MA, USA
- Harvard Medical School, Boston, MA, USA
| | - Melissa W Haskell
- Athinoula A. Martinos Center for Biomedical Imaging, Department of Radiology, Massachusetts General Hospital, Charlestown, MA, USA
- Biophysics Graduate Program, Harvard University, Cambridge, MA, USA
| | - Stephen F Cauley
- Athinoula A. Martinos Center for Biomedical Imaging, Department of Radiology, Massachusetts General Hospital, Charlestown, MA, USA
- Harvard Medical School, Boston, MA, USA
| | - Charlotte Sappo
- Athinoula A. Martinos Center for Biomedical Imaging, Department of Radiology, Massachusetts General Hospital, Charlestown, MA, USA
| | - Cristen D Lapierre
- Athinoula A. Martinos Center for Biomedical Imaging, Department of Radiology, Massachusetts General Hospital, Charlestown, MA, USA
| | - Christopher G Ha
- Athinoula A. Martinos Center for Biomedical Imaging, Department of Radiology, Massachusetts General Hospital, Charlestown, MA, USA
| | - Jason P Stockmann
- Athinoula A. Martinos Center for Biomedical Imaging, Department of Radiology, Massachusetts General Hospital, Charlestown, MA, USA
- Harvard Medical School, Boston, MA, USA
| | - Lawrence L Wald
- Athinoula A. Martinos Center for Biomedical Imaging, Department of Radiology, Massachusetts General Hospital, Charlestown, MA, USA
- Harvard Medical School, Boston, MA, USA
- Harvard-MIT Division of Health Science and Technology, Cambridge, MA, USA
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Wang H, Tam L, Kopanoglu E, Peters DC, Constable RT, Galiana G. O-space with high resolution readouts outperforms radial imaging. Magn Reson Imaging 2016; 37:107-115. [PMID: 27876569 DOI: 10.1016/j.mri.2016.11.012] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/09/2015] [Revised: 11/17/2016] [Accepted: 11/17/2016] [Indexed: 11/25/2022]
Abstract
PURPOSE While O-Space imaging is well known to accelerate image acquisition beyond traditional Cartesian sampling, its advantages compared to undersampled radial imaging, the linear trajectory most akin to O-Space imaging, have not been detailed. In addition, previous studies have focused on ultrafast imaging with very high acceleration factors and relatively low resolution. The purpose of this work is to directly compare O-Space and radial imaging in their potential to deliver highly undersampled images of high resolution and minimal artifacts, as needed for diagnostic applications. We report that the greatest advantages to O-Space imaging are observed with extended data acquisition readouts. THEORY AND METHODS A sampling strategy that uses high resolution readouts is presented and applied to compare the potential of radial and O-Space sequences to generate high resolution images at high undersampling factors. Simulations and phantom studies were performed to investigate whether use of extended readout windows in O-Space imaging would increase k-space sampling and improve image quality, compared to radial imaging. RESULTS Experimental O-Space images acquired with high resolution readouts show fewer artifacts and greater sharpness than radial imaging with equivalent scan parameters. Radial images taken with longer readouts show stronger undersampling artifacts, which can cause small or subtle image features to disappear. These features are preserved in a comparable O-Space image. CONCLUSIONS High resolution O-Space imaging yields highly undersampled images of high resolution and minimal artifacts. The additional nonlinear gradient field improves image quality beyond conventional radial imaging.
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Affiliation(s)
- Haifeng Wang
- Department of Radiology and Biomedical Imaging, Yale University, New Haven, CT 06520, USA
| | - Leo Tam
- Department of Radiology and Biomedical Imaging, Yale University, New Haven, CT 06520, USA
| | - Emre Kopanoglu
- Department of Radiology and Biomedical Imaging, Yale University, New Haven, CT 06520, USA
| | - Dana C Peters
- Department of Radiology and Biomedical Imaging, Yale University, New Haven, CT 06520, USA
| | - R Todd Constable
- Department of Radiology and Biomedical Imaging, Yale University, New Haven, CT 06520, USA; Department of Neurosurgery, Yale University, New Haven, CT 06520, USA
| | - Gigi Galiana
- Department of Radiology and Biomedical Imaging, Yale University, New Haven, CT 06520, USA.
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Wang H, Tam L, Kopanoglu E, Peters DC, Constable RT, Galiana G. Experimental O-space turbo spin echo imaging. Magn Reson Med 2016; 75:1654-61. [PMID: 25981343 PMCID: PMC4644719 DOI: 10.1002/mrm.25741] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/27/2014] [Revised: 03/23/2015] [Accepted: 03/26/2015] [Indexed: 11/08/2022]
Abstract
PURPOSE Turbo spin echo (TSE) imaging reduces imaging time by acquiring multiple echoes per repetition (TR), requiring fewer TRs. O-space can also require fewer TRs by using a combination of nonlinear magnetic gradient fields and surface coil arrays. Although to date, O-space has only been demonstrated for gradient echo imaging, it is valuable to combine these two techniques. However, collecting multiple O-space echoes per TR is difficult because of the different local k-space trajectories and variable T2-weighting. THEORY AND METHODS A practical scheme is demonstrated to combine the benefits of TSE and O-space for highly accelerated T2-weighted images. The scheme uses a modified acquisition order and filtered projection reconstruction to reduce artifacts caused by T2 decay, while retaining T2 contrast that corresponds to a specific echo time. RESULTS The experiments revealed that the proposed method can produce highly accelerated T2-weighted images. Moreover, the method can generate multiple images with different T2 contrasts from a single dataset. CONCLUSIONS The proposed O-space TSE imaging method requires fewer echoes than conventional TSE and fewer repetitions than conventional O-space imaging. It retains resilience to undersampling, clearly outperforming Cartesian SENSE at high levels of undersampling, and can generate undistorted images with a range of T2 contrast from a single acquired dataset.
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Affiliation(s)
- Haifeng Wang
- Department of Diagnostic Radiology, Yale University, New Haven, CT,
USA
| | - Leo Tam
- Department of Diagnostic Radiology, Yale University, New Haven, CT,
USA
| | - Emre Kopanoglu
- Department of Diagnostic Radiology, Yale University, New Haven, CT,
USA
| | - Dana C. Peters
- Department of Diagnostic Radiology, Yale University, New Haven, CT,
USA
| | - R. Todd Constable
- Department of Diagnostic Radiology, Yale University, New Haven, CT,
USA
- Department of Biomedical Engineering, Yale University, New Haven, CT,
USA
| | - Gigi Galiana
- Department of Diagnostic Radiology, Yale University, New Haven, CT,
USA
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Wang H, Tam LK, Constable RT, Galiana G. Fast rotary nonlinear spatial acquisition (FRONSAC) imaging. Magn Reson Med 2016; 75:1154-65. [PMID: 25950279 PMCID: PMC4637004 DOI: 10.1002/mrm.25703] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/24/2014] [Revised: 02/20/2015] [Accepted: 02/26/2015] [Indexed: 11/10/2022]
Abstract
PURPOSE Nonlinear spatial encoding magnetic fields (SEMs) have been studied to reconstruct images from a minimum number of echoes. Previous work has also explored single shot trajectories in nonlinear SEMs. However, the search continues for optimal schemes that apply nonlinear SEMs to improve spatial encoding efficiency and image quality. THEORY AND METHODS We enhance the encoding efficiency of standard linear gradient trajectories by adding a rapidly rotating nonlinear SEM of moderate amplitude, the so called FRONSAC (Fast ROtary Nonlinear Spatial ACquisition) imaging. This additional gradient greatly improves the image quality of highly undersampled single-shot trajectories, including EPI, Spiral, and Rosette trajectories. RESULTS Our simulations, including noise and dephasing effects, test the effect of adding FRONSAC gradients, demonstrating the applicability of this approach. Performance is explained by demonstrating the additional k-space sampling the nonlinear gradient provides. Studies of the optimal amplitude and frequency of the additional FRONSAC field are presented, and the role of enhanced sampling during the readout demonstrated. Dynamic field mapping in a second-order gradient system shows the proposed gradient waveforms are feasible. CONCLUSION Images resulting from highly undersampled existing k-space trajectories, such as EPI, Spiral, and Rosette, are greatly enhanced simply by adding a rotating nonlinear SEM field.
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Affiliation(s)
- Haifeng Wang
- Department of Diagnostic Radiology, Yale University, New Haven, CT, USA
| | - Leo K. Tam
- Department of Diagnostic Radiology, Yale University, New Haven, CT, USA
| | - R. Todd Constable
- Department of Diagnostic Radiology, Yale University, New Haven, CT, USA
- Department of Biomedical Engineering, Yale University, New Haven, CT, USA
- Department of Neurosurgery, Yale University, New Haven, CT, USA
| | - Gigi Galiana
- Department of Diagnostic Radiology, Yale University, New Haven, CT, USA
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Layton KJ, Kroboth S, Jia F, Littin S, Yu H, Zaitsev M. Trajectory optimization based on the signal-to-noise ratio for spatial encoding with nonlinear encoding fields. Magn Reson Med 2015; 76:104-17. [PMID: 26243290 DOI: 10.1002/mrm.25859] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/04/2014] [Revised: 07/03/2015] [Accepted: 07/07/2015] [Indexed: 11/06/2022]
Abstract
PURPOSE Multiple nonlinear gradient fields offer many potential benefits for spatial encoding including reduced acquisition time, fewer artefacts and region-specific imaging, although designing a suitable trajectory for such a setup is difficult. This work aims to optimize encoding trajectories for multiple nonlinear gradient fields based on the image signal-to-noise ratio. THEORY AND METHODS Image signal-to-noise ratio is directly linked to the covariance of the reconstructed pixels, which can be calculated recursively for each projection of the trajectory under a Bayesian formulation. An evolutionary algorithm is used to find the higher-dimensional projections that minimize the pixel covariance, incorporating receive coil profiles, intravoxel dephasing, and reconstruction regularization. The resulting trajectories are tested through simulations and experiments. RESULTS The optimized trajectories produce images with higher resolution and fewer artefacts compared with traditional approaches, particularly for high undersampling. However, higher-dimensional projection experiments strongly depend on accurate hardware and calibration. CONCLUSION Computer-based optimization provides an efficient means to explore the large trajectory space created by the use of multiple nonlinear encoding fields. The optimization framework, as presented here, is necessary to fully exploit the advantages of nonlinear fields. Magn Reson Med 76:104-117, 2016. © 2015 Wiley Periodicals, Inc.
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Affiliation(s)
- Kelvin J Layton
- Department of Radiology, Medical Physics, University Medical Center Freiburg, Freiburg, Germany
| | - Stefan Kroboth
- Department of Radiology, Medical Physics, University Medical Center Freiburg, Freiburg, Germany
| | - Feng Jia
- Department of Radiology, Medical Physics, University Medical Center Freiburg, Freiburg, Germany
| | - Sebastian Littin
- Department of Radiology, Medical Physics, University Medical Center Freiburg, Freiburg, Germany
| | - Huijun Yu
- Department of Radiology, Medical Physics, University Medical Center Freiburg, Freiburg, Germany
| | - Maxim Zaitsev
- Department of Radiology, Medical Physics, University Medical Center Freiburg, Freiburg, Germany
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Schultz G, Gallichan D, Weber H, Witschey WRT, Honal M, Hennig J, Zaitsev M. Image reconstruction in k-space from MR data encoded with ambiguous gradient fields. Magn Reson Med 2015; 73:857-64. [PMID: 24777559 PMCID: PMC4617561 DOI: 10.1002/mrm.25152] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/12/2013] [Revised: 12/09/2013] [Accepted: 01/08/2014] [Indexed: 11/11/2022]
Abstract
PURPOSE In this work, the limits of image reconstruction in k-space are explored when non-bijective gradient fields are used for spatial encoding. THEORY The image space analogy between parallel imaging and imaging with non-bijective encoding fields is partially broken in k-space. As a consequence, it is hypothesized and proven that ambiguities can only be resolved partially in k-space, and not completely as is the case in image space. METHODS Image-space and k-space based reconstruction algorithms for multi-channel radiofrequency data acquisitions are programmed and tested using numerical simulations as well as in vivo measurement data. RESULTS The hypothesis is verified based on an analysis of reconstructed images. It is found that non-bijective gradient fields have the effect that densely sampled autocalibration data, used for k-space reconstruction, provide less information than a separate scan of the receiver coil sensitivity maps, used for image space reconstruction. Consequently, in k-space only the undersampling artifact can be unfolded, whereas in image space, it is also possible to resolve aliasing that is caused by the non-bijectivity of the gradient fields. CONCLUSION For standard imaging, reconstruction in image space and in k-space is nearly equivalent, whereas there is a fundamental difference with practical consequences for the selection of image reconstruction algorithms when non-bijective encoding fields are involved.
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Affiliation(s)
- Gerrit Schultz
- Medical Physics, Department of Radiology, University Medical Center Freiburg, Freiburg, Germany
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Tam LK, Galiana G, Stockmann JP, Tagare H, Peters DC, Constable RT. Pseudo-random center placement O-space imaging for improved incoherence compressed sensing parallel MRI. Magn Reson Med 2014; 73:2212-24. [PMID: 25042143 DOI: 10.1002/mrm.25364] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/11/2013] [Revised: 06/23/2014] [Accepted: 06/24/2014] [Indexed: 11/09/2022]
Abstract
PURPOSE Nonlinear spatial encoding magnetic (SEM) field strategies such as O-space imaging have previously reported dispersed artifacts during accelerated scans. Compressed sensing (CS) has shown a sparsity-promoting convex program allows image reconstruction from a reduced data set when using the appropriate sampling. The development of a pseudo-random center placement (CP) O-space CS approach optimizes incoherence through SEM field modulation to reconstruct an image with reduced error. THEORY AND METHODS The incoherence parameter determines the sparsity levels for which CS is valid and the related transform point spread function measures the maximum interference for a single point. The O-space acquisition is optimized for CS by perturbing the Z(2) strength within 30% of the nominal value and demonstrated on a human 3T scanner. RESULTS Pseudo-random CP O-space imaging is shown to improve incoherence between the sensing and sparse domains. Images indicate pseudo-random CP O-space has reduced mean squared error compared with a typical linear SEM field acquisition method. CONCLUSION Pseudo-random CP O-space imaging, with a nonlinear SEM field designed for CS, is shown to reduce mean squared error of images at high acceleration over linear encoding methods for a 2D slice when using an eight channel circumferential receiver array for parallel imaging.
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Affiliation(s)
- Leo K Tam
- Yale University, Department of Diagnostic Radiology, New Haven, Connecticut, USA
| | - Gigi Galiana
- Yale University, Department of Diagnostic Radiology, New Haven, Connecticut, USA
| | - Jason P Stockmann
- Massachusetts General Hospital Martinos Center for Imaging, Boston, Massachusetts, USA
| | - Hemant Tagare
- Yale University, Department of Diagnostic Radiology, New Haven, Connecticut, USA.,Yale University, Department of Electrical Engineering, New Haven, Connecticut, USA.,Yale University, Department of Biomedical Engineering, New Haven, Connecticut, USA
| | - Dana C Peters
- Yale University, Department of Diagnostic Radiology, New Haven, Connecticut, USA
| | - R Todd Constable
- Yale University, Department of Diagnostic Radiology, New Haven, Connecticut, USA.,Yale University, Department of Biomedical Engineering, New Haven, Connecticut, USA.,Yale University, Department of Neurosurgery, New Haven, Connecticut, USA
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Schultz G, Gallichan D, Reisert M, Hennig J, Zaitsev M. MR image reconstruction from generalized projections. Magn Reson Med 2013; 72:546-57. [PMID: 24408880 DOI: 10.1002/mrm.24928] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/18/2013] [Revised: 07/09/2013] [Accepted: 07/29/2013] [Indexed: 11/06/2022]
Abstract
PURPOSE Currently, the time required for image reconstruction is prohibitively long if data are acquired using multidimensional imaging trajectories that make use of multichannel systems equipped with nonlinear gradients. Methods are presented that reduce the computational complexity of the iterative time-domain reconstruction algorithm down from O(N(4)) to O(N(3)). THEORY For generalized projections, a large class of multidimensional imaging trajectories, the encoding matrix can be focused to sparse bands by introducing an appropriate filter function along the frequency-encoding direction. The reconstruction can be speeded up by ignoring values below a predefined threshold level. METHODS Two methods are presented that differ in how the filter is incorporated into the reconstruction algorithm. The first method represents, without implementation of a threshold, a weighted version of the time-domain method, while the second method is equivalent to it. RESULTS Simulation and measurement results show that image reconstruction from high-resolution imaging data can be speeded up by up to two orders of magnitude. While the weighted reconstruction requires more iterations to reach an optimum than the second method, it is less sensitive to thresholding. CONCLUSION For complex spatial encoding strategies that involve nonlinear gradient fields, fast and accurate image reconstruction methods are provided that are particularly efficient for high-resolution anatomical imaging.
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Affiliation(s)
- Gerrit Schultz
- Medical Physics, Department of Radiology, University Medical Center Freiburg, Freiburg, Germany
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Karimi H, Dominguez-Viqueira W, Cunningham CH. Spatial encoding using the nonlinear field perturbations from magnetic materials. Magn Reson Med 2013; 72:399-408. [PMID: 24105884 DOI: 10.1002/mrm.24950] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/21/2013] [Revised: 08/19/2013] [Accepted: 08/20/2013] [Indexed: 11/07/2022]
Abstract
PURPOSE A proof-of-concept study was performed to assess the technical feasibility of using magnetic materials to generate spatial encoding fields. THEORY AND METHODS Spatially varying magnetic fields were generated by the placement of markers with different volume susceptibilities within the imaging volume. No linear gradients were used for spatial encoding during the signal acquisition. A signal-encoding model is described for reconstructing the images encoded with these field perturbations. Simulation and proof-of-concept experimental results are presented. Experiments were performed using field perturbations from a cylindrical marker as an example of the new encoding fields. Based on this experimental setup, annular rings were reconstructed from signals encoded with the new fields. RESULTS Simulation results were presented for different acquisition parameters. Proof-of-concept was supported by the correspondence of regions in an image reconstructed from experimental data compared to those in a conventional gradient-echo image. Experimental results showed that inclusions of dimensions 1.5 mm in size could be resolved with the experimental setup. CONCLUSION This study shows the technical feasibility of using magnetic markers to produce encoding fields. Magnetic materials will allow generating spatial encoding fields, which can be tailored to an imaging application with less complexity and at lower cost compared to the use of gradient inserts.
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Affiliation(s)
- Hirad Karimi
- Department of Medical Biophysics, University of Toronto, Toronto, Canada; Sunnybrook Research Institute, Physical Sciences Department, Toronto, Ontario, Canada
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Stockmann JP, Galiana G, Tam L, Juchem C, Nixon TW, Constable RT. In vivo O-Space imaging with a dedicated 12 cm Z2 insert coil on a human 3T scanner using phase map calibration. Magn Reson Med 2013; 69:444-55. [PMID: 22585546 PMCID: PMC3491108 DOI: 10.1002/mrm.24282] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/14/2011] [Revised: 01/28/2012] [Accepted: 03/03/2012] [Indexed: 11/11/2022]
Abstract
Recently, spatial encoding with nonlinear magnetic fields has drawn attention for its potential to achieve faster gradient switching within safety limits, tailored resolution in regions of interest, and improved parallel imaging using encoding fields that complement the sensitivity profiles of radio frequency receive arrays. Proposed methods can broadly be divided into those that use phase encoding (Cartesian-trajectory PatLoc and COGNAC) and those that acquire nonlinear projections (O-Space, Null space imaging, radial PatLoc, and 4D-RIO). Nonlinear projection data are most often reconstructed with iterative algorithms that backproject data using the full encoding matrix. Just like conventional radial sequences that use linear spatial encoding magnetic fields, nonlinear projection methods are more sensitive than phase encoding methods to imperfect calibration of the encoding fields. In this work, voxel-wise phase evolution is mapped at each acquired point in an O-Space trajectory using a variant of chemical shift imaging, capturing all spin dynamics caused by encoding fields, eddy currents, and pulse timing. Phase map calibration is then applied to data acquired from a high-power, 12 cm, Z2 insert coil with an eight-channel radio frequency transmit-receive array on a 3T human scanner. We show the first experimental proof-of-concept O-Space images on in vivo and phantom samples, paving the way for more in-depth exploration of O-Space and similar imaging methods.
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Affiliation(s)
- Jason P Stockmann
- Department of Biomedical Engineering, Yale University, New Haven, Connecticut 06520, USA.
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Layton KJ, Gallichan D, Testud F, Cocosco CA, Welz AM, Barmet C, Pruessmann KP, Hennig J, Zaitsev M. Single shot trajectory design for region-specific imaging using linear and nonlinear magnetic encoding fields. Magn Reson Med 2012; 70:684-96. [PMID: 23042707 DOI: 10.1002/mrm.24494] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/22/2012] [Revised: 07/18/2012] [Accepted: 08/18/2012] [Indexed: 11/10/2022]
Abstract
It has recently been demonstrated that nonlinear encoding fields result in a spatially varying resolution. This work develops an automated procedure to design single-shot trajectories that create a local resolution improvement in a region of interest. The technique is based on the design of optimized local k-space trajectories and can be applied to arbitrary hardware configurations that employ any number of linear and nonlinear encoding fields. The trajectories designed in this work are tested with the currently available hardware setup consisting of three standard linear gradients and two quadrupolar encoding fields generated from a custom-built gradient insert. A field camera is used to measure the actual encoding trajectories up to third-order terms, enabling accurate reconstructions of these demanding single-shot trajectories, although the eddy current and concomitant field terms of the gradient insert have not been completely characterized. The local resolution improvement is demonstrated in phantom and in vivo experiments.
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Affiliation(s)
- Kelvin J Layton
- Department of Electrical and Electronic Engineering, The University of Melbourne, Melbourne, Australia; National ICT Australia, Melbourne, Australia
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Galiana G, Stockmann JP, Tam L, Peters D, Tagare H, Constable RT. The Role of Nonlinear Gradients in Parallel Imaging: A k-Space Based Analysis. CONCEPTS IN MAGNETIC RESONANCE. PART A, BRIDGING EDUCATION AND RESEARCH 2012; 40A:253-267. [PMID: 26604857 PMCID: PMC4655121 DOI: 10.1002/cmr.a.21243] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
Sequences that encode the spatial information of an object using nonlinear gradient fields are a new frontier in MRI, with potential to provide lower peripheral nerve stimulation, windowed fields of view, tailored spatially-varying resolution, curved slices that mirror physiological geometry, and, most importantly, very fast parallel imaging with multichannel coils. The acceleration for multichannel images is generally explained by the fact that curvilinear gradient isocontours better complement the azimuthal spatial encoding provided by typical receiver arrays. However, the details of this complementarity have been more difficult to specify. We present a simple and intuitive framework for describing the mechanics of image formation with nonlinear gradients, and we use this framework to review some the main classes of nonlinear encoding schemes.
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Affiliation(s)
- Gigi Galiana
- Department of Diagnostic Radiology, Yale University, New Haven, CT
| | - Jason P Stockmann
- Department of Biomedical Engineering, Yale University, New Haven, CT
| | - Leo Tam
- Department of Biomedical Engineering, Yale University, New Haven, CT
| | - Dana Peters
- Department of Diagnostic Radiology, Yale University, New Haven, CT
| | - Hemant Tagare
- Department of Diagnostic Radiology, Yale University, New Haven, CT ; Department of Biomedical Engineering, Yale University, New Haven, CT
| | - R Todd Constable
- Department of Diagnostic Radiology, Yale University, New Haven, CT ; Department of Biomedical Engineering, Yale University, New Haven, CT ; Department of Neurosurgery, Yale University, New Haven, CT
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