1
|
Roth BJ. Can MRI Be Used as a Sensor to Record Neural Activity? SENSORS (BASEL, SWITZERLAND) 2023; 23:1337. [PMID: 36772381 PMCID: PMC9918955 DOI: 10.3390/s23031337] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 12/16/2022] [Revised: 01/17/2023] [Accepted: 01/24/2023] [Indexed: 06/18/2023]
Abstract
Magnetic resonance provides exquisite anatomical images and functional MRI monitors physiological activity by recording blood oxygenation. This review attempts to answer the following question: Can MRI be used as a sensor to directly record neural behavior? It considers MRI sensing of electrical activity in the heart and in peripheral nerves before turning to the central topic: recording of brain activity. The primary hypothesis is that bioelectric current produced by a nerve or muscle creates a magnetic field that influences the magnetic resonance signal, although other mechanisms for detection are also considered. Recent studies have provided evidence that using MRI to sense neural activity is possible under ideal conditions. Whether it can be used routinely to provide functional information about brain processes in people remains an open question. The review concludes with a survey of artificial intelligence techniques that have been applied to functional MRI and may be appropriate for MRI sensing of neural activity.
Collapse
Affiliation(s)
- Bradley J Roth
- Department of Physics, Oakland University, Rochester, MI 48309, USA
| |
Collapse
|
2
|
Serša I. Electric Current Detection Based on the MR Signal Magnitude Decay. Magn Reson Med 2022; 88:1282-1291. [PMID: 35510691 PMCID: PMC9325414 DOI: 10.1002/mrm.29278] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/08/2021] [Revised: 04/03/2022] [Accepted: 04/04/2022] [Indexed: 11/18/2022]
Abstract
Purpose Conventional current density imaging method, which relies on the detection of the magnetic field induced by the current in an image phase, is demanding and difficult to perform. In this study, a much simpler signal‐magnitude‐decay (SMD)–based current detection method is proposed. Methods Conductive test and biological samples were imaged at various TE times using the gradient‐ or spin‐echo imaging sequences with superimposed constant or bipolar currents, respectively. The SMD curve was sampled for each image voxel, which enabled voxel‐vise current density calculation by fitting an appropriate SMD model curve to the measured SMD curve. Effect of the voxel size on the signal decay and precision of the current density calculation was studied as well. Results It was shown theoretically, as well as verified by experiments on test and biological samples, that the current flowing though the sample creates an inhomogeneous magnetic field, which, as a consequence has a faster signal decay. Estimated current density from the measured signal decay increase agreed reasonably well with the actual current density, especially with the larger voxel sizes and longer times to signal acquisition. The sensitivity of the SMD method is up to 1/6 the sensitivity of the current density imaging method. Conclusion SMD method of current detection is not limited to any particular sample orientation or geometry, and any pulse sequence capable of acquisition of the current‐induced signal evolution in a voxel can be used for it. This widens the scope of its application from tissues to in vivo studies on animals and humans.
Collapse
Affiliation(s)
- Igor Serša
- Jožef Stefan Institute, Ljubljana, Slovenia.,Institute of Pathophysiology, Faculty of Medicine, University of Ljubljana, Ljubljana, Slovenia
| |
Collapse
|
3
|
Sveinsson B, Koonjoo N, Zhu B, Witzel T, Rosen MS. Detection of nanotesla AC magnetic fields using steady-state SIRS and ultra-low field MRI. J Neural Eng 2020; 17:034001. [PMID: 32268305 DOI: 10.1088/1741-2552/ab87fe] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
Abstract
OBJECTIVE Functional magnetic resonance imaging (fMRI) is commonly used to measure brain activity through the blood oxygen level dependent (BOLD) signal mechanism, but this only provides an indirect proxy signal to neuronal activity. Magnetoencephalography (MEG) provides a more direct measurement of the magnetic fields created by neuronal currents in the brain, but requires very specialized hardware and only measures these fields at the scalp. Recently, progress has been made to directly detect neuronal fields with MRI using the stimulus-induced rotary saturation (SIRS) effect, but interference from the BOLD response complicates such measurements. Here, we describe an approach to detect nanotesla-level, low-frequency alternating magnetic fields with an ultra-low field (ULF) MRI scanner, unaffected by the BOLD signal. APPROACH A steady-state implementation of the stimulus-induced rotary saturation (SIRS) method is developed. The method is designed to generate a strong signal at ultra-low magnetic field as well as allowing for efficient signal averaging, giving a high contrast-to-noise ratio (CNR). The method is tested in computer simulations and in phantom scans. MAIN RESULTS The simulations and phantom scans demonstrated the ability of the method to measure magnetic fields at different frequencies at ULF with a stronger contrast than non-steady-state approaches. Furthermore, the rapid imaging functionality of the method reduced noise efficiently. The results demonstrated sufficient CNR down to 7 nT, but the sensitivity will depend on the imaging parameters. SIGNIFICANCE A steady-state SIRS method is able to detect low-frequency alternating magnetic fields at ultra-low main magnetic field strengths with a large signal response and contrast-to-noise, presenting an important step in sensing biological fields with ULF MRI.
Collapse
Affiliation(s)
- Bragi Sveinsson
- A. A. Martinos Center for Biomedical Imaging, Massachusetts General Hospital, Boston, MA, United States of America. Department of Radiology, Harvard Medical School, Boston, MA, United States of America. Author to whom any correspondence should be addressed
| | | | | | | | | |
Collapse
|
4
|
Sadleir RJ, Fu F, Chauhan M. Functional magnetic resonance electrical impedance tomography (fMREIT) sensitivity analysis using an active bidomain finite-element model of neural tissue. Magn Reson Med 2018; 81:602-614. [PMID: 29770490 DOI: 10.1002/mrm.27351] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/28/2017] [Revised: 04/06/2018] [Accepted: 04/17/2018] [Indexed: 11/07/2022]
Abstract
PURPOSE A direct method of imaging neural activity was simulated to determine typical signal sizes. METHODS An active bidomain finite-element model was used to estimate approximate perturbations in MR phase data as a result of neural tissue activity, and when an external MR electrical impedance tomography imaging current was added to the region containing neural current sources. RESULTS Modeling-predicted, activity-related conductivity changes should produce measurable differential phase signals in practical MR electrical impedance tomography experiments conducted at moderate resolution at noise levels typical of high field systems. The primary dependence of MR electrical impedance tomography phase contrast on membrane conductivity changes, and not source strength, was demonstrated. CONCLUSION Because the injected imaging current may also affect the level of activity in the tissue of interest, this technique can be used synergistically with neuromodulation techniques such as deep brain stimulation, to examine mechanisms of action.
Collapse
Affiliation(s)
- Rosalind J Sadleir
- School of Biological and Health Systems Engineering, Arizona State University, Tempe, Arizona
| | - Fanrui Fu
- School of Biological and Health Systems Engineering, Arizona State University, Tempe, Arizona
| | - Munish Chauhan
- School of Biological and Health Systems Engineering, Arizona State University, Tempe, Arizona
| |
Collapse
|
5
|
Sadleir RJ, Fu F, Falgas C, Holland S, Boggess M, Grant SC, Woo EJ. Direct detection of neural activity in vitro using magnetic resonance electrical impedance tomography (MREIT). Neuroimage 2017; 161:104-119. [PMID: 28818695 PMCID: PMC5696120 DOI: 10.1016/j.neuroimage.2017.08.004] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/22/2017] [Revised: 07/19/2017] [Accepted: 08/01/2017] [Indexed: 11/18/2022] Open
Abstract
We describe a sequence of experiments performed in vitro to verify the existence of a new magnetic resonance imaging contrast - Magnetic Resonance Electrical Impedance Tomography (MREIT) -sensitive to changes in active membrane conductivity. We compared standard deviations in MREIT phase data from spontaneously active Aplysia abdominal ganglia in an artificial seawater background solution (ASW) with those found after treatment with an excitotoxic solution (KCl). We found significant increases in MREIT treatment cases, compared to control ganglia subject to extra ASW. This distinction was not found in phase images from the same ganglia using no imaging current. Further, significance and effect size depended on the amplitude of MREIT imaging current used. We conclude that our observations were linked to changes in cell conductivity caused by activity. Functional MREIT may have promise as a more direct method of functional neuroimaging than existing methods that image correlates of blood flow such as BOLD fMRI.
Collapse
Affiliation(s)
- Rosalind J Sadleir
- School of Biological and Health Systems Engineering, Arizona State University, 500 E. Tyler Mall, Tempe, AZ 85287-9709, USA.
| | - Fanrui Fu
- School of Biological and Health Systems Engineering, Arizona State University, 500 E. Tyler Mall, Tempe, AZ 85287-9709, USA
| | - Corey Falgas
- Department of Chemical and Biomedical Engineering, Florida A&M University-Florida State University College of Engineering, 2525 Pottsdamer Street, Tallahassee, FL 32310, USA
| | - Stephen Holland
- Department of Chemical and Biomedical Engineering, Florida A&M University-Florida State University College of Engineering, 2525 Pottsdamer Street, Tallahassee, FL 32310, USA
| | - May Boggess
- School of Mathematical and Statistical Sciences, Arizona State University, 901 S. Palm Walk, Tempe, AZ 85287-1804, USA
| | - Samuel C Grant
- Department of Chemical and Biomedical Engineering, Florida A&M University-Florida State University College of Engineering, 2525 Pottsdamer Street, Tallahassee, FL 32310, USA
| | - Eung Je Woo
- Dept. of Biomedical Engineering, College of Medicine, Kyung Hee University, 23 Kyungheedae-ro, Dongdaemun-gu, Seoul, 02447, South Korea
| |
Collapse
|
6
|
Sundaram P, Nummenmaa A, Wells W, Orbach D, Orringer D, Mulkern R, Okada Y. Direct neural current imaging in an intact cerebellum with magnetic resonance imaging. Neuroimage 2016; 132:477-490. [PMID: 26899788 DOI: 10.1016/j.neuroimage.2016.01.059] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/18/2015] [Revised: 11/10/2015] [Accepted: 01/26/2016] [Indexed: 10/22/2022] Open
Abstract
The ability to detect neuronal currents with high spatiotemporal resolution using magnetic resonance imaging (MRI) is important for studying human brain function in both health and disease. While significant progress has been made, we still lack evidence showing that it is possible to measure an MR signal time-locked to neuronal currents with a temporal waveform matching concurrently recorded local field potentials (LFPs). Also lacking is evidence that such MR data can be used to image current distribution in active tissue. Since these two results are lacking even in vitro, we obtained these data in an intact isolated whole cerebellum of turtle during slow neuronal activity mediated by metabotropic glutamate receptors using a gradient-echo EPI sequence (TR=100ms) at 4.7T. Our results show that it is possible (1) to reliably detect an MR phase shift time course matching that of the concurrently measured LFP evoked by stimulation of a cerebellar peduncle, (2) to detect the signal in single voxels of 0.1mm(3), (3) to determine the spatial phase map matching the magnetic field distribution predicted by the LFP map, (4) to estimate the distribution of neuronal current in the active tissue from a group-average phase map, and (5) to provide a quantitatively accurate theoretical account of the measured phase shifts. The peak values of the detected MR phase shifts were 0.27-0.37°, corresponding to local magnetic field changes of 0.67-0.93nT (for TE=26ms). Our work provides an empirical basis for future extensions to in vivo imaging of neuronal currents.
Collapse
Affiliation(s)
- Padmavathi Sundaram
- Department of Radiology, Boston Children's Hospital, Harvard Medical School, Boston, MA 02115, USA.
| | - Aapo Nummenmaa
- Athinoula A. Martinos Center for Biomedical Imaging, Department of Radiology, Massachusetts General Hospital, Harvard Medical School, Charlestown, MA 02129, USA.
| | - William Wells
- Department of Radiology, Brigham and Women's Hospital, Harvard Medical School, Boston, MA 02115, USA.
| | - Darren Orbach
- Department of Radiology, Boston Children's Hospital, Harvard Medical School, Boston, MA 02115, USA.
| | - Daniel Orringer
- Department of Neurosurgery, Brigham and Women's Hospital, Harvard Medical School, Boston, MA 02115, USA.
| | - Robert Mulkern
- Department of Radiology, Boston Children's Hospital, Harvard Medical School, Boston, MA 02115, USA.
| | - Yoshio Okada
- Department of Newborn Medicine, Boston Children's Hospital, Harvard Medical School, Boston, MA 02215, USA.
| |
Collapse
|
7
|
Current density imaging sequence for monitoring current distribution during delivery of electric pulses in irreversible electroporation. Biomed Eng Online 2015; 14 Suppl 3:S6. [PMID: 26356233 PMCID: PMC4565567 DOI: 10.1186/1475-925x-14-s3-s6] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022] Open
Abstract
Background Electroporation is gaining its importance in everyday clinical practice of cancer treatment. For its success it is extremely important that coverage of the target tissue, i.e. treated tumor, with electric field is within the specified range. Therefore, an efficient tool for the electric field monitoring in the tumor during delivery of electroporation pulses is needed. The electric field can be reconstructed by the magnetic resonance electric impedance tomography method from current density distribution data. In this study, the use of current density imaging with MRI for monitoring current density distribution during delivery of irreversible electroporation pulses was demonstrated. Methods Using a modified single-shot RARE sequence, where four 3000 V and 100 μs long pulses were included at the start, current distribution between a pair of electrodes inserted in a liver tissue sample was imaged. Two repetitions of the sequence with phases of refocusing radiofrequency pulses 90° apart were needed to acquire one current density image. For each sample in total 45 current density images were acquired to follow a standard protocol for irreversible electroporation where 90 electric pulses are delivered at 1 Hz. Results Acquired current density images showed that the current density in the middle of the sample increased from first to last electric pulses by 60%, i.e. from 8 kA/m2 to 13 kA/m2 and that direction of the current path did not change with repeated electric pulses significantly. Conclusions The presented single-shot RARE-based current density imaging sequence was used successfully to image current distribution during delivery of short high-voltage electric pulses. The method has a potential to enable monitoring of tumor coverage by electric field during irreversible electroporation tissue ablation.
Collapse
|
8
|
BagheriMofidi SM, Pouladian M, Jameie SB, Abbaspour Tehrani-Fard A. Computational Modeling of Neuronal Current MRI Signals with Rat Somatosensory Cortical Neurons. Interdiscip Sci 2015; 8:253-62. [PMID: 26293484 DOI: 10.1007/s12539-015-0104-0] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/04/2014] [Revised: 03/29/2015] [Accepted: 05/08/2015] [Indexed: 11/25/2022]
Abstract
Magnetic field generated by active neurons has recently been considered to determine location of neuronal activity directly with magnetic resonance imaging (MRI), but controversial results have been reported about detection of such small magnetic fields. In this study, multiple neuronal morphologies of rat tissue were modeled to investigate better estimation of MRI signal change produced by neuronal magnetic field (NMF). Ten pyramidal neurons from layer II to VI of rat somatosensory area with realistic morphology, biophysics, and neuronal density were modeled to simulate NMF of neuronal tissue, from which effects of NMF on MRI signals were obtained. Neuronal current MRI signals, which consist of relative magnitude signal change (RMSC) and phase signal change (PSC), were at least three and one orders of magnitude less than a tissue with single neuron type, respectively. Also, a reduction in voxel size could increase signal alterations. Furthermore, with selection of zenith angle of external main magnetic field related to tissue surface near to 90°, RMSC could be maximized. This value for PSC would be 90° for small voxel size and zero degree for large ones.
Collapse
Affiliation(s)
- Seyed Mehdi BagheriMofidi
- Department of Medical Radiation Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran.
| | - Majid Pouladian
- Department of Medical Radiation Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran
| | - Seyed Behnammodin Jameie
- Department of Medical Basic Sciences, Faculty of Allied Medicine, IUMS, Tehran, Iran
- Department of Anatomy, Faculty of Medicine, IUMS, Tehran, Iran
| | | |
Collapse
|
9
|
Balasubramanian M, Mulkern RV, Wells WM, Sundaram P, Orbach DB. Magnetic resonance imaging of ionic currents in solution: the effect of magnetohydrodynamic flow. Magn Reson Med 2014; 74:1145-55. [PMID: 25273917 DOI: 10.1002/mrm.25445] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/09/2014] [Revised: 07/25/2014] [Accepted: 08/15/2014] [Indexed: 11/06/2022]
Abstract
PURPOSE Reliably detecting MRI signals in the brain that are more tightly coupled to neural activity than blood-oxygen-level-dependent fMRI signals could not only prove valuable for basic scientific research but could also enhance clinical applications such as epilepsy presurgical mapping. This endeavor will likely benefit from an improved understanding of the behavior of ionic currents, the mediators of neural activity, in the presence of the strong magnetic fields that are typical of modern-day MRI scanners. THEORY Of the various mechanisms that have been proposed to explain the behavior of ionic volume currents in a magnetic field, only one-magnetohydrodynamic flow-predicts a slow evolution of signals, on the order of a minute for normal saline in a typical MRI scanner. METHODS This prediction was tested by scanning a volume-current phantom containing normal saline with gradient-echo-planar imaging at 3 T. RESULTS Greater signal changes were observed in the phase of the images than in the magnitude, with the changes evolving on the order of a minute. CONCLUSION These results provide experimental support for the MHD flow hypothesis. Furthermore, MHD-driven cerebrospinal fluid flow could provide a novel fMRI contrast mechanism.
Collapse
Affiliation(s)
- Mukund Balasubramanian
- Department of Radiology, Boston Children's Hospital, Harvard Medical School, Boston, Massachusetts, USA
| | - Robert V Mulkern
- Department of Radiology, Boston Children's Hospital, Harvard Medical School, Boston, Massachusetts, USA
| | - William M Wells
- Department of Radiology, Brigham and Women's Hospital, Harvard Medical School, Boston, Massachusetts, USA
| | - Padmavathi Sundaram
- Department of Radiology, Boston Children's Hospital, Harvard Medical School, Boston, Massachusetts, USA
| | - Darren B Orbach
- Department of Radiology, Boston Children's Hospital, Harvard Medical School, Boston, Massachusetts, USA
| |
Collapse
|
10
|
Du J, Vegh V, Reutens DC. MRI signal phase oscillates with neuronal activity in cerebral cortex: implications for neuronal current imaging. Neuroimage 2014; 94:1-11. [PMID: 24642284 DOI: 10.1016/j.neuroimage.2014.03.015] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/03/2013] [Revised: 02/06/2014] [Accepted: 03/08/2014] [Indexed: 10/25/2022] Open
Abstract
Neuronal activity produces transient ionic currents that may be detectable using magnetic resonance imaging (MRI). We examined the feasibility of MRI-based detection of neuronal currents using computer simulations based on the laminar cortex model (LCM). Instead of simulating the activity of single neurons, we decomposed neuronal activity to action potentials (AP) and postsynaptic potentials (PSP). The geometries of dendrites and axons were generated dynamically to account for diverse neuronal morphologies. Magnetic fields associated with APs and PSPs were calculated during spontaneous and stimulated cortical activity, from which the neuronal current induced MRI signal was determined. We found that the MRI signal magnitude change (<0.1 ppm) is below currently detectable levels but that the signal phase change is likely to be detectable. Furthermore, neuronal MRI signals are sensitive to temporal and spatial variations in neuronal activity but independent of the intensity of neuronal activation. Synchronised neuronal activity produces large phase changes (in the order of 0.1 mrad). However, signal phase oscillates with neuronal activity. Consequently, MRI scans need to be synchronised with neuronal oscillations to maximise the likelihood of detecting signal phase changes due to neuronal currents. These findings inform the design of MRI experiments to detect neuronal currents.
Collapse
Affiliation(s)
- Jiaxin Du
- The University of Queensland, Centre for Advanced Imaging, Brisbane, Queensland 4072, Australia
| | - Viktor Vegh
- The University of Queensland, Centre for Advanced Imaging, Brisbane, Queensland 4072, Australia.
| | - David C Reutens
- The University of Queensland, Centre for Advanced Imaging, Brisbane, Queensland 4072, Australia
| |
Collapse
|
11
|
Jiang X, Lu H, Shigeno S, Tan LH, Yang Y, Ragsdale CW, Gao JH. Octopus visual system: a functional MRI model for detecting neuronal electric currents without a blood-oxygen-level-dependent confound. Magn Reson Med 2013; 72:1311-9. [PMID: 24301336 DOI: 10.1002/mrm.25051] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/27/2013] [Revised: 09/27/2013] [Accepted: 10/28/2013] [Indexed: 11/09/2022]
Abstract
PURPOSE Despite the efforts that have been devoted to detecting the transient magnetic fields generated by neuronal firing, the conclusion that a functionally relevant signal can be measured with MRI is still controversial. For human studies of neuronal current MRI (nc-MRI), the blood-oxygen-level-dependent (BOLD) effect remains an irresolvable confound. For tissue studies where hemoglobin is removed, natural sensory stimulation is not possible. This study investigates the feasibility of detecting a physiologically induced nc-MRI signal in vivo in a BOLD-free environment. METHODS The cephalopod mollusc Octopus bimaculoides has vertebrate-like eyes, large optic lobes (OLs), and blood that does not contain hemoglobin. Visually evoked potentials were measured in the octopus retina and OL by electroretinogram and local field potential. nc-MRI scans were conducted at 9.4 Tesla to capture these activities. RESULTS Electrophysiological recording detected strong responses in the retina and OL in vivo; however, nc-MRI failed to demonstrate any statistically significant signal change with a detection threshold of 0.2° for phase and 0.2% for magnitude. Experiments in a dissected eye-OL preparation yielded similar results. CONCLUSION These findings in a large hemoglobin-free nervous system suggest that sensory evoked neuronal magnetic fields are too weak for direct detection with current MRI technology.
Collapse
Affiliation(s)
- Xia Jiang
- Brain Research Imaging Center and Department of Radiology, University of Chicago, Chicago, Illinois, USA
| | | | | | | | | | | | | |
Collapse
|
12
|
Körber R, Nieminen JO, Höfner N, Jazbinšek V, Scheer HJ, Kim K, Burghoff M. An advanced phantom study assessing the feasibility of neuronal current imaging by ultra-low-field NMR. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2013; 237:182-190. [PMID: 24252245 DOI: 10.1016/j.jmr.2013.10.011] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/29/2013] [Revised: 10/17/2013] [Accepted: 10/19/2013] [Indexed: 06/02/2023]
Abstract
In ultra-low-field (ULF) NMR/MRI, a common scheme is to magnetize the sample by a polarizing field of up to hundreds of mT, after which the NMR signal, precessing in a field on the order of several μT, is detected with superconducting quantum interference devices (SQUIDs). In our ULF-NMR system, we polarize with up to 50mT and deploy a single-stage DC-SQUID current sensor with an integrated input coil which is connected to a wire-wound Nb gradiometer. We developed this system (white noise 0.50fT/√Hz) for assessing the feasibility of imaging neuronal currents by detecting their effect on the ULF-NMR signal. Magnetoencephalography investigations of evoked brain activity showed neuronal dipole moments below 50nAm. With our instrumentation, we have studied two different approaches for neuronal current imaging. In the so-called DC effect, long-lived neuronal activity shifts the Larmor frequency of the surrounding protons. An alternative strategy is to exploit fast neuronal activity as a tipping pulse. This so-called AC effect requires the proton Larmor frequency to match the frequency of the neuronal activity, which ranges from near-DC to ∼kHz. We emulated neuronal activity by means of a single dipolar source in a physical phantom, consisting of a hollow sphere filled with an aqueous solution of CuSO4 and NaCl. In these phantom studies, with physiologically relevant dipole depths, we determined resolution limits for our set-up for the AC and the DC effect of ∼10μAm and ∼50nAm, respectively. Hence, the DC effect appears to be detectable in vivo by current ULF-NMR technology.
Collapse
Affiliation(s)
- Rainer Körber
- Physikalisch-Technische Bundesanstalt (PTB), Abbestrasse 2-12, 10587 Berlin, Germany.
| | - Jaakko O Nieminen
- Physikalisch-Technische Bundesanstalt (PTB), Abbestrasse 2-12, 10587 Berlin, Germany; Department of Biomedical Engineering and Computational Science, Aalto University School of Science, P.O. Box 12200, FI-00076 AALTO, Finland
| | - Nora Höfner
- Physikalisch-Technische Bundesanstalt (PTB), Abbestrasse 2-12, 10587 Berlin, Germany
| | - Vojko Jazbinšek
- Institute of Mathematics, Physics and Mechanics, Jadranska 19, 1000 Ljubljana, Slovenia
| | - Hans-Jürgen Scheer
- Physikalisch-Technische Bundesanstalt (PTB), Abbestrasse 2-12, 10587 Berlin, Germany
| | - Kiwoong Kim
- Korea Research Institute of Standards and Science, Daejeon 305-340, South Korea
| | - Martin Burghoff
- Physikalisch-Technische Bundesanstalt (PTB), Abbestrasse 2-12, 10587 Berlin, Germany
| |
Collapse
|
13
|
Magnetic resonance imaging at frequencies below 1 kHz. Magn Reson Imaging 2012; 31:171-7. [PMID: 22898690 DOI: 10.1016/j.mri.2012.06.014] [Citation(s) in RCA: 29] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/30/2012] [Revised: 05/31/2012] [Accepted: 06/16/2012] [Indexed: 11/23/2022]
Abstract
Within the magnetic resonance imaging (MRI) community the trend is going to higher and higher magnetic fields, ranging from 1.5 T to 7 T, corresponding to Larmor frequencies of 63.8-298 MHz. Since for high-field MRI the magnetization increases with the applied magnetic field, the signal-to-noise-ratio increases as well, thus enabling higher image resolutions. On the other hand, MRI is possible also at ultra-low magnetic fields, as was shown by different groups. The goal of our development was to reach a Larmor frequency range of the low-field MRI system corresponding to the frequency range of human brain activities ranging from near zero-frequency (near-DC) to over 1 kHz. Here, first 2D MRI images of phantoms taken at Larmor frequencies of 100 Hz and 731 Hz will be shown and discussed. These frequencies are examples of brain activity triggered by electrostimulation of the median nerve. The method will allow the magnetic fields of the brain currents to influence the magnetic resonance image, and thus lead to a direct functional imaging modality of neuronal currents.
Collapse
|
14
|
Is it possible to detect dendrite currents using presently available magnetic resonance imaging techniques? Med Biol Eng Comput 2012; 50:651-7. [PMID: 22447349 DOI: 10.1007/s11517-012-0899-3] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/30/2011] [Accepted: 03/10/2012] [Indexed: 10/28/2022]
Abstract
The action currents of a dendrite, peripheral nerve or skeletal muscle create their own magnetic field. Many investigators have attempted to detect neural and dendritic currents directly using magnetic resonance imaging that can cause the phase of the spins to change. Our goal in this paper is to use the calculated magnetic field of a dendrite to estimate the resulting phase shift in the magnetic resonance signal. The field produced by a dense collection of simultaneously active dendrites may be just detectable under the most ideal circumstances, but in almost every realistic case the field cannot be detected using current MRI technology.
Collapse
|
15
|
Buračas GT, Jung Y, Lee J, Buxton RB, Wong EC, Liu TT. On multiple alternating steady states induced by periodic spin phase perturbation waveforms. Magn Reson Med 2011; 67:1412-8. [PMID: 21826730 DOI: 10.1002/mrm.23105] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/24/2011] [Revised: 05/29/2011] [Accepted: 06/25/2011] [Indexed: 11/09/2022]
Abstract
Direct measurement of neural currents by means of MRI can potentially open a high temporal resolution (10-100 ms) window applicable for monitoring dynamics of neuronal activity without loss of the high spatial resolution afforded by MRI. Previously, we have shown that the alternating balanced steady state imaging affords high sensitivity to weak periodic currents owing to its amplification of periodic spin phase perturbations. This technique, however, requires precise synchronization of such perturbations to the radiofrequency pulses. Herein, we extend alternating balanced steady state imaging to multiple balanced alternating steady states for estimation of neural current waveforms. Simulations and phantom experiments show that the off-resonance profile of the multiple alternating steady state signal carries information about the frequency content of driving waveforms. In addition, the method is less sensitive than alternating balanced steady state to precise waveform timing relative to radiofrequency pulses. Thus, multiple alternating steady state technique is potentially applicable to MR imaging of the waveforms of periodic neuronal activity.
Collapse
Affiliation(s)
- Giedrius T Buračas
- Center for Functional MRI, Department of Radiology, University of California, San Diego, La Jolla, California 92037, USA.
| | | | | | | | | | | |
Collapse
|
16
|
Luo Q, Gao JH. Modeling magnitude and phase neuronal current MRI signal dependence on echo time. Magn Reson Med 2011; 64:1832-7. [PMID: 20665823 DOI: 10.1002/mrm.22569] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
Abstract
To enhance sensitivity in measuring neuronal current MRI (ncMRI) signal using T(2)*-weighted sequences, appropriate selection of echo time (TE) is vital for optimizing data acquisition strategy. The purpose of this study is to establish the contrast-to-noise ratio of neuronal current MRI signal dependence on TE and determine the optimum TE (TE(opt)) in achieving its highest detection power. The TE(opt) in human brain and tissue preparation at 1.5, 3, and 7 T are estimated with different voxel sizes. Our results show that TE(opt) values are different between magnitude and phase images, and TE(opt) is larger in magnitude than phase imaging. This suggests that a dual-echo data acquisition strategy would provide the best efficiency in detecting magnitude and phase neuronal current MRI signals simultaneously. Our results also indicated that the detection sensitivity will be stronger at lower magnetic fields for human brain, whereas the sensitivity will be enhanced/reduced as field strength increases for phase/magnitude imaging on tissue preparation.
Collapse
Affiliation(s)
- Qingfei Luo
- Department of Radiology, Brain Research Imaging Center, The University of Chicago, Chicago, Illinois 60637, USA
| | | |
Collapse
|
17
|
Oh T, Gilad O, Ghosh A, Schuettler M, Holder DS. A novel method for recording neuronal depolarization with recording at 125-825 Hz: implications for imaging fast neural activity in the brain with electrical impedance tomography. Med Biol Eng Comput 2011; 49:593-604. [PMID: 21448692 DOI: 10.1007/s11517-011-0761-z] [Citation(s) in RCA: 43] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/12/2010] [Accepted: 03/10/2011] [Indexed: 02/01/2023]
Abstract
Electrical impedance tomography (EIT) is a recently developed medical imaging method which has the potential to produce images of fast neuronal depolarization in the brain. Previous modelling suggested that applied current needed to be below 100 Hz but the signal-to-noise ratio (SNR) recorded with scalp electrodes during evoked responses was too low to permit imaging. A novel method in which contemporaneous evoked potentials are subtracted is presented with current applied at 225 Hz to cerebral cortex during evoked activity; although the signal is smaller than at DC by about 10×, the principal noise from the EEG is reduced by about 1000×, resulting in an improved SNR. It was validated with recording of compound action potentials in crab walking leg nerve where peak changes of -0.2% at 125 and 175 Hz tallied with biophysical modelling. In recording from rat cerebral cortex during somatosensory evoked responses, peak impedance decreases of -0.07 ± 0.006% (mean ± SE) with a SNR of >50 could be recorded at 225 Hz. This method provides a reproducible and artefact free means for recording resistance changes during neuronal activity which could form the basis for imaging fast neural activity in the brain.
Collapse
Affiliation(s)
- T Oh
- Department of Medical Physics, University College London, London, UK
| | | | | | | | | |
Collapse
|
18
|
Luo Q, Jiang X, Chen B, Zhu Y, Gao JH. Modeling neuronal current MRI signal with human neuron. Magn Reson Med 2011; 65:1680-9. [PMID: 21254209 DOI: 10.1002/mrm.22764] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/15/2010] [Revised: 11/20/2010] [Accepted: 11/24/2010] [Indexed: 11/08/2022]
Abstract
Up to date, no consensus has been achieved regarding the possibility of detecting neuronal currents by MRI (ncMRI) in human brain. To evaluate the detectability of ncMRI, an effective way is to simulate ncMRI signal with the realistic neuronal geometry and electrophysiological processes. Unfortunately, previous realistic ncMRI models are based on rat and monkey neurons. The species difference in neuronal morphology and physiology would prevent these models from simulating the ncMRI signal accurately in human subjects. The aim of this study is to bridge this gap by establishing a realistic ncMRI model specifically for human cerebral cortex. In this model, the ncMRI signal was simulated using anatomically reconstructed human pyramidal neurons and their biophysical properties. The modeling results showed that the amplitude of ncMRI signal significantly depends on the density of synchronously firing neurons and imaging conditions such as position of imaging voxel, direction of main magnetic field (B(0) ) relative to the cortical surface and echo time. The results indicated that physiologically-evoked ncMRI signal is too weak to be detected (magnitude/phase change ≤ -1.4 × 10(-6) /0.02°), but the phase signal induced by spontaneous activity may reach a detectable level (up to 0.2°) in favorable conditions.
Collapse
Affiliation(s)
- Qingfei Luo
- Department of Radiology, Brain Research Imaging Center, The University of Chicago, Chicago, Illinois 60637, USA
| | | | | | | | | |
Collapse
|
19
|
Körber R, Curio G, Hartwig S, Hilschenz I, Höfner N, Scheer HJ, Trahms L, Voigt J, Burghoff M. Simultaneous measurements of somatosensory evoked AC and near-DC MEG signals. ACTA ACUST UNITED AC 2011; 56:91-7. [DOI: 10.1515/bmt.2011.007] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
|
20
|
Huang YL, Xiong HC, Yao DZ. Direct MRI detection of the neuronal magnetic field: the effect of the dendrite branch. Phys Med Biol 2010; 55:5599-616. [PMID: 20808026 DOI: 10.1088/0031-9155/55/18/022] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
Abstract
In recent years, neuronal current MRI (nc-MRI) was proposed as a new imaging method to directly map the magnetic field change caused by neuronal activity. Nc-MRI could offer improved spatial and temporal resolution compared to blood hemodynamics-based functional magnetic resonance imaging (fMRI). In this paper, with a finite current dipole as the model of dendrite or dendrite branch, we investigated the spatial distribution of the magnetic field generated by synchronously activated neurons to evaluate the possibility of nc-MRI. Our simulations imply that the existence of a dendrite branch may not only increase the strength of the neuronal magnetic field (NMF), but also raise the non-uniform and unsymmetry of the NMF; therefore, it can enhance the detectability of the neuronal current magnetic field by MRI directly. The results show that the signal phase shift is enlarged, but it is unstable and is still very small, <<1 radian, while the magnitude signal may be strong enough for a typical MRI voxel to be detected. We suggest making further efforts to measure the magnitude signal which may induce a large effect in an nc-MRI experiment.
Collapse
Affiliation(s)
- Ying-Ling Huang
- Key Laboratory for NeuroInformation of Ministry of Education, School of Life Science and Technology, University of Electronic Science and Technology of China, Chengdu 610054, Sichuan, People's Republic of China
| | | | | |
Collapse
|
21
|
Sersa I. Enhanced sensitivity current density imaging. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2010; 204:219-224. [PMID: 20303307 DOI: 10.1016/j.jmr.2010.02.025] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/28/2009] [Revised: 02/24/2010] [Accepted: 02/24/2010] [Indexed: 05/29/2023]
Abstract
One of the major weaknesses of current density imaging (CDI) is its poor sensitivity and therefore a need for the use of high voltage in CDI. In this work, a new CDI technique with enhanced sensitivity (ES-CDI) is presented. The ES-CDI sequence overcomes the sensitivity problem in samples with a long T(2) relaxation time that allows the use of a long current encoding period. As successful CDI detection is conditioned by a sufficiently large product of current and its application time a longer current encoding period enables the use of lower current and also lower voltage therefore significantly reducing any sample damage. In addition, the ES-CDI sequence also uses fast image signal acquisition and so enables heavy signal averaging and with it associated additional CDI sensitivity increase within the experiment time of the conventional CDI experiment. The feasibility of the ES-CDI sequence was tested on a model sample filled with physiological solution. Voltage of just 1 V and current application time of 800 ms were sufficient to detect current density of 20A/m(2) with a detection limit of 0.7A/m(2).
Collapse
Affiliation(s)
- Igor Sersa
- Jozef Stefan Institute, Jamova 39, 1000 Ljubljana, Slovenia.
| |
Collapse
|
22
|
Dubey RB, Hanmandlu M, Gupta SK, Gupta SK. The brain MR Image segmentation techniques and use of diagnostic packages. Acad Radiol 2010; 17:658-71. [PMID: 20211569 DOI: 10.1016/j.acra.2009.12.017] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/12/2009] [Revised: 12/10/2009] [Accepted: 12/12/2009] [Indexed: 11/27/2022]
Abstract
RATIONALE AND OBJECTIVES This article provides a survey of segmentation methods for medical images. Usually, classification of segmentation methods is done based on the approaches adopted and the domain of application. MATERIALS AND METHODS This survey is conducted on the recent segmentation methods used in biomedical image processing and explores the methods useful for better segmentation. A critical appraisal of the current status of semiautomated and automated methods is made for the segmentation of anatomical medical images emphasizing the advantages and disadvantages. Computer-aided diagnosis (CAD) used by radiologists as a second opinion has become one of the major research areas in medical imaging and diagnostic radiology. A picture archiving communication system (PACS) is an integrated workflow system for managing images and related data that is designed to streamline operations throughout the whole patient care delivery process. RESULTS By using PACS, the medical image interpretation may be changed from conventional hard-copy images to soft-copy studies viewed on the systems workstations. CONCLUSION The automatic segmentations assist the doctors in making quick diagnosis. The CAD need not be comparable to that of physicians, but is surely complementary.
Collapse
|
23
|
Abstract
Functional MRI has become an important tool of researchers and clinicians who seek to understand patterns of neuronal activation that accompany sensory and cognitive processes. However, the interpretation of fMRI images rests on assumptions about the relationship between neuronal firing and hemodynamic response that are not firmly grounded in rigorous theory or experimental evidence. Further, the blood-oxygen-level-dependent effect, which correlates an MRI observable to neuronal firing, evolves over a period that is 2 orders of magnitude longer than the underlying processes that are thought to cause it. Here, we instead demonstrate experiments to directly image oscillating currents by MRI. The approach rests on a resonant interaction between an applied rf field and an oscillating magnetic field in the sample and, as such, permits quantitative, frequency-selective measurements of current density without spatial or temporal cancellation. We apply this method in a current loop phantom, mapping its magnetic field and achieving a detection sensitivity near the threshold required for the detection of neuronal currents. Because the contrast mechanism is under spectroscopic control, we are able to demonstrate how ramped and phase-modulated spin-lock radiation can enhance the sensitivity and robustness of the experiment. We further demonstrate the combination of these methods with remote detection, a technique in which the encoding and detection of an MRI experiment are separated by sample flow or translation. We illustrate that remotely detected MRI permits the measurement of currents in small volumes of flowing water with high sensitivity and spatial resolution.
Collapse
|
24
|
Luo Q, Lu H, Lu H, Yang Y, Gao JH. Comparison of visually evoked local field potentials in isolated turtle brain: Patterned versus blank stimulation. J Neurosci Methods 2010; 187:26-32. [PMID: 20034520 DOI: 10.1016/j.jneumeth.2009.12.005] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/23/2009] [Revised: 12/09/2009] [Accepted: 12/11/2009] [Indexed: 11/17/2022]
Affiliation(s)
- Qingfei Luo
- Department of Radiology, Brain Research Imaging Center, The University of Chicago, Chicago, IL 60637, United States
| | | | | | | | | |
Collapse
|
25
|
Rodionov R, Siniatchkin M, Michel CM, Liston AD, Thornton R, Guye M, Carmichael DW, Lemieux L. Looking for neuronal currents using MRI: an EEG-fMRI investigation of fast MR signal changes time-locked to frequent focal epileptic discharges. Neuroimage 2009; 50:1109-17. [PMID: 20044009 DOI: 10.1016/j.neuroimage.2009.12.076] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/23/2009] [Revised: 12/16/2009] [Accepted: 12/18/2009] [Indexed: 11/28/2022] Open
Abstract
RATIONALE Reproducible direct measurement of neuronal electrical activity using MRI signal changes due to local magnetic field perturbations would represent a step change in neuroimaging methods. While some previous studies using experiments based on evoked and spontaneous activity provided encouraging results no clear demonstration of neuronal current-related MR changes in the human brain has emerged to date. The availability of simultaneously acquired EEG-fMRI in patients with frequent interictal epileptic discharges (IED), which have significantly greater amplitude than evoked potentials, offers the opportunity to further investigate the phenomenon. METHODS We re-analysed simultaneously acquired EEG-fMRI data in 6 epilepsy patients with very frequent focal IED and a well-localised generator. A model of MRI signal changes due to fast activity and BOLD signal changes was used to identify fast MR signal changes, potentially directly reflecting neuronal activity. Simultaneously-acquired EEG allowed the comparison of electrical source localisation (ESI), clinical epilepsy localisation and BOLD signal changes with the fast MR signal changes. RESULTS Clusters of IED-related fast MR signal change were observed in all cases. Spatial correspondence between the IED-related fast MR, BOLD, ESI clusters and irritative zone (IZ) was observed in one slice of a single dataset. The other IED-related fast MR clusters were remote from electro-clinically determined generators of interictal activity. The sign and magnitude of the fast MR signal changes varied across regions and subjects. CONCLUSION The observed fast MR changes cannot be confidently attributed to the direct effect of neuronal currents due to lack of spatial concordance with generators of interictal activity, IED-related BOLD clusters and ESI estimates.
Collapse
Affiliation(s)
- Roman Rodionov
- Department of Clinical and Experimental Epilepsy, UCL Institute of Neurology, University College London, London, UK.
| | | | | | | | | | | | | | | |
Collapse
|
26
|
Xue Y, Chen X, Grabowski T, Xiong J. Direct MRI mapping of neuronal activity evoked by electrical stimulation of the median nerve at the right wrist. Magn Reson Med 2009; 61:1073-82. [PMID: 19466755 DOI: 10.1002/mrm.21857] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
Abstract
Magnetic source MRI (msMRI) has being developed recently for direct detections of neuronal magnetic fields to map brain activity. However, controversial results have been reported by different research groups. In this study, more evidence was provided to demonstrate that the neuronal current signal could be detected by MRI using a rapid median nerve stimulation paradigm. The experiments were performed on six normal human participants to investigate the temporal specificity of the effect, as well as inter- and intrasubject reproducibility. Significant activation of contralateral primary sensory cortex (S1) was detected 80 ms after stimulation onset (corresponding to the P80 evoked potential peak). The 80-ms latency S1 activation was observed over three independent sessions for one subject and for all six participants. The magnitude of the signal change was 0.2-0.3%. Coinciding with our expectations, no S1 activation was found when MRI data acquisitions were targeted at the N20 and P30 peaks because of mutual cancellation of magnetic fields generated by those peaks. The results demonstrated good reproducibility of S1 activations and indicated that the S1 activations most likely originated from neuronal magnetic field rather than hemodynamic response.
Collapse
Affiliation(s)
- Yiqun Xue
- Department of Biomedical Engineering, University of Iowa, Iowa City, Iowa 52242, USA
| | | | | | | |
Collapse
|
27
|
Luo Q, Lu H, Lu H, Senseman D, Worsley K, Yang Y, Gao JH. Physiologically evoked neuronal current MRI in a bloodless turtle brain: detectable or not? Neuroimage 2009; 47:1268-76. [PMID: 19539040 DOI: 10.1016/j.neuroimage.2009.06.017] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/14/2009] [Revised: 05/29/2009] [Accepted: 06/05/2009] [Indexed: 10/20/2022] Open
Abstract
Contradictory reports regarding the detection of neuronal currents have left the feasibility of neuronal current MRI (ncMRI) an open question. Most previous ncMRI studies in human subjects are suspect due to their inability to separate or eliminate hemodynamic effects. In this study, we used a bloodless turtle brain preparation that eliminates hemodynamic effects, to explore the feasibility of detecting visually-evoked ncMRI signals at 9.4 T. Intact turtle brains, with eyes attached, were dissected from the cranium and placed in artificial cerebral spinal fluid. Light flashes were delivered to the eyes to evoke neuronal activity. Local field potential (LFP) and MRI signals were measured in an interleaved fashion. Robust visually-evoked LFP signals were observed in turtle brains, but no significant signal changes synchronized with neuronal currents were found in the ncMRI images. In this study, detection thresholds of 0.1% and 0.1 degrees were set for MRI magnitude and phase signal changes, respectively. The absence of significant signal changes in the MRI images suggests that visually-evoked ncMRI signals in the turtle brain are below these detectable levels.
Collapse
Affiliation(s)
- Qingfei Luo
- Brain Research Imaging Center and Department of Radiology, The University of Chicago, Chicago, IL 60637, USA
| | | | | | | | | | | | | |
Collapse
|
28
|
Gilad O, Horesh L, Holder DS. A modelling study to inform specification and optimal electrode placement for imaging of neuronal depolarization during visual evoked responses by electrical and magnetic detection impedance tomography. Physiol Meas 2009; 30:S201-24. [DOI: 10.1088/0967-3334/30/6/s14] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
|
29
|
Gilad O, Ghosh A, Oh D, Holder DS. A method for recording resistance changes non-invasively during neuronal depolarization with a view to imaging brain activity with electrical impedance tomography. J Neurosci Methods 2009; 180:87-96. [PMID: 19427534 PMCID: PMC2813208 DOI: 10.1016/j.jneumeth.2009.03.012] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/15/2008] [Revised: 03/03/2009] [Accepted: 03/09/2009] [Indexed: 10/21/2022]
Abstract
Electrical impedance tomography (EIT) is a recently developed medical imaging method which has the potential to produce images of fast neuronal depolarization in the brain. The principle is that current remains in the extracellular space at rest but passes into the intracellular space during depolarization through open ion channels. As current passes into the intracellular space across the capacitance of cell membranes at higher frequencies, applied current needs to be below 100 Hz. A method is presented for its measurement with subtraction of the contemporaneous evoked potentials which occur in the same frequency band. Neuronal activity is evoked by stimulation and resistance is recorded from the potentials resulting from injection of a constant current square wave at 1 Hz with amplitude less than 25% of the threshold for stimulating neuronal activity. Potentials due to the evoked activity and the injected square wave are removed by subtraction. The method was validated with compound action potentials in crab walking leg nerve. Resistance changes of -0.85+/-0.4% (mean+/-SD) occurred which decreased from -0.97+/-0.43% to -0.46+/-0.16% with spacing of impedance current application electrodes from 2 to 8 mm but did not vary significantly with applied currents of 1-10 microA. These tallied with biophysical modelling, and so were consistent with a genuine physiological origin. This method appears to provide a reproducible and artefact free means for recording resistance changes during neuronal activity which could lead to the long-term goal of imaging of fast neural activity in the brain.
Collapse
Affiliation(s)
- Ori Gilad
- Department of Clinical Neurophysiology, University College London, London, UK.
| | | | | | | |
Collapse
|
30
|
Impedance changes recorded with scalp electrodes during visual evoked responses: implications for Electrical Impedance Tomography of fast neural activity. Neuroimage 2009; 47:514-22. [PMID: 19426819 DOI: 10.1016/j.neuroimage.2009.04.085] [Citation(s) in RCA: 36] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/02/2008] [Revised: 04/23/2009] [Accepted: 04/28/2009] [Indexed: 11/21/2022] Open
Abstract
Electrical Impedance Tomography (EIT) is a recently developed medical imaging method which could enable fast neural imaging in the brain by recording the resistance changes which occur as ion channels open during neuronal depolarization. In published studies in animal models with intracranial electrodes, changes of 0.005 to 3% have been reported but the amplitude of changes in the human is not known. The purpose of this work was to determine if resistance changes could be recorded non-invasively in humans during evoked activity which could form the basis for EIT of fast neural activity. Resistance was recorded with scalp electrodes during 2 Hz pattern visual evoked responses over 10 min using an insensible 1 Hz square wave constant current of 0.1-1 mA. Significant resistance decreases of 0.0010+/-0.0005% (0.30+/-0.15 microV, signal-to-noise ratio (SNR) of 2:1, n=16 recordings over 6 subjects) (mean+/-SE) were recorded. These are in broad agreement with modelling which estimated changes of 0.0039+/-0.0034% (1.03+/-0.75 microV) using an anatomically realistic finite element model. This is the first demonstration of such changes in humans and so encourages the belief that EIT could be used for neural imaging. Unfortunately, the signal-to-noise ratio was not sufficient to permit imaging at present because recording over multiple injection sites needed for imaging would require impractically long recording times. However, in the future, invasive imaging with intracranial electrodes in animal models or humans and improved signal processing or recording may still enable imaging; this would constitute a significant advance in neuroscience technology.
Collapse
|
31
|
Cassará AM, Maraviglia B, Hartwig S, Trahms L, Burghoff M. Neuronal current detection with low-field magnetic resonance: simulations and methods. Magn Reson Imaging 2009; 27:1131-9. [PMID: 19269766 DOI: 10.1016/j.mri.2009.01.015] [Citation(s) in RCA: 33] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/21/2008] [Revised: 01/10/2009] [Accepted: 01/11/2009] [Indexed: 11/29/2022]
Abstract
The noninvasive detection of neuronal currents in active brain networks [or direct neuronal imaging (DNI)] by means of nuclear magnetic resonance (NMR) remains a scientific challenge. Many different attempts using NMR scanners with magnetic fields >1 T (high-field NMR) have been made in the past years to detect phase shifts or magnitude changes in the NMR signals. However, the many physiological (i.e., the contemporarily BOLD effect, the weakness of the neuronal-induced magnetic field, etc.) and technical limitations (e.g., the spatial resolution) in observing the weak signals have led to some contradicting results. In contrast, only a few attempts have been made using low-field NMR techniques. As such, this paper was aimed at reviewing two recent developments in this front. The detection schemes discussed in this manuscript, the resonant mechanism (RM) and the DC method, are specific to NMR instrumentations with main fields below the earth magnetic field (50 microT), while some even below a few microteslas (ULF-NMR). However, the experimental validation for both techniques, with differentiating sensitivity to the various neuronal activities at specific temporal and spatial resolutions, is still in progress and requires carefully designed magnetic field sensor technology. Additional care should be taken to ensure a stringent magnetic shield from the ambient magnetic field fluctuations. In this review, we discuss the characteristics and prospect of these two methods in detecting neuronal currents, along with the technical requirements on the instrumentation.
Collapse
Affiliation(s)
- Antonino Mario Cassará
- Museo Storico della Fisica e Centro Studi e Ricerche "E. Fermi", Complesso Viminale, Rome, Italy.
| | | | | | | | | |
Collapse
|
32
|
Heller L, Barrowes BE, George JS. Modeling direct effects of neural current on MRI. Hum Brain Mapp 2009; 30:1-12. [PMID: 17990303 DOI: 10.1002/hbm.20484] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022] Open
Abstract
We investigate the effect of the magnetic field generated by neural activity on the magnitude and phase of the MRI signal in terms of a phenomenological parameter with the dimensions of length; it involves the product of the strength and duration of these currents. We obtain an analytic approximation to the MRI signal when the neuromagnetically induced phase is small inside the MRI voxel. The phase shift is the average of the MRI phase over the voxel, and therefore first order in that phase; and the reduction in the signal magnitude is one half the square of the standard deviation of the MRI phase, which is second order. The analytic approximation is compared with numerical simulations. For weak currents the agreement is excellent, and the magnitude change is generally much smaller than the phase shift. Using MEG data as a weak constraint on the current strength we find that for a net dipole moment of 10 nAm, a typical value for an evoked response, the reduction in the magnitude of the MRI signal is two parts in 10(5), and the maximum value of the overall phase shift is approximately 4 x 10(-3), obtained when the MRI voxel is displaced 2/3 the size of the neuronal activity. We also show signal changes over a large range of values of the net dipole moment. We compare these results with others in the literature. Our model overestimates the effect on the MRI signal.
Collapse
Affiliation(s)
- Leon Heller
- Physics Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
| | | | | |
Collapse
|
33
|
Chow LS, Dagens A, Fu Y, Cook GG, Paley MNJ. Comparison of BOLD and direct-MR neuronal detection (DND) in the human visual cortex at 3T. Magn Reson Med 2009; 60:1147-54. [PMID: 18956466 DOI: 10.1002/mrm.21753] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
Abstract
Direct-MR neuronal detection (DND) of transient magnetic fields has recently been investigated as a novel imaging alternative to the conventional BOLD functional MRI (fMRI) technique. However, there remain controversial issues and debate surrounding this methodology, and this study attempts clarification by comparing BOLD responses in the human visual system with those of DND. BOLD relies on indirectly measuring blood oxygenation and flow changes as a result of neuronal activity, whereas the putative DND method is based on the hypothesis that the components of the in vivo neuronal magnetic fields, which lie parallel to the B(0) field, can potentially modulate the MR signal, thus providing a means of direct detection of nerve impulses. Block paradigms of checkerboard patterns were used for visual stimulation in both DND and BOLD experiments, allowing detection based on different frequency responses. This study shows colocalization of some voxels with slow BOLD responses and putative fast DND responses using General Linear Model (GLM) analysis. Frequency spectra for the activated voxel cluster are also shown for both stimulated and control data. The mean percentage signal change for the DND responses is 0.2%, corresponding to a predicted neuronal field of 0.14 nT.
Collapse
Affiliation(s)
- Li Sze Chow
- Section of Academic Radiology, University of Sheffield, Sheffield, UK
| | | | | | | | | |
Collapse
|
34
|
Hagberg GE, Bianciardi M, Brainovich V, Cassarà AM, Maraviglia B. The effect of physiological noise in phase functional magnetic resonance imaging: from blood oxygen level-dependent effects to direct detection of neuronal currents. Magn Reson Imaging 2008; 26:1026-40. [PMID: 18479875 DOI: 10.1016/j.mri.2008.01.010] [Citation(s) in RCA: 28] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/07/2007] [Accepted: 01/14/2008] [Indexed: 11/17/2022]
Abstract
Recently, the possibility to use both magnitude and phase image sets for the statistical evaluation of fMRI has been proposed, with the prospective of increasing both statistical power and the spatial specificity. In the present work, several issues that affect the spatial and temporal stability in fMRI phase time series in the presence of physiologic noise processes are reviewed, discussed and illustrated by experiments performed at 3 T. The observed phase value is a fingerprint of the underlying voxel averaged magnetic field variations. Those related to physiological processes can be considered static or dynamic in relation to the temporal scale of a 2D acquisition and will play out on different spatial scales as well: globally across the entire images slice, and locally depending on the constituents and their relative fractions inside the MRI voxel. The 'static' respiration-induced effects lead to magneto-mechanic scan-to-scan variations in the global magnetic field but may also contribute to local BOLD fluctuations due to respiration-related variations in arterial carbon dioxide. Likewise, the 'dynamic' cardiac-related effects will lead to global susceptibility effects caused by pulsatile motion of the brain as well as local blood pressure-related changes in BOLD and changes in blood flow velocity. Finally, subject motion may lead to variations in both local and global tissue susceptibility that will be especially pronounced close to air cavities. Since dissimilar manifestations of physiological processes can be expected in phase and in magnitude images, a direct relationship between phase and magnitude scan-to-scan fluctuations cannot be assumed a priori. Therefore three different models were defined for the phase stability, each dependent on the relation between phase and magnitude variations and the best will depend on the underlying noise processes. By experiments on healthy volunteers at rest, we showed that phase stability depends on the type of post-processing and can be improved by reducing the low-frequency respiration-induced mechano-magnetic effects. Although the manifestations of physiological noise were in general more pronounced in phase than in magnitude images, due to phase wraps and global Bo effects, we suggest that a phase stability similar to that found in magnitude could theoretically be achieved by adequate correction methods. Moreover, as suggested by our experimental data regarding BOLD-related phase effects, phase stability could even supersede magnitude stability in voxels covering dense microvascular networks with BOLD-related fluctuations as the dominant noise contributor. In the interest of the quality of both BOLD-based and nc-MRI methods, future studies are required to find alternative methods that can improve phase stability, designed to match the temporal and spatial scale of the underlying neuronal activity.
Collapse
Affiliation(s)
- Gisela E Hagberg
- Laboratory of Neuroimaging, Foundation Santa Lucia IRCCS, Rome, Italy.
| | | | | | | | | |
Collapse
|
35
|
Cassarà AM, Maraviglia B. Microscopic investigation of the resonant mechanism for the implementation of nc-MRI at ultra-low field MRI. Neuroimage 2008; 41:1228-41. [PMID: 18474435 DOI: 10.1016/j.neuroimage.2008.03.051] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/14/2007] [Revised: 03/09/2008] [Accepted: 03/26/2008] [Indexed: 12/01/2022] Open
Abstract
In this paper the possible use of the resonant mechanism between some spectral components of the neuronal activity and the spin dynamics in ultra-low field MRI experiments--for the implementation of the nc-MRI techniques and proposed by Kraus et al., 2008--is investigated by means of "realistic" simulations of the neuronal activity of a modelled neuronal network. Previously characterized digital neurons are used to reproduce neuronal currents based on biophysical details and the distribution of the local magnetic field inside a MRI cubic voxel (having a dimension of 1.2 mm) is evaluated. The properties of the water proton spin dynamics as a consequence of the neuronal field and of external applied fields are extrapolated integrating the Bloch equations. The characteristics of the expected MR signals are discussed in relation to the specifics of the NMR sequence used and to the properties of the neuronal activity. The great potentialities of the technique are provided by: a) the possible easy implementation of the technique, b) the possible cheap instrumentation required; c) the flexibility of the ultra-low field systems.
Collapse
Affiliation(s)
- A M Cassarà
- Centro Studi e Ricerche Enrico Fermi, 00184, Rome, Italy.
| | | |
Collapse
|
36
|
Buracas GT, Liu TT, Buxton RB, Frank LR, Wong EC. Imaging periodic currents using alternating balanced steady-state free precession. Magn Reson Med 2008; 59:140-8. [PMID: 18050317 DOI: 10.1002/mrm.21457] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
Existing functional brain MR imaging methods detect neuronal activity only indirectly via a surrogate signal such as deoxyhemoglobin concentration in the vascular bed of cerebral parenchyma. It has been recently proposed that neuronal currents may be measurable directly using MRI (ncMRI). However, limited success has been reported in neuronal current detection studies that used standard gradient or spin echo pulse sequences. The balanced steady-state free precession (bSSFP) pulse sequence is unique in that it can afford the highest known SNR efficiency and is exquisitely sensitive to perturbations in free precession phase. It is reported herein that when a spin phase-perturbing periodic current is locked to an RF pulse train, phase perturbations are accumulated across multiple RF excitations and the spin magnetization reaches an alternating balanced steady state (ABSS) that effectively amplifies the phase perturbations due to the current. The alternation of the ABSS signal therefore is highly sensitive to weak periodic currents. Current phantom experiments employing ABSS imaging resulted in detection of magnetic field variations as small as 0.15nT in scans lasting for 36 sec, which is more sensitive than using gradient-recalled echo imaging.
Collapse
Affiliation(s)
- Giedrius T Buracas
- Department of Radiology, UCSD Center for Functional MRI, La Jolla, California 92037, USA.
| | | | | | | | | |
Collapse
|
37
|
Cassarà AM, Hagberg GE, Bianciardi M, Migliore M, Maraviglia B. Realistic simulations of neuronal activity: a contribution to the debate on direct detection of neuronal currents by MRI. Neuroimage 2007; 39:87-106. [PMID: 17936018 DOI: 10.1016/j.neuroimage.2007.08.048] [Citation(s) in RCA: 47] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/17/2007] [Revised: 08/04/2007] [Accepted: 08/22/2007] [Indexed: 11/16/2022] Open
Abstract
Many efforts have been done in order to preview the properties of the magnetic resonance (MR) signals produced by the neuronal currents using simulations. In this paper, starting with a detailed calculation of the magnetic field produced by the neuronal currents propagating over single hippocampal CA1 pyramidal neurons placed inside a cubic MR voxel of length 1.2 mm, we proceeded on the estimation of the phase and magnitude MR signals. We then extended the results to layers of parallel and synchronous similar neurons and to ensembles of layers, considering different echo times, voxel volumes and neuronal densities. The descriptions of the neurons and of their electrical activity took into account the real neuronal morphologies and the physiology of the neuronal events. Our results concern: (a) the expected time course of the MR signals produced by the neuronal currents in the brain, based on physiological and anatomical properties; (b) the different contributions of post-synaptic potentials and of action potentials to the MR signals; (c) the estimation of the equivalent current dipole and the influence of its orientation with respect to the external magnetic field on the observable MR signal variations; (d) the size of the estimated neuronal current induced phase and magnitude MR signal changes with respect to the echo time, voxel-size and neuronal density. The inclusion of realistic neuronal properties into the simulation introduces new information that can be helpful for the design of MR sequences for the direct detection of neuronal current effects and the testing of bio-electromagnetic models.
Collapse
Affiliation(s)
- A M Cassarà
- Dip. di Fisica, Gruppo G1, Università di Roma La Sapienza, Piazzale Aldo Moro, 5, 00185, Rome, Italy.
| | | | | | | | | |
Collapse
|
38
|
Mandelkow H, Halder P, Brandeis D, Soellinger M, de Zanche N, Luechinger R, Boesiger P. Heart beats brain: The problem of detecting alpha waves by neuronal current imaging in joint EEG–MRI experiments. Neuroimage 2007; 37:149-63. [PMID: 17544703 DOI: 10.1016/j.neuroimage.2007.04.034] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/27/2006] [Revised: 03/10/2007] [Accepted: 04/07/2007] [Indexed: 11/20/2022] Open
Abstract
It has been suggested recently that the influence of the neuro-magnetic field should make electrical brain activity directly detectable by MRI. To test this hypothesis, we performed combined EEG-MRI experiments which aim to localize the neuronal current sources of alpha waves (8-12 Hz), one of the most prominent EEG phenomena in humans. A detailed analysis of cross-spectral coherence between simultaneously recorded EEG and MRI time series revealed no sign of alpha waves. Instead the EEG-MRI approach was found to be hampered by artefacts due to cardiac pulsation, which extend into the frequency band of alpha waves. Separate brain displacement mapping experiments confirmed that not only the EEG but also the MRI signal is confounded by harmonics of the cardiac frequency even at 10 Hz and beyond. This well-known ballistocardiogram artefact cannot be avoided or eliminated entirely by available signal processing techniques. Therefore we must conclude that current EEG-MRI methodology based on correlation analysis lacks not only the sensitivity but also the specificity required for the reliable detection of alpha waves.
Collapse
Affiliation(s)
- H Mandelkow
- Institute for Biomedical Engineering, University and ETH Zurich, Gloriastr. 35, 8092 Zurich, Switzerland.
| | | | | | | | | | | | | |
Collapse
|
39
|
Park TS, Lee SY. Effects of neuronal magnetic fields on MRI: numerical analysis with axon and dendrite models. Neuroimage 2007; 35:531-8. [PMID: 17291782 DOI: 10.1016/j.neuroimage.2007.01.001] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/04/2006] [Revised: 12/20/2006] [Accepted: 01/04/2007] [Indexed: 11/21/2022] Open
Abstract
Whether the neuronal magnetic fields (NMFs) could cause measurable MRI signal changes in the human brain seems to be still controversial. In this study, we have numerically investigated the NMF effects on the MRI signal using two separate current source models for axons and dendrites. Since intracellular current distributions are different in axons and dendrites, the NMFs emanating from axons and dendrites are also very different from each other. Due to the quadripole configuration of the intracellular current flowing through an axon, the axonal magnetic field is bipolar causing virtually no changes in the MRI signal. On the contrary, the dendritic magnetic field is unipolar so that its effects can be accumulated during the echo time. The dendritic magnetic field has measurable effects on the MRI signal, but, it is necessary to differentiate the NMF effects from much bigger background BOLD effects to utilize the NMF effects for fMRI.
Collapse
Affiliation(s)
- Tae Seok Park
- Department of Biomedical Engineering, Kyung Hee University, 1 Seochun, Kiheung, Yongin, Kyungki 446-701, South Korea
| | | |
Collapse
|
40
|
Truong TK, Song AW. Finding neuroelectric activity under magnetic-field oscillations (NAMO) with magnetic resonance imaging in vivo. Proc Natl Acad Sci U S A 2006; 103:12598-601. [PMID: 16894177 PMCID: PMC1567924 DOI: 10.1073/pnas.0605486103] [Citation(s) in RCA: 30] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Neuroimaging techniques are among the most important tools for investigating the function of the human nervous system and for improving the clinical diagnosis of neurological disorders. However, most commonly used techniques are limited by their invasiveness or their inability to accurately localize neural activity in space or time. Previous attempts at using MRI to directly image neuroelectric activity in vivo through the detection of magnetic field changes induced by neuronal currents have been challenging because of the extremely small signal changes and confounding factors such as hemodynamic modulations. Here we describe an MRI technique that uses oscillating magnetic field gradients to significantly amplify and detect the Lorentz effect induced by neuroelectric activity, and we demonstrate its effectiveness in imaging sensory nerve activation in vivo in the human median nerve during electrical stimulation of the wrist. This direct, real-time, and noninvasive neuroimaging technique may potentially find broad applications in neurosciences.
Collapse
Affiliation(s)
- Trong-Kha Truong
- Brain Imaging and Analysis Center, Duke University, Durham, NC 27710
| | - Allen W. Song
- Brain Imaging and Analysis Center, Duke University, Durham, NC 27710
- To whom correspondence should be addressed at:
Brain Imaging and Analysis Center, Duke University Medical Center, P.O. Box 3918, Durham, NC 27710. E-mail:
| |
Collapse
|