Current Density Imaging Research Articles

MR imaging of the magnetic fields induced by injected currents can guide improvements of individualized head volume conductor models

Abstract Volume conductor models of the human head are routinely used to estimate the induced electric fields in transcranial brain stimulation (TBS) and for source localization in electro- and magnetoencephalography (EEG and MEG). Magnetic resonance current density imaging (MRCDI) has the potential to act as a non-invasive method for dose control and model validation but requires very sensitive MRI acquisition approaches. A double-echo echo-planar imaging (EPI) method is here introduced. It combines fast and sensitive imaging of the magnetic fields generated by the current flow of transcranial electric stimulation with increased robustness to physiological noise. For validation, noise floor measurements without injected currents were obtained in five subjects for an established multi-echo gradient-echo (MGRE) sequence and the new EPI method. In addition, data with current injection were acquired in each subject with a right-left (RL) and anterior-posterior (AP) electrode montage with both sequences to assess the accuracy of subject-specific detailed head models. In line with previous findings, the noise floor measurements showed that the MGRE results suffered from spatial low-frequency noise patterns, which were mostly absent in the EPI data. A recently published approach optimizes the ohmic conductivities of subject-specific head models by minimizing the difference between simulated and measured current-induced magnetic fields. Here, simulations demonstrated that the MGRE noise patterns have a larger negative impact on the optimization results than the EPI noise. For the current injection measurements, a larger discrepancy was found for the RL electrode montage compared with the AP electrode montage consistently for all subjects. This discrepancy that remained in part also after optimization of the ohmic conductivities, was similar for the data of the two sequences and larger than the measurement noise, and thus demonstrates systematic biases in the volume conductor models. We have shown that EPI-based MRCDI is superior to established techniques by mitigating the effects of previously reported spatial low-frequency noise in MRCDI if limited spatial resolution is acceptable. Additionally, the consistent inter-subject results indicate that MRCDI is capable of picking up inaccuracies in computational head models and will be useful to guide systematic improvements.

High Spatial Resolution 2D Imaging of Current Density and Pressure for Graphene Devices under High Pressure Using Nitrogen-Vacancy Centers in Diamond.

Current density imaging is helpful for discovering interesting electronic phenomena and understanding carrier dynamics, and by combining pressure distributions, several pressure-induced novel physics may be comprehended. In this work, noninvasive, high-resolution two-dimensional images of the current density and pressure gradient for graphene ribbon and hBN-graphene-hBN devices are explored using nitrogen-vacancy (NV) centers in diamond under high pressure. The two-dimensional vector current density is reconstructed by the vector magnetic field mapped by the near-surface NV center layer in the diamond. The current density images accurately and clearly reproduce the complicated structure and current flow of graphene under high pressure. Additionally, the spatial distribution of the pressure is simultaneously mapped, rationalizing the nonuniformity of the current density under high pressure. The current method opens a significant new avenue to investigate electronic transport and conductance variations in two-dimensional materials and electrical devices under high pressure as well as for nondestructive evaluation of semiconductor circuits.

A Fast Magnetic Flux Density Measurement Method With Skip-Echo Acquired Turbo Spin Echo (SATE).

The measurements of magnetic flux density ( Bz) needed in magnetic resonance electrical impedance tomography (MREIT) and magnetic resonance current density imaging (MRCDI) techniques often utilize spin echo (SE)-based sequences for data acquisition. The low imaging speed of SE-based methods significantly hampers the clinical applications of MREIT and MRCDI. Here, we propose a new sequence for substantially accelerating the acquisition of Bz measurements. A skip-echo acquired turbo spin echo (SATE) imaging sequence based on the conventional turbo spin echo (TSE) technique was proposed by adding a skip-echo module in front of the TSE acquisition module. The skip-echo module consisted of a series of refocusing pulses without acquisition. In SATE, amplitude-modulated crusher gradients were used to remove the stimulated echo pathways, and the radiofrequency (RF) pulse shape was specially selected to preserve more signals. In efficiency evaluation experiments performed on a spherical gel phantom, we demonstrated that SATE had improved measurement efficiency compared to the conventional TSE sequence via skipping one echo before acquiring signals. The accuracy of the Bz measurements by SATE was validated against those by the multi-echo injection current nonlinear encoding (ME-ICNE) method, while SATE was able to accelerate the data acquisition up to 10-fold. Volumetric coverage of Bz maps obtained in the phantom, pork, and human calf illustrated that SATE can reliably measure volumetric Bz distributions within clinically acceptable time. The proposed SATE sequence provides a fast and effective approach for volumetric coverage of Bz measurements, greatly facilitating the clinical applications of MREIT and MRCDI techniques.

Volumetric measurements of weak current-induced magnetic fields in the human brain at high resolution.

Clinical use of transcranial electrical stimulation (TES) requires accurate knowledge of the injected current distribution in the brain. MR current density imaging (MRCDI) uses measurements of the TES-induced magnetic fields to provide this information. However, sufficient sensitivity and image quality in humans in vivo has only been documented for single-slice imaging. A recently developed, optimally spoiled, acquisition-weighted, gradient echo-based 2D-MRCDI method has now been advanced for volume coverage with densely or sparsely distributed slices: The 3D rectilinear sampling (3D-DENSE) and simultaneous multislice acquisition (SMS-SPARSE) were optimized and verified by cable-loop experiments and tested with 1-mA TES experiments for two common electrode montages. Comparisons between the volumetric methods against the 2D-MRCDI showed that relatively long acquisition times of 3D-DENSE using a single slab with six slices hindered the expected sensitivity improvement in the current-induced field measurements but improved sensitivity by 61% in the Laplacian of the field, on which some MRCDI reconstruction methods rely. Also, SMS-SPARSE acquisition of three slices, with a factor 2 CAIPIRINHA (controlled aliasing in parallel imaging results in higher acceleration) acceleration, performed best against the 2D-MRCDI with sensitivity improvements for the and Laplacian noise floors of 56% and 78% (baseline without current flow) as well as 43% and 55% (current injection into head). SMS-SPARSE reached a sensitivity of 67 pT for three distant slices at 2 × 2 × 3 mm3 resolution in 10 min of total scan time, and consistently improved image quality. Volumetric MRCDI measurements with high sensitivity and image quality are well suited to characterize the TES field distribution in the human brain.

A Vectorial Current Density Imaging Method Based on Magnetic Gradient Tensor.

Magnetic current imaging is deemed an emerging powerful technique for visualizing electrical currents in electronic devices. However, the existing magnetic-field-based Fourier Transform back-evolution method is limited by its mono-function of imaging the magnitude of current density in devices under test, and subject to background noise distortion. Here, we developed a novel vectorial current density imaging method based on the detection of the magnetic field gradient generated by current carrying conductors. A closed form solution of current density inversion was analytically derived and numerically verified. Experiments were conducted by scanning tri-axial fluxgate sensor over different shapes of electrical wires. The results show that a current density resolution of 24.15 mA/mm2, probe-to-sample separation of 2 mm, and spatial resolution of 0.69 mm were achieved over a maximum scanning area of 300 mm × 300 mm. Such a method is verified to be capable of simultaneously imaging both magnitude and directions of current density, which is a promising technique for in situ noninvasive inspection for the power electronic and semiconductor industry.

Current Source Density Imaging Using Regularized Inversion of Acoustoelectric Signals.

Acoustoelectric (AE) imaging can potentially image biological currents at high spatial (~mm) and temporal (~ms) resolution. However, it does not directly map the current field distribution due to signal modulation by the acoustic field and electric lead fields. Here we present a new method for current source density (CSD) imaging. The fundamental AE equation is inverted using truncated singular value decomposition (TSVD) combined with Tikhonov regularization, where the optimal regularization parameter is found based on a modified L-curve criterion with TSVD. After deconvolution of acoustic fields, the current field can be directly reconstructed from lead field projections and the CSD image computed from the divergence of that field. A cube phantom model with a single dipole source was used for both simulation and bench-top phantom studies, where 2D AE signals generated by a 0.6 MHz 1.5D array transducer were recorded by orthogonal leads in a 3D Cartesian coordinate system. In simulations, the CSD reconstruction had significantly improved image quality and current source localization compared to AE images, and performance further improved as the fractional bandwidth (BW) increased. Similar results were obtained in the phantom with a time-varying current injected. Finally, a feasibility study using an in vivo swine heart model showed that optimally reconstructed CSD images better localized the current source than AE images over the cardiac cycle.

Transcranial acoustoelectric imaging: Towards noninvasive mapping of current densities in the human brain

Acoustoelectric Imaging (AEI) is a disruptive technology that exploits an ultrasound (US) beam to transiently interact with physiologic or artificial currents, producing a radiofrequency signature detected by one or more surface electrodes. By rapidly sweeping the US beam and simultaneously detecting the acoustoelectric modulations, 4D current density images are generated at high spatial resolution determined by the ultrasound beam focus. The principle has been used for in vivo mapping of currents in the swine heart during the cardiac activation wave. When applied to the brain, transcranial acoustoelectric imaging (tABI) overcomes limitations with electroencephalography (EEG), which suffers from poor spatial resolution and inaccuracies due to blurring of electrical signals as they pass through the brain and skull, and, unlike fMRI and PET that measure slow metabolic or hemodynamic signals, tABI directly maps fast time-varying current within a defined brain volume at the mm and ms scales. This invited presentation will describe the underlying physics and mathematics of tABI, recent progress and challenges using numerical simulations and bench-top models, and its potential impact as a cutting-edge noninvasive modality for fast and accurate electrical brain mapping in humans.

Accurate and flexible personalized head modeling and its validation using MR current density imaging

Accurate and flexible personalized head modeling and its validation using MR current density imaging

Jacobian of solutions to the conductivity equation in limited view

The aim of hybrid inverse problems such as Acousto-Electric Tomography or Current Density Imaging is the reconstruction of the electrical conductivity in a domain that can only be accessed from its exterior. In the inversion procedure, the solutions to the conductivity equation play a central role. In particular, it is important that the Jacobian of the solutions is non-vanishing. In the present paper we address a two-dimensional limited view setting, where only a part of the boundary of the domain can be controlled by a non-zero Dirichlet condition, while on the remaining boundary there is a zero Dirichlet condition. For this setting, we propose sufficient conditions on the boundary functions so that the Jacobian of the corresponding solutions is non-vanishing. In that regard we allow for discontinuous boundary functions, which requires the use of solutions in weighted Sobolev spaces. We implement the procedure of reconstructing a conductivity from power density data numerically and investigate how this limited view setting affects the Jacobian and the quality of the reconstructions.

A Novel Online State of Health Estimation Method for Electric Vehicle Pouch Cells Using Magnetic Field Imaging and Convolution Neural Networks

Lithium-ion batteries (LiBs) are used as the main power source in electric vehicles (EVs). Despite their high energy density and commercial availability, LiBs chronically suffer from non-uniform cell ageing, leading to early capacity fade in the battery packs. In this paper, a non-invasive, online characterisation method based on deep learning models is proposed for cell-level SoH estimation. For an accurate measurement of the state of health (SoH), we need to characterize electrochemical capacity fade scenarios carefully. Then, with the help of real-time monitoring, the control systems can reduce the LiB’s degradation. The proposed method, which is based on convolutional neural networks (CNN), characterises the changes in current density distributions originating from the positive electrodes in different SoH states. For training and classification by the deep learning model, current density images (CDIs) were experimentally acquired in different ageing conditions. The results confirm the efficiency of the proposed approach in online SoH estimation and the prediction of the capacity fade scenarios.

Revealing fundamentals of charge extraction in photovoltaic devices through potentiostatic photoluminescence imaging

Revealing fundamentals of charge extraction in photovoltaic devices through potentiostatic photoluminescence imaging

A Reel-to-Reel Scanning Hall Probe Microscope for Characterizing Long REBCO Conductor in Magnetic Fields Up to 5 Tesla

We have developed and routinely used a reel-to-reel (R2R) scanning Hall-probe microscopy (SHPM) system to characterize REBCO conductors developed at the University of Houston. By mapping the screening-current-induced field of a magnetized REBCO conductor, the SHPM system enables 2-dimensional imaging of critical current density (<i>J</i>_c) distribution in a contact-free, non-destructive approach. Most existing SHPM systems investigate the magnetized REBCO conductors at remnant state without external background field. However, because of the inhomogeneity in the distribution of nanoscale artificial pinning centers in advanced REBCO conductors, there is a demand for reel-to-reel in-field examination over long conductor lengths. We have been developing a new R2R SHPM, capable of measuring the <i>J</i>_c profile of long REBCO conductors at the temperature of 63.5&#x2013;77 K and in an applied field up to 5 T. With optimal data acquisition and processing techniques, we overcame the challenge of measuring weak screening-current-field signals in a strong background field. R2R <i>J</i>_c mapping has been performed on long REBCO conductors with a spatial resolution as low as 0.15 mm² and a longitudinal scanning speed comparable with our existing system. Our previous study revealed a good correlation between the REBCO conductors&#x2019; 65-K in-field <i>J</i>_c and their <i>J</i>_c over a wide span of temperatures and fields. Using this correlation, the in-field R2R SHPM will serve not only as a means of quality control, but also provide insight into high-field performance of advanced REBCO conductors at low temperatures.

Electric Current Detection Based on the MR Signal Magnitude Decay.

PurposeConventional 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.MethodsConductive 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.ResultsIt 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.ConclusionSMD 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.

Non-invasive current density imaging of lithium-ion batteries

The rapid pace of replacing fossil fuel propelled transport by electric vehicles is critically dependent on high-performing, high energy density batteries. Optimal and safe use of existing battery cells and development of much-needed novel battery chemistries and geometries require a multitude of diagnostic and monitoring tools. While structural and chemical information is readily extracted through a host of imaging techniques, non-invasive functional detection of interior battery processes remains limited. Here we introduce sensitive magnetometry performed outside the battery, revealing internal current distribution. As a key application, we use a sensor array to image the internal current flow of a pouch cell cycling between charge states. We find good agreement between measured and modelled fields with sufficient resolution to detect percent-level deviations around high current density areas. This opens the path towards rapid and reliable assessment throughout the battery life cycle, from battery development and manufacturing quality assurance to optimised use.

Magnetic Resonance Current Density Imaging (MR-CDI).

Current density imaging (CDI) was developed with the aim of determining the three-dimensional distribution of externally applied electric current pathways inside a conductive medium, using measurements of magnetic flux density [Formula: see text] data. While the B field may be measurable using instruments such as a magnetometer, in magnetic resonance current density imaging (MR-CDI), an MRI scanner is used to measure the magnetic flux density data induced by current flow. In MR-CDI, the object must be rotated inside the MRI machine to find all three components of the B-field, as only the component of B parallel to the magnet main magnetic field can be measured. In principle, once the all three components of the B field have been obtained from an MR imaging experiment, the current density distribution [Formula: see text] can be reconstructed from Ampere's law [Formula: see text]. However, the need to rotate the object within the MRI scanner limits the usability of this technique. To overcome this problem, researchers have investigated the current density reconstruction problem using only one component of the magnetic flux density Bq, where q = x, y, z. In this chapter, we discuss numerical algorithms developed to reconstruct the distribution of J information from the measured B-field.

SNR and total acquisition time analysis of multi-echo FLASH pulse sequence for current density imaging

Magnetic Resonance Current Density Imaging (MRCDI) is an imaging modality providing cross-sectional current density (J¯) information inside the body. The clinical applicability of MRCDI is highly dependent on the sensitivity of the acquired noisy current-induced magnetic flux density (B∼z) distributions.Here, a novel analysis is developed to investigate the combined effect of relevant parameters of the RF spoiled gradient echo (FLASH) pulse sequence on the SNR level and the total acquisition time (TAT) of the acquired B∼z images. The proposed analysis then is expanded for a multi-echo FLASH (ME-FLASH) pulse sequence to take advantage of combining the multiple echoes to achieve B∼zcomb distribution with a higher SNR than the one achievable with a single echo acquisition.The optimized sequence parameters to acquire a B∼z distribution with the highest possible SNR for a given acquisition time or the desired SNR in the shortest scan time are estimated using the proposed analysis. The analysis also provides different sets of sequence parameters to acquire B∼z distributions with the same SNR at almost the same TAT. Furthermore, the effects of intensive utilization of the gradients and the magnetohydrodynamic (MHD) flow velocity on the acquired B∼z distribution in MRCDI experiments is investigated.The analytical results of the proposed analysis are validated experimentally using an imaging phantom having the conductivity and the relaxation parameters of the brain white matter tissue.

Human in-vivo magnetic resonance current density imaging of the brain by optimizing head tissue conductivities

Abstract Introduction: Magnetic resonance current density imaging (MRCDI) aims to reconstruct the current flow of transcranial electrical stimulation (TES) in the brain from MR-measurements of the current-induced magnetic field Bz. Aim: We test the performance of a standard reconstruction algorithm (“projected current density algorithm”, PCD, Jeong et al. 2014) for human brain data. We compare it with current flow simulations using personalized head models. Methods:1. We generated ground-truth data for the TES current flow and Bz-field using a detailed head model and SimNIBS (www.simnibs.org). We applied the PCD algorithm to the Bz -field and quantified the reconstruction performance by comparison with the ground-truth current flow. We additionally compared the PCD results with simulations using a simple head model (“3c” with scalp, bone and a homogeneous intracranial compartment). 2. We reconstructed the current flow from in-vivo MRCDI data (Göksu et al, 2018) with the PCD algorithm. We also used head models of different complexities (“3c” and “4c”: scalp, skull, CSF & brain) and optimized their conductivities to minimize the root-mean-square difference between the measured and simulated Bz. Results: 1. For simulated Bz data, the PCD algorithm only coarsely reconstructed the true current flow. Even the simple head model performed better. 2. For measured Bz data, current flows obtained with personalized head models and fitted conductivities explained the measurements better than the current flow reconstructed with the PCD algorithm. This was already the case for the simple head model (3c). The more detailed model (4c) resulted in further statistically significant improvements. However, for all models, the unexplained variance stayed above the noise floor, indicating remaining differences to unknown true current flow. Conclusions: The PCD algorithm has low accuracy for MRCDI data of the brain. However, MRCDI is useful for evaluations and improvements of current flow simulations with anatomically detailed personalized head models. Keywords: magnetic resonance current density imaging, personalized electric field calculation, dose control, transcranial electrical stimulation

Four-channel current switching device to enable multi-electrode magnetic resonance current density imaging.

Neurostimulation with multiple scalp electrodes has shown enhanced effects in recent studies. However, visualizations of stimulation-induced internal current distributions in brain is only possible through simulated current distributions obtained from computer model of human head. While magnetic resonance current density imaging (MRCDI) has a potential for direct in-vivo measurement of currents induced in brain with multi-electrode stimulation, existing MRCDI methods are only developed for two-electrode neurostimulation. A major bottleneck is the lack of a current switching device which is typically used to convert the DC current of neurostimulation devices into user-defined waveforms of positive and negative polarity with delays between them. In this work, we present a design of a four-electrode current switching device to enable simultaneous switching of current flowing through multiple scalp electrodes.

Nanoscale magnetic field imaging for 2D materials

Nanometer-scale imaging of magnetization and current density is the key to deciphering the mechanisms behind a variety of new and poorly understood condensed matter phenomena. The recently discovered correlated states hosted in atomically layered materials such as twisted bilayer graphene or van der Waals heterostructures are noteworthy examples. Manifestations of these states range from superconductivity, to highly insulating states, to magnetism. Their fragility and susceptibility to spatial inhomogeneities limits their macroscopic manifestation and complicates conventional transport or magnetization measurements, which integrate over an entire sample. In contrast, techniques for imaging weak magnetic field patterns with high spatial resolution overcome inhomogeneity by measuring the local fields produced by magnetization and current density. Already, such imaging techniques have shown the vulnerability of correlated states in twisted bilayer graphene to twist-angle disorder and revealed the complex current flows in quantum Hall edge states. Here, we review the state-of-the-art techniques most amenable to the investigation of such systems, because they combine the highest magnetic field sensitivity with the highest spatial resolution and are minimally invasive: magnetic force microscopy, scanning superconducting quantum interference device microscopy, and scanning nitrogen-vacancy center microscopy. We compare the capabilities of these techniques, their required operating conditions, and assess their suitability to different types of source contrast, in particular magnetization and current density. Finally, we focus on the prospects for improving each technique and speculate on its potential impact, especially in the rapidly growing field of two-dimensional (2D) materials.

On the reconstruction of magnetic resonance current density images of the human brain: Pitfalls and perspectives

Magnetic resonance current density imaging (MRCDI) of the human brain aims to reconstruct the current density distribution caused by transcranial electric stimulation from MR-based measurements of the current-induced magnetic fields. So far, the MRCDI data acquisition achieves only a low signal-to-noise ratio, does not provide a full volume coverage and lacks data from the scalp and skull regions. In addition, it is only sensitive to the component of the current-induced magnetic field parallel to the scanner field. The reconstruction problem thus involves coping with noisy and incomplete data, which makes it mathematically challenging. Most existing reconstruction methods have been validated using simulation studies and measurements in phantoms with simplified geometries. Only one reconstruction method, the projected current density algorithm, has been applied to human in-vivo data so far, however resulting in blurred current density estimates even when applied to noise-free simulated data.We analyze the underlying causes for the limited performance of the projected current density algorithm when applied to human brain data. In addition, we compare it with an approach that relies on the optimization of the conductivities of a small number of tissue compartments of anatomically detailed head models reconstructed from structural MR data. Both for simulated ground truth data and human in-vivo MRCDI data, our results indicate that the estimation of current densities benefits more from using a personalized volume conductor model than from applying the projected current density algorithm. In particular, we introduce a hierarchical statistical testing approach as a principled way to test and compare the quality of reconstructed current density images that accounts for the limited signal-to-noise ratio of the human in-vivo MRCDI data and the fact that the ground truth of the current density is unknown for measured data. Our results indicate that the statistical testing approach constitutes a valuable framework for the further development of accurate volume conductor models of the head. Our findings also highlight the importance of tailoring the reconstruction approaches to the quality and specific properties of the available data.