Current Density Imaging Research Articles

Software Toolbox for Low-Frequency Conductivity and Current Density Imaging Using MRI.

Low-frequency conductivity and current density imaging using MRI includes magnetic resonance electrical impedance tomography (MREIT), diffusion tensor MREIT (DT-MREIT), conductivity tensor imaging (CTI), and magnetic resonance current density imaging (MRCDI). MRCDI and MREIT provide current density and isotropic conductivity images, respectively, using current-injection phase MRI techniques. DT-MREIT produces anisotropic conductivity tensor images by incorporating diffusion weighted MRI into MREIT. These current-injection techniques are finding clinical applications in diagnostic imaging and also in transcranial direct current stimulation (tDCS), deep brain stimulation (DBS), and electroporation where treatment currents can function as imaging currents. To avoid adverse effects of nerve and muscle stimulations due to injected currents, conductivity tensor imaging (CTI) utilizes B1 mapping and multi-b diffusion weighted MRI to produce low-frequency anisotropic conductivity tensor images without injecting current. This paper describes numerical implementations of several key mathematical functions for conductivity and current density image reconstructions in MRCDI, MREIT, DT-MREIT, and CTI. To facilitate experimental studies of clinical applications, we developed a software toolbox for these low-frequency conductivity and current density imaging methods. This MR-based conductivity imaging (MRCI) toolbox includes 11 toolbox functions which can be used in the MATLAB environment. The MRCI toolbox is available at http://iirc.khu.ac.kr/software.html . Its functions were tested by using several experimental datasets, which are provided together with the toolbox. Users of the toolbox can focus on experimental designs and interpretations of reconstructed images instead of developing their own image reconstruction softwares. We expect more toolbox functions to be added from future research outcomes. Low-frequency conductivity and current density imaging using MRI includes magnetic resonance electrical impedance tomography (MREIT), diffusion tensor MREIT (DT-MREIT), conductivity tensor imaging (CTI), and magnetic resonance current density imaging (MRCDI). MRCDI and MREIT provide current density and isotropic conductivity images, respectively, using current-injection phase MRI techniques. DT-MREIT produces anisotropic conductivity tensor images by incorporating diffusion weighted MRI into MREIT. These current-injection techniques are finding clinical applications in diagnostic imaging and also in transcranial direct current stimulation (tDCS), deep brain stimulation (DBS), and electroporation where treatment currents can function as imaging currents. To avoid adverse effects of nerve and muscle stimulations due to injected currents, conductivity tensor imaging (CTI) utilizes B1 mapping and multi-b diffusion weighted MRI to produce low-frequency anisotropic conductivity tensor images without injecting current. This paper describes numerical implementations of several key mathematical functions for conductivity and current density image reconstructions in MRCDI, MREIT, DT-MREIT, and CTI. To facilitate experimental studies of clinical applications, we developed a software toolbox for these low-frequency conductivity and current density imaging methods. This MR-based conductivity imaging (MRCI) toolbox includes 11 toolbox functions which can be used in the MATLAB environment. The MRCI toolbox is available at http://iirc.khu.ac.kr/software.html . Its functions were tested by using several experimental datasets, which are provided together with the toolbox. Users of the toolbox can focus on experimental designs and interpretations of reconstructed images instead of developing their own image reconstruction softwares. We expect more toolbox functions to be added from future research outcomes.

Tissue Acoustoelectric Effect Modeling From Solid Mechanics Theory.

The acoustoelectric (AE) effect is a basic physical phenomenon, which underlies the changes made in the conductivity of a medium by the application of focused ultrasound. Recently, based on the AE effect, several biomedical imaging techniques have been widely studied, such as ultrasound-modulated electrical impedance tomography and ultrasound current source density imaging. To further investigate the mechanism of the AE effect in tissue and to provide guidance for such techniques, we have modeled the tissue AE effect using the theory of solid mechanics. Both bulk compression and thermal expansion of tissue are considered and discussed. Computation simulation shows that the muscle AE effect result, conductivity change rate, is 3.26×10-3 with 4.3-MPa peak pressure, satisfying the theoretical value. Bulk compression plays the main role for muscle AE effect, while thermal expansion makes almost no contribution to it. In addition, the AE signals of porcine muscle are measured at different focal positions. With the same magnitude order and the same change trend, the experiment result confirms that the simulation result is effective. Both simulation and experimental results validate that tissue AE effect modeling using solid mechanics theory is feasible, which is of significance for the further development of related biomedical imaging techniques.

Comparisons between in-vivo current density images and computational models in human TACS recipients

Comparisons between in-vivo current density images and computational models in human TACS recipients

Alternative luminescence image evaluation – Comparison with lock-in thermography

It was shown recently that previous approaches for quantitative luminescence image evaluation based on the model of independent diodes inevitably lead to erroneous results for imaging saturation current densities. However, the pioneering work of Fuyuki on electroluminescence imaging of solar cells was not based on this model. There it was claimed that the calibration constant of the local luminescence signal should be proportional to the local effective diffusion length. With increasing diffusion length, however, the luminescence reaches a saturation value. Recently a simple formula for the calibration constant was proposed, which describes both the proportionality for small diffusion lengths and the saturation property for large ones. While this non-linear Fuyuki PL evaluation method was previously only applied to standard BSF cells, in this work it is applied to modern multicrystalline PERC cells processed from different high performance multicrystalline silicon materials. The results are compared to that of dark lock-in thermography (DLIT) and Laplacian PL investigations of these cells. It is found that saturation current density images obtained from the alternative luminescence evaluation methods are close to that based on DLIT in low lifetime regions, but show a much better spatial resolution. In high lifetime regions, however, this alternative PL evaluation is generally less reliable than DLIT. These alternative kinds of luminescence image evaluation may replace previous approaches of quantitative PL evaluation based on the model of independent diodes.

Realistic Electric Field Mapping of Anisotropic Muscle During Electrical Stimulation Using a Combination of Water Diffusion Tensor and Electrical Conductivity.

PurposeTo realistically map the electric fields of biological tissues using a diffusion tensor magnetic resonance electrical impedance tomography (DT-MREIT) method to estimate tissue response during electrical stimulation.MethodsImaging experiments were performed using chunks of bovine muscle. Two silver wire electrodes were positioned inside the muscle tissue for electrical stimulation. Electric pulses were applied with a 100-V amplitude and 100-μs width using a voltage stimulator. During electrical stimulation, we collected DT-MREIT data from a 3T magnetic resonance imaging scanner. We adopted the projected current density method to calculate the electric field. Based on the relation between the water diffusion tensor and the conductivity tensor, we computed the position-dependent scale factor using the measured magnetic flux density data. Then, a final conductivity tensor map was reconstructed using the multiplication of the water diffusion tensor and the scale factor.ResultsThe current density images from DT-MREIT data represent the internal current flows that exist not only in the electrodes but also in surrounding regions. The reconstructed electric filed map from our anisotropic conductivity tensor with the projected current density shows coverage that is more than 2 times as wide, and higher signals in both the electrodes and surrounding tissues, than the previous isotropic method owing to the consideration of tissue anisotropy.ConclusionsAn electric field map obtained by an anisotropic reconstruction method showed different patterns from the results of the previous isotropic reconstruction method. Since accurate electric field mapping is important to correctly estimate the coverage of the electrical treatment, future studies should include more rigorous validations of the new method through in vivo and in situ experiments.

Nanoscale Imaging of Current Density with a Single-Spin Magnetometer.

Charge transport in nanostructures and thin films is fundamental to many phenomena and processes in science and technology, ranging from quantum effects and electronic correlations in mesoscopic physics, to integrated charge- or spin-based electronic circuits, to photoactive layers in energy research. Direct visualization of the charge flow in such structures is challenging due to their nanometer size and the itinerant nature of currents. In this work, we demonstrate noninvasive magnetic imaging of current density in two-dimensional conductor networks including metallic nanowires and carbon nanotubes. Our sensor is the electronic spin of a diamond nitrogen-vacancy center attached to a scanning tip and operated under ambient conditions. Using a differential measurement technique, we detect DC currents down to a few μA with a current density noise floor of ∼2 × 104 A/cm2. Reconstructed images have a spatial resolution of typically 50 nm, with a best-effort value of 22 nm. Current density imaging offers a new route for studying electronic transport and conductance variations in two-dimensional materials and devices, with many exciting applications in condensed matter physics and materials science.

Multishot echo-planar MREIT for fast imaging of conductivity, current density, and electric field distributions.

Magnetic resonance electrical impedance tomography (MREIT) sequences typically use conventional spin or gradient echo-based acquisition methods for reconstruction of conductivity and current density maps. Use of MREIT in functional and electroporation studies requires higher temporal resolution and faster sequences. Here, single and multishot echo planar imaging (EPI) based MREIT sequences were evaluated to see whether high-quality MREIT phase data could be obtained for rapid reconstruction of current density, conductivity, and electric fields. A gel phantom with an insulating inclusion was used as a test object. Ghost artifact, geometric distortion, and MREIT correction algorithms were applied to the data. The EPI-MREIT-derived phase-projected current density and conductivity images were compared with simulations and spin-echo images as a function of EPI shot number. Good agreement among measures in simulated, spin echo, and EPI data was achieved. Current density errors were stable and below 9% as the shot number decreased from 64 to 2, but increased for single-shot images. Conductivity reconstruction relative contrast ratios were stable as the shot number decreased. The derived electric fields also agreed with the simulated data. The EPI methods can be combined successfully with MREIT reconstruction algorithms to achieve fast imaging of current density, conductivity, and electric field. Magn Reson Med 79:71-82, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

The Impact of Anisotropy on the Accuracy of Conductivity Imaging: A Quantitative Validation Study.

We present a quantitative validation study to assess the accuracy of low-frequency conductivity imaging methods, based on a testing current measured using Current Density Imaging (CDI). We tested the proposed procedure to study the influence of tissue anisotropy on the accuracy of conductivity reconstruction methods, using a finite element model of anisotropic brain tissue. Simulations were carried out for three different levels of tissue anisotropy to compare the results obtained by our recently developed anisotropic conductivity method with those obtained by our well-established conductivity method that assumes isotropic conductivity. The validation results clearly show that the conductivity imaging method which takes into account tissue anisotropy yields significantly superior accuracy.

Magnetic field and current density imaging using off-line lock-in analysis

In the current paper the application of a custom developed 2-dimenional scanning magnetic field microscope based on tunnel-magnetoresistive sensors and subsequent qualitative and quantitative analysis is described. To improve sensitivity and to enable the detection and evaluation of phase deviations, an off-line lock-in approach was employed by driving the samples under test with an injected current at a fixed signal frequency. Amplitude and phase evaluation was based on simultaneous acquisition of the reference and the measurement signal obtained from the magnetic field sensor. This off-line lock-in approach enables not just the detection but also the estimation of changes in signal phase caused by capacitive, inductive or ohmic coupling of the induced currents. Furthermore assessed magnetic fields were converted into the current density by solving the inverse magnetic problem and post processing of the acquired signals. For verification of the developed set-up the current density distribution was computed from experimentally acquired magnetic fields for a two-wire test structure. In addition quantitative values of the current density were derived for a calibration pattern containing defined structures. Finally, to evaluate the practical relevance a power MOSFET with unknown defect was analysed and an area of unexpectedly increased magnetic field intensity was observed.

Effective Diffusion Length and Bulk Saturation Current Density Imaging in Solar Cells by Spectrally Filtered Luminescence Imaging

Most methods for interpreting electroluminescence (EL) or photoluminescence (PL) images of solar cells evaluate the local diode voltages but not the local luminescence intensity itself. One exception is the Fuyuki approximation, which assumes that the local value of the luminescence signal is proportional to the local effective diffusion length. This dependence has been derived for infinitely thick solar cells and neglects self-absorption of the luminescence photons. However, for real solar cells and imaging conditions, with increasing diffusion length, the luminescence signal approaches a limiting value; hence, the Fuyuki approximation no longer holds. In this paper, we compare EL and PL images of multicrystalline solar cells using different kinds of light filtering and find that gentle shortpass filtering is useful for avoiding optical artifacts. Based on earlier calculations, a physically founded formula for the dependence of the gently shortpass-filtered luminescence signal on the bulk diffusion length, for a given rear surface recombination velocity, is presented. Since this formula only barely allows us to calculate the diffusion length from the luminescence signal, a simplified approximate formula is proposed, and its accuracy is checked. This method is tested on EL and ${V_{{{\rm oc}}}}$ PL images of solar cells. We find that for a typical industrial multicrystalline Al-backside solar cell, the obtained effective diffusion length images correlate well with such images obtained by spectral LBIC image evaluation. In addition, the saturation current density images correlate well with such images obtained by dark lock-in thermography, which show a much lower spatial resolution. The main limitation of the proposed method is that it is basically approximate and needs some fitting parameters.

Polarity detection in ultrasound current source density imaging.

Modulating the electric dipole field with ultrasound pulse, ultrasound current source density imaging (UCSDI) can detect current direction and form spatial 3D imaging of dipole changing in one period of treatment. As ultrasound pulse passes through the conductive media, it convolves/correlates with the inner product of the electric field of a dipole and lead field of a pair of detectors, making the shifting frequency of polarity lower than the center frequency of the ultrasound pulse. After acoustoelectric (AE) signal is shifted to base band, the AE voltage is positive at anode and negative at cathode. In the simulation, the lead fields of detectors and electric field of dipole were calculated by the finite element (FE) method; the convolution and correlation in the computation of AE signal were accelerated using 3-D fast Fourier transforms. The current direction and amplitude are encoded in the phase and amplitude of the AE signal. Based on the analysis of polarity algorithms on the simulated and in-vitro ultrasound current source density images, it is concluded that the cross-correlation method is significantly better than the autocorrelation method to extract the frequency shift for high pulse bandwidth.

Interpretation of very low frequency electromagnetic measurements in terms of normalized current density over variable topography

A 2D inversion approach is developed to interpret VLF electromagnetic measurement recorded over variable topography. To depict the variable topography accurately, an octree mesh discretization is incorporated. Subsurface structure is modeled in terms of apparent current density distribution and compared with the inversion results for actual resistivity distribution obtained using numerical techniques. The study demonstrates that the results obtained using both approaches (current density and resistivity distribution) are comparable, but due to analytical expression, current density imaging is faster. The conjugate gradient method is used to reduce the computation time and storage space when solving the matrix equations, resulting in feasible and practical imaging inversion of VLF data. The preconditioned matrix, which is determined by the distances between the blocks and observation points, has an important function in improving the resolution. In case of flat earth, preconditioned conjugate gradient inversion of data results in images that are comparable to those obtained using resistivity inversion. We also test whether topography variation in the order of skin depth is significant to incorporate topography in the modeling. The example of a topographical field VLF data inversion shows the efficacy of the presented approach to appraise the subsurface structure in terms of current density.

Complementary Detection of Multiple Electrical Sources in Tissue Using Acoustoelectric Effects

Accurate 3-D mapping of multiple bioelectric sources in nerve fibers with high spatial resolution is challenging for the diagnosis and treatment of a variety of neural abnormalities. Ultrasound current source density imaging exploits the acoustoelectric (AE) effect, an interaction between electrical current and acoustic pressure waves propagating through a conducting material, and has distinct advantages over conventional electrophysiology (i.e., without ultrasound) for mapping electrical current flow in tissue. Ultrasound current source density imaging and two complementary Wheatstone bridge circuits were used to simultaneously detect two separate current flows induced in tissue phantoms. It has been found that the addition and subtraction of AE signals acquired by two circuits are independent components, regardless of whether the two sources are positioned at the same or different depths. In the ultrasound field, the AE signal from the bridge circuits is stronger, with a higher signal-to-noise ratio, than without a bridge circuit. Both experimental and simulated AE images depend on the magnitude and direction of the current, as well as the geometry (shape and thickness) and location of the current sources in the ultrasound field (2.25-MHz transducer). The experimental results are consistent with simulations consisting of multiple current sources. Real-time 3-D ultrasound current source density images of multiple current flows co-registered with convention pulse echo ultrasound potentially facilitate monitoring of neurologic disorders.

Modeling Current Density Maps Using Aliev-Panfilov Electrophysiological Heart Model.

Most existing studies of cardiac arrhythmia rely on surface measurements through optical or electrical mapping techniques. Current density imaging (CDI) is a method which enables us to study current pathways inside the tissue. However, this method entails implementation complexities for beating ex vivo hearts. Hence, this work presents an approach to simulate and study the current distributions in different cardiac electrophysiological states. The results are corroborated by experimental data, and they indicate that different states were distinguishable. The CDI simulations can be used for studying cardiac arrhythmias under simulation conditions which are otherwise impossible or difficult to be implemented experimentally.

Imaging of complex-valued tensors for two-dimensional Maxwell’s equations

Abstract This paper concerns the imaging of a complex-valued anisotropic tensor γ = σ + 𝜾 ⁢ ω ⁢ ε ${\gamma=\sigma+\boldsymbol{\iota}\omega\varepsilon}$ from knowledge of several inter magnetic fields H, where H satisfies the anisotropic Maxwell system on a bounded domain X ⊂ ℝ 2 ${X\subset\mathbb{R}^{2}}$ with prescribed boundary conditions on ∂ ⁡ X ${\partial X}$ . We show that γ can be uniquely reconstructed with a loss of two derivatives from errors in the acquisition H. A minimum number of five well-chosen functionals guaranties a local reconstruction of γ in dimension two. The explicit inversion procedure is presented in several numerical simulations, which demonstrate the influence of the choice of boundary conditions on the stability of the reconstruction. This problem finds applications in the medical imaging modalities Current Density Imaging and Magnetic Resonance Electrical Impedance Tomography.

Improved empirical method for calculating short circuit current density images of silicon solar cells from saturation current density images and vice versa

An empirical dependence of the short circuit current density Jsc as a function of the dark saturation current density J01 is proposed, which describes this dependence down to a bulk lifetime of 1ns. This method avoids artifacts, which appear when applying the previously proposed quadratic dependence. The parameters of the new dependence are fitted to PC1D simulations and to experimental LBIC results for various wavelengths and AM 1.5 for a typical industrial BSF-type solar cell and a PERC cell. This dependence can also be used to calculate J01 images from LBIC-based Jsc images. It turns out that this method is more reliable in BSF than in PERC cells.

2D surface defect images applying Tikhonov regularized inversion and ECT

This paper presents an inversion problem solution to obtain the geometrical profile of defects in a 2D surface view using an eddy current method with sinusoidal excitation. The inversion model deals with the perturbation of the eddy currents when a spatially uniform excitation magnetic field distribution is imposed in the vicinity of a metal surface. An adequate experimental setup was used to measure the magnetic field around a crack region. A planar excitation coil was used to generate the uniform magnetic field distribution around the points under measurement, and a giant magneto-resistance (GMR) was used as a sensing element. Tikhonov regularization was applied to the inversion problem algorithm. Five different geometric defects machined in an aluminum plate were tested experimentally using the inversion algorithm. Finite element simulations are provided to validate the 2D eddy current density images obtained by the regularized inversion process.

Feature-based MRI data fusion for cardiac arrhythmia studies

Current practices in studying cardiac arrhythmias primarily use electrical or optical surface recordings of a heart, spatially limited transmural recordings, and mathematical models. However, given that such arrhythmias occur on a 3D myocardial tissue, information obtained from such practices lack in dimension, completeness, and are sometimes prone to oversimplification. The combination of complementary Magnetic-Resonance Imaging (MRI)-based techniques such as Current Density Imaging (CDI) and Diffusion Tensor Imaging (DTI) could provide more depth to current practices in assessing the cardiac arrhythmia dynamics in entire cross sections of myocardium. In this work, we present an approach utilizing feature-based data fusion methods to demonstrate that complimentary information obtained from electrical current distribution and structural properties within a heart could be quantified and enhanced. Twelve (12) pairs of CDI and DTI image data sets were gathered from porcine hearts perfused through a Langendorff setup. Images were fused together using feature-based data fusion techniques such as Joint Independent Component Analysis (jICA), Canonical Correlation Analysis (CCA), and their combination (CCA+jICA). The results suggest that the complimentary information of cardiac states from CDI and DTI are enhanced and are better classified with the use of data fusion methods. For each data set, an increase in mean correlations of fused images were observed with 38% increase from CCA+jICA compared to the original images while mean mutual information of the fused images from jICA and CCA+jICA increased by approximately three-fold. We conclude that MRI-based techniques present potential viable tools in furthering studies for cardiac arrhythmias especially Ventricular Fibrillation.

Auditory P3a and P3b neural generators in schizophrenia: An adaptive sLORETA P300 localization approach

The present study investigates the neural substrates underlying cognitive processing in schizophrenia (Sz) patients. To this end, an auditory 3-stimulus oddball paradigm was used to identify P3a and P3b components, elicited by rare-distractor and rare-target tones, respectively. Event-related potentials (ERP) were recorded from 31 Sz patients and 38 healthy controls. The P3a and P3b brain-source generators were identified by time-averaging of low-resolution brain electromagnetic tomography (LORETA) current density images. In contrast with the commonly used fixed window of interest (WOI), we proposed to apply an adaptive WOI, which takes into account subjects' P300 latency variability. Our results showed different P3a and P3b source activation patterns in both groups. P3b sources included frontal, parietal and limbic lobes, whereas P3a response generators were localized over bilateral frontal and superior temporal regions. These areas have been related to the discrimination of auditory stimulus and to the inhibition (P3a) or the initiation (P3b) of motor response in a cognitive task. In addition, differences in source localization between Sz and control groups were observed. Sz patients showed lower P3b source activity in bilateral frontal structures and the cingulate. P3a generators were less widespread for Sz patients than for controls in right superior, medial and middle frontal gyrus. Our findings suggest that target and distractor processing involves distinct attentional subsystems, both being altered in Sz. Hence, the study of neuroelectric brain information can provide further insights to understand cognitive processes and underlying mechanisms in Sz.

The development of an experimental setup to measure acousto-electric interaction signal

Abstract A new method is desirable for secure efficiency of FES treatment of degenerated denervated muscles. Degeneration of denervaed muscles as a consequence of spinal injuries are treated with functional electrical stimulation (FES). So far, no effective method to monitor the effectiveness of the treatment over the whole treated muscle is available. The most common method is placing finger on appropriate tendons and sense the movement. We suggest new approach. As pressure wave changes locally electrical conductivity in its propagation direction of the medium, a change in voltage is detected when electrical field is applied simultaneously at that location. This change in voltage is called acousto-electric interaction (AEI) signal. By recording AEI signal a distribution of electrical activity can be mapped, known as ultrasound current source density imaging (UCSDI). In this paper, an experimental setup to investigate the AEI signal is developed. The signal is measured and compared to calculated values. Debye effect and AEI signal is detected.