Low-frequency dominant electrical conductivity imaging of in vivo human brain using high-frequency conductivity at Larmor-frequency and spherical mean diffusivity without external injection current.

Diffusion weighted imaging based on random Brownian motion of water molecules within a voxel provides information on the micro-structure of biological tissues through water molecule diffusivity. As the electrical conductivity is primarily determined by the concentration and mobility of ionic charge carriers, the macroscopic electrical conductivity of biological tissues is also related to the diffusion of electrical ions. This paper aims to investigate the low-frequency electrical conductivity by relying on a pre-defined biological model that separates the brain into the intracellular (restricted) and extracellular (hindered) compartments. The proposed method uses B1 mapping technique, which provides a high-frequency conductivity distribution at Larmor frequency, and the spherical mean technique, which directly estimates the microscopic tissue structure based on the water molecule diffusivity and neurite orientation distribution. The total extracellular ion concentration, which is separated from the high-frequency conductivity, is recovered using the estimated diffusivity parameters and volume fraction in each compartment. We propose a method to reconstruct the low-frequency dominant conductivity tensor by taking into consideration the extracted extracellular diffusion tensor map and the reconstructed electrical parameters. To demonstrate the reliability of the proposed method, we conducted two phantom experiments. The first one used a cylindrical acrylic cage filled with an agar in the background region and four anomalies for the effect of ion concentration on the electrical conductivity. The other experiment, in which the effect of ion mobility on the conductivity was verified, used cell-like materials with thin insulating membranes suspended in an electrolyte. Animal and human brain experiments were conducted to visualize the low-frequency dominant conductivity tensor images. The proposed method using a conventional MRI scanner can predict the internal current density map in the brain without directly injected external currents.

Decomposition of high-frequency electrical conductivity into extracellular and intracellular compartments based on two-compartment model using low-to-high multi-b diffusion MRI.

BACKGROUND: As an object's electrical passive property, the electrical conductivity is proportional to the mobility and concentration of charged carriers that reflect the brain micro-structures. The measured multi-b diffusion-weighted imaging (Mb-DWI) data by controlling the degree of applied diffusion weights can quantify the apparent mobility of water molecules within biological tissues. Without any external electrical stimulation, magnetic resonance electrical properties tomography (MREPT) techniques have successfully recovered the conductivity distribution at a Larmor-frequency. METHODS: This work provides a non-invasive method to decompose the high-frequency conductivity into the extracellular medium conductivity based on a two-compartment model using Mb-DWI. To separate the intra- and extracellular micro-structures from the recovered high-frequency conductivity, we include higher b-values DWI and apply the random decision forests to stably determine the micro-structural diffusion parameters. RESULTS: To demonstrate the proposed method, we conducted phantom and human experiments by comparing the results of reconstructed conductivity of extracellular medium and the conductivity in the intra-neurite and intra-cell body. The phantom and human experiments verify that the proposed method can recover the extracellular electrical properties from the high-frequency conductivity using a routine protocol sequence of MRI scan. CONCLUSION: We have proposed a method to decompose the electrical properties in the extracellular, intra-neurite, and soma compartments from the high-frequency conductivity map, reconstructed by solving the electro-magnetic equation with measured B1 phase signals.

Angular resolution enhancement technique for diffusion-weighted imaging (DWI) using predicted diffusion gradient directions.

Anisotropic diffusion MRI techniques using single-shell or multi-shell acquisitions have been proposed as a means to overcome some limitations imposed by diffusion tensor imaging (DTI), especially in complex models of fibre orientation distribution in voxels. A long acquisition time for the angular resolution of diffusion MRI is a major obstacle to practical clinical implementations. In this paper, we propose a novel method to improve angular resolution of diffusion MRI acquisition using given diffusion gradient (DG) directions. First, we define a local diffusion pattern map of diffusion MR signals on a single shell in given DG directions. Using the local diffusion pattern map, we design a prediction scheme to determine the best DG direction to be synthesized within a nearest neighborhood DG directions group. Second, the local diffusion pattern map and the spherical distance on the shell are combined to determine a synthesized diffusion signal in the new DG direction. Using the synthesized and measured diffusion signals on a single sphere, we estimate a spin orientation distribution function (SDF) with human brain data. Although the proposed method is applied to SDF, a basic idea is to increase the angular resolution using the measured diffusion signals in various DG directions. The method can be applicable to different acquired multi-shell data or diffusion spectroscopic imaging (DSI) data. We validate the proposed method by comparing the recovered SDFs using the angular resolution enhanced diffusion signals with the recovered SDF using the measured diffusion data. The developed method provides an enhanced SDF resolution and improved multiple fiber structure by incorporating synthesized signals. The proposed method was also applied neurite orientation dispersion and density imaging (NODDI) using multi-shell acquisitions.

Functional MRI study with conductivity signal changes during visual stimulation.

BACKGROUND: Although blood oxygen level-dependent (BOLD) functional MRI (fMRI) is a standard method, major BOLD signals primarily originate from intravascular sources. Magnetic resonance electrical properties tomography (MREPT)-based fMRI signals may provide additional insights into electrical activity caused by alterations in ion concentrations and mobilities. PURPOSE: This study aimed to investigate the neuronal response of conductivity during visual stimulation and compare it with BOLD. MATERIALS AND METHODS: A total of 30 young, healthy volunteers participated in two independent experiments using BOLD and MREPT techniques with a visual stimulation paradigm at 3 T MRI. The first set of MREPT fMRI data was obtained using a multi-echo spin-echo (SE) echo planar imaging (EPI) sequence from 14 participants. The second set of MREPT fMRI data was collected from 16 participants using both a single-echo SE-EPI and a single-echo three-dimensional (3D) balanced fast-field-echo (bFFE) sequence. We reconstructed the time-course Larmor frequency conductivity to evaluate hemodynamics. RESULTS: Conductivity values slightly increased during visual stimulation. Activation strengths were consistently stronger with BOLD than with conductivity for both SE-EPI MREPT and bFFE MREPT. Additionally, the activated areas were always larger with BOLD than MREPT. Some participants also exhibited decreased conductivity values during visual stimulations. In Experiment 1, conductivity showed significant differences between the fixation and visual stimulation blocks in the secondary visual cortex (SVC) and cuneus, with conductivity differences of 0.43 % and 0.47 %, respectively. No significant differences in conductivity were found in the cerebrospinal fluid (CSF) areas between the two blocks. In Experiment 2, significant conductivity differences were observed between the two blocks in the SVC, cuneus, and lingual gyrus for SE-EPI MREPT, with differences of 0.90 %, 0.67 %, and 0.24 %, respectively. Again, no significant differences were found in the CSF areas. CONCLUSION: Conductivity values increased slightly during visual stimulation in the visual cortex areas but were much weaker than BOLD responses. The conductivity change during visual stimulation was less than 1 % compared to the fixation block. No significant differences in conductivity were observed between the primary visual cortex (PVC)-CSF and SVC-CSF during fixation and visual stimulations, suggesting that the observed conductivity changes may not be related to CSF changes in the visual cortex but rather to diffusion changes. Future research should explore the potential of MREPT to detect neuronal electrical activity and hemodynamic changes, with further optimization of the MREPT technique.

Increased extra-neurite conductivity of brain in patients with Alzheimer's disease: A pilot study.

The objectives of this study were to investigate how the extra-neurite conductivity (EC) and intra-neurite conductivity (IC) were reflected in Alzheimer's disease (AD) patients compared with old cognitively normal (CN) people and patients with amnestic mild cognitive impairment (MCI) and to evaluate the association between those conductivity values and cognitive decline. To do this, high-frequency conductivity (HFC) at the Larmor frequency was obtained using MRI-based electrical property tomography (MREPT) and was decomposed into EC and IC using information of multi-shell multi-gradient direction diffusion tensor images. This prospective single-center study included 20 patients with mild or moderate AD, 25 patients with amnestic MCI, and 21 old CN participants. After decomposing EC and IC from HFC for all participants, we performed voxel-based and regions-of-interest analyses to compare conductivity between the three participant groups and to evaluate the association with either age or the Mini-Mental State Examination (MMSE) scores. We found increased EC in AD compared to CN and MCI. EC was significantly negatively associated with MMSE scores in the insula, and middle temporal gyrus. EC might be used as an imaging biomarker for helping to monitor cognitive function.

High frequency conductivity decomposition by solving physically constraint underdetermined inverse problem in human brain.

The developed magnetic resonance electrical properties tomography (MREPT) can visualize the internal conductivity distribution at Larmor frequency by measuring the B1 transceive phase data from magnetic resonance imaging (MRI). The recovered high-frequency conductivity (HFC) value is highly complex and heterogeneous in a macroscopic imaging voxel. Using high and low b-value diffusion weighted imaging (DWI) data, the multi-compartment spherical mean technique (MC-SMT) characterizes the water molecule movement within and between intra- and extra-neurite compartments by analyzing the microstructures and underlying architectural organization of brain tissues. The proposed method decomposes the recovered HFC into the conductivity values in the intra- and extra-neurite compartments via the recovered intra-neurite volume fraction (IVF) and the diffusion patterns using DWI data. As a form of decomposition of intra- and extra-neurite compartments, the problem to determine the intra- and extra-neurite conductivity values from the HFC is still an underdetermined inverse problem. To solve the underdetermined problem, we use the compartmentalized IVF as a criterion to decompose the electrical properties because the ion-concentration and mobility have different characteristics in the intra- and extra-neurite compartments. The proposed method determines a representative apparent intra- and extra-neurite conductivity values by changing the underdetermined equation for a voxel into an over-determined minimization problem over a local window consisting of surrounding voxels. To suppress the noise amplification and estimate a feasible conductivity, we define a diffusion pattern distance to weight the over-determined system in the local window. To quantify the proposed method, we conducted a simulation experiment. The simulation experiments show the relationships between the noise reduction and the spatial resolution depending on the designed local window sizes and diffusion pattern distance. Human brain experiments (five young healthy volunteers and a patient with brain tumor) were conducted to evaluate and validate the reliability of the proposed method. To quantitatively compare the results with previously developed methods, we analyzed the errors for reconstructed extra-neurite conductivity using existing methods and indirectly verified the feasibility of the proposed method.

Application of High-Frequency Conductivity Map Using MRI to Evaluate It in the Brain of Alzheimer's Disease Patients.

Background: The previous studies reported increased concentrations of metallic ions, imbalanced Na+ and K+ ions, and the increased mobility of protons by microstructural disruptions in Alzheimer's disease (AD). Purpose: (1) to apply a high-frequency conductivity (HFC) mapping technique using a clinical 3T MRI system, (2) compare HFC values in the brains of participants with AD, amnestic mild cognitive impairment (MCI), and cognitively normal (CN) elderly people, (3) evaluate the relationship between HFC values and cognitive decline, and (4) explore usefulness of HFC values as an imaging biomarker to evaluate the differentiation of AD from CN. Materials and Methods: This prospective study included 74 participants (23 AD patients, 27 amnestic MCI patients, and 24 CN elderly people) to explore the clinical application of HFC mapping in the brain from March 2019 to August 2021. We performed statistical analyses to compare HFC maps between the three participant groups, evaluate the association of HFC maps with Mini-Mental State Examination (MMSE) scores, and to evaluate the differentiation between the participant groups for HFC values for some brain areas. Results: We obtained a good HFC map non-invasively. The HFC value was higher in the AD group than in the CN and MCI groups. MMSE scores were negatively associated with HFC values. Age was positively associated with HFC values. The HFC value in the insula has a high area under the receiver operating characteristic (ROC) curve (AUC) value to differentiate AD patients from the CN participants (Sensitivity [SE] = 82, Specificity [SP] =97, AUC = 0.902, p < 0.0001), better than gray matter volume (GMV) in hippocampus (SE = 79, SP = 83, AUC = 0.880, p < 0.0001). The classification for differentiating AD from CN was highest by adding the hippocampal GMV to the insular HFC value (SE = 87, SP = 87, AUC = 0.928, p < 0.0001). Conclusion: High-frequency conductivity values were significantly increased in the AD group compared to the CN group and increased with age and disease severity. HFC values of the insula along with the GMV of the hippocampus can be used as an imaging biomarker to improve the differentiation of AD from CN.

High-frequency conductivity at Larmor-frequency in human brain using moving local window multilayer perceptron neural network.

Magnetic resonance electrical properties tomography (MREPT) aims to visualize the internal high-frequency conductivity distribution at Larmor frequency using the B1 transceive phase data. From the magnetic field perturbation by the electrical field associated with the radiofrequency (RF) magnetic field, the high-frequency conductivity and permittivity distributions inside the human brain have been reconstructed based on the Maxwell's equation. Starting from the Maxwell's equation, the complex permittivity can be described as a second order elliptic partial differential equation. The established reconstruction algorithms have focused on simplifying and/or regularizing the elliptic partial differential equation to reduce the noise artifact. Using the nonlinear relationship between the Maxwell's equation, measured magnetic field, and conductivity distribution, we design a deep learning model to visualize the high-frequency conductivity in the brain, directly derived from measured magnetic flux density. The designed moving local window multi-layer perceptron (MLW-MLP) neural network by sliding local window consisting of neighboring voxels around each voxel predicts the high-frequency conductivity distribution in each local window. The designed MLW-MLP uses a family of multiple groups, consisting of the gradients and Laplacian of measured B1 phase data, as the input layer in a local window. The output layer of MLW-MLP returns the conductivity values in each local window. By taking a non-local mean filtering approach in the local window, we reconstruct a noise suppressed conductivity image while maintaining spatial resolution. To verify the proposed method, we used B1 phase datasets acquired from eight human subjects (five subjects for training procedure and three subjects for predicting the conductivity in the brain).

Extracellular electrical conductivity property imaging by decomposition of high-frequency conductivity at Larmor-frequency using multi-b-value diffusion-weighted imaging.

Magnetic resonance electrical properties tomography (MREPT) uses the B1 mapping technique to provide the high-frequency conductivity distribution at Larmor frequency that simultaneously reflects the intracellular and extracellular effects. In biological tissues, the electrical conductivity can be described as the concentration and mobility of charge carriers. For the water molecule diffusivity, diffusion weighted imaging (DWI) measures the random Brownian motion of water molecules within biological tissues. The DWI data can quantitatively access the mobility of microscopic water molecules within biological tissues. By measuring multi-b-value DWI data and the recovered high-frequency conductivity at Larmor frequency, we propose a new method to decompose the conductivity into the total ion concentration and mobility in the extracellular space (ECS) within a routinely applicable MR scan time. Using the measured multi-b-value DWI data, a constrained compartment model is designed to estimate the extracellular volume fraction and extracellular mean diffusivity. With the extracted extracellular volume fraction and water molecule diffusivity, we directly reconstruct the low-frequency electrical properties including the extracellular mean conductivity and extracellular conductivity tensor. To demonstrate the proposed method by comparing the ion concentration and the ion mobility, we conducted human experiments for the proposed low-frequency conductivity imaging. Human experiments verify that the proposed method can recover the low-frequency electrical properties using a conventional MRI scanner.

Anisotropic conductivity tensor imaging for transcranial direct current stimulation (tDCS) using magnetic resonance diffusion tensor imaging (MR-DTI).

Transcranial direct current stimulation (tDCS) is a widely used non-invasive brain stimulation technique by applying low-frequency weak direct current via electrodes attached on the head. The tDCS using a fixed current between 1 and 2 mA has relied on computational modelings to achieve optimal stimulation effects. Recently, by measuring the tDCS current induced magnetic field using an MRI scanner, the internal current pathway has been successfully recovered. However, up to now, there is no technique to visualize electrical properties including the electrical anisotropic conductivity, effective extracellular ion-concentration, and electric field using only the tDCS current in-vivo. By measuring the apparent diffusion coefficient (ADC) and the magnetic flux density induced by the tDCS, we propose a method to visualize the electrical properties. We reconstruct the scale parameter, which connects the anisotropic conductivity tensor to the diffusion tensor of water molecules, by introducing a repetitive scheme called the diffusion tensor J-substitution algorithm using the recovered current density and the measured ADCs. We investigate the proposed method to explain why the iterative scheme converges to the internal conductivity. We verified the proposed method with an anesthetized canine brain to visualize electrical properties including the electrical properties by tDCS current.

Anisotropic conductivity tensor by analyzing diffusion tensor for electrical brain stimulation (EBS).

Electrical brain stimulation (EBS) is a promising medical treatment method for brain neurological disorders through the direct or indirect excitation by injecting an electric current. At present, it is difficult to directly measure the distribution of the electric current delivered by electrodes inside tissues. By applying low-frequency ([Formula: see text]1 kHz) external electrical brain stimulation (EBS), the low-frequency conductivity around the cells is uneven due to asymmetric cellular structures. We propose a method of electrical property imaging using the measured one component magnetic flux density by EBS and diffusion tensor imaging (DTI). The low-frequency electrical anisotropic conductivity tensor can be decomposed into the ion concentration and the mobility tensor of charge carriers. By analyzing the role of the diffusion tensor, we reconstruct the apparent anisotropic tensor by EBS using the [Formula: see text]-component of measured magnetic flux density data and the estimated diffusion tensor. Using only the measured [Formula: see text]-component of magnetic flux density, the orthotropic conductivity tensor can be approximately recovered. The orthotropic conductivity tensor is not exact, but only reflects the extracellular space (ECS) effects. By comparing the components of orthotropic tensor and diffusion tensor, we stably determine a scale factor which primarily reflects the concentration of total ions in the extracellular space (ECS). Animal experiments verify that the proposed method recovers the anisotropic conductivity tensor which can visualize electrical properties during EBS of the brain. A direct reconstruction method for the apparent anisotropic conductivity tensor imaging during EBS was proposed to analyze unknown effects to brain tissue.

Extracellular Total Electrolyte Concentration Imaging for Electrical Brain Stimulation (EBS).

Techniques for electrical brain stimulation (EBS), in which weak electrical stimulation is applied to the brain, have been extensively studied in various therapeutic brain functional applications. The extracellular fluid in the brain is a complex electrolyte that is composed of different types of ions, such as sodium (Na+), potassium (K+), and calcium (Ca+). Abnormal levels of electrolytes can cause a variety of pathological disorders. In this paper, we present a novel technique to visualize the total electrolyte concentration in the extracellular compartment of biological tissues. The electrical conductivity of biological tissues can be expressed as a product of the concentration and the mobility of the ions. Magnetic resonance electrical impedance tomography (MREIT) investigates the electrical properties in a region of interest (ROI) at low frequencies (below 1 kHz) by injecting currents into the brain region. Combining with diffusion tensor MRI (DT-MRI), we analyze the relation between the concentration of ions and the electrical properties extracted from the magnetic flux density measurements using the MREIT technique. By measuring the magnetic flux density induced by EBS, we propose a fast non-iterative technique to visualize the total extracellular electrolyte concentration (EEC), which is a fundamental component of the conductivity. The proposed technique directly recovers the total EEC distribution associated with the water transport mobility tensor.

Microelectrode array analysis of hippocampal network dynamics following theta-burst stimulation via current source density reconstruction by Gaussian interpolation.

BACKGROUND: Multielectrode arrays (MEAs) have been used to understand electrophysiological network dynamics by recording real-time activity in groups of cells. The extent to which the collection of such data enables hypothesis testing on the level of circuits and networks depends largely on the sophistication of the analyses applied. NEW METHOD: We studied the systemic temporal variations of endogenous signaling within an organotypic hippocampal network following theta-burst stimulation (TBS) to the Schaffer collateral-commissural pathways. The recovered current source density (CSD) information from the raw grid of extracellular potentials by using a Gaussian interpolation method increases spatial resolution and avoids border artifacts by numerical differentials. RESULTS: We compared total sink and source currents in DG, CA3, and CA1; calculated accumulated correlation coefficients to compare pre- with post-stimulation CSD dynamics in each region; and reconstructed functional connectivity maps for regional cross-correlations with respect to temporal CSD variations. The functional connectivity maps for potential correlations pre- and post-TBS were compared to investigate the neural network as a whole, revealing differences post-TBS. COMPARISON WITH EXISTING METHOD(S): Previous MEA work on plasticity in hippocampal evoked potentials has focused on synchronicity across the hippocampus within isolated subregions. Such analyses ignore the complex relationships among diverse components of the hippocampal circuitry, thus failing to capture network-level behaviors integral to understanding hippocampal function. CONCLUSIONS: The proposed method of recovering current source density to examine whole-hippocampal function is sensitive to experimental manipulation and is worth further examination in the context of network-level analyses of neural signaling.