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

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.

Estimation of brain tissue response by electrical stimulation in a subject-specific model implemented by conductivity tensor imaging

Electrical stimulation such as transcranial direct current stimulation (tDCS) is widely used to treat neuropsychiatric diseases and neurological disorders. Computational modeling is an important approach to understand the mechanisms underlying tDCS and optimize treatment planning. When applying computational modeling to treatment planning, uncertainties exist due to insufficient conductivity information inside the brain. In this feasibility study, we performed in vivo MR-based conductivity tensor imaging (CTI) experiments on the entire brain to precisely estimate the tissue response to the electrical stimulation. A recent CTI method was applied to obtain low-frequency conductivity tensor images. Subject-specific three-dimensional finite element models (FEMs) of the head were implemented by segmenting anatomical MR images and integrating a conductivity tensor distribution. The electric field and current density of brain tissues following electrical stimulation were calculated using a conductivity tensor-based model and compared to results using an isotropic conductivity model from literature values. The current density by the conductivity tensor was different from the isotropic conductivity model, with an average relative difference |rD| of 52 to 73%, respectively, across two normal volunteers. When applied to two tDCS electrode montages of C3-FP2 and F4-F3, the current density showed a focused distribution with high signal intensity which is consistent with the current flowing from the anode to the cathode electrodes through the white matter. The gray matter tended to carry larger amounts of current densities regardless of directional information. We suggest this CTI-based subject-specific model can provide detailed information on tissue responses for personalized tDCS treatment planning.

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.

Measurement of extracellular volume fraction using magnetic resonance-based conductivity tensor imaging

Conductivity tensor imaging (CTI) using MRI is an advanced method that can non-invasively measure the electrical properties of living tissues. The contrast of CTI is based on underlying hypothesis about the proportionality between the mobility and diffusivity of ions and water molecules inside tissues. The experimental validation of CTI in both in vitro and in vivo settings is required as a reliable tool to assess tissue conditions. The changes in extracellular space can be indicators for disease progression, such as fibrosis, edema, and cell swelling. In this study, we conducted a phantom imaging experiment to test the feasibility of CTI for measuring the extracellular volume fraction in biological tissue. To mimic tissue conditions with different extracellular volume fractions, four chambers of giant vesicle suspension (GVS) with different vesicle densities were included in the phantom. The reconstructed CTI images of the phantom were compared with the separately-measured conductivity spectra of the four chambers using an impedance analyzer. Moreover, the values of the estimated extracellular volume fraction in each chamber were compared with those measured by a spectrophotometer. As the vesicle density increased, we found that the extracellular volume fraction, extracellular diffusion coefficient, and low-frequency conductivity decreased, while the intracellular diffusion coefficient slightly increased. On the other hand, the high-frequency conductivity could not clearly distinguish the four chambers. The extracellular volume fraction measured by the spectrophotometer and CTI method in each chamber were quite comparable, i.e., (1.00, 0.98 ± 0.01), (0.59, 0.63 ± 0.02), (0.40, 0.40 ± 0.05), and (0.16, 0.18 ± 0.02). The prominent factor influencing the low-frequency conductivity at different GVS densities was the extracellular volume fraction. Further studies are needed to validate the CTI method as a tool to measure the extracellular volume fractions in living tissues with different intracellular and extracellular compartments.

Measurement of extracellular volume fraction using magnetic resonance-based conductivity tensor imaging

Conductivity tensor imaging (CTI) using MRI is an advanced method that can non-invasively measure the electrical properties of living tissues. The contrast of CTI is based on underlying hypothesis about the proportionality between the mobility and diffusivity of ions and water molecules inside tissues. The experimental validation of CTI in both in vitro and in vivo settings is required as a reliable tool to assess tissue conditions. The changes in extracellular space can be indicators for disease progression, such as fibrosis, edema, and cell swelling. In this study, we conducted a phantom imaging experiment to test the feasibility of CTI for measuring the extracellular volume fraction in biological tissue. To mimic tissue conditions with different extracellular volume fractions, four chambers of giant vesicle suspension (GVS) with different vesicle densities were included in the phantom. The reconstructed CTI images of the phantom were compared with the separately-measured conductivity spectra of the four chambers using an impedance analyzer. Moreover, the values of the estimated extracellular volume fraction in each chamber were compared with those measured by a spectrophotometer. As the vesicle density increased, we found that the extracellular volume fraction, extracellular diffusion coefficient, and low-frequency conductivity decreased, while the intracellular diffusion coefficient slightly increased. On the other hand, the high-frequency conductivity could not clearly distinguish the four chambers. The extracellular volume fraction measured by the spectrophotometer and CTI method in each chamber were quite comparable, i.e., (1.00, 0.98 ± 0.01), (0.59, 0.63 ± 0.02), (0.40, 0.40 ± 0.05), and (0.16, 0.18 ± 0.02). The prominent factor influencing the low-frequency conductivity at different GVS densities was the extracellular volume fraction. Further studies are needed to validate the CTI method as a tool to measure the extracellular volume fractions in living tissues with different intracellular and extracellular compartments.

Measurement and image-based estimation of dielectric properties of biological tissues —past, present, and future—

The dielectric properties of biological tissues are fundamental pararmeters that are essential for electromagnetic modeling of the human body. The primary database of dielectric properties compiled in 1996 on the basis of dielectric measurements at frequencies from 10 Hz to 20 GHz has attracted considerable attention in the research field of human protection from non-ionizing radiation. This review summarizes findings on the dielectric properties of biological tissues at frequencies up to 1 THz since the database was developed. Although the 1996 database covered general (normal) tissues, this review also covers malignant tissues that are of interest in the research field of medical applications. An intercomparison of dielectric properties based on reported data is presented for several tissue types. Dielectric properties derived from image-based estimation techniques developed as a result of recent advances in dielectric measurement are also included. Finally, research essential for future advances in human body modeling is discussed.

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.

Conductivity Tensor Imaging of the Human Brain Using Water Mapping Techniques

Conductivity tensor imaging (CTI) has been recently proposed to map the conductivity tensor in 3D using magnetic resonance imaging (MRI) at the frequency range of the brain at rest, i.e., low-frequencies. Conventional CTI mapping methods process the trans-receiver phase of the MRI signal using the MR electric properties tomography (MR-EPT) technique, which in turn involves the application of the Laplace operator. This results in CTI maps with a low signal-to-noise ratio (SNR), artifacts at tissue boundaries and a limited spatial resolution. In order to improve on these aspects, a methodology independent from the MR-EPT method is proposed. This relies on the strong assumption for which electrical conductivity is univocally pre-determined by water concentration. In particular, CTI maps are calculated by combining high-frequency conductivity derived from water maps and multi b-value diffusion tensor imaging (DTI) data. Following the implementation of a pipeline to optimize the pre-processing of diffusion data and the fitting routine of a multi-compartment diffusivity model, reconstructed conductivity images were evaluated in terms of the achieved spatial resolution in five healthy subjects scanned at rest. We found that the pre-processing of diffusion data and the optimization of the fitting procedure improve the quality of conductivity maps. We achieve reproducible measurements across healthy participants and, in particular, we report conductivity values across subjects of 0.55 ± 0.01Sm, 0.3 ± 0.01Sm and 2.15 ± 0.02Sm for gray matter (GM), white matter (WM), and cerebrospinal fluid (CSF), respectively. By attaining an actual spatial resolution of the conductivity tensor close to 1 mm in-plane isotropic, partial volume effects are reduced leading to good discrimination of tissues with similar conductivity values, such as GM and WM. The application of the proposed framework may contribute to a better definition of the head tissue compartments in electroencephalograpy/magnetoencephalography (EEG/MEG) source imaging and be used as biomarker for assessing conductivity changes in pathological conditions, such as stroke and brain tumors.

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.

Identification of Brain Damage after Seizures Using an MR-Based Electrical Conductivity Imaging Method

Previous imaging studies have shown the morphological malformation and the alterations of ionic mobility, water contents, electrical properties, or metabolites in seizure brains. Magnetic resonance electrical properties tomography (MREPT) is a recently developed technique for the measurement of electrical tissue properties with a high frequency that provides cellular information regardless of the cell membrane. In this study, we examined the possibility of MREPT as an applicable technique to detect seizure-induced functional changes in the brain of rats. Ultra-high field (9.4 T) magnetic resonance imaging (MRI) was performed, 2 h, 2 days, and 1 week after the injection of N-methyl-D-aspartate (NMDA; 75 mg/kg). The conductivity images were reconstructed from B1 phase images using a magnetic resonance conductivity imaging (MRCI) toolbox. The high-frequency conductivity was significantly decreased in the hippocampus among various brain regions of NMDA-treated rats. Nissl staining showed shrunken cell bodies and condensed cytoplasm potently at 2 h after NMDA treatment, and neuronal cell loss at all time points in the hippocampus. These results suggest that the reduced electrical conductivity may be associated with seizure-induced neuronal loss in the hippocampus. Magnetic resonance (MR)-based electrical conductivity imaging may be an applicable technique to non-invasively identify brain damage after a seizure.