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The developed magnetic resonance electrical properties tomography (MREPT) techniques visualize the internal conductivity distribution at Larmor frequency by measuring the B1 transceive phase data. In biological tissues, electrical conductivity is influenced by ion concentrations and mobility. To visualize the anisotropic conductivity tensor of biological tissues, we use the Einstein–Smoluchowski equation, which links the diffusion coefficient to particle mobility. By assuming a correlation between ion mobility and water diffusivity, we aim to decompose the internal isotropic conductivity at Larmor frequency into anisotropic conductivity tensors within the intra- and extra-neurite compartments. The multi-compartment spherical mean technique (MC-SMT), utilizing both high and low b-value diffusion-weighted imaging (DWI) data, characterizes the diffusion of water molecules within and across the intra- and extra-neurite compartments by analyzing the microstructural intricacies and the foundational architectural arrangement of the brain’s tissues. By analyzing the relationships between the measured DWI data, the microscopic diffusion signal, and the fiber orientation distribution function, we predict the DWI data for the intra- and extra-neurite compartments using spherical harmonic decomposition. Using the predicted DWI data for the intra- and extra-neurite compartments, we develop a conductivity tensor imaging method that operates specifically within the separated compartments. Human brain experiments, involving four healthy volunteers and a brain tumor patient, were performed to assess and confirm the reliability of the proposed method. •Intra-neurite volume fraction and diffusion patterns reconstructed using DWI data with multiple b-values.•Prediction of intra- and extra-neurite DWI data.•Conductivity tensor imaging for intra- and extra-neurite compartments using the predicted DWI data.

Magnetic resonance imaging (MRI) often uses gadolinium-based contrast agents (GBCAs) to improve the characterization of imaging contrast, owing to their strong paramagnetic properties. Magnetic resonance electrical properties tomography (MREPT) visualizes the conductivity distribution of biological tissues at the Larmor frequency using the field phase signal. In this paper, we investigate the effect of GBCA on brain conductivity. To compare the differences of reconstructed noisy conductivity maps before and after the GBCA injection, we propose a method to remove the background low-frequency noise artifact based on an elliptic partial differential equation. By analyzing the relationship between electrical conductivity and magnetic permeability, the objective of this study is to develop a cost-effective and accessible initial screening imaging tool for diagnosing and monitoring the treatment of Alzheimer’s disease (AD) pathophysiology. To investigate vascular damage in AD, we define a conductivity heterogeneity volume fraction (CHVF) caused by GBCA leakage. Using CHVF, we develop three indices to characterize mild cognitive impairment (MCI) and AD. To verify the proposed method, we studied a total of 42 participants, including 14 individuals diagnosed with AD, 18 participants with MCI, and 10 cognitively normal (CN) participants. Finally, we designed a radar chart informed by the CHVF analysis, to exhibit the pertinent parameters for MCI and AD patients, facilitating the evaluation and ongoing monitoring of each patient’s diagnosis and treatment regimen.

•Novel method to estimating low-frequency electrical property imaging is proposed.•The method is based on the B1 mapping technique, which provides a high-frequency conductivity distribution at Larmor frequency, and the multi-compartment model based on the spherical mean technique, which estimates the microscopic tissue structure.•The low-frequency dominant electrical parameters including the total ion concentration and mean diffusivity in the extra-neurite space are reconstructed.•The low-frequency anisotropic conductivity tensor is recovered by combining with the extracted extra-neurite diffusion tensor map and the reconstructed electrical parameters.•The method uses a conventional MRI scanner without any additional device to inject external currents. 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.

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.

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).

Purpose: No prior clinical studies have quantitatively evaluated the effect of low-dose radiation therapy (LDRT) on Alzheimer’s disease (AD) brain changes using multi-modal MRI. This study examined the feasibility of using conductivity, diffusion, and brain tissue volume measures to detect treatment effects in patients with AD receiving LDRT. Methods: Nine patients with mild AD were enrolled in three groups. Three patients in each group were assigned to the control group (0 cGy) and the treated groups [24 cGy/6 fractions (4 cGy for each fraction) and 300 cGy/6 fractions (50 cGy for each fraction)]. Conductivity, diffusivity, and brain tissue volume were acquired at baseline and 6 months post-treatment and were evaluated to assess within-group MRI changes and evaluate associations between MRI measures and Mini-Mental State Examination (MMSE) scores. Results: Region-of-interest (ROI) analyses identified substantial changes in high-frequency conductivity (HFC) (e.g., left insula), cerebrospinal fluid (CSF) volumes (e.g., anterior cingulate, limbic regions), and diffusion tensor imaging (DTI) metrics, such as axial diffusivity (AxD) and fractional anisotropy (FA), in fusiform, thalamic, hippocampal, and occipital areas. Correlation analysis showed strong associations between MRI measures and cognition, most notably HFC in the left fusiform gyrus (r = 0.843, p = 0.0043) after treatment. Diffusion indices across multiple regions also showed significant positive or negative correlations with MMSE. Conclusions: This exploratory clinical study demonstrates that LDRT induces measurable physiological and microstructural alterations in the brain detectable via conductivity and diffusion MRI. Conductivity emerged as the sensitive biomarker, showing strong cognitive correlations. These exploratory findings suggest that multi-modal quantitative MRI can serve as an effective tool for evaluating treatment response in clinical LDRT for AD.

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.

Purpose Previous studies have utilized texture analyses on T1-weighted images and quantitative susceptibility maps in Alzheimer’s disease (AD) patients. This study aims to evaluate 3D texture analyses of high-frequency conductivity (HFC) maps at Larmor frequency, acquired from a 3T MRI system, as a potential imaging biomarker for AD Methods HFC maps were generated for 18 AD patients, 25 individuals with amnestic mild cognitive impairment (MCI), and 21 cognitively normal (CN) elderly participants using a six-echo turbo spin-echo pulse sequence on a clinical 3T MRI. Differences among the three groups were assessed by comparing the first- and second-order texture parameters of HFC images in the insular region, using a one-way analysis of covariance with age as a covariate Results For the first-order analysis, the mean HFC was elevated in AD patients compared to the other groups. Significant differences were observed in the second-order texture parameters, including angular second moment, inverse difference moment, sum of squares, entropy, sum of entropy, difference of entropy, and sum of average, across the subject groups Conclusion The findings indicate that AD patients have more complex and diverse patterns in HFCs within the insula compared to the CN and MCI groups. Thus, texture analysis of HFC images can effectively differentiate AD from other conditions

Diffusion tensor magnetic resonance electrical impedance tomography (DT-MREIT) is a newly developed technique that combines MR-based measurements of magnetic flux density with diffusion tensor MRI (DT-MRI) data to reconstruct electrical conductivity tensor distributions. DT-MREIT techniques normally require injection of two independent current patterns for unique reconstruction of conductivity characteristics. In this paper, we demonstrate an algorithm that can be used to reconstruct the position dependent scale factor relating conductivity and diffusion tensors, using flux density data measured from only one current injection. We demonstrate how these images can also be used to reconstruct electric field and current density distributions. Reconstructions were performed using a mimetic algorithm and simulations of magnetic flux density from complementary electrode montages, combined with a small-scale machine learning approach. In a biological tissue phantom, we found that the method reduced relative errors between single-current and two-current DT-MREIT results to around 10%. For in vivo human experimental data the error was about 15%. These results suggest that incorporation of machine learning may make it easier to recover electrical conductivity tensors and electric field images during neuromodulation therapy without the need for multiple current administrations.

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 (M b -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 M b -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.