Electrical Properties Tomography Research Articles

REC-NN: A reconstruction error compensation neural network for Magnetic Resonance Electrical Property Tomography (MREPT).

Electrical properties (EPs) are expected as biomarkers for early cancer detection. Magnetic resonance electrical properties tomography (MREPT) is a technique to non-invasively estimate the EPs of tissues from MRI measurements. While noise sensitivity and artifact problems of MREPT are being solved progressively through recent efforts, the loss of tissue contrast emerges as an obstacle to the clinical applications of MREPT. To solve the problem, we propose a reconstruction error compensation neural network scheme (REC-NN) for a typical analytic MREPT method, Stab-EPT. Two NN structures: one with only ResNet blocks, and the other hybridizing ResNet blocks with an encoder-decoder structure. Results of experiments with digital brain phantoms show that, compared with Stab-EPT, and conventional NN based reconstruction, REC-NN improves both reconstruction accuracy and tissue contrast. It is found that, the encoder-decoder structure could improve the compensation accuracy of EPs in homogeneous region but showed worse reconstruction than only ResNet structure for tumorous tissues unseen in the training samples. Future research is required to address overcompensation problems, optimization of NN structure and application to clinical data.

An Adaptative Savitzky-Golay Kernel for Laplacian Estimation in Magnetic Resonance Electrical Property Tomography.

Magnetic Resonance electrical property tomography (MR-EPT) is a non-invasive imaging modality that reconstructs the living biological tissue's conductivity σ and εr permittivity using spatial derivatives of the measured RF field, also termed B1 data, in a magnetic resonance imaging system. The spatial derivative operator, particularly the Laplacian, amplifies the noise in the reconstructed electrical property (EP) maps, hence decreasing accuracy and increasing boundary artifacts. We propose a novel adaptative convolution kernel for generating numerical derivatives based on 3D Savitzky-Golay (SG) filters and local segmentation in a magnitude image. In comparison to typical SG kernel, the proposed kernel allows arbitrary shapes and sizes to vary with local tissue. It provides an automatic trade-off between noise and resolution, thereby significantly enhancing reconstruction accuracy and eliminating boundary artifacts.

Quantitative Assessment of Intervertebral Disc Composition by MRI: Sensitivity to Diurnal Variation.

Whether diurnal variation exists in quantitative MRI indices such as the T1rho relaxation time (T1ρ) of the intervertebral disc (IVD) is yet to be explored. This prospective study aimed to evaluate the diurnal variation in T1ρ, apparent diffusion coefficient (ADC), and electrical conductivity (σ) of lumbar IVD and its relationship with other MRI or clinical indices. Lumbar spine MRI, including T1ρ imaging, diffusion-weighted imaging (DWI), and electric properties tomography (EPT), was conducted on 17 sedentary workers twice (morning and evening) on the same day. The T1ρ, ADC, and σ of IVD were compared between the time points. Their diurnal variation, if any, was tested for correlation with age, body mass index (BMI), IVD level, Pfirrmann grade, scan interval, and diurnal variation in IVD height index. The results showed a significant decrease in T1ρ and ADC and a significant increase in the σ of IVD in the evening. T1ρ variation had a weak correlation with age and scan interval, and ADC variation with scan interval. Diurnal variation exists for the T1ρ, ADC, and σ of lumbar IVD, which should be accounted for in image interpretation. This variation is thought to be due to diurnal variations in intradiscal water, proteoglycan, and sodium ion concentration.

Use of machine learning to improve the estimation of conductivity and permittivity based on longitudinal relaxation time T1 in magnetic resonance at 7 T

Electrical property tomography (EPT) is a noninvasive method that uses magnetic resonance imaging (MRI) to estimate the conductivity and permittivity of tissues, and hence, can be used as a biomarker. One branch of EPT is based on the correlation of water and relaxation time T1 with the conductivity and permittivity of tissues. This correlation was applied to a curve-fitting function to estimate electrical properties, it was found to have a high correlation between permittivity and T1 however the computation of conductivity based on T1 requires to estimate the water content. In this study, we developed multiple phantoms with several ingredients that modify the conductivity and permittivity and explored the use of machine learning algorithms to have a direct estimation of conductivity and permittivity based on MR images and the relaxation time T1. To train the algorithms, each phantom was measured using a dielectric measurement device to acquire the true conductivity and permittivity. MR images were taken for each phantom, and the T1 values were measured. Then, the acquired data were tested using curve fitting, regression learning, and neural fit models to estimate the conductivity and permittivity values based on the T1 values. In particular, the regression learning algorithm based on Gaussian process regression showed high accuracy with a coefficient of determination R2 of 0.96 and 0.99 for permittivity and conductivity, respectively. The estimation of permittivity using regression learning demonstrated a lower mean error of 0.66% compared to the curve fitting method, which resulted in a mean error of 3.6%. The estimation of conductivity also showed that the regression learning approach had a lower mean error of 0.49%, whereas the curve fitting method resulted in a mean error of 6%. The findings suggest that utilizing regression learning models, specifically Gaussian process regression, can result in more accurate estimations for both permittivity and conductivity compared to other methods.

Repeatability of brain phase-based magnetic resonance electric properties tomography methods and effect of compressed SENSE and RF shimming

Magnetic resonance electrical properties tomography (MREPT) is an emerging imaging modality to noninvasively measure tissue conductivity and permittivity. Implementation of MREPT in the clinic requires repeatable measurements at a short scan time and an appropriate protocol. The aim of this study was to investigate the repeatability of conductivity measurements using phase-based MREPT and the effects of compressed SENSE (CS), and RF shimming on the precision of conductivity measurements. Conductivity measurements using turbo spin echo (TSE) and three-dimensional balanced fast field echo (bFFE) with CS factors were repeatable. Conductivity measurement using bFFE phase showed smaller mean and variance that those measured by TSE. The conductivity measurements using bFFE showed minimal deviation with CS factors up to 8, with deviation increasing at CS factors > 8. Subcortical structures produced less consistent measurements than cortical parcellations at higher CS factors. RF shimming using full slice coverage 2D dual refocusing echo acquisition mode (DREAM) and full coverage 3D dual TR approaches further improved measurement precision. BFFE is a more optimal sequence than TSE for phase-based MREPT in brain. Depending on the area of the brain being measured, the scan can be safely accelerated with compressed SENSE without sacrifice of precision, offering the potential to employ MREPT in clinical research and applications. RF shimming with better field mapping further improves precision of the conductivity measures.

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.

Repeatability and Reproducibility Uncertainty in Magnetic Resonance-Based Electric Properties Tomography of a Homogeneous Phantom.

Uncertainty assessment is a fundamental step in quantitative magnetic resonance imaging because it makes comparable, in a strict metrological sense, the results of different scans, for example during a longitudinal study. Magnetic resonance-based electric properties tomography (EPT) is a quantitative imaging technique that retrieves, non-invasively, a map of the electric properties inside a human body. Although EPT has been used in some early clinical studies, a rigorous experimental assessment of the associated uncertainty has not yet been performed. This paper aims at evaluating the repeatability and reproducibility uncertainties in phase-based Helmholtz-EPT applied on homogeneous phantom data acquired with a clinical 3 T scanner. The law of propagation of uncertainty is used to evaluate the uncertainty in the estimated conductivity values starting from the uncertainty in the acquired scans, which is quantified through a robust James-Stein shrinkage estimator to deal with the dimensionality of the problem. Repeatable errors are detected in the estimated conductivity maps and are quantified for various values of the tunable parameters of the EPT implementation. The spatial dispersion of the estimated electric conductivity maps is found to be a good approximation of the reproducibility uncertainty, evaluated by changing the position of the phantom after each scan. The results underpin the use of the average conductivity (calculated by weighting the local conductivity values by their uncertainty and taking into account the spatial correlation) as an estimate of the conductivity of the homogeneous phantom.

Technical note: Multi-receiver combination method for phase-based electrical property tomography of the breast.

Phase-based electrical property tomography (EPT) is a technique that allows conductivity reconstruction with only phase of the B1 field under the assumption that the magnitude of the B1 fields are homogeneous. The more this assumption is violated, the less accurate the reconstructed conductivity. Thus, a method that ensures homogeneity of field is important for breast image using multi-receiver coil. To develop a method for multi-receiver combination for phase-based EPT usable for breast EPT imaging in the clinic. Theory of the proposed method is presented. To validate the proposed method, the phantom and in-vivo experiments were conducted. Conductivity images were reconstructed using the transceive phase of the combined image and results were compared with another combination method. The proposed method's conductivity results were more stable than those of the previous method when was not homogeneous and when the homogeneous contrast region was small. The phantom and in-vivo results indicate that the proposed method produces improved conductivity images than the previous method. The proposed combination method also increased the conductivity contrast between benign and cancerous tissues. The proposed method produced more stable multi-receiver combination for phase-based EPT of the breast in a clinical environment.

Physics Informed Neural Networks (PINN) for Low Snr Magnetic Resonance Electrical Properties Tomography (MREPT).

Electrical properties (EPs) of tissues facilitate early detection of cancerous tissues. Magnetic resonance electrical properties tomography (MREPT) is a technique to non-invasively probe the EPs of tissues from MRI measurements. Most MREPT methods rely on numerical differentiation (ND) to solve partial differential Equations (PDEs) to reconstruct the EPs. However, they are not practical for clinical data because ND is noise sensitive and the MRI measurements for MREPT are noisy in nature. Recently, Physics informed neural networks (PINNs) have been introduced to solve PDEs by substituting ND with automatic differentiation (AD). To the best of our knowledge, it has not been applied to MREPT due to the challenges in using PINN on MREPT as (i) a PINN requires part of ground-truth EPs as collocation points to optimize the network's AD, (ii) the noisy input data disrupts the optimization of PINNs despite the noise-filtering nature of NNs and additional denoising processes. In this work, we propose a PINN-MREPT model based on a canonical analytic MREPT model. A reference padding layer with known EPs was added to surround the region of interest for providing additive collocation points. Moreover, an optimizable diffusion coefficient was embedded in the analytic MREPT model used in the PINN-MREPT. The noise robustness of the proposed PINN-MREPT for single-sample reconstruction was tested by using numerical phantoms of human brain with extra tumor-like tissues at different noise levels. The results of numerical experiments show that PINN-MREPT outperforms two typical numerical MREPT methods in terms of reconstruction accuracy, sensitivity to the extra tissues, and the correlations of line profiles in the regions of interest. The advantage of the PINN-MREPT is shown by the results of an experiment on phantom measurement, too. Moreover, it is found that the diffusion term plays an important role to achieve a noise-robust PINN-MREPT. This is an important step moving forward to a clinical application of MREPT.

MR Electrical Properties Tomography (MREPT) at 9.4T to Assess Treatment Response of Choline Kinase Inhibition on GL261 Glioblastoma

Abstract AIMS To monitor changes in tissue-conductivity based MR parameter in response to JAS239 treatment in preclinical glioblastoma model. METHOD C57BL/6 mice were injected intracranially with 5x105 GL261 glioblastoma cells and tumours were observed on T2 weighted MRI. Mice were imaged on day 0 (baseline), day 3 , 6 of treatment and post-treatment day 10. For MREPT, multi-slice-multi-echo sequence was used. Laplacian algorithm was employed to obtain the phase-based MREPT image reconstruction. RESULTS Saline treated mice showed a greater increase in tumour volume compared to JAS239 treated animals with respect to baseline. Percentage changes in conductivity values with respect to baseline from saline treated mice were compared to JAS239 treated animals. JAS239 group showed a slight increase in mean conductivity on day 3 and 6 compared to saline group. There were no statistically (p> 0.05) significant differences between the two groups. 4 days after treatment completion (Day10), the mean of conductivity values of JAS239 treated animals compared to saline treated animals showed no statistically (p> 0.05) significant differences. These results may indicate that GL261 tumour model is treatment resistant. Our findings agree with a study conducted by Bhaduri et al, where tumours were treated with JAS239. CONCLUSION EPT technique provides unique data on tissue conductivity which can be used to improve the assessment of treatment response in glioblastoma. MREPT parameter might be insensitive to evaluate choline kinase inhibitor. For future work, this technique can be incorporated into multiparametric MRI to complement diffusion and perfusion-weighted imaging of assessing treatment response in glioblastoma.

A Method for Electrical Property Tomography Based on a Three-Dimensional Integral Representation of the Electric Field.

Magnetic resonance electrical properties tomography (MREPT) noninvasively reconstructs high-resolution electrical property (EP) maps using MRI scanners and is useful for diagnosing cancerous tissues. However, conventional MREPT methods have limitations: sensitivity to noise in the numerical Laplacian operation, difficulty in reconstructing three-dimensional (3D) EPs and convergence not guaranteed in the iterative process. We propose a novel, iterative 3D reconstruction MREPT method without a numerical Laplacian operation. We derive an integral representation of the electric field using its Helmholtz decomposition with Maxwell's equations, under the assumption that the EPs are known on the boundary of the region of interest with the approximation that the unmeasurable magnetic field components are zero. Then, we solve the simultaneous equations composed of the integral representation and Ampere's law using a convex projection algorithm whose convergence is theoretically guaranteed. The efficacy of the proposed method was validated through numerical simulations and a phantom experiment. The results showed that this method is effective in reconstructing 3D EPs and is robust to noise. It was also shown that our proposed method with the unmeasurable component H- enhances the accuracy of the EPs in a background and that with all the components of the magnetic field reduces the artifacts at the center of the slices except when all the components of the electric field are close to zero.

Noninvasive Assessment of the Cerebrospinal Fluid and Its Composition by Electric Properties Tomography [Presidential Award Proceedings

Noninvasive Assessment of the Cerebrospinal Fluid and Its Composition by Electric Properties Tomography [Presidential Award Proceedings

Brain Tissue Conductivity in Focal Cerebral Ischemia.

Cerebral ischemia leads to oxygen depletion with rapid breakdown of transmembrane transporters and subsequent impaired electrolyte haemostasis. Electric properties tomography (EPT) is a new contrast in MRI which delivers information on tissue electrical conductivity. In the clinical realm it has been mostly used for tumour mapping. Ischemic cerebral stroke is another promising but neglected application. It might deliver additional information on tissue viability and possible response to therapy. The aim of this study was to demonstrate tissue conductivity in a rodent model of stroke. Further, we aimed to compare electric conductivity in ischemic and non-ischemic cerebral tissue. Two male Wistar rats were used in this study and were subjected to permanent MCAO. The animals were scanned in a 3 Tesla system (Philips Achieva/Best, the Netherlands) using a dedicated solenoid animal coil (Philips/Hamburg, Germany). In addition to diffusion weighted imaging (DWI), EPT was performed using a steady-state free-precession (SSFP) sequence (repetition time/echo time=4.5/2.3ms, measured voxel size=0.6×0.6×1.2 mm3, flip angle=38°, number of excitations=4). From the transceive phase ϕ of these SSFP scans, conductivity σ was estimated by the equation σ=Δϕ/(2μ0ω) with Δ the Laplacian operator, μ0 the magnetic permeability, and ω the Larmor frequency. Subsequently, a median filter was applied, which was locally restricted to voxels with comparable signal magnitude. The animals exhibited an infarct as demonstrated on DWI. Conductivity within the infarcted region was 60-70 % of the conductivity of not affected contralateral tissue (0.39±0.07S/m and 0.31±0.14S/m vs. 0.64±0.15S/m and 0.66±0.16S/m, respectively). Infarcted tissue exhibited decreased conductivity. Further in-vivo experiments with examination of the influence of reperfusion status and temporal evolution of the infarcted areas should be conducted. Depiction of the ischemic penumbra and possibly subclassification of the DWI lesion still seemsto be a fruitful target for further studies.

Phantom Construction and Equipment Configurations for Characterizing Electrical Properties Using MRI.

Phantom objects are commonly employed in MRI systems as stable substitutes for biological tissues to ensure systems for measuring images are operating correctly and safely. For magnetic resonance electrical impedance tomography (MREIT) and magnetic resonance electrical property tomography (MREPT), conductivity or permittivity phantoms play an important role in checking MRI pulse sequences, MREIT equipment performance, and algorithm validation. The construction of these phantoms is explained in this chapter. In the first part, materials used for phantom construction are introduced. Ingredients for modifying the electromagnetic properties and relaxation times are presented, and the advantages and disadvantages of aqueous, gel, and hybrid conductivity phantoms are explained. The devices and methods used to confirm phantom electromagnetic properties are explained. Next, different types of MREIT electrode materials and the constant current sources used for MREIT studies are discussed. In the last section, we present the results of previous MREIT and MREPT studies.

Physics-Coupled Neural Network Magnetic Resonance Electrical Property Tomography (MREPT) for Conductivity Reconstruction.

The electrical property (EP) of human tissues is a quantitative biomarker that facilitates early diagnosis of cancerous tissues. Magnetic resonance electrical properties tomography (MREPT) is an imaging modality that reconstructs EPs by the radio-frequency field in an MRI system. MREPT reconstructs EPs by solving analytic models numerically based on Maxwell's equations. Most MREPT methods suffer from artifacts caused by inaccuracy of the hypotheses behind the models, and/or numerical errors. These artifacts can be mitigated by adding coefficients to stabilize the models, however, the selection of such coefficient has been empirical, which limit its medical application. Alternatively, end-to-end Neural networks-based MREPT (NN-MREPT) learns to reconstruct the EPs from training samples, circumventing Maxwell's equations. However, due to its pattern-matching nature, it is difficult for NN-MREPT to produce accurate reconstructions for new samples. In this work, we proposed a physics-coupled NN for MREPT (PCNN-MREPT), in which an analytic model, cr-MREPT, works with diffusion and convection coefficients, learned by NNs from the difference between the reconstructed and ground-truth EPs to reduce artifacts. With two simulated datasets, three generalization experiments in which test samples deviate gradually from the training samples, and one noise-robustness experiment were conducted. The results show that the proposed PCNN-MREPT achieves higher accuracy than two representative analytic methods. Moreover, compared with an end-to-end NN-MREPT, the proposed method attained higher accuracy in two critical generalization tests. This is an important step to practical MREPT medical diagnoses.

OD164 - MRI safety application of the magnetic resonance-based electric properties tomography

OD164 - MRI safety application of the magnetic resonance-based electric properties tomography

Complex B1+ mapping with Carr-Purcell spin echoes and its application to electrical properties tomography.

PurposeTo present a new complex‐valued B1 + mapping method for electrical properties tomography using Carr‐Purcell spin echoes.MethodsA Carr‐Purcell (CP) echo train generates pronounced flip‐angle dependent oscillations that can be used to estimate the magnitude of B1 +. To this end, a dictionary is used that takes into account the slice profile as well as T2 relaxation along the echo train. For validation, the retrieved B1 + map is compared with the actual flip angle imaging (AFI) method in a phantom (79 ε0, 0.34 S/m). Moreover, the phase of the first echo reflects the transceive phase. Overall, the CP echo train yields an estimate of the complex‐valued B1 +, allowing electrical properties tomography with both permittivity and conductivity. The presented method is evaluated in phantom scans as well as for in vivo brain at 3 T.ResultsIn the phantom, the obtained magnitude B1 + maps retrieved from the CP echo train and the AFI method show excellent agreement, and both the reconstructed estimated permittivity (79 ± 3) ε0 and conductivity (0.35 ± 0.04) S/m values are in accordance with expectations. In the brain, the obtained electrical properties are also close to expectations. In addition to the retrieved complex B1 + information, the decay of the CP echo trains also yields an estimate for T2.ConclusionThe CP sequence can be used to simultaneously provide both B1 + magnitude and phase estimations, and therefore allows for full reconstruction of the electrical properties.

Mapping electric bulk conductivity in the human heart.

To explore the technical feasibility of mapping the electric bulk conductivity in the human heart, and to determine quantitative conductivity values of myocardium and blood from a small group of volunteers. Using a 3T MR system, 6 healthy male volunteers were measured. For all volunteers, a time-resolved 2D sequence over the cardiac cycle was applied (electrocardiogram [ECG]-triggered SSFP acquired in breath-hold). From these data, a dedicated, so-called "2D conductivity" has been derived in the framework of electrical properties tomography (EPT). To validate the concept of 2D conductivity, a static 3D sequence (ECG-triggered and respiratory-gated SSFP 3D whole heart acquisition, allowing the full 3D reconstruction of conductivity) as well as a Q-flow sequence (for investigating the relation between flow and reconstruction errors of the conductivity) have been applied for one of the volunteers. For both, blood and myocardium, quantitative values of obtained 2D conductivity were approximately two-thirds of the obtained 3D conductivity, as expected from Maxwell's equations. Furthermore, the quantitative conductivity values agreed with corresponding literature values. Conductivity of left-ventricular blood volume showed characteristic over- and under-shooting at specific time points during the cardiac cycle for all volunteers investigated. This over- and under-shooting correlated with the phase pattern caused by blood flow into/out of the ventricle. The study demonstrated the technical feasibility of cardiac conductivity measurements using standard MR systems and standard MR sequences, and therefore, may open new options for MR-based cardiac diagnosis.

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 ± 0.01, 0.3 ± 0.01 and 2.15 ± 0.02 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.

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).