Feasibility of undersampled spiral trajectories in MREPT for fast conductivity imaging.

PURPOSE: To investigate spiral-based imaging including trajectories with undersampling as a fast and robust alternative for phase-based magnetic resonance electrical properties tomography (MREPT) techniques. METHODS: Spiral trajectories with various undersampling ratios were prescribed to acquire images from an experimental phantom and a healthy volunteer at 3T. The non-Cartesian acquisitions were reconstructed using SPIRiT, and conductivity maps were derived using phase-based cr-MREPT. The resulting maps were compared between different sampling trajectories. Additionally, a conductivity map was obtained using a Cartesian balanced SSFP acquisition from the volunteer to comparatively demonstrate the robustness of the proposed method. RESULTS: The phantom and volunteer results illustrate the benefits of the spiral acquisitions. Specifically, undersampled spiral acquisitions display improved robustness against field inhomogeneity artifacts and lowered SD values with shortened readout times. Furthermore, average of conductivity values measured for the cerebrospinal fluid with the spiral acquisitions were 1.703 S/m, indicating a close agreement with the theoretical values of 1.794 S/m. CONCLUSION: A spiral-based acquisition framework for conductivity imaging with and without undersampling is presented. Overall, spiral-based acquisitions improved robustness against field inhomogeneity artifacts, while achieving whole head coverage with multiple averages in less than a minute.

A reusable 3D printed brain-like phantom for benchmarking electrical properties tomography reconstructions.

PURPOSE: In MR electrical properties tomography (MR-EPT), electrical properties (EPs, conductivity and permittivity) are reconstructed from MR measurements. Phantom measurements are important to characterize the performance of MR-EPT reconstruction methods, since they allow knowledge of reference EPs values. To assess reconstruction methods in a more realistic scenario, it is important to test the methods using phantoms with realistic shapes, internal structures, and dielectric properties. In this work, we present a 3D printing procedure for the creation of realistic brain-like phantoms to benchmark MR-EPT reconstructions. METHODS: We created two brain-like geometries with three different compartments using 3D printing. The first geometry was filled once, while the second geometry was filled three times with different saline-gelatin solutions, resulting in a total of four phantoms with different EPs. The saline solutions were characterized using a probe. 3D MR-EPT reconstructions were performed from MR measurements at 3T. The reconstructed conductivity values were compared to reference values of the saline-gelatin solutions. The measured fields were also compared to simulated fields using the same phantom geometry and electrical properties. RESULTS: The measured fields were consistent with simulated fields. Reconstructed conductivity values were consistent with the reference (probe) conductivity values. This indicated the suitability of such phantoms for benchmarking MR-EPT reconstructions. CONCLUSION: We presented a new workflow to 3D print realistic brain-like phantoms in an easy and affordable way. These phantoms are suitable to benchmark MR-EPT reconstructions, but can also be used for benchmarking other quantitative MR methods.

Phantom evaluation of electrical conductivity mapping by MRI: Comparison to vector network analyzer measurements and spatial resolution assessment.

PURPOSE: To evaluate the performance of various MR electrical properties tomography (MR-EPT) methods at 3 T in terms of absolute quantification and spatial resolution limit for electrical conductivity. METHODS: Absolute quantification as well as spatial resolution performance were evaluated on homogeneous phantoms and a phantom with holes of different sizes, respectively. Ground-truth conductivities were measured with an open-ended coaxial probe connected to a vector network analyzer (VNA). Four widely used MR-EPT reconstruction methods were investigated: phase-based Helmholtz (PB), phase-based convection-reaction (PB-cr), image-based (IB), and generalized-image-based (GIB). These methods were compared using the same complex images from a 1 mm-isotropic UTE sequence. Alternative transceive phase acquisition sequences were also compared in PB and PB-cr. RESULTS: In large homogeneous phantoms, all methods showed a strong correlation with ground truth conductivities (r > 0.99); however, GIB was the best in terms of accuracy, spatial uniformity, and robustness to boundary artifacts. In the resolution phantom, the normalized root-mean-squared error of all methods grew rapidly (>0.40) when the hole size was below 10 mm, with simplified methods (PB and IB), or below 5 mm, with generalized methods (PB-cr and GIB). CONCLUSION: VNA measurements are essential to assess the accuracy of MR-EPT. In this study, all tested MR-EPT methods correlated strongly with the VNA measurements. The UTE sequence is recommended for MR-EPT, with the GIB method providing good accuracy for structures down to 5 mm. Structures below 5 mm may still be detected in the conductivity maps, but with significantly lower accuracy.

MR-based electrical property tomography using a physics-informed network at 3 and 7 T.

Magnetic resonance electrical propert tomography promises to retrieve electrical properties (EPs) quantitatively and non-invasively in vivo, providing valuable information for tissue characterization and pathology diagnosis. However, its clinical implementation has been hindered by, for example, B1 measurement accuracy, reconstruction artifacts resulting from inaccuracies in underlying models, and stringent hardware/software requirements. To address these challenges, we present a novel approach aimed at accurate and high-resolution EPs reconstruction based on water content maps by using a physics-informed network (PIN-wEPT). The proposed method utilizes standard clinical protocols and conventional multi-channel receive arrays that have been routinely equipped in clinical settings, thus eliminating the need for specialized RF sequence/coil configurations. Compared with the original wEPT method, the network generates accurate water content maps that effectively eliminate the influence of B → 1 + and B → 1 - by incorporating data mismatch with electrodynamic constraints derived from the Helmholtz equation. Subsequent regression analysis develops a broad relationship between water content and EPs across various types of brain tissue. A series of numerical simulations was conducted at 7 T to assess the feasibility and performance of the method, which encompassed four normal head models and models with tumorous tissues incorporated, and the results showed normalized mean square error below 1.0% in water content, below 11.7% in conductivity, and below 1.1% in permittivity reconstructions for normal brain tissues. Moreover, in vivo validations conducted over five healthy subjects at both 3 and 7 T showed reasonably good consistency with empirical EPs values across the white matter, gray matter, and cerebrospinal fluid. The PIN-wEPT method, with its demonstrated efficacy, flexibility, and compatibility with current MRI scanners, holds promising potential for future clinical application.

Combining deep learning and 3D contrast source inversion in MR-based electrical properties tomography.

Magnetic resonance electrical properties tomography (MR-EPT) is a technique used to estimate the conductivity and permittivity of tissues from MR measurements of the transmit magnetic field. Different reconstruction methods are available; however, all these methods present several limitations, which hamper the clinical applicability. Standard Helmholtz-based MR-EPT methods are severely affected by noise. Iterative reconstruction methods such as contrast source inversion electrical properties tomography (CSI-EPT) are typically time-consuming and are dependent on their initialization. Deep learning (DL) based methods require a large amount of training data before sufficient generalization can be achieved. Here, we investigate the benefits achievable using a hybrid approach, that is, using MR-EPT or DL-EPT as initialization guesses for standard 3D CSI-EPT. Using realistic electromagnetic simulations at 3 and 7 T, the accuracy and precision of hybrid CSI reconstructions are compared with those of standard 3D CSI-EPT reconstructions. Our results indicate that a hybrid method consisting of an initial DL-EPT reconstruction followed by a 3D CSI-EPT reconstruction would be beneficial. DL-EPT combined with standard 3D CSI-EPT exploits the power of data-driven DL-based EPT reconstructions, while the subsequent CSI-EPT facilitates a better generalization by providing data consistency.

High-frequency electrical properties tomography at 9.4T as a novel contrast mechanism for brain tumors.

PURPOSE: To establish high-frequency magnetic resonance electrical properties tomography (MREPT) as a novel contrast mechanism for the assessment of glioblastomas using a rat brain tumor model. METHODS: Six F98 intracranial tumor bearing rats were imaged longitudinally 8, 11 and 14 days after tumor cell inoculation. Conductivity and mean diffusivity maps were generated using MREPT and Diffusion Tensor Imaging. These maps were co-registered with T2 -weighted images and volumes of interests (VOIs) were segmented from the normal brain, ventricles, edema, viable tumor, tumor rim, and tumor core regions. Longitudinal changes in conductivity and mean diffusivity (MD) values were compared in these regions. A correlation analysis was also performed between conductivity and mean diffusivity values. RESULTS: The conductivity of ventricles, edematous area and tumor regions (tumor rim, viable tumor, tumor core) was significantly higher (P < .01) compared to the contralateral cortex. The conductivity of the tumor increased over time while MD from the tumor did not change. A marginal positive correlation was noted between conductivity and MD values for tumor rim and viable tumor, whereas this correlation was negative for the tumor core. CONCLUSION: We demonstrate a novel contrast mechanism based on ionic concentration and mobility, which may aid in providing complementary information to water diffusion in probing the microenvironment of brain tumors.

MR electrical properties imaging using a generalized image-based method.

PURPOSE: To develop a fast and easy-to-use electrical properties tomography (EPT) method based on a single MR scan, avoiding both the need of a B1 -map and transceive phase assumption, and that is robust against noise. THEORY: Derived from Maxwell's equations, conductivity, and permittivity are reconstructed from a new partial differential equation involving the product of the RF fields and its derivatives. This also allows us to clarify and revisit the relevance of common assumptions of MREPT. METHODS: Our new governing equation is solved using a 3D finite-difference scheme and compared to previous frameworks. The benefits of our method over selected existing MREPT methods are demonstrated for different simulation models, as well as for both an inhomogeneous agar phantom gel and in vivo brain data at 3T. RESULTS: Simulation and experimental results are illustrated to highlight the merits of the proposed method over existing methods. We show the validity of our algorithm in versatile configurations, with many transition regions notably. Complex admittivity maps are also provided as a complementary MR contrast. CONCLUSION: Because it avoids time-consuming RF field mapping and generalizes the use of standard MR image for electrical properties reconstruction, this contribution is promising as a new step forward for clinical applications.

Brain Tissue Conductivity Measurements with MR-Electrical Properties Tomography: An In Vivo Study.

First in vivo brain conductivity reconstructions using Helmholtz MR-Electrical Properties Tomography (MR-EPT) have been published. However, a large variation in the reconstructed conductivity values is reported and these values differ from ex vivo conductivity measurements. Given this lack of agreement, we performed an in vivo study on eight healthy subjects to provide reference in vivo brain conductivity values. MR-EPT reconstructions were performed at 3 T for eight healthy subjects. Mean conductivity and standard deviation values in the white matter, gray matter and cerebrospinal fluid (σWM, σGM, and σCSF) were computed for each subject before and after erosion of regions at tissue boundaries, which are affected by typical MR-EPT reconstruction errors. The obtained values were compared to the reported ex vivo literature values. To benchmark the accuracy of in vivo conductivity reconstructions, the same pipeline was applied to simulated data, which allow knowledge of ground truth conductivity. Provided sufficient boundary erosion, the in vivo σWM and σGM values obtained in this study agree for the first time with literature values measured ex vivo. This could not be verified for the CSF due to its limited spatial extension. Conductivity reconstructions from simulated data verified conductivity reconstructions from in vivo data and demonstrated the importance of discarding voxels at tissue boundaries. The presented σWM and σGM values can therefore be used for comparison in future studies employing different MR-EPT techniques.

bSSFP phase correction and its use in magnetic resonance electrical properties tomography.

PURPOSE: Balanced steady-state free precession (bSSFP) sequence is widely used because of its high SNR and high speed. However, bSSFP images suffer from "banding artifact" caused by B0 inhomogeneity. In this article, we propose a method to remove this artifact in bSSFP phase images and investigate the usage of the corrected phase images in phase-based magnetic resonance electrical properties tomography (MREPT). THEORY AND METHODS: Two bSSFP phase images, obtained with different excitation frequencies, are collaged to get rid of the regions containing banding artifacts. Phase of the collaged bSSFP image is the sum of the transceive phase of the RF system and an error term that depends on B0 and T2 . By using B0 and T2 maps, this error is eliminated from bSSFP phase images by using pixel-wise corrections. Conductivity maps are obtained from the uncorrected and the corrected phase images using the phase-based cr-MREPT method. RESULTS: Phantom and human experiment results of the proposed method are illustrated for both phase images and conductivity maps. It is shown that uncorrected phase images yield unacceptable conductivity images. When only B0 information is used for phase correction conductivity, reconstructions are substantially improved, and yet T2 information is still needed to fully recover accurate and undistorted conductivity images. CONCLUSIONS: With the proposed technique, B0 sensitivity of the bSSFP phase images can be removed by using B0 and T2 maps. It is also shown that corrected bSSFP phase images are of sufficient quality to be used in conductivity imaging.

Electrical properties tomography: Available contrast and reconstruction capabilities.

MR-based electrical properties tomography converts the MRI transmit/receive RF field measurements to tissue electrical property maps through dedicated reconstruction algorithms. Recent reports showed that despite limitations, electrical properties tomography holds promise for generating additional contrast for tumor detection and patient-specific modeling of tissue-RF field interactions. This review summarizes the available tissue electrical property contrasts and compares them with the capabilities of the most commonly used electrical properties tomography reconstruction method. Future directions and prospects of clinical translation are discussed.

Redesign of the Laplacian kernel for improvements in conductivity imaging using MRI.

PURPOSE: To develop an electrical property tomography reconstruction method that achieves improvements over standard method by redesigning the Laplacian kernel. THEORY AND METHODS: A decomposition property of the governing PET equation shows the possibility of redesigning the Laplacian kernel for conductivity reconstruction. Hence, the discrete Laplacian operator used for electrical property tomography reconstruction is redesigned to have a Gaussian-like envelope, which enables manipulation of the spatial and spectral response. The characteristics of the proposed kernel are investigated through numerical simulations and in vivo brain experiments. RESULTS: The proposed method reduces textured noise, which hampers observing features of the conductivity image. Furthermore, the proposed scheme can mitigate the propagation of local phase error such as flow-induced phase. By doing so, the proposed method can recover feature information in conductivity (or resistivity) images. Lastly, the proposed kernel can be extended to other electrical property tomography reconstructions, improving the quality of images. CONCLUSION: An alternative design of the Laplacian kernel for conductivity imaging has been developed to mitigate the textured noise and the propagation of local phase artifact.

Correlation of quantitative conductivity mapping and total tissue sodium concentration at 3T/4T.

PURPOSE: To investigate the correlation between electrical conductivity and sodium concentration, both measured in vivo, in the human brain. METHODS: Conductivity measurements were performed on samples with different sodium (Na+ ) and agarose concentrations using a dielectric probe, and the correlation between conductivity and Na+ content was evaluated. Subsequently, brain conductivity and total Na+ content maps were measured in 8 healthy subjects using phase-based MREPT and sodium MRI, respectively. After co-registration and spatial normalization to the 1 mm 152 MNI brain atlas, the relationship between conductivity and tissue sodium concentration (TSC) was examined within different brain regions. RESULTS: The conductivities of agarose gels increased linearly with NaCl concentration, while remaining almost independent of agarose content. When measured in healthy subjects, conductivities showed positive correlation with total tissue sodium concentration (R = 0.39, P < 0.005). The same trend was found in gray matter (R = 0.36, P < 0.005) and in white matter (R = 0.28, P < 0.05). CONCLUSION: Tissue conductivity shows a positive correlation with total sodium concentration. Conductivity might serve as a novel technique to visualize the total tissue electrolyte concentration, although refinements in the consideration of e.g., tissue water content, would be necessary to improve the quantitative value.

Error analysis of helmholtz-based MR-electrical properties tomography.

PURPOSE: MR electrical properties tomography (MR-EPT) aims to measure tissue electrical properties by computing spatial derivatives of measured B1+ data. This computation is very sensitive to spatial fluctuations caused, for example, by noise and Gibbs ringing. In this work, the error arising from the computation of spatial derivatives using finite difference kernels (FD error) has been investigated. In relation to this FD error, it has also been investigated whether mitigation strategies such as Gibbs ringing correction and Gaussian apodization can be beneficial for conductivity reconstructions. METHODS: Conductivity reconstructions were performed on a phantom (by means of simulations and MR measurements at 3T) and on a human brain model. The accuracy was evaluated as a function of image resolution, FD kernel size, k-space windowing, and signal-to-noise ratio. The impact of mitigation strategies was also investigated. RESULTS: The adopted small FD kernel is highly sensitive to spatial fluctuations, whereas the large FD kernel is more noise-robust. However, large FD kernels lead to extended numerical boundary error propagation, which severely hampers the MR-EPT reconstruction accuracy for highly spatially convoluted tissue structures such as the human brain. Mitigation strategies slightly improve the accuracy of conductivity reconstructions. For the adopted derivative kernels and the investigated scenario, MR-EPT conductivity reconstructions show low accuracy: less than 37% of the voxels have a relative error lower than 30%. CONCLUSION: The numerical error introduced by the computation of spatial derivatives using FD kernels is one of the major causes of limited accuracy in Helmholtz-based MR-EPT reconstructions. Magn Reson Med 80:90-100, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

Gradient-based electrical conductivity imaging using MR phase.

PURPOSE: To develop a fast, practically applicable, and boundary artifact free electrical conductivity imaging method that does not use transceive phase assumption, and that is more robust against the noise. THEORY: Starting from the Maxwell's equations, a new electrical conductivity imaging method that is based solely on the MR transceive phase has been proposed. Different from the previous phase based electrical properties tomography (EPT) method, a new formulation was derived by including the gradients of the conductivity into the equations. METHODS: The governing partial differential equation, which is in the form of a convection-reaction-diffusion equation, was solved using a three-dimensional finite-difference scheme. To evaluate the performance of the proposed method numerical simulations, phantom and in vivo human experiments have been conducted at 3T. RESULTS: Simulation and experimental results of the proposed method and the conventional phase-based EPT method were illustrated to show the superiority of the proposed method over the conventional method, especially in the transition regions and under noisy data. CONCLUSION: With the contributions of the proposed method to the phase-based EPT approach, a fast and reliable electrical conductivity imaging appears to be feasible, which is promising for clinical diagnoses and local SAR estimation. Magn Reson Med 77:137-150, 2017. © 2016 Wiley Periodicals, Inc.

Variation in the dielectric properties of freshly excised colorectal cancerous tissues at different tumor stages.

The study was designed to identify differences in the dielectric properties of ex vivo colorectal cancerous tissues at different tumor stages. To date, 130 freshly excised colorectal cancerous specimens underwent measurement of both relative permittivity and conductivity on the serosal and mucosal surfaces of the carcinoma nidus, and the mucosa of the surgical resection margin ranging from 50 to 500 MHz at the Larmor frequencies. Tumor node metastasis staging was determined according to pathological reports for each patient. There were statistically significant differences in the relative permittivity of both colorectal cancerous serosa and mucosa among stages ≤I, II, III, and IV and between stages ≤II and ≥III (P < 0.05) at most frequencies under 300 MHz; statistically significant differences in conductivity were also observed for most of the measured frequencies (P < 0.05). The significant differences in dielectric characteristics among tumor stages, especially between early and advanced stages, have value for selecting appropriate surgical strategies. The presented ex vivo data provide important information for magnetic resonance electrical properties tomography in vivo system because the frequencies of 64 MHz (1.5T) and 128 MHz (3T) are usually used in clinical settings. Bioelectromagnetics. 38:522-532, 2017. © 2017 Wiley Periodicals, Inc.

MR-based conductivity imaging using multiple receiver coils.

PURPOSE: To propose a signal combination method for MR-based tissue conductivity mapping using a standard clinical scanner with multiple receiver coils. METHODS: The theory of the proposed method is presented with two practical approaches, a coil-specific approach and a subject-specific approach. Conductivity maps were reconstructed using the transceive phase of the combined signal. The sensitivities of the coefficients used for signal combination were analyzed and the method was compared with other signal combination methods. For validation, multiple receiver brain coils and multiple receiver breast coils were used in phantom, in vivo brain, and in vivo breast studies. RESULTS: The variation among the conductivity estimates was <15% as determined by the coefficient sensitivity tests. Compared with other signal combination methods, the proposed method yielded fewer artifacts in the conductivity estimates. CONCLUSION: MR-based tissue conductivity mapping is feasible when using a standard clinical MR scanner with multiple receiver coils. The proposed method reduces systematic errors in phase-based conductivity mapping that can occur due to the inhomogeneous magnitude of the combined receive profile. Magn Reson Med 76:530-539, 2016. © 2015 Wiley Periodicals, Inc.

Simultaneous imaging of dual-frequency electrical conductivity using a combination of MREIT and MREPT.

PURPOSE: To propose a single magnetic resonance scan conductivity imaging technique providing dual-frequency characteristics of tissue conductivity. METHODS: Using a modified spin-echo pulse sequence, the magnetic flux density induced by externally injected currents and the B1+ phase map with injected current effects removed were acquired simultaneously. The low-frequency conductivity was reconstructed from the measured magnetic flux density by the projected current density method, while the high-frequency conductivity was reconstructed using the B1+ maps. Three different conductivity phantoms were used to demonstrate low- and high-frequency conductivity characteristics. RESULTS: A conductivity spectrum at two frequencies was successfully acquired with the proposed scheme. Magnetic resonance electrical impedance tomography is advantageous for seeing an anomaly itself wrapped with a thin insulating membrane. In addition, if the membrane is porous, the membrane property can be quantitatively visualized with magnetic resonance electrical impedance tomography. Magnetic resonance electrical properties tomography does not detect such membranes, which enable it to probe things inside an insulating membrane. CONCLUSION: Considering these pros and cons and also the fact that the conductivity of biological tissue changes with frequency, a dual-frequency conductivity imaging incorporating both magnetic resonance electrical impedance tomography and magnetic resonance electrical properties tomography in future animal and human experiments is suggested.

Bias correction for phase-based cr-MREPT using low resolution B1+ magnitude.

ObjectiveFull-form Magnetic Resonance Electrical Properties Tomography (MREPT) requires bothB1+magnitude and phase information. SinceB1+phase can be obtained faster and with higher SNR compared toB1+magnitude, several phase-based methods have been developed for conductivity imaging. However, phase-based methods suffer from a concave bias due to the assumption that∇|B1+|is negligible in the ROI.ApproachIn this paper, we re-derive the central equation of phase-based cr-MREPT without assuming that∇|B1+|is negligible and thus propose a correction method directly integrated into the equation system.Main resultsProposed method successfully corrects the concave bias on both simulated and experimental data and significantly increases image quality.SignificanceThe proposed correction method depends on a very low-resolution|B1+|map, and therefore the imaging time does not increase significantly for obtainingB1+magnitude. Moreover, correction can be achieved using simulatedB1+magnitude, hence completely removing the additional imaging requirement.

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.

Magnetic resonance electrical properties tomography for small anomalies using boundary conditions: A simulation study.

PURPOSE: Magnetic resonance electrical property tomography (MREPT) is an emerging imaging modality using measured B1 maps from magnetic resonance imaging (MRI) to measure a distribution of electric conductivity and permittivity of the subject at the Larmor frequency. Conventional MREPT approaches at single transmit channel system using the Helmholtz equation rely on an assumption that conductivity and permittivity of the subject are locally homogeneous. For small tissue structures and tissue boundaries, in which the assumption of locally homogeneous conductivity and permittivity does not hold, the reconstructed conductivity values deviated from the actual values, so called "Boundary Artifacts." The aim of this study is to propose new reconstruction processes based on time-harmonic Maxwell's equations to reconstruct conductivity for small tissue structures and tissue boundaries. METHODS: Instead of removing the electric fields from the equations as done in the Helmholtz equation, three key identities of circularly polarized and longitudinal components of electric fields, circularly polarized component of magnetic fields, and electric properties from time-harmonic Maxwell's equations are derived. Based on the three key identities, the proposed reconstruction methods determine conductivity, permittivity, and circularly polarized component and longitudinal component of electric fields using the measured H1+ . In each iterative step, estimated conductivity, permittivity, electric fields, and artifact-free mask region, Ω, where the contribution of the boundary artifacts is small, were updated. Using the estimated values in the artifact-free mask region as boundary conditions, the estimates beyond the mask region were updated. EM simulations were performed on three types of numerical phantoms with very small regions of homogeneous conductivity and permittivity. The performance of the proposed methods was evaluated using the simulated electric and magnetic fields. RESULTS: For the numerical simulation model, the proposed methods significantly reduced the boundary artifacts compared to conventional methods using Helmholtz equations. In addition, previous methods using the Helmholtz equation could measure conductivity of only large anomalies, but the proposed method can measure the conductivity of the small compartments whose size is 2-3 voxels. The proposed approaches are compatible with spatial filtering which can be used to reduce noise. If a good image segmentation is available as a prior information, better initial boundary conditions can be estimated, and thus the proposed approach can be more accurate for small tissue structures. CONCLUSIONS: The proposed reconstruction method not only determines electrical properties, but also circularly polarized component and longitudinal component of electric fields using an iterative process. The proposed method can quantitatively detect the conductivity of the small anomalies better than conventional methods.