Quantitative analysis of the reconstruction errors of the currently popular algorithm of magnetic resonance electrical property tomography at the interfaces of adjacent tissues

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.

Changes of in vivo electrical conductivity in the brain and torso related to age, fat fraction and sex using MRI

This work was inspired by the observation that a majority of MR-electrical properties tomography studies are based on direct comparisons with ex vivo measurements carried out on post-mortem samples in the 90's. As a result, the in vivo conductivity values obtained from MRI in the megahertz range in different types of tissues (brain, liver, tumors, muscles, etc.) found in the literature may not correspond to their ex vivo equivalent, which still serves as a reference for electromagnetic modelling. This study aims to pave the way for improving current databases since the definition of personalized electromagnetic models (e.g. for Specific Absorption Rate estimation) would benefit from better estimation. Seventeen healthy volunteers underwent MRI of both brain and thorax/abdomen using a three-dimensional ultrashort echo-time (UTE) sequence. We estimated conductivity (S/m) in several classes of macroscopic tissue using a customized reconstruction method from complex UTE images, and give general statistics for each of these regions (mean-median-standard deviation). These values are used to find possible correlations with biological parameters such as age, sex, body mass index and/or fat volume fraction, using linear regression analysis. In short, the collected in vivo values show significant deviations from the ex vivo values in conventional databases, and we show significant relationships with the latter parameters in certain organs for the first time, e.g. a decrease in brain conductivity with age.

A database for MR-based electrical properties tomography with in silico brain data-ADEPT

PURPOSE

Several reconstruction methods for MR-based electrical properties tomography (EPT) have been developed. However, the lack of common data makes it difficult to objectively compare their performances. This is, however, a necessary precursor for standardizing and introducing this technique in the clinical setting. To enable objective comparison of the performances of reconstruction methods and provide common data for their training and testing, we created ADEPT, a database of simulated data for brain MR-EPT reconstructions.

METHODS

ADEPT is a database containing in silico data for brain EPT reconstructions. This database was created from 25 different brain models, with and without tumors. Rigid geometric augmentations were applied, and different electrical properties were assigned to white matter, gray matter, CSF, and tumors to generate 120 different brain models. These models were used as input for finite-difference time-domain simulations in Sim4Life, used to compute the electromagnetic fields needed for MR-EPT reconstructions.

RESULTS

Electromagnetic fields from 84 healthy and 36 tumor brain models were simulated. The simulated fields relevant for MR-EPT reconstructions (transmit and receive RF fields and transceive phase) and their ground-truth electrical properties are made publicly available through ADEPT. Additionally, nonattainable fields such as the total magnetic field and the electric field are available upon request.

CONCLUSION

ADEPT will serve as reference database for objective comparisons of reconstruction methods and will be a first step toward standardization of MR-EPT reconstructions. Furthermore, it provides a large amount of data that can be exploited to train data-driven methods. It can be accessed from  https://doi.org/10.34894/V0HBJ8.

Data-driven electrical conductivity brain imaging using 3 T MRI

Magnetic resonance electrical properties tomography (MR-EPT) is a non-invasive measurement technique that derives the electrical properties (EPs, e.g., conductivity or permittivity) of tissues in the radiofrequency range (64 MHz for 1.5 T and 128 MHz for 3 T MR systems). Clinical studies have shown the potential of tissue conductivity as a biomarker. To date, model-based conductivity reconstructions rely on numerical assumptions and approximations, leading to inaccuracies in the reconstructed maps. To address such limitations, we propose an artificial neural network (ANN)-based non-linear conductivity estimator trained on simulated data for conductivity brain imaging. Network training was performed on 201 synthesized T2-weighted spin-echo (SE) data obtained from the finite-difference time-domain (FDTD) electromagnetic (EM) simulation. The dataset was composed of an approximated T2-w SE magnitude and transceive phase information. The proposed method was tested three in-silico and in-vivo on two volunteers and three patients' data. For comparison purposes, various conventional phase-based EPT reconstruction methods were used that ignoreB 1 + magnitude information, such as Savitzky-Golay kernel combined with Gaussian filter (S-G Kernel), phase-based convection-reaction EPT (cr-EPT), magnitude-weighted polynomial-fitting phase-based EPT (Poly-Fit), and integral-based phase-based EPT (Integral-based). From the in-silico experiments, quantitative analysis showed that the proposed method provides more accurate and improved quality (e.g., high structural preservation) conductivity maps compared to conventional reconstruction methods. Representatively, in the healthy brain in-silico phantom experiment, the proposed method yielded mean conductivity values of 1.97 ± 0.20 S/m for CSF, 0.33 ± 0.04 S/m for WM, and 0.52 ± 0.08 S/m for GM, which were closer to the ground-truth conductivity (2.00, 0.30, 0.50 S/m) than the integral-based method (2.56 ± 2.31, 0.39 ± 0.12, 0.68 ± 0.33 S/m). In-vivo ANN-based conductivity reconstructions were also of improved quality compared to conventional reconstructions and demonstrated network generalizability and robustness to in-vivo data and pathologies. The reported in-vivo brain conductivity values were in agreement with literatures. In addition, the proposed method was observed for various SNR levels (SNR levels = 10, 20, 40, and 58) and repeatability conditions (the eight acquisitions with the number of signal averages = 1). The preliminary investigations on brain tumor patient datasets suggest that the network trained on simulated dataset can generalize to unforeseen in-vivo pathologies, thus demonstrating its potential for clinical applications.

Improving phase-based conductivity reconstruction by means of deep learning-based denoising of B 1 + phase data for 3T MRI

PURPOSE

To denoise B 1 + phase using a deep learning method for phase-based in vivo electrical conductivity reconstruction in a 3T MR system.

METHODS

For B 1 + phase deep-learning denoising, a convolutional neural network (U-net) was chosen. Training was performed on data sets from 10 healthy volunteers. Input data were the real and imaginary components of single averaged spin-echo data (SNR = 45), which was used to approximate the B 1 + phase. For label data, multiple signal-averaged spin-echo data (SNR = 128) were used. Testing was performed on in silico and in vivo data. Reconstructed conductivity maps were derived using phase-based conductivity reconstructions. Additionally, we investigated the usability of the network to various SNR levels, imaging contrasts, and anatomical sites (ie, T₁ , T₂ , and proton density-weighted brain images and proton density-weighted breast images. In addition, conductivity reconstructions from deep learning-based denoised data were compared with conventional image filters, which were used for data denoising in electrical properties tomography (ie, the Gaussian filtering and the Savitzky-Golay filtering).

RESULTS

The proposed deep learning-based denoising approach showed improvement for B 1 + phase for both in silico and in vivo experiments with reduced quantitative error measures compared with other methods. Subsequently, this resulted in an improvement of reconstructed conductivity maps from the denoised B 1 + phase with deep learning.

CONCLUSION

The results suggest that the proposed approach can be used as an alternative preprocessing method to denoise B 1 + maps for phase-based conductivity reconstruction without relying on image filters or signal averaging.

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.

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.

A robust electrical conductivity imaging method with total variation and wavelet regularization

PURPOSE

This study aims to develop and evaluate a robust conductivity imaging method that combines total variation and wavelet regularization to enhance the accuracy of conductivity maps.

THEORY AND METHODS

The proposed approach is based on a gradient-based method. The central equation is derived from Maxwell's equation and describes the relationship between conductivity and the transceive phase. A linear system equation is obtained via a finite-difference method and solved using a least-squares method. Total variation and wavelet transform regularization terms are added to the minimization problem and solved using the Split Bregman method to improve reconstruction stability. The proposed approach is compared with conventional and gradient-based methods. Numerical simulations are performed to validate the accuracy of the developed method, and the effects of noise are determined. Phantom and in vivo experiments are conducted at 3 T to verify the clinical applicability of the proposed method.

RESULTS

Numerical simulations show that the proposed method is more robust than other methods and can suppress the effects of noise. The quantitative conductivity value of the phantom experiment agrees with the measured value. The in vivo experiment results present a clear structure, and the conductivity value of the tumor region is significantly higher than that around healthy tissues.

CONCLUSION

The proposed electrical conductivity imaging method can improve the quality of conductivity reconstruction, and thus, has future clinical applications.

Magnetic resonance electrical property mapping at 21.1 T: a study of conductivity and permittivity in phantoms, ex vivo tissue and in vivo ischemia

Electrical properties (EP), namely conductivity and permittivity, can provide endogenous contrast for tissue characterization. Using electrical property tomography (EPT), maps of EP can be generated from conventional MRI data. This report investigates the feasibility and accuracy of EPT at 21.1 T for multiple RF coils and modes of operation using phantoms. Additionally, it demonstrates the EP of the in vivo rat brain with and without ischemia. Helmholtz-based EPT was implemented in its Full-form, which demands the complex [Formula: see text] field, and a simplified form requiring either just the [Formula: see text] field phase for conductivity or the [Formula: see text] field magnitude for permittivity. Experiments were conducted at 21.1 T using birdcage and saddle coils operated in linear or quadrature transceive mode, respectively. EPT approaches were evaluated using a phantom, ex and in vivo Sprague-Dawley rats under naïve conditions and ischemic stroke via transient middle cerebral artery occlusion. Different conductivity reconstruction approaches applied to the phantom displayed average errors of 12%-73% to the target acquired from dielectric probe measurements. Permittivity reconstructions showed higher agreement and an average 3%-8% error to the target depending on reconstruction approach. Conductivity and permittivity of ex and in vivo rodent brain were measured. Elevated EP in the ischemia region correlated with the increased sodium content and the influx of water intracellularly following ischemia in the lesion were detected. The Full-form technique generated from the linear birdcage provided the best accuracy for EP of the phantom. Phase-based conductivity and magnitude-based permittivity mapping provided reasonable estimates but also demonstrated the limitations of Helmholtz-based EPT at 21.1 T. Permittivity reconstruction was improved significantly over lower fields, suggesting a novel metric for in vivo brain studies. EPT applied to ischemic rat brain proved sensitivity to physiological changes, motivating the future application of more advanced reconstruction approaches.

Numerical Experiments on the Contrast Capability of Magnetic Resonance Electrical Property Tomography

Purpose:

Magnetic resonance electrical property tomography (MR EPT) is a technique for non-invasively obtaining the electric property (EP) distribution of biological tissues, with a promising potential for application in the early detection of tumors. However, the contrast capability (CC) of this technique has not been fully studied. This work aims to theoretically explore the CC for detecting the variation of EP values and the size of the imaging region.

Methods:

A simulation scheme was specifically designed to evaluate the CC of MR EPT. The simulation study has the advantage that the magnetic field can be accurately obtained. EP maps of the designed phantom embedded with target regions of designated various sizes and EPs were reconstructed using the homogeneous Helmholtz equation based on B1+ with different signal-to-noise ratios (SNRs). The CC was estimated by determining the smallest detectable EP contrast when the target region size was as large as the Laplacian kernel and the smallest detectable target region size when the EP contrast was the same as the difference between healthy and malignant tissues in the brain, based on the reconstructed EP maps.

Results:

Using noise free B1+, the smallest detectable contrast_σ and contrast_εr were 1% and 3%, respectively, and the smallest detectable target region size was 1 mesh unit (the base unit size used in the simulation) for conductivity and relative permittivity. The smallest detectable EP contrast and target region size were decreased as the B1+ SNR increased.

Conclusion:

The CC of MR EPT was related with the SNR of the magnetic field. A small EP contrast and size were necessary for detection at a high-SNR magnetic field. Obtaining a high-SNR magnetic field is important for improving the CC of MR EPT.

Automated gradient-based electrical properties tomography in the human brain using 7 Tesla MRI

Electrical properties of the brain tissues may yield useful biomarkers for neurological disorders and diseases, as well as contribute to safety assurance of ultra-high-field MRI. It has been reported that using B₁ maps from a multi-channel RF coil, the spatial variation of the electrical properties can be robustly retrieved. The absolute electrical property values can then be obtained by spatial integration, given that an integration seed point is assigned. In this study, we propose to exploit automatically detected seed points based on tissue piece-wise homogeneity (Helmholtz equation) for spatial integration. Numerical simulations of a numerical brain model and experiments involving 12 healthy volunteers were performed to demonstrate its feasibility and robustness in various noisy conditions and head positions. For in vivo imaging, we consistently observed higher conductivity and permittivity values in the white and gray matter compared to tabulated ex vivo probe measurement results found in the literature, a discrepancy that may be attributed to ex vivo experimental constraints. Our results suggest that the proposed technique produces consistent brain electrical properties in vivo that may contribute to improving diagnostic and therapeutic decisions.

Opening a new window on MR-based Electrical Properties Tomography with deep learning

In the radiofrequency (RF) range, the electrical properties of tissues (EPs: conductivity and permittivity) are modulated by the ionic and water content, which change for pathological conditions. Information on tissues EPs can be used e.g. in oncology as a biomarker. The inability of MR-Electrical Properties Tomography techniques (MR-EPT) to accurately reconstruct tissue EPs by relating MR measurements of the transmit RF field to the EPs limits their clinical applicability. Instead of employing electromagnetic models posing strict requirements on the measured MRI quantities, we propose a data driven approach where the electrical properties reconstruction problem can be casted as a supervised deep learning task (DL-EPT). DL-EPT reconstructions for simulations and MR measurements at 3 Tesla on phantoms and human brains using a conditional generative adversarial network demonstrate high quality EPs reconstructions and greatly improved precision compared to conventional MR-EPT. The supervised learning approach leverages the strength of electromagnetic simulations, allowing circumvention of inaccessible MR electromagnetic quantities. Since DL-EPT is more noise-robust than MR-EPT, the requirements for MR acquisitions can be relaxed. This could be a major step forward to turn electrical properties tomography into a reliable biomarker where pathological conditions can be revealed and characterized by abnormalities in tissue electrical properties.

Mapping electrical properties heterogeneity of tumor using boundary informed electrical properties tomography (BIEPT) at 7T

PURPOSES

To develop and evaluate a boundary informed electrical properties tomography (BIEPT) technique for high-resolution imaging of tumor electrical properties (EPs) heterogeneity on a rodent tumor xenograft model.

METHODS

Tumor EP distributions were inferred from a reference area external to the tumor, as well as internal EP spatial variations derived from a plurality of relative transmit B1 measurements at 7T. Edge sparsity constraint was enforced to enhance numerical stability. Phantom experiments were performed to determine the imaging accuracy and sensitivity for structures of various EP values, as well as geometrical sizes down to 1.5 mm. Numerical simulation of a realistic rodent model was used to quantify the algorithm performance in the presence of noise. Eleven athymic rats with human breast cancer xenograft were imaged in vivo, and representative pathological samples were acquired for comparison.

RESULTS

Reconstructed EPs of the phantoms correspond well to the ground truth acquired from dielectric probe measurements, with the smallest structure reliably detectable being 3 mm. EPs heterogeneity inside a tumor is successfully retrieved in both simulated and experimental cases. In vivo tumor imaging results demonstrate similar local features and spatial patterns to anatomical MRI and pathological slides. The imaged conductivity of necrotic tissue is higher than that of viable tissues, which agrees with our expectation.

CONCLUSION

BIEPT enables robust detection of tumor EPs heterogeneity with high accuracy and sensitivity to small structures. The retrieved quantitative EPs reflect tumor pathological features (e.g., necrosis). These results provide strong rationale to further expand BIEPT studies toward pathological conditions where EPs may yield valuable, non-invasive biomarkers.

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.

MR-based electrical property tomography using a modified finite difference scheme

Magnetic resonance electrical property tomography (MR-EPT) reconstructs electrical properties (EPs) from measured magnetic fields in magnetic resonance imaging (MRI) systems. In this study, an MR-EPT method was proposed that utilized a new finite difference approximation of the involved differential wave equation. Compared with existing MR-EPT approaches, the construction of the system matrix involves applying the first derivative twice based on a larger number of neighbouring finite-difference grids, which is different from a standard Laplacian operator on a regular grid structure, leading to a better conditioned linear inverse problem. With improved noise robustness, more faithful EPs can be obtained by the proposed method, particularly at tissue boundaries and regions with a poorly measured magnetic field (low signal-to-noise ratio). Numerical simulations with a specially designed multi-slice phantom and an anatomically accurate head model (Duke) have demonstrated that the proposed method can provide a more faithful reconstruction of EPs compared to existing methods, which usually offer unreliable solutions associated with traditional finite difference approximation of the central wave equation and unrealistic assumptions. Experiments on a 9.4 T MRI system have been conducted to validate the simulations.

In vivo imaging of electrical properties of an animal tumor model with an 8-channel transceiver array at 7 T using electrical properties tomography

PURPOSE

To develop and evaluate a technique for imaging electrical properties ((EPs), conductivity and permittivity) of an animal tumor model in vivo using MRI.

METHODS

Electrical properties were reconstructed from the calculated EP gradient, which was derived using two sets of measured transmit B1 magnitude and relative phase maps with the sample and radiofrequency (RF) coil oriented in the positive and negative z-directions, respectively. An eight-channel transceiver microstrip array RF coil fitting the size of the animal was developed for generating and mapping B1 fields to reconstruct EPs. The technique was evaluated at 7 tesla using a physical phantom and in vivo on two Copenhagen rats with subcutaneously implanted AT-1 rat prostate cancer on a hind limb.

RESULTS

The reconstructed EPs in the phantom experiment was in good agreement with the target EP map determined by a dielectric probe. Reconstructed conductivity map of the animals revealed the boundary between tumor and healthy tissue consistent with the boundary indicated by T1 -weighted MRI.

CONCLUSION

A technique for imaging EP of an animal tumor model using MRI has been developed with high sensitivity, accuracy, and resolution, as demonstrated in the phantom experiment. Further animal experiments are needed to demonstrate its translational value for tumor diagnosis. Magn Reson Med 78:2157-2169, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

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.

Electrical Properties Tomography Based on $B_{{1}}$ Maps in MRI: Principles, Applications, and Challenges

OBJECTIVE

The purpose is to provide a comprehensive review of the electrical properties tomography (EPT) technique, which was introduced to image the electrical properties (EPs) of tissue noninvasively by exploiting the measured field data of MRI.

METHODS

We reviewed the principle of EPT, reconstruction methods, biomedical applications such as tumor imaging, and existing challenges. As a key application of EPT, the estimation of specific absorption rate (SAR) due to MRI was discussed in the background of elevated risk of tissue heating at high field.

RESULTS AND CONCLUSION

Since the originally proposed local, homogeneous Helmholtz equation-based reconstruction algorithm, advanced EPT algorithms have emerged to address the challenges of EPT, including reconstruction error near tissue boundaries, noise sensitivity, inaccurate phase estimation, and elimination of the unmeasurable component, along with demonstrations of in vivo experiments. EPT techniques have been applied to investigate EPs of both healthy and pathological tissues in vivo and factors contributing to various EP value, including sodium, water content, etc. More studies are anticipated to consolidate the current findings. EPT-based subject-specific SAR estimation has led to in vivo demonstration of its feasibility and prediction of temperature increase of phantom during MRI scans merely using measured data.

SIGNIFICANCE

EPT has the advantage of high resolution and practical feasibility in a clinical setup for imaging the biomedically interesting EPs of tissue in the radiofrequency range. EPT-based SAR estimation is another promising topic for predicting tissue heating of individual subjects during a specific MRI scan.

Electric properties tomography: Biochemical, physical and technical background, evaluation and clinical applications

Electric properties tomography (EPT) derives the patient's electric properties, i.e. conductivity and permittivity, using standard magnetic resonance (MR) systems and standard MR sequences. Thus, EPT does not apply externally mounted electrodes, currents or radiofrequency (RF) probes, as is the case in competing techniques. EPT is quantitative MR, i.e. it yields absolute values of conductivity and permittivity. This review summarizes the physical equations underlying EPT, the corresponding basic and advanced reconstruction techniques and practical numerical aspects to realize these reconstruction techniques. MR sequences which map the field information required for EPT are outlined, and experiments to validate EPT in phantom and in vivo studies are described. Furthermore, the review describes the clinical findings which have been obtained with EPT so far, and attempts to understand the physiologic background of these findings.

A regularized, model-based approach to phase-based conductivity mapping using MRI

PURPOSE

To develop a novel regularized, model-based approach to phase-based conductivity mapping that uses structural information to improve the accuracy of conductivity maps.

THEORY AND METHODS

The inverse of the three-dimensional Laplacian operator is used to model the relationship between measured phase maps and the object conductivity in a penalized weighted least-squares optimization problem. Spatial masks based on structural information are incorporated into the problem to preserve data near boundaries. The proposed Inverse Laplacian method was compared against a restricted Gaussian filter in simulation, phantom, and human experiments.

RESULTS

The Inverse Laplacian method resulted in lower reconstruction bias and error due to noise in simulations than the Gaussian filter. The Inverse Laplacian method also produced conductivity maps closer to the measured values in a phantom and with reduced noise in the human brain, as compared to the Gaussian filter.

CONCLUSION

The Inverse Laplacian method calculates conductivity maps with less noise and more accurate values near boundaries. Improving the accuracy of conductivity maps is integral for advancing the applications of conductivity mapping. Magn Reson Med 78:2011-2021, 2017. © 2016 International Society for Magnetic Resonance in Medicine.