Complex B1 mapping and electrical properties imaging of the human brain using a 16-channel transceiver coil at 7T

Parallel transmit (pTx) with online pulse design for task-based fMRI at 7 T

PURPOSE

Parallel transmission (pTx) is an approach to improve image uniformity for ultra-high field imaging. In this study, we modified an echo planar imaging (EPI) sequence to design subject-specific pTx pulses online. We compared its performance against EPI with conventional circularly polarised (CP) pulses.

METHODS

We compared the pTx-EPI and CP-EPI sequences in a short EPI acquisition protocol and for two different functional paradigms in six healthy volunteers (2 female, aged 23-36 years, mean age 29.2 years). We chose two paradigms that are typically affected by signal dropout at 7 T: a visual objects localiser to determine face/scene selective brain regions and a semantic-processing task.

RESULTS

Across all subjects, pTx-EPI improved whole-brain mean temporal signal-to-noise ratio (tSNR) by 11.0% compared to CP-EPI. We also compared the ability of pTx-EPI and CP-EPI to detect functional activation for three contrasts over the two paradigms: face > object and scene > object for the visual objects localiser and semantic association > pattern matching for the semantic-processing paradigm. Across all three contrasts, pTx-EPI showed higher median z-scores and detected more active voxels in relevant areas, as determined from previous 3 T studies.

CONCLUSION

We have demonstrated a workflow for EPI acquisitions with online per-subject pulse calculations. We saw improved performance in both tSNR and functional acquisitions from pTx-EPI. Thus, we believe that online calculation pTx-EPI is robust enough for future fMRI studies, especially where activation is expected in brain areas liable to significant signal dropout.

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

Purpose

To present a new complex‐valued B₁⁺ mapping method for electrical properties tomography using Carr‐Purcell spin echoes.

Methods

A 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.

Results

In 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.

Conclusion

The CP sequence can be used to simultaneously provide both B₁⁺ magnitude and phase estimations, and therefore allows for full reconstruction of the electrical properties.

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.

Electrical Properties Tomography: A Methodological Review

Electrical properties tomography (EPT) is an imaging method that uses a magnetic resonance (MR) system to non-invasively determine the spatial distribution of the conductivity and permittivity of the imaged object. This manuscript starts by providing clear definitions about the data required for, and acquired in, EPT, followed by comprehensively formulating the physical equations underlying a large number of analytical EPT techniques. This thorough mathematical overview of EPT harmonizes several EPT techniques in a single type of formulation and gives insight into how they act on the data and what their data requirements are. Furthermore, the review describes machine learning-based algorithms. Matlab code of several differential and iterative integral methods is available upon request.

Effect of radiofrequency inhomogeneity on water-content based electrical properties tomography and its correction by flip angle maps

Water-content based electrical properties tomography (wEPT) can retrieve electrical properties (EPs) from water-content maps. B₁⁺ field information is not involved in the traditional magnetic resonance electrical properties tomography approach. wEPT can be performed through conventional MR scanning, such as T₁-weighted spin-echo imaging, which provides convenient access to multiple clinical applications. However, the inhomogeneous radiofrequency (RF) field induced by RF coils would cause inaccuracy in wEPT reconstructions during MR scanning. We conducted a detailed investigation to evaluate the effect of inhomogeneous RF field on wEPT reconstructions to guarantee that EP mapping is desired for clinical practice. Two important considerations are involved, namely, multiple typical coil configurations and various flip angles (FAs). We proposed a correction scheme with actual FA mapping to calibrate the RF inhomogeneity and finally validated it by using human imaging at 3 T. This study illustrates a detailed evaluation for wEPT under imperfect RF homogeneity and further provides a feasible correction procedure to mitigate it. The profound knowledge of wEPT provided in our work will benefit its performance in 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.

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.

Magnetic-Resonance-Based Electrical Property Mapping Using Global Maxwell Tomography With an 8-Channel Head Coil at 7 Tesla: A Simulation Study

OBJECTIVE

Global Maxwell Tomography (GMT) is a recently introduced volumetric technique for noninvasive estimation of electrical properties (EP) from magnetic resonance measurements. Previous work evaluated GMT using ideal radiofrequency (RF) excitations. The aim of this simulation study was to assess GMT performance with a realistic RF coil.

METHODS

We designed a transmit-receive RF coil with 8 decoupled channels for 7T head imaging. We calculated the RF transmit field ( B₁⁺) inside heterogeneous head models for different RF shimming approaches, and used them as input for GMT to reconstruct EP for all voxels.

RESULTS

Coil tuning/decoupling remained relatively stable when the coil was loaded with different head models. Mean error in EP estimation changed from [Formula: see text] to [Formula: see text] and from [Formula: see text] to [Formula: see text] for relative permittivity and conductivity, respectively, when changing head model without re-tuning the coil. Results slightly improved when an SVD-based RF shimming algorithm was applied, in place of excitation with one coil at a time. Despite errors in EP, RF transmit field ( B₁⁺) and absorbed power could be predicted with less than [Formula: see text] error over the entire head. GMT could accurately detect a numerically inserted tumor.

CONCLUSION

This work demonstrates that GMT can reliably reconstruct EP in realistic simulated scenarios using a tailored 8-channel RF coil design at 7T. Future work will focus on construction of the coil and optimization of GMT's robustness to noise, to enable in-vivo GMT experiments.

SIGNIFICANCE

GMT could provide accurate estimations of tissue EP, which could be used as biomarkers and could enable patient-specific estimation of RF power deposition, which is an unsolved problem for ultra-high-field magnetic resonance imaging.

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.

Integral MR-EPT With the Calculation of Coil Current Distributions

Many integral equation (IE)-based magnetic resonance electrical property tomography (MR-EPT) methods use unloaded incident radio-frequency (RF) fields from simulations that may not fully reflect the real situation and thus lead to reconstruction errors. To improve the accuracy of IE-based MR-EPT methods, a novel approach that enables the calculation of loaded coil current distributions and avoids the explicit use of incident RF fields is presented in this paper. In the proposed method, a hybrid source composed of the current source from the coil and the contrast source from the subject are introduced in the integral equations. Because the loaded coil current distributions can be extracted from the reconstructed hybrid source, the simulated incident RF fields are eliminated from the problem formulations. To improve the convergence performance, a modified conjugate gradient (CG) scheme was used where the gradients of the current source and contrast source were balanced through using different weighting parameters. The proposed method was verified through full-wave simulations at 9.4 and 7 T involving a heterogeneous ball and an anatomical head phantom. The numerical results indicated that by using the proposed method, an accurate coil current distributions and EPs profiles can be reconstructed and the desirable robustness against noise can also be achieved.

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.

Variation in Reported Human Head Tissue Electrical Conductivity Values

Electromagnetic source characterisation requires accurate volume conductor models representing head geometry and the electrical conductivity field. Head tissue conductivity is often assumed from previous literature, however, despite extensive research, measurements are inconsistent. A meta-analysis of reported human head electrical conductivity values was therefore conducted to determine significant variation and subsequent influential factors. Of 3121 identified publications spanning three databases, 56 papers were included in data extraction. Conductivity values were categorised according to tissue type, and recorded alongside methodology, measurement condition, current frequency, tissue temperature, participant pathology and age. We found variation in electrical conductivity of the whole-skull, the spongiform layer of the skull, isotropic, perpendicularly- and parallelly-oriented white matter (WM) and the brain-to-skull-conductivity ratio (BSCR) could be significantly attributed to a combination of differences in methodology and demographics. This large variation should be acknowledged, and care should be taken when creating volume conductor models, ideally constructing them on an individual basis, rather than assuming them from the literature. When personalised models are unavailable, it is suggested weighted average means from the current meta-analysis are used. Assigning conductivity as: 0.41 S/m for the scalp, 0.02 S/m for the whole skull, or when better modelled as a three-layer skull 0.048 S/m for the spongiform layer, 0.007 S/m for the inner compact and 0.005 S/m for the outer compact, as well as 1.71 S/m for the CSF, 0.47 S/m for the grey matter, 0.22 S/m for WM and 50.4 for the BSCR.

Noninvasive Estimation of Electrical Properties From Magnetic Resonance Measurements via Global Maxwell Tomography and Match Regularization

OBJECTIVE

In this paper, we introduce global Maxwell tomography (GMT), a novel volumetric technique that estimates electric conductivity and permittivity by solving an inverse scattering problem based on magnetic resonance measurements.

METHODS

GMT relies on a fast volume integral equation solver, MARIE, for the forward path, and a novel regularization method, match regularization, designed specifically for electrical property estimation from noisy measurements. We performed simulations with three different tissue-mimicking numerical phantoms of different complexity, using synthetic transmit sensitivity maps with realistic noise levels as the measurements. We performed an experiment at 7 T using an eight-channel coil and a uniform phantom.

RESULTS

We showed that GMT could estimate relative permittivity and conductivity from noisy magnetic resonance measurements with an average error as low as 0.3% and 0.2%, respectively, over the entire volume of the numerical phantom. Voxel resolution did not affect GMT performance and is currently limited only by the memory of the graphics processing unit. In the experiment, GMT could estimate electrical properties within 5% of the values measured with a dielectric probe.

CONCLUSION

This work demonstrated the feasibility of GMT with match regularization, suggesting that it could be effective for accurate in vivo electrical property estimation. GMT does not rely on any symmetry assumption for the electromagnetic field, and can be generalized to estimate also the spin magnetization, at the expense of increased computational complexity.

SIGNIFICANCE

GMT could provide insight into the distribution of electromagnetic fields inside the body, which represents one of the key ongoing challenges for various diagnostic and therapeutic applications.

CONtrast Conformed Electrical Properties Tomography (CONCEPT) Based on Multi- Channel Transmission and Alternating Direction Method of Multipliers

In magnetic resonance-based electrical properties tomography (EPT), circularly polarized magnetic field B1 from a transmit radiofrequency (RF) coil is measured and utilized to infer the electrical conductivity and permittivity of biological tissues. Compared with a quadrature RF coil, a multi-channel transmit coil provides a plurality of unique transmit B1 patterns that help to alleviate the under-determinedness of EPT reconstruction problem, and it also allows to circumvent the "transceive phase assumption" that fails at ultra-high-field MRI. Here, a new approach, contrast conformed electrical properties tomography or CONCEPT, is proposed based on the multi-channel transmission that retrieves electrical properties (EPs) by solving a linear partial differential equation with discriminated L1 and L2 norm regularization informed by intermediate EP gradient. The theory of CONCEPT and a fast reconstruction algorithm based on the alternating direction method of multipliers are described and evaluated using numerical simulations, phantom experiment, and analysis of in vivo human brain data at 7 T MRI. Compared with the multi-channel gradient-based EPT (gEPT) method, this new technology does not require receive- B1 sensitivity profiles and does not rely on symmetry assumption regarding RF coil design and imaged target. Moreover, it is not dependent on external prior information, such as integration seed point or anatomical MRI, which can be sources of bias in reconstructed EP values. By deriving EPs from transmit B1 profiles only, CONCEPT can be used with RF coils that include receive-only arrays with large channel count which can, in turn, offer substantial gains in signal-to-noise ratio. It also holds potentials to image unsymmetrical body organs and diseased brain. CONCEPT provides solutions for the practical problems during the implementation of gEPT, thus representing a more generalized framework in the context of multi-channel RF transmission.

A surface loop array for in vivo small animal MRI/fMRI on 7T human scanners

Small animals such as non-human primate (NHP) and rodent are valuable models in frontier neuroscience researches, and comparative research between the animal model and human is helpful to understand and reveal the functional brain circuits in cognition and underlying mechanism in psychological disease. Small animals can be trained or anesthetized to endure long-term and multiple imaging scans; however, the concomitant needs in subcortical structure and function investigations pose major challenges in, e.g. spatial resolution, scan time efficiency, spatial/temporal signal-to-noise-ratio, as well as apparatus mechanical fixation. In addition, comparative investigations across species are also expected to be conducted under similar physical environment (such as the main magnetic field strength, RF pulse shape, sequence protocols, gradient waveform, system stability, etc in MRI), in order to avoid possible deviation in signal detection under different platforms, as well as to reduce experiment complexity. We have proposed a novel 5-channel surface coil that is equipped on 7T human MRI scanners and designed for small animal structural and functional MRI. Through a series of in vivo experiments over an anesthetized rat and macaque, the presented coil shows its main characteristics in, i.e. flexible coil mounting, reduced FOV, high temporal SNR, and parallel imaging capability. Such design is able to compensate the relatively lower gradient slew rate of human scanners versus those with smaller bores, and thus effectively facilitates in vivo microscopic structural MR images being obtained within a shortened and safe period of anesthesia; besides, it also enables high-resolution functional MRI (i.e. spin-echo based) being achieved with reasonable temporal resolution, distortion level and functional contrast.

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.

Reference-Based Integral MR-EPT:Simulation and Experiment Studies on the 9.4T MRI

Current integral-equation (IE) based MR electrical properties tomography (EPT) methods utilize simulated incident radio-frequency (RF) fields, which are inaccurate and lead to reconstruction errors. To improve the accuracy and practicability of IE-based MR-EPT methods, a new approach is presented that obtains the incident fields using reference subjects and RF field mapping techniques. The Incident field approximation (IFA) is first demonstrated in this paper. This approximation assumes that two imaged subjects with similar coil/subject interactions will have similar incident RF fields, thus one can feed the estimation of the incident fields within the imaged subject into the calculation of those within a homogeneous subject (reference subject). This is done by measuring the total RF fields ( field) of the reference using field mapping techniques, using the known EPs of the reference subject and by rearranging Ampere's Law and the integral equations. The calculated incident RF fields are then used to reconstruct the EPs' distribution with a three-dimensional (3D) integral-based MR-EPT method. Numerical simulation results indicated that the incident RF fields obtained from the reference subject provide accurate 3D reconstruction of EPs with less than 16% root mean square error (RMSE) in noise-free scenario while the conventional IE method had more than 28% RMSE. The phantom-based experiments at 9.4T MRI system have also been conducted to evaluate the performance of the proposed method and the results indicated that the proposed method achieved desirable robustness against the noise in practical scenario with less than 21% RMSE while the conventional differential equation-based method showed worse than 37% RMSE.

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.

3-D Contrast Source Inversion-Electrical Properties Tomography

Contrast source inversion-electrical properties tomography (CSI-EPT) is an iterative reconstruction method to retrieve the electrical properties (EPs) of tissues from magnetic resonance data. The method is based on integral representations of the electromagnetic field and has been shown to allow EP reconstructions of small structures as well as tissue boundaries with compelling accuracy. However, to date, the CSI-EPT has been implemented for 2-D configurations only, which limits its applicability. In this paper, a full 3-D extension of the CSI-EPT method is presented, to enable CSI-EPT to be applied to realistic 3-D scenarios. Here, we demonstrate a proof-of-principle of 3-D CSI-EPT and present the reconstructions of a 3-D abdominal body section and a 3-D head model using different settings of the transmit coil. Numerical results show that the full 3-D approach yields accurate reconstructions of the EPs, even at tissue boundaries and is most accurate in regions where the absolute value of the electric field is highest.

Phase-sensitive B1 mapping: Effects of relaxation and RF spoiling

PURPOSE

To develop a phase-based B₁ mapping technique accounting for the effects of imperfect RF spoiling and magnetization relaxation.

THEORY AND METHODS

The technique is based on a multi-gradient-echo sequence with 2 successive orthogonal radiofrequency (RF) excitation pulses followed by the train of gradient echoes measurements. We have derived a theoretical expression relating the MR signal phase produced by the 2 successive RF pulses to the B₁ field and B₀ -related frequency shift. The expression takes into account effects of imperfections of RF spoiling and T₁ and T2* relaxations.

RESULTS

Our computer simulations and experiments revealed that imperfections of RF spoiling cause significant errors in B₁ mapping if not accounted for. By accounting for these effects along with effects of magnetization relaxation and frequency shift, we demonstrated the high accuracy of our approach. The technique has been tested on spherical phantoms and a healthy volunteer.

CONCLUSION

In this paper, we have proposed, implemented, and demonstrated the accuracy of a new phase-based technique for fast and robust B₁ mapping based on the measured MR signal phase, frequency, and relaxation. Because imperfect RF spoiling effects are accounted for, this technique can be applied with short TRs and therefore substantially reduces the scan time. Magn Reson Med 80:101-111, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

Investigating the Influence of Spatial Constraints on Ultimate Receive Coil Performance for Monkey Brain MRI at 7 T

The RF receive coil array has become increasingly vital in current MR imaging practice due to its extended spatial coverage, maintained high SNR, and improved capability of accelerating data acquisition. The performance of a coil array is intrinsically determined by the current patterns generated in coil elements as well as by the induced electromagnetic fields inside the object. Investigations of the ultimate performance constrained by a specific coil space, which defines all possible current patterns flowing within, offer the opportunity to evaluate coil-space parameters (i.e., coverage, coil-to-object distance, layer thickness, and coil element type) without the necessity of considering the realistic coil element geometry, coil elements layout, and number of receive channels in modeling. In this paper, to mimic 7-T monkey RF head coil design, seven hypothetical ultimate coil arrays with different coil-space configurations were mounted over a numerical macaque head model; by using Huygens's surface approximation method, the influences of coil-space design parameters were systematically investigated through evaluating the spatial constrained ultimate intrinsic SNR and ultimate g-factor. Moreover, simulations were also conducted by using four coil arrays with limited number of loop-only elements, in order to explore to what extent the ultimate coil performance can be achieved by using practical coil designs, and hence several guidelines in RF coil design for monkey brain imaging at 7 T have been tentatively concluded. It is believed that the present analysis will offer important implications in novel receive array design for monkey brain MR imaging at ultra-high field.

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.

Predicting temperature increase through local SAR estimation by B1 mapping: a phantom validation at 7T

It has been shown that Electrical Properties d(EPs) of biological tissues can be derived from MR-based B1 measurement. A strong appeal for these `Electrical Property Tomography' (EPT) methods is to estimate real-time and subject-specific local specific absorption rate (SAR) induced by RF transmission. In order to investigate the feasibility of EPT-based local SAR estimation, following previously proposed EPT protocols, induced local SAR has been firstly estimated under one B1 shim setting for a heating sequence at 7T; whereas with the same acquired B1 information, induced local SAR under a different B1 shim setting has been further predicted. Both of the SAR results have been compared to measured temperature changes using MRI Thermometry based on the proton chemical shift.

The technological future of 7 T MRI hardware

In this article we present our projections of future hardware developments on 7 T human MRI systems. These include compact cryogen-light magnets, improved gradient performance, integrated RF-receive and direct current shimming coil arrays, new RF technology with adaptive impedance matching, patient-specific specific absorption rate estimation and monitoring, and increased integration of physiological monitoring systems. Copyright © 2015 John Wiley & Sons, Ltd.

Simultaneous Quantitative Imaging of Electrical Properties and Proton Density From B1 Maps Using MRI

Electrical conductivity and permittivity of biological tissues are important diagnostic parameters and are useful for calculating subject-specific specific absorption rate distribution. On the other hand, water proton density also has clinical relevance for diagnosis purposes. These two kinds of tissue properties are inevitably associated in the technique of electrical properties tomography (EPT), which can be used to map in vivo electrical properties based on the measured B1 field distribution at Larmor frequency using magnetic resonance imaging (MRI). The signal magnitude in MR images is locally proportional to both the proton density of tissue and the receive B1 field; this is a source of artifact in receive B1-based EPT reconstruction because these two quantities cannot easily be disentangled. In this study, a new method was proposed for simultaneously extracting quantitative conductivity, permittivity and proton density from the measured magnitude of transmit B1 field, proton density-weighted receive B1 field, and transceiver phase, in a multi-channel radiofrequency (RF) coil using MRI, without specific assumptions to derive the proton density distribution. We evaluated the spatial resolution, sensitivity to contrast, and accuracy of the method using numerical simulations of B1 field in a phantom and in a realistic human head model. Using the proposed method, conductivity, permittivity and proton density were then experimentally obtained ex vivo in a pork tissue sample on a 7T MRI scanner equipped with a 16-channel microstrip transceiver RF coil.

B1-based SAR reconstruction using contrast source inversion-electric properties tomography (CSI-EPT)

Specific absorption rate (SAR) assessment is essential for safety purposes during MR acquisition. Online SAR assessment is not trivial and requires, in addition, knowledge of the electric tissue properties and the electric fields in the human anatomy. In this study, the potential of the recently developed CSI-EPT method to reconstruct SAR distributions is investigated. This method is based on integral representations for the electromagnetic field and attempts to reconstruct the tissue parameters and the electric field strength based on \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$B_{1}^{ + }$$\end{document}B1+ field data only. Full three-dimensional FDTD simulations using a female pelvis model are used to validate two-dimensional CSI reconstruction results in the central transverse plane of a 3T body coil. Numerical experiments demonstrate that the reconstructed SAR distributions are in good agreement with the SAR distributions as determined via 3D FDTD simulations and show that these distributions can be computed very efficiently in the central transverse plane of a body coil with the two-dimensional approach of CSI-EPT.

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.

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.

CSI-EPT: A Contrast Source Inversion Approach for Improved MRI-Based Electric Properties Tomography

Electric properties tomography (EPT) is an imaging modality to reconstruct the electric conductivity and permittivity inside the human body based on B1(+) maps acquired by a magnetic resonance imaging (MRI) system. Current implementations of EPT are based on the local Maxwell equations and assume piecewise constant media. The accuracy of the reconstructed maps may therefore be sensitive to noise and reconstruction errors occur near tissue boundaries. In this paper, we introduce a multiplicative regularized CSI-EPT method (contrast source inversion-electric properties tomography) where the electric tissue properties are retrieved in an iterative fashion based on a contrast source inversion approach. The method takes the integral representations for the electromagnetic field as a starting point and the tissue parameters are obtained by iteratively minimizing an objective function which measures the discrepancy between measured and modeled data and the discrepancy in satisfying a consistency equation known as the object equation. Furthermore, the objective function consists of a multiplicative Total Variation factor for noise suppression during the reconstruction process. Finally, the presented implementation is able to simultaneously include more than one B1(+) data set acquired by complementary RF excitation settings. We have performed in vivo simulations using a female pelvis model to compute the B1(+) fields. Three different RF excitation settings were used to acquire complementary B1(+) fields for an improved overall reconstruction. Numerical results illustrate the improved reconstruction near tissue boundaries and the ability of CSI-EPT to reconstruct small tissue structures.

Multichannel Double-Row Transmission Line Array for Human MR Imaging at Ultrahigh Fields

OBJECTIVE

In microstrip transmission line (MTL) transmit/receive (transceive) arrays used for ultrahigh field MRI, the array length is often constrained by the required resonant frequency, limiting the image coverage. The purpose of this study is to increase the imaging coverage and also improve its parallel imaging capability by utilizing a double-row design.

METHODS

A 16-channel double-row MTL transceive array was designed, constructed, and tested for human head imaging at 7 T. Array elements between two rows were decoupled by using the induced current elimination or magnetic wall decoupling technique. In vivo human head images were acquired, and g-factor results were calculated to evaluate the performance of this double-row array.

RESULTS

Testing results showed that all coil elements were well decoupled with a better than -18 dB transmission coefficient between any two elements. The double-row array improves the imaging quality of the lower portion of the human head, and has low g-factors even at high acceleration rates.

CONCLUSION

Compared with a regular single-row MTL array, the double-row array demonstrated a larger imaging coverage along the z-direction with improved parallel imaging capability.

SIGNIFICANCE

The proposed technique is particularly suitable for the design of large-sized transceive arrays with large channel counts, which ultimately benefits the imaging performance in human MRI.

Gradient-based magnetic resonance electrical properties imaging of brain tissues

Electrical properties tomography (EPT) holds promise for noninvasively mapping at high spatial resolution the electrical conductivity and permittivity of biological tissues in vivo using a magnetic resonance imaging (MRI) scanner. In the present study, we have developed a novel gradient-based EPT approach with greatly improved tissue boundary reconstruction and largely elevated robustness against measurement noise compared to existing techniques. Using a 7 Tesla MRI system, we report, for the first time, high-quality in vivo human brain electrical property images with refined structural details, which can potentially merit clinical diagnosis (such as cancer detection) and high-field MRI applications (quantification of local specific absorption rate) in the future.

Quantitative prediction of radio frequency induced local heating derived from measured magnetic field maps in magnetic resonance imaging: A phantom validation at 7 T

Electrical Properties Tomography (EPT) technique utilizes measurable radio frequency (RF) coil induced magnetic fields (B1 fields) in a Magnetic Resonance Imaging (MRI) system to quantitatively reconstruct the local electrical properties (EP) of biological tissues. Information derived from the same data set, e.g., complex numbers of B1 distribution towards electric field calculation, can be used to estimate, on a subject-specific basis, local Specific Absorption Rate (SAR). SAR plays a significant role in RF pulse design for high-field MRI applications, where maximum local tissue heating remains one of the most constraining limits. The purpose of the present work is to investigate the feasibility of such B1-based local SAR estimation, expanding on previously proposed EPT approaches. To this end, B1 calibration was obtained in a gelatin phantom at 7 T with a multi-channel transmit coil, under a particular multi-channel B1-shim setting (B1-shim I). Using this unique set of B1 calibration, local SAR distribution was subsequently predicted for B1-shim I, as well as for another B1-shim setting (B1-shim II), considering a specific set of parameter for a heating MRI protocol consisting of RF pulses plaid at 1% duty cycle. Local SAR results, which could not be directly measured with MRI, were subsequently converted into temperature change which in turn were validated against temperature changes measured by MRI Thermometry based on the proton chemical shift.

Magnetic-resonance-based electrical properties tomography: a review

Frequency-dependent electrical properties (EPs; conductivity and permittivity) of biological tissues provide important diagnostic information (e.g., tumor characterization), and also play an important role in quantifying radiofrequency (RF) coil induced specific absorption rate (SAR), which is a major safety concern in high- and ultrahigh-field magnetic resonance imaging (MRI) applications. Cross-sectional imaging of EPs has been pursued for decades. Recently introduced electrical properties tomography (EPT) approaches utilize the measurable RF magnetic field induced by the RF coil in an MRI system to quantitatively reconstruct the EP distribution in vivo and noninvasively with a spatial resolution of a few millimeters or less. This paper reviews the EPT approach from its basic theory in electromagnetism to the state-of-the-art research outcomes. Emphasizing on the imaging reconstruction methods rather than experimentation techniques, we review the developed imaging algorithms, validation results in physical phantoms and biological tissues, as well as their applications in in vivo tumor detection and subject-specific SAR prediction. Challenges for future research are also discussed.

Gradient-based electrical properties tomography (gEPT): A robust method for mapping electrical properties of biological tissues in vivo using magnetic resonance imaging

PURPOSE

To develop high-resolution electrical properties tomography (EPT) methods and investigate a gradient-based EPT (gEPT) approach that aims to reconstruct the electrical properties (EP), including conductivity and permittivity, of an imaged sample from experimentally measured B1 maps with improved boundary reconstruction and robustness against measurement noise.

THEORY AND METHODS

Using a multichannel transmit/receive stripline head coil with acquired B1 maps for each coil element, and by assuming negligible Bz component compared to transverse B1 components, a theory describing the relationship between B1 field, EP value, and their spatial gradient has been proposed. The final EP images were obtained through spatial integration over the reconstructed EP gradient. Numerical simulation, physical phantom, and in vivo human experiments at 7 T have been conducted to evaluate the performance of the proposed method.

RESULTS

Reconstruction results were compared with target EP values in both simulations and phantom experiments. Human experimental results were compared with EP values in literature. Satisfactory agreement was observed with improved boundary reconstruction. Importantly, the proposed gEPT method proved to be more robust against noise when compared to previously described nongradient-based EPT approaches.

CONCLUSION

The proposed gEPT approach holds promises to improve EP mapping quality by recovering the boundary information and enhancing robustness against noise.

Single acquisition electrical property mapping based on relative coil sensitivities: A proof-of-concept demonstration

PURPOSE

All methods presented to date to map both conductivity and permittivity rely on multiple acquisitions to compute quantitatively the magnitude of radiofrequency transmit fields, B1+. In this work, we propose a method to compute both conductivity and permittivity based solely on relative receive coil sensitivities ( B1-) that can be obtained in one single measurement without the need to neither explicitly perform transmit/receive phase separation nor make assumptions regarding those phases.

THEORY AND METHODS

To demonstrate the validity and the noise sensitivity of our method we used electromagnetic finite differences simulations of a 16-channel transceiver array. To experimentally validate our methodology at 7 Tesla, multi compartment phantom data was acquired using a standard 32-channel receive coil system and two-dimensional (2D) and 3D gradient echo acquisition. The reconstructed electric properties were correlated to those measured using dielectric probes.

RESULTS

The method was demonstrated both in simulations and in phantom data with correlations to both the modeled and bench measurements being close to identity. The noise properties were modeled and understood.

CONCLUSION

The proposed methodology allows to quantitatively determine the electrical properties of a sample using any MR contrast, with the only constraint being the need to have 4 or more receive coils and high SNR. Magn Reson Med 74:185-195, 2015. © 2014 Wiley Periodicals, Inc.

Anisotropic conductivity tensor imaging in MREIT using directional diffusion rate of water molecules

Magnetic resonance electrical impedance tomography (MREIT) is an emerging method to visualize electrical conductivity and/or current density images at low frequencies (below 1 KHz). Injecting currents into an imaging object, one component of the induced magnetic flux density is acquired using an MRI scanner for isotropic conductivity image reconstructions. Diffusion tensor MRI (DT-MRI) measures the intrinsic three-dimensional diffusion property of water molecules within a tissue. It characterizes the anisotropic water transport by the effective diffusion tensor. Combining the DT-MRI and MREIT techniques, we propose a novel direct method for absolute conductivity tensor image reconstructions based on a linear relationship between the water diffusion tensor and the electrical conductivity tensor. We first recover the projected current density, which is the best approximation of the internal current density one can obtain from the measured single component of the induced magnetic flux density. This enables us to estimate a scale factor between the diffusion tensor and the conductivity tensor. Combining these values at all pixels with the acquired diffusion tensor map, we can quantitatively recover the anisotropic conductivity tensor map. From numerical simulations and experimental verifications using a biological tissue phantom, we found that the new method overcomes the limitations of each method and successfully reconstructs both the direction and magnitude of the conductivity tensor for both the anisotropic and isotropic regions.

Convection-reaction equation based magnetic resonance electrical properties tomography (cr-MREPT)

Images of electrical conductivity and permittivity of tissues may be used for diagnostic purposes as well as for estimating local specific absorption rate distributions. Magnetic resonance electrical properties tomography (MREPT) aims at noninvasively obtaining conductivity and permittivity images at radio-frequency frequencies of magnetic resonance imaging systems. MREPT algorithms are based on measuring the B1 field which is perturbed by the electrical properties of the imaged object. In this study, the relation between the electrical properties and the measured B1 field is formulated for the first time as a well-known convection-reaction equation. The suggested novel algorithm, called "cr-MREPT," is based on the solution of this equation on a triangular mesh, and in contrast to previously proposed algorithms, it is applicable in practice not only for regions where electrical properties are relatively constant but also for regions where they vary. The convective field of the convection-reaction equation depends on the spatial derivatives of the B1 field, and in the regions where its magnitude is low, a spot-like artifact is observed in the reconstructed electrical properties images. For eliminating this artifact, two different methods are developed, namely "constrained cr-MREPT" and "double-excitation cr-MREPT." Successful reconstructions are obtained using noisy and noise-free simulated data, and experimental data from phantoms.

2D Magnetic resonance electrical property tomography based on B1(-) field mapping

Magnetic Resonance Electrical Property Tomography (MREPT) is a method to visualize electrical conductivity and permittivity distributions in the object. Traditional MREPT relies on either the radio frequency (RF) transmit field (B(+)1) mapping, or using a transmit/receive RF coil, to compute tissue's electrical conductivity and permittivity. This paper introduces an alternative approach based on the reconstructed receive field (B(-)1) By solving a system of homogeneous equations consisting of the signal ratios from multi-channel receive coils, the receive field distribution with both magnitude and phase can be computed. Similar to (B(+)1) based MREPT method, the conductivity and permittivity in the imaging object can be calculated from the (B(-)1) field. We demonstrated the feasibility to image electrical property contrasts through computer simulated studies and phantom experiments. Although this study focuses on the 2D reconstruction, the presented method can be extended to full 3D. This method can be applied to regular MR imaging collected with multi-channel receive coils, and therefore, tissue anomaly based on electrical properties can potentially be revealed with a higher imaging quality, providing useful information for clinical diagnosis.

Determining electrical properties based on B(1) fields measured in an MR scanner using a multi-channel transmit/receive coil: a general approach

Electrical properties tomography (EPT) is a recently developed noninvasive technology to image the electrical conductivity and permittivity of biological tissues at Larmor frequency in magnetic resonance scanners. The absolute phase of the complex radio-frequency magnetic field (B1) is necessary for electrical property calculation. However, due to the lack of practical methods to directly measure the absolute B1 phases, current EPT techniques have been achieved with B1 phase estimation based on certain assumptions on object anatomy, coil structure and/or electromagnetic wave behavior associated with the main magnetic field, limiting EPT from a larger variety of applications. In this study, using a multi-channel transmit/receive coil, the framework of a new general approach for EPT has been introduced, which is independent on the assumptions utilized in previous studies. Using a human head model with realistic geometry, a series of computer simulations at 7 T were conducted to evaluate the proposed method under different noise levels. Results showed that the proposed method can be used to reconstruct the conductivity and permittivity images with noticeable accuracy and stability. The feasibility of this approach was further evaluated in a phantom experiment at 7 T.