Error analysis of nonconstant admittivity for MR-based electric property imaging

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

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

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

PURPOSE

To evaluate the performance of various MR electrical properties tomography (MR-EPT) methods at 3 T in terms of absolute quantification and spatial resolution limit for electrical conductivity.

METHODS

Absolute quantification as well as spatial resolution performance were evaluated on homogeneous phantoms and a phantom with holes of different sizes, respectively. Ground-truth conductivities were measured with an open-ended coaxial probe connected to a vector network analyzer (VNA). Four widely used MR-EPT reconstruction methods were investigated: phase-based Helmholtz (PB), phase-based convection-reaction (PB-cr), image-based (IB), and generalized-image-based (GIB). These methods were compared using the same complex images from a 1 mm-isotropic UTE sequence. Alternative transceive phase acquisition sequences were also compared in PB and PB-cr.

RESULTS

In large homogeneous phantoms, all methods showed a strong correlation with ground truth conductivities (r > 0.99); however, GIB was the best in terms of accuracy, spatial uniformity, and robustness to boundary artifacts. In the resolution phantom, the normalized root-mean-squared error of all methods grew rapidly (>0.40) when the hole size was below 10 mm, with simplified methods (PB and IB), or below 5 mm, with generalized methods (PB-cr and GIB).

CONCLUSION

VNA measurements are essential to assess the accuracy of MR-EPT. In this study, all tested MR-EPT methods correlated strongly with the VNA measurements. The UTE sequence is recommended for MR-EPT, with the GIB method providing good accuracy for structures down to 5 mm. Structures below 5 mm may still be detected in the conductivity maps, but with significantly lower accuracy.

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

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

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

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

Mapping electric bulk conductivity in the human heart

PURPOSE

To explore the technical feasibility of mapping the electric bulk conductivity in the human heart, and to determine quantitative conductivity values of myocardium and blood from a small group of volunteers.

METHODS

Using a 3T MR system, 6 healthy male volunteers were measured. For all volunteers, a time-resolved 2D sequence over the cardiac cycle was applied (electrocardiogram [ECG]-triggered SSFP acquired in breath-hold). From these data, a dedicated, so-called "2D conductivity" has been derived in the framework of electrical properties tomography (EPT). To validate the concept of 2D conductivity, a static 3D sequence (ECG-triggered and respiratory-gated SSFP 3D whole heart acquisition, allowing the full 3D reconstruction of conductivity) as well as a Q-flow sequence (for investigating the relation between flow and reconstruction errors of the conductivity) have been applied for one of the volunteers.

RESULTS

For both, blood and myocardium, quantitative values of obtained 2D conductivity were approximately two-thirds of the obtained 3D conductivity, as expected from Maxwell's equations. Furthermore, the quantitative conductivity values agreed with corresponding literature values. Conductivity of left-ventricular blood volume showed characteristic over- and under-shooting at specific time points during the cardiac cycle for all volunteers investigated. This over- and under-shooting correlated with the phase pattern caused by blood flow into/out of the ventricle.

CONCLUSION

The study demonstrated the technical feasibility of cardiac conductivity measurements using standard MR systems and standard MR sequences, and therefore, may open new options for MR-based cardiac diagnosis.

Comparison of Five Conductivity Tensor Models and Image Reconstruction Methods Using MRI

Imaging of the electrical conductivity distribution inside the human body has been investigated for numerous clinical applications. The conductivity tensors of biological tissue have been obtained from water diffusion tensors by applying several models, which may not cover the entire phenomenon. Recently, a new conductivity tensor imaging (CTI) method was developed through a combination of B1 mapping, and multi-b diffusion weighted imaging. In this study, we compared the most recent CTI method with the four existing models of conductivity tensors reconstruction. Two conductivity phantoms were designed to evaluate the accuracy of the models. Applied to five human brains, the conductivity tensors using the four existing models and CTI were imaged and compared with the values from the literature. The conductivity image of the phantoms by the CTI method showed relative errors between 1.10% and 5.26%. The images by the four models using DTI could not measure the effects of different ion concentrations subsequently due to prior information of the mean conductivity values. The conductivity tensor images obtained from five human brains through the CTI method were comparable to previously reported literature values. The images by the four methods using DTI were highly correlated with the diffusion tensor images, showing a coefficient of determination (R2) value of 0.65 to 1.00. However, the images by the CTI method were less correlated with the diffusion tensor images and exhibited an averaged R2 value of 0.51. The CTI method could handle the effects of different ion concentrations as well as mobilities and extracellular volume fractions by collecting and processing additional B1 map data. It is necessary to select an application-specific model taking into account the pros and cons of each model. Future studies are essential to confirm the usefulness of these conductivity tensor imaging methods in clinical applications, such as tumor characterization, EEG source imaging, and treatment planning for electrical stimulation.

Noncontrast-Enhanced MR-Based Conductivity Imaging for Breast Cancer Detection and Lesion Differentiation

BACKGROUND

There is increasing interest in noncontrast-enhanced MRI due to safety concerns for gadolinium contrast agents.

PURPOSE

To investigate the clinical feasibility of MR-based conductivity imaging for breast cancer detection and lesion differentiation.

STUDY TYPE

Prospective.

SUBJECTS

One hundred and ten women, with 112 known cancers and 17 benign lesions (biopsy-proven), scheduled for preoperative MRI.

FIELD STRENGTH/SEQUENCE

Non-fat-suppressed T2-weighted turbo spin-echo sequence (T2WI), dynamic contrast-enhanced MRI and diffusion-weighted imaging (DWI) at 3T.

ASSESSMENT

Cancer detectability on each imaging modality was qualitatively evaluated on a per-breast basis: the conductivity maps derived from T2WI were independently reviewed by three radiologists (R1-R3). T2WI, DWI, and pre-operative digital mammography were independently reviewed by three other radiologists (R4-R6). Conductivity and apparent diffusion coefficient (ADC) measurements (mean, minimum, and maximum) were performed for 112 cancers and 17 benign lesions independently by two radiologists (R1 and R2). Tumor size was measured from surgical specimens.

STATISTICAL TESTS

Cancer detection rates were compared using generalized estimating equations. Multivariable logistic regression analysis was performed to identify factors associated with cancer detectability. Discriminating ability of conductivity and ADC was evaluated by using the areas under the receiver operating characteristic curve (AUC).

RESULTS

Conductivity imaging showed lower cancer detection rates (20%-32%) compared to T2WI (62%-71%), DWI (85%-90%), and mammography (79%-88%) (all P < 0.05). Fatty breast on MRI (odds ratio = 11.8, P < 0.05) and invasive tumor size (odds ratio = 1.7, P < 0.05) were associated with cancer detectability of conductivity imaging. The maximum conductivity showed comparable ability to the mean ADC in discriminating between cancers and benign lesions (AUC = 0.67 [95% CI: 0.59, 0.75] vs. 0.84 [0.76, 0.90], P = 0.06 (R1); 0.65 [0.56, 0.73] vs. 0.82 [0.74, 0.88], P = 0.07 (R2)).

DATA CONCLUSION

Although conductivity imaging showed suboptimal performance in breast cancer detection, the quantitative measurement of conductivity showed the potential for lesion differentiation.

EVIDENCE LEVEL

1 TECHNICAL EFFICACY: Stage 2.

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.

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.

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.

In Vivo Measurement of Brain Tissue Response After Irradiation: Comparison of T2 Relaxation, Apparent Diffusion Coefficient, and Electrical Conductivity

Radiation therapy (RT) has been widely used as a powerful treatment tool to address cancerous tissues because of its ability to control cell growth. Its ionizing radiation damages the DNA of cancerous tissues, leading to cell death. Medical imaging, however, still has limitations regarding the reliability of its assessment of tissue response and in predicting the treatment effect because of its inability to provide contrast information on the gradual, minute tissue changes after RT. A recently developed magnetic resonance (MR)-based conductivity imaging method may provide direct, highly sensitive information on this tissue response because its contrast mechanism is based on the concentration and mobility of ions in intracellular and extracellular spaces. In this feasibility study, we applied T2-weighted, diffusion-weighted, and electrical conductivity imaging to mouse brain, thus, using the MR imaging to map the tissue response after radiation exposure. To evaluate the degree of response, we measured the T2 relaxation, apparent diffusion coefficient (ADC), and electrical conductivity of brain tissues before and after irradiation. The conductivity images, which showed significantly higher sensitivity than other MR imaging methods, indicated that the contrast is distinguishable in different ways at different areas of the brain. Future studies will focus on verifying these results and the long-term evaluation of conductivity changes using various irradiation methods for clinical applications.

Electrical conductivity-based contrast imaging for characterizing prostatic tissues: in vivo animal feasibility study

Background

Electrical conductivity-based magnetic resonance (MR) imaging may provide unique information on tissue condition because its contrast originates from the concentration and mobility of ions in the cellular space. We imaged the conductivity of normal canine prostate in vivo and evaluated tissue contrast in terms of both the conductivity distribution and anatomical significance.

Methods

Five healthy laboratory beagles were used. After clipping the pelvis hair, we attached electrodes and placed each dog inside the bore of an MRI scanner. During MR scanning, we injected imaging currents into two mutually orthogonal directions between two pairs of electrodes. A multi spin echo pulse sequence was used to obtain the MR magnitude and magnetic flux density images. The projected current density algorithm was used to reconstruct the conductivity image.

Results

Conductivity images showed unique contrast depending on the prostatic tissues. From the conductivity distribution, conductivity was highest in the center area and lower in the order of the middle and outer areas of prostatic tissues. The middle and outer areas were, respectively, 11.2 and 25.5% lower than the center area. Considering anatomical significance, conductivity was highest in the central zone and lower in the order of the transitional and peripheral zones in all prostates. The transitional and peripheral zones were, respectively, 7.5 and 17.8% lower than the central zone.

Conclusions

Current conductivity-based MR imaging can differentiate prostatic tissues without using any contrast media or additional MR scans. The electrical conductivity images with unique contrast to tissue condition can provide a prior information on tissues in situ to be used for human imaging.

Conductivity Tensor Imaging of In Vivo Human Brain and Experimental Validation Using Giant Vesicle Suspension

Human brain mapping of low-frequency electrical conductivity tensors can realize patient-specific volume conductor models for neuroimaging and electrical stimulation. We report experimental validation and in vivo human experiments of a new electrodeless conductivity tensor imaging (CTI) method. From CTI imaging of a giant vesicle suspension using a 9.4-T MRI scanner, the relative error in the reconstructed conductivity tensor image was found to be less than 1.7% compared with the measured value using an impedance analyzer. In vivo human brain imaging experiments of five subjects were followed using a 3-T clinical MRI scanner. With the spatial resolution of 1.87 mm, the white matter conductivity showed considerably more position dependency compared with the gray matter and cerebrospinal fluid (CSF). The anisotropy ratio of the white matter was in the range of 1.96-3.25 with a mean value of 2.43, whereas that of the gray matter was in the range of 1.12-1.19 with a mean value of 1.16. The three diagonal components of the reconstructed conductivity tensors were from 0.08 to 0.27 S/m for the white matter, from 0.20 to 0.30 S/m for the gray matter, and from 1.55 to 1.82 S/m for the CSF. The reconstructed conductivity tensor images exhibited significant inter-subject variabilities in terms of frequency and position dependencies. The high-frequency and low-frequency conductivity values can quantify the total and extracellular water contents, respectively, at every pixel. Their difference can quantify the intracellular water content at every pixel. The CTI method can separately quantify the contributions of ion concentrations and mobility to the conductivity tensor.

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.

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.

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

PURPOSE

To develop an electrical property tomography reconstruction method that achieves improvements over standard method by redesigning the Laplacian kernel.

THEORY AND METHODS

A decomposition property of the governing PET equation shows the possibility of redesigning the Laplacian kernel for conductivity reconstruction. Hence, the discrete Laplacian operator used for electrical property tomography reconstruction is redesigned to have a Gaussian-like envelope, which enables manipulation of the spatial and spectral response. The characteristics of the proposed kernel are investigated through numerical simulations and in vivo brain experiments.

RESULTS

The proposed method reduces textured noise, which hampers observing features of the conductivity image. Furthermore, the proposed scheme can mitigate the propagation of local phase error such as flow-induced phase. By doing so, the proposed method can recover feature information in conductivity (or resistivity) images. Lastly, the proposed kernel can be extended to other electrical property tomography reconstructions, improving the quality of images.

CONCLUSION

An alternative design of the Laplacian kernel for conductivity imaging has been developed to mitigate the textured noise and the propagation of local phase artifact.

Electrodeless conductivity tensor imaging (CTI) using MRI: basic theory and animal experiments

The electrical conductivity is a passive material property primarily determined by concentrations of charge carriers and their mobility. The macroscopic conductivity of a biological tissue at low frequency may exhibit anisotropy related with its structural directionality. When expressed as a tensor and properly quantified, the conductivity tensor can provide diagnostic information of numerous diseases. Imaging conductivity distributions inside the human body requires probing it by externally injecting conduction currents or inducing eddy currents. At low frequency, the Faraday induction is negligible and it has been necessary in most practical cases to inject currents through surface electrodes. Here we report a novel method to reconstruct conductivity tensor images using an MRI scanner without current injection. This electrodeless method of conductivity tensor imaging (CTI) utilizes B1 mapping to recover a high-frequency isotropic conductivity image which is influenced by contents in both extracellular and intracellular spaces. Multi-b diffusion weighted imaging is then utilized to extract the effects of the extracellular space and incorporate its directional structural property. Implementing the novel CTI method in a clinical MRI scanner, we reconstructed in vivo conductivity tensor images of canine brains. Depending on the details of the implementation, it may produce conductivity contrast images for conductivity weighted imaging (CWI). Clinical applications of CTI and CWI may include imaging of tumor, ischemia, inflammation, cirrhosis, and other diseases. CTI can provide patient-specific models for source imaging, transcranial dc stimulation, deep brain stimulation, and electroporation.

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.

Software Toolbox for Low-Frequency Conductivity and Current Density Imaging Using MRI

OBJECTIVE

Low-frequency conductivity and current density imaging using MRI includes magnetic resonance electrical impedance tomography (MREIT), diffusion tensor MREIT (DT-MREIT), conductivity tensor imaging (CTI), and magnetic resonance current density imaging (MRCDI). MRCDI and MREIT provide current density and isotropic conductivity images, respectively, using current-injection phase MRI techniques. DT-MREIT produces anisotropic conductivity tensor images by incorporating diffusion weighted MRI into MREIT. These current-injection techniques are finding clinical applications in diagnostic imaging and also in transcranial direct current stimulation (tDCS), deep brain stimulation (DBS), and electroporation where treatment currents can function as imaging currents. To avoid adverse effects of nerve and muscle stimulations due to injected currents, conductivity tensor imaging (CTI) utilizes B1 mapping and multi-b diffusion weighted MRI to produce low-frequency anisotropic conductivity tensor images without injecting current. This paper describes numerical implementations of several key mathematical functions for conductivity and current density image reconstructions in MRCDI, MREIT, DT-MREIT, and CTI.

METHODS

To facilitate experimental studies of clinical applications, we developed a software toolbox for these low-frequency conductivity and current density imaging methods. This MR-based conductivity imaging (MRCI) toolbox includes 11 toolbox functions which can be used in the MATLAB environment.

RESULTS

The MRCI toolbox is available at http://iirc.khu.ac.kr/software.html . Its functions were tested by using several experimental datasets, which are provided together with the toolbox.

CONCLUSION

Users of the toolbox can focus on experimental designs and interpretations of reconstructed images instead of developing their own image reconstruction softwares. We expect more toolbox functions to be added from future research outcomes.

OBJECTIVE

Low-frequency conductivity and current density imaging using MRI includes magnetic resonance electrical impedance tomography (MREIT), diffusion tensor MREIT (DT-MREIT), conductivity tensor imaging (CTI), and magnetic resonance current density imaging (MRCDI). MRCDI and MREIT provide current density and isotropic conductivity images, respectively, using current-injection phase MRI techniques. DT-MREIT produces anisotropic conductivity tensor images by incorporating diffusion weighted MRI into MREIT. These current-injection techniques are finding clinical applications in diagnostic imaging and also in transcranial direct current stimulation (tDCS), deep brain stimulation (DBS), and electroporation where treatment currents can function as imaging currents. To avoid adverse effects of nerve and muscle stimulations due to injected currents, conductivity tensor imaging (CTI) utilizes B1 mapping and multi-b diffusion weighted MRI to produce low-frequency anisotropic conductivity tensor images without injecting current. This paper describes numerical implementations of several key mathematical functions for conductivity and current density image reconstructions in MRCDI, MREIT, DT-MREIT, and CTI.

METHODS

To facilitate experimental studies of clinical applications, we developed a software toolbox for these low-frequency conductivity and current density imaging methods. This MR-based conductivity imaging (MRCI) toolbox includes 11 toolbox functions which can be used in the MATLAB environment.

RESULTS

The MRCI toolbox is available at http://iirc.khu.ac.kr/software.html . Its functions were tested by using several experimental datasets, which are provided together with the toolbox.

CONCLUSION

Users of the toolbox can focus on experimental designs and interpretations of reconstructed images instead of developing their own image reconstruction softwares. We expect more toolbox functions to be added from future research outcomes.

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.

Fast Spin Echo Imaging-Based Electric Property Tomography With K-Space Weighting via ${T}_{2}$ Relaxation (rEPT)

Magnetic resonance electrical property tomography (MREPT) is a technique used to extract the electrical properties of tissues (conductivity in particular) using a magnetic resonance imaging system. In this paper, we propose an improved data acquisition scheme for the electrical property tomography technique by utilizing T ₂ modulation in fast spin echo (FSE) imaging. This technique was motivated by a numerical analysis of conductivity reconstruction in the frequency domain; results reveal the spatial frequency-dependent noise texture of conventional methods. A data-acquisition scheme using the FSE sequence was formulated to concentrate the signal within a specific frequency range where notable noise amplification is observed in the conventional method. Through numerical studies, the performance of the proposed acquisition was investigated. Furthermore, a compensation scheme was applied to reduce quantification errors due to tissue-specific T ₂ modulation, which is inherent in FSE imaging. The technique was applied to phantom and in vivo experiments. Results showed improved conductivity contrasts in both experiments, as compared with conventional MREPT methods.

Realistic Electric Field Mapping of Anisotropic Muscle During Electrical Stimulation Using a Combination of Water Diffusion Tensor and Electrical Conductivity

Purpose

To realistically map the electric fields of biological tissues using a diffusion tensor magnetic resonance electrical impedance tomography (DT-MREIT) method to estimate tissue response during electrical stimulation.

Methods

Imaging experiments were performed using chunks of bovine muscle. Two silver wire electrodes were positioned inside the muscle tissue for electrical stimulation. Electric pulses were applied with a 100-V amplitude and 100-μs width using a voltage stimulator. During electrical stimulation, we collected DT-MREIT data from a 3T magnetic resonance imaging scanner. We adopted the projected current density method to calculate the electric field. Based on the relation between the water diffusion tensor and the conductivity tensor, we computed the position-dependent scale factor using the measured magnetic flux density data. Then, a final conductivity tensor map was reconstructed using the multiplication of the water diffusion tensor and the scale factor.

Results

The current density images from DT-MREIT data represent the internal current flows that exist not only in the electrodes but also in surrounding regions. The reconstructed electric filed map from our anisotropic conductivity tensor with the projected current density shows coverage that is more than 2 times as wide, and higher signals in both the electrodes and surrounding tissues, than the previous isotropic method owing to the consideration of tissue anisotropy.

Conclusions

An electric field map obtained by an anisotropic reconstruction method showed different patterns from the results of the previous isotropic reconstruction method. Since accurate electric field mapping is important to correctly estimate the coverage of the electrical treatment, future studies should include more rigorous validations of the new method through in vivo and in situ experiments.

An MR-Based Viscosity-Type Regularization Method for Electrical Property Tomography

Here, a method based on viscosity-type regularization is proposed for magnetic resonance electrical property tomography (MREPT) to mitigate persistent artifacts when it is used to reconstruct a map of electrical properties based on data from a magnetic resonance imaging scanner. The challenges for solving the corresponding partial differential equation (PDE) are discussed in detail. The existing artifacts in the numerical results are pointed out and classified. The methods in the literature for MREPT are mainly based on an assumption of local homogeneity, which makes the approach simple but leads to artifacts in the transition region where electrical properties vary rapidly. Recent work has focused on eliminating the assumption of local homogeneity, and one of the solutions is convection–reaction MREPT that is based on a first-order PDE. Numerical solutions of the PDE have persistent artifacts in certain regions and global spurious oscillations. Here, a method based on viscosity-type regularization is proposed to effectively mitigate the aforementioned problems. Finite difference method is used for discretizing the governing PDE. Numerical experiments are presented to analyze the problem in detail. Electrical properties of different phantoms are successfully retrieved. The efficiency, accuracy, and noise tolerance of the proposed method are illustrated with numerical results.

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.

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.

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

This work quantitatively analyzed the reconstruction errors (REs) of electrical property (EP) images using a currently popular algorithm of magnetic resonance electrical property tomography (MREPT), which occurred along the tissue interfaces. Transmitted magnetic fields B1+ were acquired at 3 T using a birdcage coil loaded with a phantom consisting of various adjacent tissues. Homogeneous Helmholtz was employed to calculate the EP maps by Laplacian computation of central differences. The maps of absolute REs (aREs) and relative REs (rREs) were calculated. The maximum and mean rREs, in addition to rRE distributions at the interfaces, were presented. Reconstructed EP maps showed various REs along different interface boundaries. Among all the investigated tissue interfaces, the kidney-fat interface presented the maximum mean rREs for both conductivity and relative permittivity. The minimum mean rRE of conductivity was observed at the spleen-muscle interface, and the minimum mean rRE of relative permittivity was detected along the lung-heart interface. The mean rREs ranged from 0.3986 to 36.11 for conductivity and 0.2218 to 11.96 for relative permittivity. Overall, this research indicates that different REs occur at various tissue boundaries, as shown by the currently popular algorithm of MREPT. Thus, REs should be considered when applying MREPT to reconstruct the EP distributions inside the human body. Copyright © 2016 John Wiley & Sons, Ltd.

Electrical conductivity and permittivity maps of brain tissues derived from water content based on T1 -weighted acquisition

PURPOSE

To develop an electrical properties tomography (EPT) technique that can provide in vivo electrical conductivity and permittivity images of biological tissue without performing complex-valued radiofrequency field measurements.

THEORY AND METHODS

Electrical conductivity and permittivity images are modeled as a monotonic function of tissues' water content (W) under the principle of Maxwell's mixture theory. Water content maps are estimated from two spin-echo images having different repetition times (TRs). For the modeling functions, physically measured parameters (electrical properties, water content, and T₁ ) of brain cerebrospinal fluid (CSF), gray matter, and white matter are used as landmark literature references. The formulations are validated by a developed electrolyte-protein phantom and by human brain studies at 3 Tesla (T).

RESULTS

The electrical properties (EPs) of the phantom estimated by the proposed method match well with the values measured on the bench. The conductivity and permittivity maps from all experiments show uncompromised spatial resolution without boundary artifacts and higher contrast when compared with water content maps.

CONCLUSIONS

Human brain and phantom EP images suggest that water content is a dominating factor in determining the electrical properties of tissues. Despite possible literature inaccuracies, the proposed method offers EP maps that can provide complementary information to current approaches, to facilitate EPT scans in clinical applications. Magn Reson Med 77:1094-1103, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

An Inverse Problems Approach to MR-EPT Image Reconstruction

Magnetic Resonance-Electrical Properties Tomography (MR-EPT) is an imaging modality that maps the spatial distribution of the electrical conductivity and permittivity using standard MRI systems. The presence of a body within the scanner alters the RF field, and by mapping these alterations it is possible to recover the electrical properties. The field is time-harmonic, and can be described by the Helmholtz equation. Approximations to this equation have been previously used to estimate conductivity and permittivity in terms of first or second derivatives of RF field data. Using these same approximations, an inverse approach to solving the MR-EPT problem is presented here that leverages a forward model for describing the magnitude and phase of the field within the imaging domain, and a fitting approach for estimating the electrical properties distribution. The advantages of this approach are that 1) differentiation of the measured data is not required, thus reducing noise sensitivity, and 2) different regularization schemes can be adopted, depending on prior knowledge of the distribution of conductivity or permittivity, leading to improved image quality. To demonstrate the developed approach, both Quadratic (QR) and Total Variation (TV) regularization methods were implemented and evaluated through numerical simulation and experimentally acquired data. The proposed inverse approach to MR-EPT reconstruction correctly identifies contrasts and accurately reconstructs the geometry in both simulations and experiments. The TV regularized scheme reconstructs sharp spatial transitions, which are difficult to reconstruct with other, more traditional approaches.

Correlation between conductivity and prognostic factors in invasive breast cancer using magnetic resonance electric properties tomography (MREPT)

PURPOSE

To investigate the correlation between conductivity and prognostic factors of invasive breast cancer using magnetic resonance electric properties tomography (MREPT).

METHODS

This retrospective study was approved by the Institutional Review Board, and verbal informed consent was obtained prior to breast MRI. This study included 65 women with surgically confirmed invasive breast cancers measuring 1 cm or larger on T2-weighted fast spin echo (FSE). Phase-based MREPT and the coil combination technique were used to reconstruct conductivity. Simple and multiple linear regression analysis were used to find an independent factor associated with conductivity.

RESULTS

In total tumours, tumours with HER-2 overexpression showed lower conductivity than those without, and HER-2 overexpression was independently associated with conductivity. In 37 tumours 2 cm or larger, tumours with high mitosis or PR positivity showed higher conductivity than those without, and high mitosis and PR positivity were independently associated with conductivity. In 28 tumours 1-2 cm in size, there were no differences in conductivity according to the prognostic factors.

CONCLUSION

Conductivity values measured using MREPT are associated with the HER-2 overexpression status, and may provide information about mitosis and the PR status of invasive breast cancers 2 cm or larger.

KEY POINTS

• In all tumours, HER-2 overexpression was independently associated with conductivity. • In tumours ≥ 2 cm, high mitosis and PR positivity were associated with conductivity. • Conductivity is associated with the HER-2 overexpression status of invasive breast cancers.

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.

Tissue electrical property mapping from zero echo-time magnetic resonance imaging

The capability of magnetic resonance imaging (MRI) to produce spatially resolved estimation of tissue electrical properties (EPs) in vivo has been a subject of much recent interest. In this work we introduce a method to map tissue EPs from low-flip-angle, zero-echo-time (ZTE) imaging. It is based on a new theoretical formalism that allows calculation of EPs from the product of transmit and receive radio-frequency (RF) field maps. Compared to conventional methods requiring separation of the transmit RF field (B(1)(+)) from acquired MR images, the proposed method has such advantages as: 1) reduced theoretical error, 2) higher acquisition speed, and 3) flexibility in choice of different transmit and receive RF coils. The method is demonstrated in electrical conductivity and relative permittivity mapping in a salt water phantom, as well as in vivo measurement of brain conductivity in healthy volunteers. The phantom results show the validity and scan-time efficiency of the proposed method applied to a piece-wise homogeneous object. Quality of in vivo EP results was limited by reconstruction errors near tissue boundaries, which highlights need for image segmentation in EP mapping in a heterogeneous medium. Our results show the feasibility of rapid EP mapping from MRI without B(1)(+) mapping.

Frequency-dependent conductivity contrast for tissue characterization using a dual-frequency range conductivity mapping magnetic resonance method

Electrical conductivities of biological tissues show frequency-dependent behaviors, and these values at different frequencies may provide clinically useful diagnostic information. MR-based tissue property mapping techniques such as magnetic resonance electrical impedance tomography (MREIT) and magnetic resonance electrical property tomography (MREPT) are widely used and provide unique conductivity contrast information over different frequency ranges. Recently, a new method for data acquisition and reconstruction for low- and high-frequency conductivity images from a single MR scan was proposed. In this study, we applied this simultaneous dual-frequency range conductivity mapping MR method to evaluate its utility in a designed phantom and two in vivo animal disease models. Magnetic flux density and B(1)(+) phase map for dual-frequency conductivity images were acquired using a modified spin-echo pulse sequence. Low-frequency conductivity was reconstructed from MREIT data by the projected current density method, while high-frequency conductivity was reconstructed from MREPT data by B(1)(+) mapping. Two different conductivity phantoms comprising varying ion concentrations separated by insulating films with or without holes were used to study the contrast mechanism of the frequency-dependent conductivities related to ion concentration and mobility. Canine brain abscess and ischemia were used as in vivo models to evaluate the capability of the proposed method to identify new electrical properties-based contrast at two different frequencies. The simultaneous dual-frequency range conductivity mapping MR method provides unique contrast information related to the concentration and mobility of ions inside tissues. This method has potential to monitor dynamic changes of the state of disease.

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.

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.