B1-based specific energy absorption rate determination for nonquadrature radiofrequency excitation

Investigation of alternative RF power limit control methods for 0.5T, 1.5T, and 3T parallel transmission cardiac imaging: A simulation study

PURPOSE

To investigate safety and performance aspects of parallel-transmit (pTx) RF control-modes for a body coil atB 0 ≤ 3 T $$ {B}_0\le 3\mathrm{T} $$ .

METHODS

Electromagnetic simulations of 11 human voxel models in cardiac imaging position were conducted forB 0 = 0.5 T $$ {B}_0=0.5\mathrm{T} $$ ,1.5 T $$ 1.5\mathrm{T} $$ and3 T $$ 3\mathrm{T} $$ and a body coil with a configurable number of transmit channels (1, 2, 4, 8, 16). Three safety modes were considered: the 'SAR-controlled mode' (SCM), where specific absorption rate (SAR) is limited directly, a 'phase agnostic SAR-controlled mode' (PASCM), where phase information is neglected, and a 'power-controlled mode' (PCM), where the voltage amplitude for each channel is limited. For either mode, safety limits were established based on a set of 'anchor' simulations and then evaluated in 'target' simulations on previously unseen models. The comparison allowed to derive safety factors accounting for varying patient anatomies. All control modes were compared in terms of theB 1 + $$ {B}_1^{+} $$ amplitude and homogeneity they permit under their respective safety requirements.

RESULTS

Large safety factors (approximately five) are needed if only one or two anchor models are investigated but they shrink with increasing number of anchors. The achievableB 1 + $$ {B}_1^{+} $$ is highest for SCM but this advantage is reduced when the safety factor is included. PCM appears to be more robust against variations of subjects. PASCM performance is mostly in between SCM and PCM. Compared to standard circularly polarized (CP) excitation, pTx offers minorB 1 + $$ {B}_1^{+} $$ improvements if local SAR limits are always enforced.

CONCLUSION

PTx body coils can safely be used atB 0 ≤ 3 T $$ {B}_0\le 3\mathrm{T} $$ . Uncertainties in patient anatomy must be accounted for, however, by simulating many models.

Ultrafast B1 mapping with RF-prepared 3D FLASH acquisition: Correcting the bias due to T1 -induced k-space filtering effect

Purpose

The traditional radiofrequency (RF)‐prepared B₁ mapping technique consists of one scan with an RF preparation module for flip angle‐encoding and a second scan without this module for normalizing. To reduce the T₁‐induced k‐space filtering effect, this method is limited to 2D FLASH acquisition with a two‐parameter method. A novel 3D RF‐prepared three‐parameter method for ultrafast B₁‐mapping is proposed to correct the T₁‐induced quantification bias.

Theory

The point spread function analysis of FLASH shows that the prepared longitudinal magnetization before the FLASH acquisition and the image signal obeys a linear (not proportional) relationship. The intercept of the linear function causes the quantification bias and can be captured by a third saturated scan.

Methods

Using the 2D double‐angle method (DAM) as the reference, a 3D RF‐prepared three‐parameter protocol with 9 s duration was compared with the two‐parameter method, as well as the saturated DAM (SDAM) method, the dual refocusing echo acquisition mode (DREAM) method, and the actual flip‐angle imaging (AFI) method, for B₁ mapping of brain, breast, and abdomen with different orientations and shim settings at 3T.

Results

The 3D RF‐prepared three‐parameter method with complex‐subtraction delivered consistently lower RMS error, error mean, error standard deviation, and higher concordance correlation coefficients values than the two‐parameter method, the three‐parameter method with magnitude‐subtraction, the multi‐slice DREAM and the 3D AFI, and were close to the results of 2D or multi‐slice SDAM.

Conclusion

The proposed ultrafast 3D RF‐prepared three‐parameter method with complex‐subtraction was demonstrated with high accuracy for B₁ mapping of brain, breast, and abdomen.

Progress in Understanding Radiofrequency Heating and Burn Injuries for Safer MR Imaging

RF electromagnetic wave exposure during MRI scans induces heat and occasionally causes burn injuries to patients. Among all the types of physical injuries that have occurred during MRI examinations, RF burn injuries are the most common ones. The number of RF burn injuries increases as the static magnetic field of MRI systems increases because higher RFs lead to higher heating. The commonly believed mechanisms of RF burn injuries are the formation of a conductive loop by the patient's posture or cables, such as an electrocardiogram lead; however, the mechanisms of RF burn injuries that occur at the contact points, such as the bore wall and the elbow, remain unclear. A comprehensive understanding of RF heating is needed to address effective countermeasures against all RF burn injuries for safe MRI examinations. In this review, we summarize the occurrence of RF burn injury cases by categorizing RF burn injuries reported worldwide in recent decades. Safety standards and regulations governing RF heating that occurs during MRI examinations are presented, along with their theoretical and physiological backgrounds. The experimental assessment techniques for RF heating are then reviewed, and the development of numerical simulation techniques is explained. In addition, a comprehensive theoretical interpretation of RF burn injuries is presented. By including the results of recent experimental and numerical simulation studies on RF heating, this review describes the progress achieved in understanding RF heating from the standpoint of MRI burn injury prevention.

Radio-Frequency Vector Magnetic Field Mapping in Magnetic Resonance Imaging

A method is presented to measure the radio-frequency (RF) vector magnetic field inside an object using magnetic resonance imaging (MRI). Conventional " [Formula: see text] mapping" in MRI can measure the proton co-rotating component ( [Formula: see text] of the RF field produced by a transmit coil. Here we show that by repeating [Formula: see text] mapping on the same object and coil at multiple (8) specific orientations with respect to the main magnet, the magnitudes and relative phases of all (x, y, z) Cartesian components of the RF field can be determined unambiguously. We demonstrate the method on a circularly polarized volume coil and a loop coil tuned at 123.25 MHz in a 3 Tesla MRI scanner, with liquid phantoms. The volume coil measurement showed the axial component of the RF field, which is normally unmeasurable in MRI, away from the center of the coil. The measured RF vector field maps of both coils compared favorably with numerical simulation, with volumetric normalized root-mean-square difference in the range of 7~20%. While the proposed method cannot be applied to human imaging at present, applications to phantoms and small animals could provide a useful experimental tool to validate RF simulation and verify certain assumptions in [Formula: see text] map-based electrical properties tomography (EPT).

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.

Individualized SAR calculations using computer vision-based MR segmentation and a fast electromagnetic solver

PURPOSE

We propose a fast, patient-specific workflow for on-line specific absorption rate (SAR) supervision. An individualized electromagnetic model is created while the subject is on the table, followed by rapid SAR estimates for that individual. Our goal is an improved correspondence between the patient and model, reducing reliance on general anatomical body models.

METHODS

A 3D fat-water 3T acquisition (~2 minutes) is automatically segmented using a computer vision algorithm (~1 minute) into what we found to be the most important electromagnetic tissue classes: air, bone, fat, and soft tissues. We then compute the individual's EM field exposure and global and local SAR matrices using a fast electromagnetic integral equation solver. We assess the approach in 10 volunteers and compare to the SAR seen in a standard generic body model (Duke).

RESULTS

The on-the-table workflow averaged 7'44″. Simulation of the simplified Duke models confirmed that only air, bone, fat, and soft tissue classes are needed to estimate global and local SAR with an error of 6.7% and 2.7%, respectively, compared to the full model. In contrast, our volunteers showed a 16.0% and 20.3% population variability in global and local SAR, respectively, which was mostly underestimated by the Duke model.

CONCLUSION

Timely construction and deployment of a patient-specific model is computationally feasible. The benefit of resolving the population heterogeneity compared favorably to the modest modeling error incurred. This suggests that individualized SAR estimates can improve electromagnetic safety in MRI and possibly reduce conservative safety margins that account for patient-model mismatch, especially in non-standard patients.

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.

Transceive phase mapping using the PLANET method and its application for conductivity mapping in the brain

Purpose

To demonstrate feasibility of transceive phase mapping with the PLANET method and its application for conductivity reconstruction in the brain.

Methods

Accuracy and precision of transceive phase (ϕ^±) estimation with PLANET, an ellipse fitting approach to phase‐cycled balanced steady state free precession (bSSFP) data, were assessed with simulations and measurements and compared to standard bSSFP. Measurements were conducted on a homogeneous phantom and in the brain of healthy volunteers at 3 tesla. Conductivity maps were reconstructed with Helmholtz‐based electrical properties tomography. In measurements, PLANET was also compared to a reference technique for transceive phase mapping, i.e., spin echo.

Results

Accuracy and precision of ϕ^± estimated with PLANET depended on the chosen flip angle and TR. PLANET‐based ϕ^± was less sensitive to perturbations induced by off‐resonance effects and partial volume (e.g., white matter + myelin) than bSSFP‐based ϕ^±. For flip angle = 25° and TR = 4.6 ms, PLANET showed an accuracy comparable to that of reference spin echo but a higher precision than bSSFP and spin echo (factor of 2 and 3, respectively). The acquisition time for PLANET was ~5 min; 2 min faster than spin echo and 8 times slower than bSSFP. However, PLANET simultaneously reconstructed T₁, T₂, B₀ maps besides mapping ϕ^±. In the phantom, PLANET‐based conductivity matched the true value and had the smallest spread of the three methods. In vivo, PLANET‐based conductivity was similar to spin echo‐based conductivity.

Conclusion

Provided that appropriate sequence parameters are used, PLANET delivers accurate and precise ϕ^± maps, which can be used to reconstruct brain tissue conductivity while simultaneously recovering T₁, T₂, and B₀ maps.

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.

MRI-based, wireless determination of the transfer function of a linear implant: Introduction of the transfer matrix

PURPOSE

We introduce the transfer matrix (TM) that makes MR-based wireless determination of transfer functions (TFs) possible. TFs are implant specific measures for RF-safety assessment of linear implants. The TF relates an incident tangential electric field on an implant to a scattered electric field at its tip that generally governs local heating. The TM extends this concept and relates an incident tangential electric field to a current distribution in the implant therewith characterizing the RF response along the entire implant. The TM is exploited to measure TFs with MRI without hardware alterations.

THEORY AND METHODS

A model of rightward and leftward propagating attenuated waves undergoing multiple reflections is used to derive an analytical expression for the TM. This allows parameterization of the TM of generic implants, e.g., (partially) insulated single wires, in a homogeneous medium in a few unknowns that simultaneously describe the TF. These unknowns can be determined with MRI making it possible to measure the TM and, therefore, also the TF.

RESULTS

The TM is able to predict an induced current due to an incident electric field and can be accurately parameterized with a limited number of unknowns. Using this description the TF is determined accurately (with a Pearson correlation coefficient R ≥ 0.9 between measurements and simulations) from MRI acquisitions.

CONCLUSION

The TM enables measuring of TFs with MRI of the tested generic implant models. The MR-based method does not need hardware alterations and is wireless hence making TF determination in more realistic scenarios conceivable.

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.

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.

Parallel transmission for ultrahigh-field imaging

The development of MRI systems operating at or above 7 T has provided researchers with a new window into the human body, yielding improved imaging speed, resolution and signal-to-noise ratio. In order to fully realise the potential of ultrahigh-field MRI, a range of technical hurdles must be overcome. The non-uniformity of the transmit field is one of such issues, as it leads to non-uniform images with spatially varying contrast. Parallel transmission (i.e. the use of multiple independent transmission channels) provides previously unavailable degrees of freedom that allow full spatial and temporal control of the radiofrequency (RF) fields. This review discusses the many ways in which these degrees of freedom can be used, ranging from making more uniform transmit fields to the design of subject-tailored RF pulses for both uniform excitation and spatial selection, and also the control of the specific absorption rate. © 2015 The Authors. NMR in Biomedicine published by John Wiley & Sons Ltd.

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.

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.

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.

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.

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.

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.

Transmit and receive RF fields determination from a single low-tip-angle gradient-echo scan by scaling of SVD data

PURPOSE

A new method, called Transmit and Receive Patterns from Low-Tip-angle gradient-Echo Images (TRIPLET), is described which simultaneously maps the B1+ and B1- fields of a transmit/receive radiofrequency coil array. The input data are low-tip-angle gradient-echo images, which can be acquired in a relatively short scanning time.

THEORY AND METHODS

For each voxel in the field of view, a matrix can be assembled with the low-tip-angle gradient-echo image values of the radiofrequency coil array. Applying the singular value decomposition to those matrices, datasets are obtained which show a high resemblance with the true B1+ and B1- fields. These datasets are a voxel-wise scaled version of the true radiofrequency maps. The channel independent scaling parameters can be found by implicitly forcing the reconstructed fields to be solutions of the Maxwell equations. This is achieved by introducing a multipole expansion consisting of Bessel/Fourier functions.

RESULTS

Two FDTD simulated radiofrequency fields for two coil array combinations at 7 T and a measured, in vivo dataset at 7 T are investigated to illustrate the singular value decomposition analysis of the low-tip-angle gradient-echo images and to show how the B1+ and B1- fields can be reconstructed by Transmit and Receive Patterns from Low-Tip-angle gradient-Echo Images.

CONCLUSION

The Transmit and Receive Patterns from Low-Tip-angle gradient-Echo Images algorithm can convert the datasets from singular value decomposition analysis of low-tip-angle gradient-echo images to true B1+ and B1- fields.

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.

From complex B(1) mapping to local SAR estimation for human brain MR imaging using multi-channel transceiver coil at 7T

Elevated specific absorption rate (SAR) associated with increased main magnetic field strength remains a major safety concern in ultra-high-field (UHF) magnetic resonance imaging (MRI) applications. The calculation of local SAR requires the knowledge of the electric field induced by radio-frequency (RF) excitation, and the local electrical properties of tissues. Since electric field distribution cannot be directly mapped in conventional MR measurements, SAR estimation is usually performed using numerical model-based electromagnetic simulations which, however, are highly time consuming and cannot account for the specific anatomy and tissue properties of the subject undergoing a scan. In the present study, starting from the measurable RF magnetic fields (B1) in MRI, we conducted a series of mathematical deduction to estimate the local, voxel-wise and subject-specific SAR for each single coil element using a multi-channel transceiver array coil. We first evaluated the feasibility of this approach in numerical simulations including two different human head models. We further conducted experimental study in a physical phantom and in two human subjects at 7T using a multi-channel transceiver head coil. Accuracy of the results is discussed in the context of predicting local SAR in the human brain at UHF MRI using multi-channel RF transmission.

Recent progress and future challenges in MR electric properties tomography

MR Electric Properties Tomography (EPT) is a lately developed medical imaging modality capable of visualizing both conductivity and permittivity of the patient at the Larmor frequency using B 1 maps. The paper discusses the development of EPT reconstructions, EPT sequences, EPT experiments, and challenging issues of EPT.

Iterative separation of transmit and receive phase contributions and B1(+)-based estimation of the specific absorption rate for transmit arrays

OBJECT

The specific absorption rate (SAR) can be determined from radiofrequency transmit fields measured via magnetic resonance imaging.

MATERIALS AND METHODS

The proposed method estimates the SAR solely from the complex transmit field (B1(+)) by taking into account the particular properties of the electromagnetic field generated by an 8-channel transmit array. It is further based on an iterative consistency check between the measured B1(+) magnitude and an appropriate field estimate fulfilling Maxwell's equations. For testing the method, simulations and phantom experiments were performed for a multi-transmit array at 3T using a cylindrical phantom.

RESULTS

The method's robustness with respect to the assumptions made about electric tissue properties as well as its stability under different initial conditions regarding the signal phase was shown. A high sensitivity to signal noise was found. Robust reconstruction results were achieved including information from more than two transmit elements. The validity of the experimental results was confirmed by a qualitative comparison to simulated electromagnetic fields.

CONCLUSIONS

The method allows the determination of the SAR as well as the transmit phase of the individual channels of a multi-transmit array. With additional B0 inhomogeneity measurements, a reconstruction of the receive phase is feasible independent of the receive coil type in use.