Extraction of conductivity and permittivity using magnetic resonance imaging

Feasibility of undersampled spiral trajectories in MREPT for fast conductivity imaging

PURPOSE

To investigate spiral-based imaging including trajectories with undersampling as a fast and robust alternative for phase-based magnetic resonance electrical properties tomography (MREPT) techniques.

METHODS

Spiral trajectories with various undersampling ratios were prescribed to acquire images from an experimental phantom and a healthy volunteer at 3T. The non-Cartesian acquisitions were reconstructed using SPIRiT, and conductivity maps were derived using phase-based cr-MREPT. The resulting maps were compared between different sampling trajectories. Additionally, a conductivity map was obtained using a Cartesian balanced SSFP acquisition from the volunteer to comparatively demonstrate the robustness of the proposed method.

RESULTS

The phantom and volunteer results illustrate the benefits of the spiral acquisitions. Specifically, undersampled spiral acquisitions display improved robustness against field inhomogeneity artifacts and lowered SD values with shortened readout times. Furthermore, average of conductivity values measured for the cerebrospinal fluid with the spiral acquisitions were 1.703 S/m, indicating a close agreement with the theoretical values of 1.794 S/m.

CONCLUSION

A spiral-based acquisition framework for conductivity imaging with and without undersampling is presented. Overall, spiral-based acquisitions improved robustness against field inhomogeneity artifacts, while achieving whole head coverage with multiple averages in less than a minute.

Feasibility of Magnetic Resonance-Based Conductivity Imaging as a Tool to Estimate the Severity of Hypoxic-Ischemic Brain Injury in the First Hours After Cardiac Arrest

BACKGROUND

Early identification of the severity of hypoxic-ischemic brain injury (HIBI) after cardiac arrest can be used to help plan appropriate subsequent therapy. We evaluated whether conductivity of cerebral tissue measured using magnetic resonance-based conductivity imaging (MRCI), which provides contrast derived from the concentration and mobility of ions within the imaged tissue, can reflect the severity of HIBI in the early hours after cardiac arrest.

METHODS

Fourteen minipigs were resuscitated after 5 min or 12 min of untreated cardiac arrest. MRCI was performed at baseline and at 1 h and 3.5 h after return of spontaneous circulation (ROSC).

RESULTS

In both groups, the conductivity of cerebral tissue significantly increased at 1 h after ROSC compared with that at baseline (P = 0.031 and 0.016 in the 5-min and 12-min groups, respectively). The increase was greater in the 12-min group, resulting in significantly higher conductivity values in the 12-min group (P = 0.030). At 3.5 h after ROSC, the conductivity of cerebral tissue in the 12-min group remained increased (P = 0.022), whereas that in the 5-min group returned to its baseline level.

CONCLUSIONS

The conductivity of cerebral tissue was increased in the first hours after ROSC, and the increase was more prominent and lasted longer in the 12-min group than in the 5-min group. Our findings suggest the promising potential of MRCI as a tool to estimate the severity of HIBI in the early hours after cardiac arrest.

Editorial for "Problem Solving MRI to Reduce False-Positive Biopsy Related to Breast US: Conductivity vs. DWI vs. Abbreviated Contrast-Enhanced MRI"

Level of Evidence

5

Technical Efficacy Stage

3

Data-driven electrical conductivity brain imaging using 3 T MRI

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

Quantification of tissue property and perfusion uncertainties in hyperthermia treatment planning: Multianalysis using polynomial chaos expansion

INTRODUCTION

Hyperthermia treatment planning (HTP) tools can guide treatment delivery, particularly with locoregional radiative phased array systems. Uncertainties in tissue and perfusion property values presently lead to quantitative inaccuracy of HTP, leading to sub-optimal treatment. Assessment of these uncertainties would allow for better judgement of the reliability of treatment plans and improve their value for treatment guidance. However, systematically investigating the impact of all uncertainties on treatment plans is a complex, high-dimensional problem and too computationally expensive for traditional Monte Carlo approaches. This study aims to systematically quantify the treatment-plan impact of tissue property uncertainties by investigating their individual contribution to, and combined impact on predicted temperature distributions.

METHODS

A novel Polynomial Chaos Expansion (PCE)-based HTP uncertainty quantification was developed and applied for locoregional hyperthermia of modelled tumours in the pancreatic head, prostate, rectum, and cervix. Patient models were based on the Duke and Ella digital human models. Using Plan2Heat, treatment plans were created to optimise tumour temperature (represented by T90) for treatment using the Alba4D system. For all 25-34 modelled tissues, the impact of tissue property uncertainties was analysed individually i.e., electrical and thermal conductivity, permittivity, density, specific heat capacity and perfusion. Next, combined analyses were performed on the top 30 uncertainties with the largest impact.

RESULTS

Uncertainties in thermal conductivity and heat capacity were found to have negligible impact on the predicted temperature ( < 1 × 10-10 °C), density and permittivity uncertainties had a small impact (< 0.3 °C). Uncertainties in electrical conductivity and perfusion can lead to large variations in predicted temperature. However, variations in muscle properties result in the largest impact at locations that could limit treatment quality, with a standard deviation up to almost 6 °C (pancreas) and 3.5 °C (prostate) for perfusion and electrical conductivity, respectively. The combined influence of all significant uncertainties leads to large variations with a standard deviation up to 9.0, 3.6, 3.7 and 4.1 °C for the pancreatic, prostate, rectal and cervical cases, respectively.

CONCLUSION

Uncertainties in tissue and perfusion property values can have a large impact on predicted temperatures from hyperthermia treatment planning. PCE-based analysis helps to identify all major uncertainties, their impact and judge the reliability of treatment plans.

Field and Temperature Shaping for Microwave Hyperthermia: Recent Treatment Planning Tools to Enhance SAR-Based Procedures

The aim of the article is to provide a summary of the work carried out in the framework of a research project funded by the Italian Ministry of Research. The main goal of the activity was to introduce multiple tools for reliable, affordable, and high-performance microwave hyperthermia for cancer therapy. The proposed methodologies and approaches target microwave diagnostics, accurate in vivo electromagnetic parameters estimation, and improvement in treatment planning using a single device. This article provides an overview of the proposed and tested techniques and shows their complementarity and interconnection. To highlight the approach, we also present a novel combination of specific absorption rate optimization via convex programming with a temperature-based refinement method implemented to mitigate the effect of thermal boundary conditions on the final temperature map. To this purpose, numerical tests were carried out for both simple and anatomically detailed 3D scenarios for the head and neck region. These preliminary results show the potential of the combined technique and improvements in the temperature coverage of the tumor target with respect to the case wherein no refinement is adopted.

Technical note: Multi-receiver combination method for phase-based electrical property tomography of the breast

BACKGROUND

Phase-based electrical property tomography (EPT) is a technique that allows conductivity reconstruction with only phase of the B₁ field under the assumption that the magnitude of the B₁ fields are homogeneous. The more this assumption is violated, the less accurate the reconstructed conductivity. Thus, a method that ensures homogeneity of | B 1 - | $| {{\rm{B}}_1^ - } |$ field is important for breast image using multi-receiver coil.

PURPOSE

To develop a method for multi-receiver combination for phase-based EPT usable for breast EPT imaging in the clinic.

METHODS

Theory of the proposed method is presented. To validate the proposed method, the phantom and in-vivo experiments were conducted. Conductivity images were reconstructed using the transceive phase of the combined image and results were compared with another combination method.

RESULTS

The proposed method's conductivity results were more stable than those of the previous method when | B 1 + | $| {{\rm{B}}_1^ + } |$ was not homogeneous and when the homogeneous contrast region was small. The phantom and in-vivo results indicate that the proposed method produces improved conductivity images than the previous method. The proposed combination method also increased the conductivity contrast between benign and cancerous tissues.

CONCLUSION

The proposed method produced more stable multi-receiver combination for phase-based EPT of the breast in a clinical environment.

Physics Informed Neural Networks (PINN) for Low Snr Magnetic Resonance Electrical Properties Tomography (MREPT)

Electrical properties (EPs) of tissues facilitate early detection of cancerous tissues. Magnetic resonance electrical properties tomography (MREPT) is a technique to non-invasively probe the EPs of tissues from MRI measurements. Most MREPT methods rely on numerical differentiation (ND) to solve partial differential Equations (PDEs) to reconstruct the EPs. However, they are not practical for clinical data because ND is noise sensitive and the MRI measurements for MREPT are noisy in nature. Recently, Physics informed neural networks (PINNs) have been introduced to solve PDEs by substituting ND with automatic differentiation (AD). To the best of our knowledge, it has not been applied to MREPT due to the challenges in using PINN on MREPT as (i) a PINN requires part of ground-truth EPs as collocation points to optimize the network's AD, (ii) the noisy input data disrupts the optimization of PINNs despite the noise-filtering nature of NNs and additional denoising processes. In this work, we propose a PINN-MREPT model based on a canonical analytic MREPT model. A reference padding layer with known EPs was added to surround the region of interest for providing additive collocation points. Moreover, an optimizable diffusion coefficient was embedded in the analytic MREPT model used in the PINN-MREPT. The noise robustness of the proposed PINN-MREPT for single-sample reconstruction was tested by using numerical phantoms of human brain with extra tumor-like tissues at different noise levels. The results of numerical experiments show that PINN-MREPT outperforms two typical numerical MREPT methods in terms of reconstruction accuracy, sensitivity to the extra tissues, and the correlations of line profiles in the regions of interest. The advantage of the PINN-MREPT is shown by the results of an experiment on phantom measurement, too. Moreover, it is found that the diffusion term plays an important role to achieve a noise-robust PINN-MREPT. This is an important step moving forward to a clinical application of MREPT.

Application of High-Frequency Conductivity Map Using MRI to Evaluate It in the Brain of Alzheimer's Disease Patients

Background

The previous studies reported increased concentrations of metallic ions, imbalanced Na+ and K+ ions, and the increased mobility of protons by microstructural disruptions in Alzheimer's disease (AD).

Purpose

(1) to apply a high-frequency conductivity (HFC) mapping technique using a clinical 3T MRI system, (2) compare HFC values in the brains of participants with AD, amnestic mild cognitive impairment (MCI), and cognitively normal (CN) elderly people, (3) evaluate the relationship between HFC values and cognitive decline, and (4) explore usefulness of HFC values as an imaging biomarker to evaluate the differentiation of AD from CN.

Materials and Methods

This prospective study included 74 participants (23 AD patients, 27 amnestic MCI patients, and 24 CN elderly people) to explore the clinical application of HFC mapping in the brain from March 2019 to August 2021. We performed statistical analyses to compare HFC maps between the three participant groups, evaluate the association of HFC maps with Mini-Mental State Examination (MMSE) scores, and to evaluate the differentiation between the participant groups for HFC values for some brain areas.

Results

We obtained a good HFC map non-invasively. The HFC value was higher in the AD group than in the CN and MCI groups. MMSE scores were negatively associated with HFC values. Age was positively associated with HFC values. The HFC value in the insula has a high area under the receiver operating characteristic (ROC) curve (AUC) value to differentiate AD patients from the CN participants (Sensitivity [SE] = 82, Specificity [SP] =97, AUC = 0.902, p < 0.0001), better than gray matter volume (GMV) in hippocampus (SE = 79, SP = 83, AUC = 0.880, p < 0.0001). The classification for differentiating AD from CN was highest by adding the hippocampal GMV to the insular HFC value (SE = 87, SP = 87, AUC = 0.928, p < 0.0001).

Conclusion

High-frequency conductivity values were significantly increased in the AD group compared to the CN group and increased with age and disease severity. HFC values of the insula along with the GMV of the hippocampus can be used as an imaging biomarker to improve the differentiation of AD from CN.

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.

Physics-Coupled Neural Network Magnetic Resonance Electrical Property Tomography (MREPT) for Conductivity Reconstruction

The electrical property (EP) of human tissues is a quantitative biomarker that facilitates early diagnosis of cancerous tissues. Magnetic resonance electrical properties tomography (MREPT) is an imaging modality that reconstructs EPs by the radio-frequency field in an MRI system. MREPT reconstructs EPs by solving analytic models numerically based on Maxwell's equations. Most MREPT methods suffer from artifacts caused by inaccuracy of the hypotheses behind the models, and/or numerical errors. These artifacts can be mitigated by adding coefficients to stabilize the models, however, the selection of such coefficient has been empirical, which limit its medical application. Alternatively, end-to-end Neural networks-based MREPT (NN-MREPT) learns to reconstruct the EPs from training samples, circumventing Maxwell's equations. However, due to its pattern-matching nature, it is difficult for NN-MREPT to produce accurate reconstructions for new samples. In this work, we proposed a physics-coupled NN for MREPT (PCNN-MREPT), in which an analytic model, cr-MREPT, works with diffusion and convection coefficients, learned by NNs from the difference between the reconstructed and ground-truth EPs to reduce artifacts. With two simulated datasets, three generalization experiments in which test samples deviate gradually from the training samples, and one noise-robustness experiment were conducted. The results show that the proposed PCNN-MREPT achieves higher accuracy than two representative analytic methods. Moreover, compared with an end-to-end NN-MREPT, the proposed method attained higher accuracy in two critical generalization tests. This is an important step to practical MREPT medical diagnoses.

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

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

In vivo electrical conductivity measurement of muscle, cartilage, and peripheral nerve around knee joint using MR-electrical properties tomography

This study aimed to investigate whether in vivo MR-electrical properties tomography (MR-EPT) is feasible in musculoskeletal tissues by evaluating the conductivity of muscle, cartilage, and peripheral nerve around the knee joint, and to explore whether these measurements change after exercise. This prospective study was approved by the institutional review board. On February 2020, ten healthy volunteers provided written informed consent and underwent MRI of the right knee using a three-dimensional balanced steady-state free precession (bSSFP) sequence. To test the effect of loading, the subjects performed 60 squatting exercises after baseline MRI, immediately followed by post-exercise MRI with the same sequences. After reconstruction of conductivity map based on the bSSFP sequence, conductivity of muscles, cartilages, and nerves were measured. Measurements between the baseline and post-exercise MRI were compared using the paired t-test. Test–retest reliability for baseline conductivity was evaluated using the intraclass correlation coefficient. The baseline and post-exercise conductivity values (mean ± standard deviation) [S/m] of muscles, cartilages, and nerves were 1.73 ± 0.40 and 1.82 ± 0.50 (p = 0.048), 2.29 ± 0.47 and 2.51 ± 0.37 (p = 0.006), and 2.35 ± 0.57 and 2.36 ± 0.57 (p = 0.927), respectively. Intraclass correlation coefficient for the baseline conductivity of muscles, cartilages, and nerves were 0.89, 0.67, and 0.89, respectively. In conclusion, in vivo conductivity measurement of musculoskeletal tissues is feasible using MR-EPT. Conductivity of muscles and cartilages significantly changed with an overall increase after exercise.

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

Purpose

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

Methods

A Carr‐Purcell (CP) echo train generates pronounced flip‐angle dependent oscillations that can be used to estimate the magnitude of B₁⁺. To this end, a dictionary is used that takes into account the slice profile as well as T₂ relaxation along the echo train. For validation, the retrieved B₁⁺ map is compared with the actual flip angle imaging (AFI) method in a phantom (79 ε₀, 0.34 S/m). Moreover, the phase of the first echo reflects the transceive phase. Overall, the CP echo train yields an estimate of the complex‐valued B₁⁺, allowing electrical properties tomography with both permittivity and conductivity. The presented method is evaluated in phantom scans as well as for in vivo brain at 3 T.

Results

In the phantom, the obtained magnitude B₁⁺ maps retrieved from the CP echo train and the AFI method show excellent agreement, and both the reconstructed estimated permittivity (79 ± 3) ε₀ and conductivity (0.35 ± 0.04) S/m values are in accordance with expectations. In the brain, the obtained electrical properties are also close to expectations. In addition to the retrieved complex B₁⁺ information, the decay of the CP echo trains also yields an estimate for T₂.

Conclusion

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

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.

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

PURPOSE

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

METHODS

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

RESULTS

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

CONCLUSION

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

Transceive phase corrected 2D contrast source inversion-electrical properties tomography

PURPOSE

To remove the necessity of the tranceive phase assumption for CSI-EPT and show electrical properties maps reconstructed from measured data obtained using a standard 3T birdcage body coil setup.

METHODS

The existing CSI-EPT algorithm is reformulated to use the transceive phase rather than relying on the transceive phase assumption. Furthermore, the radio frequency (RF)-shield is numerically implemented to accurately model the RF fields inside the MRI scanner. We verify that the reformulated two-dimensional (2D) CSI-EPT algorithm can reconstruct electrical properties maps given 2D electromagnetic simulations. Afterward, the algorithm is tested with three-dimensional (3D) FDTD simulations to investigate if the 2D CSI-EPT can retrieve the electrical properties for 3D RF fields. Finally, an MR experiment at 3T with a phantom is performed.

RESULTS

From the results of the 2D simulations, it is seen that CSI-EPT can reconstruct the electrical properties using MRI accessible quantities. For 3D simulations, it is observed that the electrical properties are underestimated, nonetheless, CSI-EPT has a lower standard deviation than the standard Helmholtz based methods. Finally, the first CSI-EPT reconstructions based on measured data are presented showing comparable accuracy and precision to reconstructions based on simulated data, and demonstrating the feasibility of CSI-EPT.

CONCLUSIONS

The CSI-EPT algorithm was rewritten to use MRI accessible quantities. This allows for CSI-EPT to fully exploit the benefits of the higher static magnetic field strengths with a standard quadrature birdcage coil setup.

Silent zero TE MR neuroimaging: Current state-of-the-art and future directions

Magnetic Resonance Imaging (MRI) scanners produce loud acoustic noise originating from vibrational Lorentz forces induced by rapidly changing currents in the magnetic field gradient coils. Using zero echo time (ZTE) MRI pulse sequences, gradient switching can be reduced to a minimum, which enables near silent operation.Besides silent MRI, ZTE offers further interesting characteristics, including a nominal echo time of TE = 0 (thus capturing short-lived signals from MR tissues which are otherwise MR-invisible), 3D radial sampling (providing motion robustness), and ultra-short repetition times (providing fast and efficient scanning).In this work we describe the main concepts behind ZTE imaging with a focus on conceptual understanding of the imaging sequences, relevant acquisition parameters, commonly observed image artefacts, and image contrasts. We will further describe a range of methods for anatomical and functional neuroimaging, together with recommendations for successful implementation.

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.

Reliable Method for Fabricating Tissue-Mimicking Materials With Designated Relative Permittivity and Conductivity at 128 MHz

Artificial materials that can simultaneously mimic the relative permittivity and conductivity of various human tissues are usually used in medical applications. However, the method of precisely designing these materials with designated values of both relative permittivity and conductivity at 3 T MRI resonance frequency is lacking. In this study, a reliable method is established to determine the compositions of artificial dielectric materials with designated relative permittivity and conductivity at 128 MHz. Sixty dielectric materials were produced using oil, sodium chloride, gelatin, and deionized water as the main raw materials. The dielectric properties of these dielectric materials were measured using the open-ended coaxial line method at 128 MHz. Nonlinear least-squares Marquardt-Levenberg algorithm was used to obtain the formula, establishing the relationship between the compositions of the dielectric materials and their dielectric properties at 128 MHz. The dielectric properties of the blood, gall bladder, muscle, skin, lung, and bone at 128 MHz were selected to verify the reliability of the obtained formula. For the obtained formula, the coefficient of determination and the expanded uncertainties with a coverage factor of k = 2 were 0.991% and 4.9% for relative permittivity and 0.992% and 6.4% for conductivity. For the obtained artificial materials measured using the open-ended coaxial line method, the maximal difference of relative permittivity and conductivity were 1.0 and 0.02 S/m, respectively, with respect to the designated values. In conclusion, the compositions of tissue-mimicking material can be quickly determined after the establishment of the formulas with the expanded uncertainties of less than 10%. Bioelectromagnetics. 2021;42:86-94. © 2020 Bioelectromagnetics Society.

Configuration-based electrical properties tomography

PURPOSE

To introduce phase-based conductivity mapping from a configuration space analysis.

METHODS

The frequency response function of balanced SSFP (bSSFP) is used to perform a configuration space analysis. It is shown that the transceive phase for conductivity mapping can be directly obtained by a simple fast Fourier transform of a series of phase-cycled bSSFP scans. For validation, transceive phase and off-resonance mapping with fast Fourier transform is compared with phase estimation using a recently proposed method, termed PLANET. Experiments were performed in phantoms and for in vivo brain imaging at 3 T using a quadrature head coil.

RESULTS

For fast Fourier transform, aliasing can lead to systematic phase errors. This bias, however, decreases rapidly with increasing sampling points. Interestingly, Monte Carlo simulations revealed a lower uncertainty for the transceive phase and the off-resonance using fast Fourier transform as compared with PLANET. Both methods, however, essentially retrieve the same phase information from a set of phase-cycled bSSFP scans. As a result, configuration-based conductivity mapping was successfully performed using eight phase-cycled bSSFP scans in the phantoms and for brain tissues. Overall, the retrieved values were in good agreement with expectations. Conductivity estimation and mapping of the field inhomogeneities can therefore be performed in conjunction with the estimation of other quantitative parameters, such as relaxation, using configuration theory.

CONCLUSIONS

Phase-based conductivity mapping can be estimated directly from a simple Fourier analysis, such as in conjunction with relaxometry, using a series of phase-cycled bSSFP scans.

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.

Deep Learning-Based Development of Personalized Human Head Model With Non-Uniform Conductivity for Brain Stimulation

Electromagnetic stimulation of the human brain is a key tool for neurophysiological characterization and the diagnosis of several neurological disorders. Transcranial magnetic stimulation (TMS) is a commonly used clinical procedure. However, personalized TMS requires a pipeline for individual head model generation to provide target-specific stimulation. This process includes intensive segmentation of several head tissues based on magnetic resonance imaging (MRI), which has significant potential for segmentation error, especially for low-contrast tissues. Additionally, a uniform electrical conductivity is assigned to each tissue in the model, which is an unrealistic assumption based on conventional volume conductor modeling. This study proposes a novel approach for fast and automatic estimation of the electric conductivity in the human head for volume conductor models without anatomical segmentation. A convolutional neural network is designed to estimate personalized electrical conductivity values based on anatomical information obtained from T1- and T2-weighted MRI scans. This approach can avoid the time-consuming process of tissue segmentation and maximize the advantages of position-dependent conductivity assignment based on the water content values estimated from MRI intensity values. The computational results of the proposed approach provide similar but smoother electric field distributions of the brain than that provided by conventional approaches.

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.

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

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

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

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

Variation in Reported Human Head Tissue Electrical Conductivity Values

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

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

OBJECTIVE

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

METHODS

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

RESULTS

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

CONCLUSION

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

SIGNIFICANCE

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

Developments in Electrical-Property Tomography Based on the Contrast-Source Inversion Method

The main objective of electrical-property tomography (EPT) is to retrieve dielectric tissue parameters from B ^ 1 + data as measured by a magnetic-resonance (MR) scanner. This is a so-called hybrid inverse problem in which data are defined inside the reconstruction domain of interest. In this paper, we discuss recent and new developments in EPT based on the contrast-source inversion (CSI) method. After a short review of the basics of this method, two- and three-dimensional implementations of CSI-EPT are presented along with a very efficient variant of 2D CSI-EPT called first-order induced current EPT (foIC-EPT). Practical implementation issues that arise when applying the method to measured data are addressed as well, and the limitations of a two-dimensional approach are extensively discussed. Tissue-parameter reconstructions of an anatomically correct male head model illustrate the performance of two- and three-dimensional CSI-EPT. We show that 2D implementation only produces reliable reconstructions under very special circumstances, while accurate reconstructions can be obtained with 3D CSI-EPT.

Use of dielectric padding to eliminate low convective field artifact in cr-MREPT conductivity images

PURPOSE

Convection-reaction equation-based magnetic resonance electrical properties tomography (cr-MREPT) provides conductivity images that are boundary artifact-free and robust against noise. However, these images suffer from the low convective field (LCF) artifact. We propose to use dielectric pads to alter the transmit magnetic field (B₁ ⁺ ), shift the LCF region, and eliminate the LCF artifact.

METHODS

Computer simulations were conducted to analyze the effects of pad electrical properties, pad thickness, pad height, arc angle, and thickness of the pad-object gap. In 3T MR experiments, water pads and BaTiO₃ pads were used with agar-saline phantoms. Two data sets (e.g., with the pad located on the left or on the right of the object [phantom]) were acquired, and the corresponding linear systems were simultaneously solved to get LCF artifact-free conductivity images.

RESULTS

A pad needed to have 180° arc angle and the same height with the phantom for maximum benefit. Increasing the pad thickness and/or the relative permittivity of the pad increased the LCF shift, whereas excessive amounts of these parameters caused errors in conductivity reconstructions because the effect of neglected B_z terms became noticeable. Conductivity of the pad, on the other hand, had minimal effect on elimination of the LCF artifact. Combining 2 data sets (i.e., with 2 different dielectric pad positions) resulted in more accurate conductivity maps (low L² -errors) as opposed to no pad or single pad cases in experiments and simulations.

CONCLUSIONS

Using the proposed technique, LCF artifact is significantly removed, and the reconstructed conductivity values are improved.

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.

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

PURPOSE

Balanced steady-state free precession (bSSFP) sequence is widely used because of its high SNR and high speed. However, bSSFP images suffer from "banding artifact" caused by B₀ inhomogeneity. In this article, we propose a method to remove this artifact in bSSFP phase images and investigate the usage of the corrected phase images in phase-based magnetic resonance electrical properties tomography (MREPT).

THEORY AND METHODS

Two bSSFP phase images, obtained with different excitation frequencies, are collaged to get rid of the regions containing banding artifacts. Phase of the collaged bSSFP image is the sum of the transceive phase of the RF system and an error term that depends on B₀ and T₂ . By using B₀ and T₂ maps, this error is eliminated from bSSFP phase images by using pixel-wise corrections. Conductivity maps are obtained from the uncorrected and the corrected phase images using the phase-based cr-MREPT method.

RESULTS

Phantom and human experiment results of the proposed method are illustrated for both phase images and conductivity maps. It is shown that uncorrected phase images yield unacceptable conductivity images. When only B₀ information is used for phase correction conductivity, reconstructions are substantially improved, and yet T₂ information is still needed to fully recover accurate and undistorted conductivity images.

CONCLUSIONS

With the proposed technique, B₀ sensitivity of the bSSFP phase images can be removed by using B₀ and T₂ maps. It is also shown that corrected bSSFP phase images are of sufficient quality to be used in conductivity imaging.

Electrical properties tomography: Available contrast and reconstruction capabilities

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

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

PURPOSE

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

THEORY AND METHODS

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

RESULTS

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

CONCLUSION

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

Dictionary-based electric properties tomography

PURPOSE

To develop and validate a new algorithm called "dictionary-based electric properties tomography" (dbEPT) for deriving tissue electric properties from measured B₁ maps.

METHODS

Inspired by Magnetic Resonance fingerprinting, dbEPT uses a dictionary of local patterns ("atoms") of B₁ maps and corresponding electric properties distributions, derived from electromagnetic field simulations. For reconstruction, a pattern from a measured B₁ map is compared with the B₁ atoms of the dictionary. The B₁ atom showing the best match with the measured B₁ pattern yields the optimum electric properties pattern that is chosen for reconstruction. Matching was performed through machine learning algorithms. Two dictionaries, using transmit and transceive phases, were evaluated. The spatial distribution of local matching distance between optimal atom and measured pattern yielded a reconstruction reliability map. The method was applied to reconstruct conductivity of 4 volunteers' brains. A conventional, Helmholtz-based Electric properties tomography (EPT) reconstruction was performed for reference. Noise performance was studied through phantom simulations.

RESULTS

Quantitative values of conductivity agree with literature values. Results of the 2 dictionaries exhibit only minor differences. Somewhat larger differences are visible between dbEPT and Helmholtz-based EPT. Quantified by the correlation between conductivity and anatomic images, dbEPT depicts brain details more clearly than Helmholtz-based EPT. Matching distance is minimal in homogeneous brain ventricles and increases with tissue heterogeneity. Central processing unit time was approximately 2 minutes per dictionary training and 3 minutes per brain conductivity reconstruction using standard hardware equipment.

CONCLUSION

A new, dictionary-based approach for reconstructing electric properties is presented. Its conductivity reconstruction is able to overcome the EPT transceive-phase problem.

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.

3-D Contrast Source Inversion-Electrical Properties Tomography

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

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.