Electrical Properties Tomography in the Human Brain at 1.5, 3, and 7T: A Comparison Study

A reusable 3D printed brain-like phantom for benchmarking electrical properties tomography reconstructions

PURPOSE

In MR electrical properties tomography (MR-EPT), electrical properties (EPs, conductivity and permittivity) are reconstructed from MR measurements. Phantom measurements are important to characterize the performance of MR-EPT reconstruction methods, since they allow knowledge of reference EPs values. To assess reconstruction methods in a more realistic scenario, it is important to test the methods using phantoms with realistic shapes, internal structures, and dielectric properties. In this work, we present a 3D printing procedure for the creation of realistic brain-like phantoms to benchmark MR-EPT reconstructions.

METHODS

We created two brain-like geometries with three different compartments using 3D printing. The first geometry was filled once, while the second geometry was filled three times with different saline-gelatin solutions, resulting in a total of four phantoms with different EPs. The saline solutions were characterized using a probe. 3D MR-EPT reconstructions were performed from MR measurements at 3T. The reconstructed conductivity values were compared to reference values of the saline-gelatin solutions. The measured fields were also compared to simulated fields using the same phantom geometry and electrical properties.

RESULTS

The measured fields were consistent with simulated fields. Reconstructed conductivity values were consistent with the reference (probe) conductivity values. This indicated the suitability of such phantoms for benchmarking MR-EPT reconstructions.

CONCLUSION

We presented a new workflow to 3D print realistic brain-like phantoms in an easy and affordable way. These phantoms are suitable to benchmark MR-EPT reconstructions, but can also be used for benchmarking other quantitative MR methods.

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

PURPOSE

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

METHODS

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

RESULTS

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

CONCLUSION

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

MR-based electrical property tomography using a physics-informed network at 3 and 7 T

Magnetic resonance electrical propert tomography promises to retrieve electrical properties (EPs) quantitatively and non-invasively in vivo, providing valuable information for tissue characterization and pathology diagnosis. However, its clinical implementation has been hindered by, for example, B1 measurement accuracy, reconstruction artifacts resulting from inaccuracies in underlying models, and stringent hardware/software requirements. To address these challenges, we present a novel approach aimed at accurate and high-resolution EPs reconstruction based on water content maps by using a physics-informed network (PIN-wEPT). The proposed method utilizes standard clinical protocols and conventional multi-channel receive arrays that have been routinely equipped in clinical settings, thus eliminating the need for specialized RF sequence/coil configurations. Compared with the original wEPT method, the network generates accurate water content maps that effectively eliminate the influence ofB → 1 + $$ {\overrightarrow{B}}_1^{+} $$ andB → 1 - $$ {\overrightarrow{B}}_1^{-} $$ by incorporating data mismatch with electrodynamic constraints derived from the Helmholtz equation. Subsequent regression analysis develops a broad relationship between water content and EPs across various types of brain tissue. A series of numerical simulations was conducted at 7 T to assess the feasibility and performance of the method, which encompassed four normal head models and models with tumorous tissues incorporated, and the results showed normalized mean square error below 1.0% in water content, below 11.7% in conductivity, and below 1.1% in permittivity reconstructions for normal brain tissues. Moreover, in vivo validations conducted over five healthy subjects at both 3 and 7 T showed reasonably good consistency with empirical EPs values across the white matter, gray matter, and cerebrospinal fluid. The PIN-wEPT method, with its demonstrated efficacy, flexibility, and compatibility with current MRI scanners, holds promising potential for future clinical application.

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

PURPOSE

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

METHODS

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

RESULTS

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

CONCLUSION

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

Fast high-resolution electric properties tomography using three-dimensional quantitative transient-state imaging-based water fraction estimation

In this study, we aimed to develop a fast and robust high-resolution technique for clinically feasible electrical properties tomography based on water content maps (wEPT) using Quantitative Transient-state Imaging (QTI), a multiparametric transient state-based method that is similar to MR fingerprinting. Compared with the original wEPT implementation based on standard spin-echo acquisition, QTI provides robust electrical properties quantification towards B1 + inhomogeneities and full quantitative relaxometry data. To validate the proposed approach, 3D QTI data of 12 healthy volunteers were acquired on a 1.5 T scanner. QTI-provided T1 maps were used to compute water content maps of the tissues using an empirical relationship based on literature ex-vivo measurements. Assuming that electrical properties are modulated mainly by tissue water content, the water content maps were used to derive electrical conductivity and relative permittivity maps. The proposed technique was compared with a conventional phase-only Helmholtz EPT (HH-EPT) acquisition both within whole white matter, gray matter, and cerebrospinal fluid masks, and within different white and gray matter subregions. In addition, QTI-based wEPT was retrospectively applied to four multiple sclerosis adolescent and adult patients, compared with conventional contrast-weighted imaging in terms of lesion delineation, and quantitatively assessed by measuring the variation of electrical properties in lesions. Results obtained with the proposed approach agreed well with theoretical predictions and previous in vivo findings in both white and gray matter. The reconstructed maps showed greater anatomical detail and lower variability compared with standard phase-only HH-EPT. The technique can potentially improve delineation of pathology when compared with conventional contrast-weighted imaging and was able to detect significant variations in lesions with respect to normal-appearing tissues. In conclusion, QTI can reliably measure conductivity and relative permittivity of brain tissues within a short scan time, opening the way to the study of electric properties in clinical settings.

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.

Use of machine learning to improve the estimation of conductivity and permittivity based on longitudinal relaxation time T1 in magnetic resonance at 7 T

Electrical property tomography (EPT) is a noninvasive method that uses magnetic resonance imaging (MRI) to estimate the conductivity and permittivity of tissues, and hence, can be used as a biomarker. One branch of EPT is based on the correlation of water and relaxation time T1 with the conductivity and permittivity of tissues. This correlation was applied to a curve-fitting function to estimate electrical properties, it was found to have a high correlation between permittivity and T1 however the computation of conductivity based on T1 requires to estimate the water content. In this study, we developed multiple phantoms with several ingredients that modify the conductivity and permittivity and explored the use of machine learning algorithms to have a direct estimation of conductivity and permittivity based on MR images and the relaxation time T1. To train the algorithms, each phantom was measured using a dielectric measurement device to acquire the true conductivity and permittivity. MR images were taken for each phantom, and the T1 values were measured. Then, the acquired data were tested using curve fitting, regression learning, and neural fit models to estimate the conductivity and permittivity values based on the T1 values. In particular, the regression learning algorithm based on Gaussian process regression showed high accuracy with a coefficient of determination R² of 0.96 and 0.99 for permittivity and conductivity, respectively. The estimation of permittivity using regression learning demonstrated a lower mean error of 0.66% compared to the curve fitting method, which resulted in a mean error of 3.6%. The estimation of conductivity also showed that the regression learning approach had a lower mean error of 0.49%, whereas the curve fitting method resulted in a mean error of 6%. The findings suggest that utilizing regression learning models, specifically Gaussian process regression, can result in more accurate estimations for both permittivity and conductivity compared to other methods.

Repeatability of brain phase-based magnetic resonance electric properties tomography methods and effect of compressed SENSE and RF shimming

Magnetic resonance electrical properties tomography (MREPT) is an emerging imaging modality to noninvasively measure tissue conductivity and permittivity. Implementation of MREPT in the clinic requires repeatable measurements at a short scan time and an appropriate protocol. The aim of this study was to investigate the repeatability of conductivity measurements using phase-based MREPT and the effects of compressed SENSE (CS), and RF shimming on the precision of conductivity measurements. Conductivity measurements using turbo spin echo (TSE) and three-dimensional balanced fast field echo (bFFE) with CS factors were repeatable. Conductivity measurement using bFFE phase showed smaller mean and variance that those measured by TSE. The conductivity measurements using bFFE showed minimal deviation with CS factors up to 8, with deviation increasing at CS factors > 8. Subcortical structures produced less consistent measurements than cortical parcellations at higher CS factors. RF shimming using full slice coverage 2D dual refocusing echo acquisition mode (DREAM) and full coverage 3D dual TR approaches further improved measurement precision. BFFE is a more optimal sequence than TSE for phase-based MREPT in brain. Depending on the area of the brain being measured, the scan can be safely accelerated with compressed SENSE without sacrifice of precision, offering the potential to employ MREPT in clinical research and applications. RF shimming with better field mapping further improves precision of the conductivity measures.

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.

Correlation analysis between the complex electrical permittivity and relaxation time of tissue mimicking phantoms in 7 T MRI

Dielectric relaxation theory describes the complex permittivity of a material in an alternating field; in particular, Debye theory relates the time it takes for an applied field to achieve the maximum polarization and the electrical properties of the material. Although, Debye’s equations were proposed for electrical polarization, in this study, we investigate the correlation between the magnetic longitudinal relaxation time T1 and the complex electrical permittivity of tissue-mimicking phantoms using a 7 T magnetic resonance scanner. We created phantoms that mimicked several human tissues with specific electrical properties. The electrical properties of the phantoms were measured using bench-test equipment. T1 values were acquired from phantoms using MRI. The measured values were fitted with functions based on dielectric estimations, using relaxation times of electrical polarization, and the mixture theory for dielectrics. The results show that, T1 and the real permittivity are correlated; therefore, the correlation can be approximated with a rational function in the case of water-based phantoms. The correlation between index loss and T1 was determined using a fitting function based on the Debye equation and mixture theory equation, in which the fraction of the materials was taken into account. This phantom study and analysis provide an insight into the application relaxation times used for estimating dielectric properties. Currently, the measurement of electrical properties based on dielectric relaxation theory is based on an antenna, sometimes invasive, that irradiates an electric field into a small sample; thus, it is not possible to create a map of electrical properties for a complex structure such as the human body. This study could be further used to compute the electrical properties maps of tissues by scanning images and measuring T1 maps.

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.

Interstitial Fluid Behavior and Diseases

Living things comprise a typical hierarchical and porous medium, and their most fundamental logical architectures are interstitial structures encapsulating parenchymal structures. The recent discovery of the efficient transport mechanisms of interstitial streams has provided a new understanding of these complex activities. The substance transport of interstitial streams follows mesoscopic fluid behavior dynamics, which is intimately associated with material transfer in nanoconfined spaces and a unique signal transmission. Accordingly, the evaluation of interstitial stream transport behavior at the mesoscopic scale is essential. In this review, recent advances in physical and chemical properties, the substance transport model, and the characterization methods of interstitial streams at the mesoscopic scale, as well as the relationships between interstitial streams and disease are summarized. Interstitial stream transport can be used as a basis to fully mine hierarchal behavior in images to expand imaging behavior into an omics field. By starting from the perspective of soft matter, a new understanding can be gained of health and disease and quantitative physical markers for research, clinical diagnosis, and treatment can be provided, as well as prognosis evaluation in complex diseases such as cancer and Alzheimer's disease. This will provide a foundation for the development of medicine of soft matter.

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.

Progress in Imaging the Human Torso at the Ultrahigh Fields of 7 and 10.5 T

Especially after the launch of 7 T, the ultrahigh magnetic field (UHF) imaging community achieved critically important strides in our understanding of the physics of radiofrequency interactions in the human body, which in turn has led to solutions for the challenges posed by such UHFs. As a result, the originally obtained poor image quality has progressed to the high-quality and high-resolution images obtained at 7 T and now at 10.5 T in the human torso. Despite these tremendous advances, work still remains to further improve the image quality and fully capitalize on the potential advantages UHF has to offer.

An insight into electrical resistivity of white matter and brain tumors

BACKGROUND

There is a lack of information regarding electrical properties of white matter and brain tumors.

OBJECTIVE

To investigate the feasibility of in-vivo measurement of electrical resistivity during brain surgery and establish a better understanding of the resistivity patterns of brain tumors in correlation to the white matter.

METHODS

A bipolar probe was used to measure electrical resistivity during surgery in a prospective cohort of patients with brain tumors. For impedance measurement, the probe applied a constant current of 0.7 μA with a frequency of 140 Hz. The measurement was performed in the white matter within and outside peritumoral edema as well as in non-enhancing, enhancing and necrotic tumor areas. Resistivity values expressed in ohmmeter (Ω∗m) were compared between different intracranial tissues and brain tumors.

RESULTS

Ninety-two patients (gliomas WHO II:16, WHO III:10, WHO IV:33, metastasis:33) were included. White matter outside peritumoral edema had higher resistivity values (13.3 ± 1.7 Ω∗m) than within peritumoral edema (8.5 ± 1.6 Ω∗m), and both had higher values than brain tumors including non-enhancing (WHO II:6.4 ± 1.3 Ω∗m, WHO III:6.3 ± 0.9 Ω∗m), enhancing (WHO IV:5 ± 1 Ω∗m, metastasis:5.4 ± 1.3 Ω∗m) and necrotic tumor areas (WHO IV:3.9 ± 1.1 Ω∗m, metastasis:4.3 ± 1.3 Ω∗m), p=<0.001. No difference was found between low-grade and anaplastic gliomas, p = 0.808, while resistivity values in both were higher than the highest values found in glioblastomas, p = 0.003 and p = 0.004, respectively.

CONCLUSIONS

The technique we applied enabled us to measure electrical resistivity of white matter and brain tumors in-vivo presumably with a significant effect with regard to dielectric polarization. Our results suggest that there are significant differences within different areas and subtypes of brain tumors and that white matter exhibits higher electrical resistivity than brain tumors.

High-frequency electrical properties tomography at 9.4T as a novel contrast mechanism for brain tumors

PURPOSE

To establish high-frequency magnetic resonance electrical properties tomography (MREPT) as a novel contrast mechanism for the assessment of glioblastomas using a rat brain tumor model.

METHODS

Six F98 intracranial tumor bearing rats were imaged longitudinally 8, 11 and 14 days after tumor cell inoculation. Conductivity and mean diffusivity maps were generated using MREPT and Diffusion Tensor Imaging. These maps were co-registered with T2 -weighted images and volumes of interests (VOIs) were segmented from the normal brain, ventricles, edema, viable tumor, tumor rim, and tumor core regions. Longitudinal changes in conductivity and mean diffusivity (MD) values were compared in these regions. A correlation analysis was also performed between conductivity and mean diffusivity values.

RESULTS

The conductivity of ventricles, edematous area and tumor regions (tumor rim, viable tumor, tumor core) was significantly higher (P < .01) compared to the contralateral cortex. The conductivity of the tumor increased over time while MD from the tumor did not change. A marginal positive correlation was noted between conductivity and MD values for tumor rim and viable tumor, whereas this correlation was negative for the tumor core.

CONCLUSION

We demonstrate a novel contrast mechanism based on ionic concentration and mobility, which may aid in providing complementary information to water diffusion in probing the microenvironment of brain tumors.

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.

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.

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.

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.

MRI-based transfer function determination through the transfer matrix by jointly fitting the incident and scattered B1+ field

PURPOSE

A purely experimental method for MRI-based transfer function (TF) determination is presented. A TF characterizes the potential for radiofrequency heating of a linear implant by relating the incident tangential electric field to a scattered electric field at its tip. We utilize the previously introduced transfer matrix (TM) to determine transfer functions solely from the MR measurable quantities, that is, the B 1 + and transceive phase distributions. This technique can extend the current practice of phantom-based TF assessment with dedicated experimental setup toward MR-based methods that have the potential to assess the TF in more realistic situations.

THEORY AND METHODS

An analytical description of the B 1 + magnitude and transceive phase distribution around a wire-like implant was derived based on the TM. In this model, the background field is described using a superposition of spherical and cylindrical harmonics while the transfer matrix is parameterized using a previously introduced attenuated wave model. This analytical description can be used to estimate the transfer matrix and transfer function based on the measured B 1 + distribution.

RESULTS

The TF was successfully determined for 2 mock-up implants: a 20-cm bare copper wire and a 20-cm insulated copper wire with 10 mm of insulation stripped at both endings in respectively 4 and 3 different trajectories. The measured TFs show a strong correlation with a reference determined from simulations and between the separate experiments with correlation coefficients above 0.96 between all TFs. Compared to the simulated TF, the maximum deviation in the estimated tip field is 9.4% and 12.2% for the bare and insulated wire, respectively.

CONCLUSIONS

A method has been developed to measure the TF of medical implants using MRI experiments. Jointly fitting the incident and scattered B 1 + distributions with an analytical description based on the transfer matrix enables accurate determination of the TF of 2 test implants. The presented method no longer needs input from simulated data and can therefore, in principle, be used to measure TF's in test animals or corpses.

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.

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.

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.

Evolution of UHF Body Imaging in the Human Torso at 7T: Technology, Applications, and Future Directions

The potential value of ultrahigh field (UHF) magnetic resonance imaging (MRI) and spectroscopy to biomedical research and in clinical applications drives the development of technologies to overcome its many challenges. The increased difficulties of imaging the human torso compared with the head include its overall size, the dimensions and location of its anatomic targets, the increased prevalence and magnitude of physiologic effects, the limited availability of tailored RF coils, and the necessary transmit chain hardware. Tackling these issues involves addressing notoriously inhomogeneous transmit B1 (B1) fields, limitations in peak B1, larger spatial variations of the static magnetic field B0, and patient safety issues related to implants and local RF power deposition. However, as research institutions and vendors continue to innovate, the potential gains are beginning to be realized. Solutions overcoming the unique challenges associated with imaging the human torso are reviewed as are current studies capitalizing on the benefits of UHF in several anatomies and applications. As the field progresses, strategies associated with the RF system architecture, calibration methods, RF pulse optimization, and power monitoring need to be further integrated into the MRI systems making what are currently complex processes more streamlined. Meanwhile, the UHF MRI community must seize the opportunity to build upon what have been so far proof of principle and feasibility studies and begin to further explore the true impact in both research and the clinic.

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.

Accuracy and precision of electrical permittivity mapping at 3T: the impact of three B 1 + mapping techniques

Purpose

To investigate the sequence‐specific impact of B1+ amplitude mapping on the accuracy and precision of permittivity reconstruction at 3T in the pelvic region.

Methods

B1+ maps obtained with actual flip angle imaging (AFI), Bloch–Siegert (BS), and dual refocusing echo acquisition mode (DREAM) sequences, set to a clinically feasible scan time of 5 minutes, were compared in terms of accuracy and precision with electromagnetic and Bloch simulations and MR measurements. Permittivity maps were reconstructed based on these B1+ maps with Helmholtz‐based electrical properties tomography. Accuracy and precision in permittivity were assessed. A 2‐compartment phantom with properties and size similar to the human pelvis was used for both simulations and measurements. Measurements were also performed on a female volunteer’s pelvis.

Results

Accuracy was evaluated with noiseless simulations on the phantom. The maximum B1+ bias relative to the true B1+ distribution was 1% for AFI and BS and 6% to 15% for DREAM. This caused an average permittivity bias relative to the true permittivity of 7% to 20% for AFI and BS and 12% to 35% for DREAM. Precision was assessed in MR experiments. The lowest standard deviation in permittivity, found in the phantom for BS, measured 22.4 relative units and corresponded to a standard deviation in B1+ of 0.2% of the B1+ average value. As regards B1+ precision, in vivo and phantom measurements were comparable.

Conclusions

Our simulation framework quantitatively predicts the different impact of B1+ mapping techniques on permittivity reconstruction and shows high sensitivity of permittivity reconstructions to sequence‐specific bias and noise perturbation in the B1+ map. These findings are supported by the experimental results.

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.

An MR technique for simultaneous quantitative imaging of water content, conductivity and susceptibility, with application to brain tumours using a 3T hybrid MR-PET scanner

Approaches for the quantitative mapping of water content, electrical conductivity and susceptibility have been developed independently. The purpose of this study is to develop a method for simultaneously acquiring quantitative water content, electrical conductivity and susceptibility maps based on a 2D multi-echo gradient echo sequence. Another purpose is to investigate the changes in these properties caused by brain tumours. This was done using a 3T hybrid magnetic resonance imaging and positron emission tomography (MR-PET) scanner. Water content maps were derived after performing T₂* and transmit-receive field bias corrections to magnitude images essentially reflecting only the H₂O content contrast. Phase evolution during the multi-echo train was used to generate field maps and derive quantitative susceptibility, while the conductivity maps were retrieved from the phase value at zero echo time. Performance of the method is demonstrated on phantoms and two healthy volunteers. In addition, the method was applied to three patients with brain tumours and a comparison to maps obtained from PET using O-(2-[18 F]fluoroethyl)-L-tyrosine and clinical MR images is presented. The combined information of the water content, conductivity and susceptibility may provide additional information about the tissue viability. Future studies can benefit from the evaluation of these contrasts with shortened acquisition times.

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.

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.

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.

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.

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

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

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

PURPOSE

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

METHODS

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

RESULTS

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

CONCLUSION

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

Error analysis of helmholtz-based MR-electrical properties tomography

PURPOSE

MR electrical properties tomography (MR-EPT) aims to measure tissue electrical properties by computing spatial derivatives of measured B1+ data. This computation is very sensitive to spatial fluctuations caused, for example, by noise and Gibbs ringing. In this work, the error arising from the computation of spatial derivatives using finite difference kernels (FD error) has been investigated. In relation to this FD error, it has also been investigated whether mitigation strategies such as Gibbs ringing correction and Gaussian apodization can be beneficial for conductivity reconstructions.

METHODS

Conductivity reconstructions were performed on a phantom (by means of simulations and MR measurements at 3T) and on a human brain model. The accuracy was evaluated as a function of image resolution, FD kernel size, k-space windowing, and signal-to-noise ratio. The impact of mitigation strategies was also investigated.

RESULTS

The adopted small FD kernel is highly sensitive to spatial fluctuations, whereas the large FD kernel is more noise-robust. However, large FD kernels lead to extended numerical boundary error propagation, which severely hampers the MR-EPT reconstruction accuracy for highly spatially convoluted tissue structures such as the human brain. Mitigation strategies slightly improve the accuracy of conductivity reconstructions. For the adopted derivative kernels and the investigated scenario, MR-EPT conductivity reconstructions show low accuracy: less than 37% of the voxels have a relative error lower than 30%.

CONCLUSION

The numerical error introduced by the computation of spatial derivatives using FD kernels is one of the major causes of limited accuracy in Helmholtz-based MR-EPT reconstructions. Magn Reson Med 80:90-100, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

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.

Noninvasive electrical conductivity measurement by MRI: a test of its validity and the electrical conductivity characteristics of glioma

OBJECTIVES

This study noninvasively examined the electrical conductivity (σ) characteristics of diffuse gliomas using MRI and tested its validity.

METHODS

MRI including a 3D steady-state free precession (3D SSFP) sequence was performed on 30 glioma patients. The σ maps were reconstructed from the phase images of the 3D SSFP sequence. The σ histogram metrics were extracted and compared among the contrast-enhanced (CET) and noncontrast-enhanced tumour components (NCET) and normal brain parenchyma (NP). Difference in tumour σ histogram metrics among tumour grades and correlation of σ metrics with tumour grades were tested. Validity of σ measurement using this technique was tested by correlating the mean tumour σ values measured using MRI with those measured ex vivo using a dielectric probe.

RESULTS

Several σ histogram metrics of CET and NCET of diffuse gliomas were significantly higher than NP (Bonferroni-corrected p ≤ .045). The maximum σ of NCET showed a moderate positive correlation with tumour grade (r = .571, Bonferroni-corrected p = .018). The mean tumour σ measured using MRI showed a moderate positive correlation with the σ measured ex vivo (r = .518, p = .040).

CONCLUSIONS

Tissue σ can be evaluated using MRI, incorporation of which may better characterise diffuse gliomas.

KEY POINTS

• This study tested the validity of noninvasive electrical conductivity measurements by MRI. • This study also evaluated the electrical conductivity characteristics of diffuse glioma. • Gliomas have higher electrical conductivity values than the normal brain parenchyma. • Noninvasive electrical conductivity measurement can be helpful for better characterisation of glioma.

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

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

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

PURPOSE

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

THEORY AND METHODS

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

RESULTS

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

CONCLUSION

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