Electric properties tomography: Biochemical, physical and technical background, evaluation and clinical applications

Investigation of electrical conductivity changes during brain functional activity in 3T MRI

Blood oxygenation level-dependent functional magnetic resonance imaging (fMRI) is widely used to visualize brain activation regions by detecting hemodynamic responses associated with increased metabolic demand. Although alternative MRI methods have been employed to monitor functional activities, the investigation of in-vivo electrical property changes during brain function remains limited. In this study, the relationship between fMRI signals and electrical conductivity (measured at the Larmor frequency) changes was explored using phase-based electrical property tomography. Results revealed consistent patterns: conductivity changes showed negative correlations, with conductivity decreasing in functionally active regions whereas B1 phase mapping exhibited positive correlations around the activation regions. These observations were consistent across the motor and visual cortex activations To further substantiate these findings, electromagnetic radio-frequency simulations that modeled activation states with varying conductivities were conducted, demonstrating trends similar to in-vivo results for B1 phase and conductivity. Notably, we observed that false-positive activation signals could occur depending on the level of noise and the reconstruction method applied. These findings suggested that in-vivo electrical conductivity changes can indeed be measured during brain activity. However, further investigation is needed to fully understand the underlying mechanisms driving these measurements.

Gadolinium based contrast agent induced electrical conductivity heterogeneity analysis in the brain of Alzheimer's disease

Magnetic resonance imaging (MRI) often uses gadolinium-based contrast agents (GBCAs) to improve the characterization of imaging contrast, owing to their strong paramagnetic properties. Magnetic resonance electrical properties tomography (MREPT) visualizes the conductivity distribution of biological tissues at the Larmor frequency using the [Formula: see text] field phase signal. In this paper, we investigate the effect of GBCA on brain conductivity. To compare the differences of reconstructed noisy conductivity maps before and after the GBCA injection, we propose a method to remove the background low-frequency noise artifact based on an elliptic partial differential equation. By analyzing the relationship between electrical conductivity and magnetic permeability, the objective of this study is to develop a cost-effective and accessible initial screening imaging tool for diagnosing and monitoring the treatment of Alzheimer's disease (AD) pathophysiology. To investigate vascular damage in AD, we define a conductivity heterogeneity volume fraction (CHVF) caused by GBCA leakage. Using CHVF, we develop three indices to characterize mild cognitive impairment (MCI) and AD. To verify the proposed method, we studied a total of 42 participants, including 14 individuals diagnosed with AD, 18 participants with MCI, and 10 cognitively normal (CN) participants. Finally, we designed a radar chart informed by the CHVF analysis, to exhibit the pertinent parameters for MCI and AD patients, facilitating the evaluation and ongoing monitoring of each patient's diagnosis and treatment regimen.

Effect of Ethanol on Brain Electrical Tissue Conductivity in Social Drinkers

BACKGROUND

How the biophysics of electrical conductivity measures relate to brain activity is poorly understood. The sedative, ethanol, reduces metabolic activity but its impact on brain electrical conductivity is unknown.

PURPOSE

To investigate whether ethanol reduces brain electrical tissue conductivity.

STUDY TYPE

Prospective.

SUBJECTS

Fifty-two healthy volunteers (aged 18-37 years, 22 females, 30 males).

FIELD STRENGTH/SEQUENCE

3 T, T1-weighted, multi-shot, turbo-field echo (TFE); 3D balanced fast-field echo (bFFE).

ASSESSMENT

Brain gray and white matter tissue conductivity measured with phase-based magnetic resonance electrical properties tomography (MREPT) compared before and 20 minutes after ethanol consumption (0.7 g/kg body weight). Differential conductivity whole brain maps were generated for three subgroups: those with strong ( ∆ σ max  > 0.1 S/m; N = 33), weak (0.02 S/m ≤  ∆ σ max  ≤ 0.1 S/m; N = 9) conductivity decrease, and no significant response ( ∆ σ max  < 0.02 S/m, N = 10). Maps were compared in the strong response group where breath alcohol rose between scans, vs. those where it fell.

STATISTICAL TESTS

Average breath alcohol levels were compared to the differential conductivity maps using linear regression. T-maps were generated (threshold P < 0.05 and P < 0.001; minimum cluster 48 mm3). Differential conductivity maps were compared with ANOVA.

RESULTS

Whole-group analysis showed decreased conductivity that did not survive statistical thresholding. Strong responders (N = 33) showed a consistent pattern of significantly decreased conductivity ( ∆ σ max  > 0.1 S/m) in frontal/occipital and cerebellar white matter. The weak response group (N = 9) showed a similar pattern of conductivity decrease (0.02 S/m ≤  ∆ σ max  ≤ 0.1 S/m). There was no significant relationship with breath alcohol levels, alcohol use, age, ethnicity, or sex. The strong responders' regional response was different between ascending (N = 12) or descending (N = 20) alcohol during the scan.

DATA CONCLUSION

Ethanol reduces brain tissue conductivity in a participant-dependent and spatially dependent fashion.

EVIDENCE LEVEL

1 TECHNICAL EFFICACY: Stage 2.

A joint three-plane physics-constrained deep learning based polynomial fitting approach for MR electrical properties tomography

Magnetic resonance electrical properties tomography can extract the electrical properties of in-vivo tissue. To estimate tissue electrical properties, various reconstruction algorithms have been proposed. However, physics-based reconstructions are prone to various artifacts such as noise amplification and boundary artifact. Deep learning-based approaches are robust to these artifacts but need extensive training datasets and suffer from generalization to unseen data. To address these issues, we introduce a joint three-plane physics-constrained deep learning framework for polynomial fitting MR-EPT by merging physics-based weighted polynomial fitting with deep learning. Within this framework, deep learning is used to discern the optimal polynomial fitting weights for a physics based polynomial fitting reconstruction on the complex B1+ data. For the prediction of optimal fitting coefficients, three neural networks were separately trained on simulated heterogeneous brain models to predict optimal polynomial weighting parameters in three orthogonal planes. Then, the network weights were jointly optimized to estimate the polynomial weights in each plane for a combined conductivity reconstruction. Based on this physics-constrained deep learning approach, we achieved an improvement of conductivity estimation accuracy in comparison to a single plane estimation and a reduction of computational load. The results demonstrate that the proposed method based on 3D data exhibits superior performance in comparison to conventional polynomial fitting methods in terms of capturing anatomical detail and homogeneity. Crucially, in-vivo application of the proposed method showed that the method generalizes well to in-vivo data, without introducing significant errors or artifacts. This generalization makes the presented method a promising candidate for use in clinical applications.

Robust stochastic optimisation strategies for locoregional hyperthermia treatment planning using polynomial chaos expansion

Objective.Conventional temperature optimization in hyperthermia treatment planning aims to maximize tumour temperature (e.g.T90; the temperature reached in at least 90% of the tumour) while enforcing hard constraints on normal tissue temperature (max(Ttissue) ⩽45 °C). This method generally incorrectly assumes that tissue/perfusion properties are known, typically relying on average values from the literature. To enhance the reliability of temperature optimization in clinical applications, we developed new robust optimization strategies to reduce the impact of tissue/perfusion property uncertainties.Approach.Within the software package Plan2Heat, temperature calculations during optimization apply efficient superposition of precomputed distributions, represented by a temperature matrix (T-matrix). We extended this method using stochastic polynomial chaos expansion models to compute an averageT-matrix (Tavg) and a covariance matrixCto account for uncertainties in tissue/perfusion properties. Three new strategies were implemented usingTavgandCduring optimization: (1)Tavg90 maximization, hard constraint on max(Ttissue), (2)Tavg90 maximization, hard constraint on max(Ttissue) variation, and (3) combinedTavg90 maximization and variation minimization, hard constraint on max(Ttissue). Conventional and new optimization strategies were tested in a cervical cancer patient. 100 test cases were generated, randomly sampling tissue-property probability distributions. TumourT90 and hot spots (max(Ttissue) >45 °C) were evaluated for each sample.Main Results.Conventional optimization had 28 samples without hot spots, with a medianT90 of 39.7 °C. For strategies (1), (2) and (3), the number of samples without hot spots was increased to 33, 41 and 36, respectively. MedianT90 was reduced lightly, by ∼0.1 °C-0.3 °C, for strategies (1-3). Tissue volumes exceeding 45 °C and variation in max(Ttissue) were less for the novel strategies.Significance.Optimization strategies that account for tissue-property uncertainties demonstrated fewer, and reduced in volume, normal tissue hot spots, with only a marginal reduction in tumourT90. This implies a potential clinical utility in reducing the need for, or the impact of, device setting adjustments during hyperthermia treatment.

Functional MRI study with conductivity signal changes during visual stimulation

BACKGROUND

Although blood oxygen level-dependent (BOLD) functional MRI (fMRI) is a standard method, major BOLD signals primarily originate from intravascular sources. Magnetic resonance electrical properties tomography (MREPT)-based fMRI signals may provide additional insights into electrical activity caused by alterations in ion concentrations and mobilities.

PURPOSE

This study aimed to investigate the neuronal response of conductivity during visual stimulation and compare it with BOLD.

MATERIALS AND METHODS

A total of 30 young, healthy volunteers participated in two independent experiments using BOLD and MREPT techniques with a visual stimulation paradigm at 3 T MRI. The first set of MREPT fMRI data was obtained using a multi-echo spin-echo (SE) echo planar imaging (EPI) sequence from 14 participants. The second set of MREPT fMRI data was collected from 16 participants using both a single-echo SE-EPI and a single-echo three-dimensional (3D) balanced fast-field-echo (bFFE) sequence. We reconstructed the time-course Larmor frequency conductivity to evaluate hemodynamics.

RESULTS

Conductivity values slightly increased during visual stimulation. Activation strengths were consistently stronger with BOLD than with conductivity for both SE-EPI MREPT and bFFE MREPT. Additionally, the activated areas were always larger with BOLD than MREPT. Some participants also exhibited decreased conductivity values during visual stimulations. In Experiment 1, conductivity showed significant differences between the fixation and visual stimulation blocks in the secondary visual cortex (SVC) and cuneus, with conductivity differences of 0.43 % and 0.47 %, respectively. No significant differences in conductivity were found in the cerebrospinal fluid (CSF) areas between the two blocks. In Experiment 2, significant conductivity differences were observed between the two blocks in the SVC, cuneus, and lingual gyrus for SE-EPI MREPT, with differences of 0.90 %, 0.67 %, and 0.24 %, respectively. Again, no significant differences were found in the CSF areas.

CONCLUSION

Conductivity values increased slightly during visual stimulation in the visual cortex areas but were much weaker than BOLD responses. The conductivity change during visual stimulation was less than 1 % compared to the fixation block. No significant differences in conductivity were observed between the primary visual cortex (PVC)-CSF and SVC-CSF during fixation and visual stimulations, suggesting that the observed conductivity changes may not be related to CSF changes in the visual cortex but rather to diffusion changes. Future research should explore the potential of MREPT to detect neuronal electrical activity and hemodynamic changes, with further optimization of the MREPT technique.

Fast bias-corrected conductivity mapping using stimulated echoes

OBJECTIVE

To demonstrate the potential of a double angle stimulated echo (DA-STE) method for fast and accurate "full" homogeneous Helmholtz-based electrical properties tomography using a simultaneous B 1 + magnitude and transceive phase measurement.

METHODS

The combination of a spin and stimulated echo can be used to yield an estimate of both B 1 + magnitude and transceive phase and thus provides the means for "full" EPT reconstruction. An interleaved 2D acquisition scheme is used for rapid acquisition. The method was validated in a saline phantom and compared to a double angle method based on two single gradient echo acquisitions (GRE-DAM). The method was evaluated in the brain of a healthy volunteer.

RESULTS

The B 1 + magnitude obtained with DA-STE showed excellent agreement with the GRE-DAM method. Conductivity values based on the "full" EPT reconstruction also agreed well with the expectations in the saline phantom. In the brain, the method delivered conductivity values close to literature values.

DISCUSSION

The method allows the use of the "full" Helmholtz-based EPT reconstruction without the need for additional measurements. As a result, quantitative conductivity values are improved compared to phase-based EPT reconstructions. DA-STE is a fast complex- B 1 + mapping technique that could render EPT clinically relevant at 3 T.

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.

A wideband model to evaluate the dielectric properties of biological tissues from magnetic resonance acquisitions

Objective. Aim of this work is to illustrate and experimentally validate a model to evaluate the dielectric properties of biological tissues on a wide frequency band using the magnetic resonance imaging (MRI) technique.Approach. The dielectric behaviour of biological tissues depends on frequency, according to the so-called relaxation mechanisms. The adopted model derives the dielectric properties of biological tissues in the frequency range 10 MHz-20 GHz considering the presence of two relaxation mechanisms whose parameters are determined from quantities derived from MRI acquisitions. In particular, the MRI derived quantities are the water content and the dielectric properties of the tissue under study at the frequency of the MR scanner.Main results.The model was first theoretically validated on muscle and fat using literature data in the frequency range 10 MHz-20 GHz. Results showed capabilities of reconstructing dielectric properties with errors within 16%. Then the model was applied to ex vivo muscle and liver tissues, comparing the MRI-derived properties with data measured by the open probe technique in the frequency range 10 MHz-3 GHz, showing promising results.Significance. The use of medical techniques based on the application of electromagnetic fields (EMFs) is significantly increasing. To provide safe and effective treatments, it is necessary to know how human tissues react to the applied EMF. Since this information is embedded in the dielectric properties of biological tissues, an accurate and precise dielectric characterization is needed. Biological tissues are heterogenous, and their characteristics depend on several factors. Consequently, it is necessary to characterize dielectric propertiesin vivofor each specific patient. While this aim cannot be reached with traditional measurement techniques, through the adopted model these properties can be reconstructedin vivoon a wide frequency band from non-invasive MRI acquisitions.

Magnetic Resonance Electrical Properties Tomography Based on Modified Physics- Informed Neural Network and Multiconstraints

This paper presents a novel method based on leveraging physics-informed neural networks for magnetic resonance electrical property tomography (MREPT). MREPT is a noninvasive technique that can retrieve the spatial distribution of electrical properties (EPs) of scanned tissues from measured transmit radiofrequency (RF) in magnetic resonance imaging (MRI) systems. The reconstruction of EP values in MREPT is achieved by solving a partial differential equation derived from Maxwell's equations that lacks a direct solution. Most conventional MREPT methods suffer from artifacts caused by the invalidation of the assumption applied for simplification of the problem and numerical errors caused by numerical differentiation. Existing deep learning-based (DL-based) MREPT methods comprise data-driven methods that need to collect massive datasets for training or model-driven methods that are only validated in trivial cases. Hence we proposed a model-driven method that learns mapping from a measured RF, its spatial gradient and Laplacian to EPs using fully connected networks (FCNNs). The spatial gradient of EP can be computed through the automatic differentiation of FCNNs and the chain rule. FCNNs are optimized using the residual of the central physical equation of convection-reaction MREPT as the loss function ( L) . To alleviate the ill condition of the problem, we added multiconstraints, including the similarity constraint between permittivity and conductivity and the l1 norm of spatial gradients of permittivity and conductivity, to the L . We demonstrate the proposed method with a three-dimensional realistic head model, a digital phantom simulation, and a practical phantom experiment at a 9.4T animal MRI system.

Changes of in vivo electrical conductivity in the brain and torso related to age, fat fraction and sex using MRI

This work was inspired by the observation that a majority of MR-electrical properties tomography studies are based on direct comparisons with ex vivo measurements carried out on post-mortem samples in the 90's. As a result, the in vivo conductivity values obtained from MRI in the megahertz range in different types of tissues (brain, liver, tumors, muscles, etc.) found in the literature may not correspond to their ex vivo equivalent, which still serves as a reference for electromagnetic modelling. This study aims to pave the way for improving current databases since the definition of personalized electromagnetic models (e.g. for Specific Absorption Rate estimation) would benefit from better estimation. Seventeen healthy volunteers underwent MRI of both brain and thorax/abdomen using a three-dimensional ultrashort echo-time (UTE) sequence. We estimated conductivity (S/m) in several classes of macroscopic tissue using a customized reconstruction method from complex UTE images, and give general statistics for each of these regions (mean-median-standard deviation). These values are used to find possible correlations with biological parameters such as age, sex, body mass index and/or fat volume fraction, using linear regression analysis. In short, the collected in vivo values show significant deviations from the ex vivo values in conventional databases, and we show significant relationships with the latter parameters in certain organs for the first time, e.g. a decrease in brain conductivity with age.

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.

Unrolled Optimization via Physics-Assisted Convolutional Neural Network for MR-Based Electrical Properties Tomography: A Numerical Investigation

Magnetic Resonance imaging based Electrical Properties Tomography (MR-EPT) is a non-invasive technique that measures the electrical properties (EPs) of biological tissues. In this work, we present and numerically investigate the performance of an unrolled, physics-assisted method for 2D MR-EPT reconstructions, where a cascade of Convolutional Neural Networks is used to compute the contrast update. Each network takes in input the EPs and the gradient descent direction (encoding the physics underlying the adopted scattering model) and returns as output the updated contrast function. The network is trained and tested in silico using 2D slices of realistic brain models at 128 MHz. Results show the capability of the proposed procedure to reconstruct EPs maps with quality comparable to that of the popular Contrast Source Inversion-EPT, while significantly reducing the computational time.

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.

An Adaptative Savitzky-Golay Kernel for Laplacian Estimation in Magnetic Resonance Electrical Property Tomography. ANNUAL INTERNATIONAL CONFERENCE OF THE IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. ANNUAL INTERNATIONAL CONFERENCE 2023;2023:1-4. [PMID: 38083553 DOI: 10.1109/embc40787.2023.10341200]

Magnetic Resonance electrical property tomography (MR-EPT) is a non-invasive imaging modality that reconstructs the living biological tissue's conductivity σ and εr permittivity using spatial derivatives of the measured RF field, also termed B1 data, in a magnetic resonance imaging system. The spatial derivative operator, particularly the Laplacian, amplifies the noise in the reconstructed electrical property (EP) maps, hence decreasing accuracy and increasing boundary artifacts. We propose a novel adaptative convolution kernel for generating numerical derivatives based on 3D Savitzky-Golay (SG) filters and local segmentation in a magnitude image. In comparison to typical SG kernel, the proposed kernel allows arbitrary shapes and sizes to vary with local tissue. It provides an automatic trade-off between noise and resolution, thereby significantly enhancing reconstruction accuracy and eliminating boundary artifacts.

Quantitative Assessment of Intervertebral Disc Composition by MRI: Sensitivity to Diurnal Variation

Whether diurnal variation exists in quantitative MRI indices such as the T1rho relaxation time (T1ρ) of the intervertebral disc (IVD) is yet to be explored. This prospective study aimed to evaluate the diurnal variation in T1ρ, apparent diffusion coefficient (ADC), and electrical conductivity (σ) of lumbar IVD and its relationship with other MRI or clinical indices. Lumbar spine MRI, including T1ρ imaging, diffusion-weighted imaging (DWI), and electric properties tomography (EPT), was conducted on 17 sedentary workers twice (morning and evening) on the same day. The T1ρ, ADC, and σ of IVD were compared between the time points. Their diurnal variation, if any, was tested for correlation with age, body mass index (BMI), IVD level, Pfirrmann grade, scan interval, and diurnal variation in IVD height index. The results showed a significant decrease in T1ρ and ADC and a significant increase in the σ of IVD in the evening. T1ρ variation had a weak correlation with age and scan interval, and ADC variation with scan interval. Diurnal variation exists for the T1ρ, ADC, and σ of lumbar IVD, which should be accounted for in image interpretation. This variation is thought to be due to diurnal variations in intradiscal water, proteoglycan, and sodium ion concentration.

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.

Advanced Radio Frequency Applicators for Thermal Magnetic Resonance Theranostics of Brain Tumors

Thermal Magnetic Resonance (ThermalMR) is a theranostic concept that combines diagnostic magnetic resonance imaging (MRI) with targeted thermal therapy in the hyperthermia (HT) range using a radiofrequency (RF) applicator in an integrated system. ThermalMR adds a therapeutic dimension to a diagnostic MRI device. Focused, targeted RF heating of deep-seated brain tumors, accurate non-invasive temperature monitoring and high-resolution MRI are specific requirements of ThermalMR that can be addressed with novel concepts in RF applicator design. This work examines hybrid RF applicator arrays combining loop and self-grounded bow-tie (SGBT) dipole antennas for ThermalMR of brain tumors, at magnetic field strengths of 7.0 T, 9.4 T and 10.5 T. These high-density RF arrays improve the feasible transmission channel count, and provide additional degrees of freedom for RF shimming not afforded by using dipole antennas only, for superior thermal therapy and MRI diagnostics. These improvements are especially relevant for ThermalMR theranostics of deep-seated brain tumors because of the small surface area of the head. ThermalMR RF applicators with the hybrid loop+SGBT dipole design outperformed applicators using dipole-only and loop-only designs, with superior MRI performance and targeted RF heating. Array variants with a horse-shoe configuration covering an arc (270°) around the head avoiding the eyes performed better than designs with 360° coverage, with a 1.3 °C higher temperature rise inside the tumor while sparing healthy tissue. Our EMF and temperature simulations performed on a virtual patient with a clinically realistic intracranial tumor provide a technical foundation for implementation of advanced RF applicators tailored for ThermalMR theranostics of brain tumors.

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.

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.

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.

Brain Tissue Conductivity in Focal Cerebral Ischemia

BACKGROUND

Cerebral ischemia leads to oxygen depletion with rapid breakdown of transmembrane transporters and subsequent impaired electrolyte haemostasis. Electric properties tomography (EPT) is a new contrast in MRI which delivers information on tissue electrical conductivity. In the clinical realm it has been mostly used for tumour mapping. Ischemic cerebral stroke is another promising but neglected application. It might deliver additional information on tissue viability and possible response to therapy.

AIM

The aim of this study was to demonstrate tissue conductivity in a rodent model of stroke. Further, we aimed to compare electric conductivity in ischemic and non-ischemic cerebral tissue.

MATERIALS AND METHODS

Two male Wistar rats were used in this study and were subjected to permanent MCAO. The animals were scanned in a 3 Tesla system (Philips Achieva/Best, the Netherlands) using a dedicated solenoid animal coil (Philips/Hamburg, Germany). In addition to diffusion weighted imaging (DWI), EPT was performed using a steady-state free-precession (SSFP) sequence (repetition time/echo time = 4.5/2.3 ms, measured voxel size = 0.6 × 0.6 × 1.2 mm3, flip angle = 38°, number of excitations = 4). From the transceive phase ϕ of these SSFP scans, conductivity σ was estimated by the equation σ = Δϕ/(2μ0ω) with Δ the Laplacian operator, μ0 the magnetic permeability, and ω the Larmor frequency. Subsequently, a median filter was applied, which was locally restricted to voxels with comparable signal magnitude.

RESULTS

The animals exhibited an infarct as demonstrated on DWI. Conductivity within the infarcted region was 60-70 % of the conductivity of not affected contralateral tissue (0.39 ± 0.07 S/m and 0.31 ± 0.14 S/m vs. 0.64 ± 0.15 S/m and 0.66 ± 0.16 S/m, respectively).

DISCUSSION

Infarcted tissue exhibited decreased conductivity. Further in-vivo experiments with examination of the influence of reperfusion status and temporal evolution of the infarcted areas should be conducted. Depiction of the ischemic penumbra and possibly subclassification of the DWI lesion still seems to be a fruitful target for further studies.

Assessment of vertebral fractures and edema of the thoracolumbar spine based on water-fat and susceptibility-weighted images derived from a single ultra-short echo time scan

PURPOSE

To develop a methodology to simultaneously perform single echo Dixon water-fat imaging and susceptibility-weighted imaging (SWI) based on a single echo time (TE) ultra-short echo time (UTE) (sUTE) scan to assess vertebral fractures and degenerative bone changes in the thoracolumbar spine.

METHODS

A methodology was developed to solve the smoothness-constrained inverse water-fat problem to separate water and fat while removing unwanted low-frequency phase terms. Additionally, the corrected UTE phase was used for SWI. UTE imaging (TE: 0.14 ms, 3T MRI) was performed in the lumbar spine of nine patients with vertebral fractures and bone marrow edema (BME). All images were reviewed by two radiologists. Water- and fat-separated images were analyzed in comparison with short-tau inversion recovery (STIR) and with respect to BME visibility. The visibility of fracture lines and cortical outlining of the UTE magnitude images were analyzed in comparison with computed tomography.

RESULTS

Unwanted phase components, dominated by the B₁ phase, were removed from the UTE phase images. The rating of the diagnostic quality of BME visualization showed a high preference for the sUTE-Dixon water- and fat-separated images in comparison with STIR. The UTE magnitude images enabled better visualizing fracture lines compared with STIR and slightly better visibility of cortical outlining. With increasing SWI weighting osseous structures and fatty tissues were enhanced.

CONCLUSION

The proposed sUTE-Dixon-SWI methodology allows the removal of unwanted low-frequency phases and enables water-fat separation and SWI processing from a single complex UTE image. The methodology can be used for the simultaneous assessment of vertebral fractures and BME of the thoracolumbar spine.

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.

Receiver phase alignment using fitted SVD derived sensitivities from routine prescans

Magnetic resonance imaging radio frequency arrays are composed of multiple receive coils that have their signals combined to form an image. Combination requires an estimate of the radio frequency coil sensitivities to align signal phases and prevent destructive interference. At lower fields this can be accomplished using a uniform physical reference coil. However, at higher fields, uniform volume coils are lacking and, when available, suffer from regions of low receive sensitivity that result in poor sensitivity estimation and combination. Several approaches exist that do not require a physical reference coil but require manual intervention, specific prescans, or must be completed post-acquisition. This makes these methods impractical for large multi-volume datasets such as those collected for novel types of functional MRI or quantitative susceptibility mapping, where magnitude and phase are important. This pilot study proposes a fitted SVD method which utilizes existing combination methods to create a phase sensitive combination method targeted at large multi-volume datasets. This method uses any multi-image prescan to calculate the relative receive sensitivities using voxel-wise singular value decomposition. These relative sensitivities are fitted to the solid harmonics using an iterative least squares fitting algorithm. Fits of the relative sensitivities are used to align the phases of the receive coils and improve combination in subsequent acquisitions during the imaging session. This method is compared against existing approaches in the human brain at 7 Tesla by examining the combined data for the presence of singularities and changes in phase signal-to-noise ratio. Two additional applications of the method are also explored, using the fitted SVD method in an asymmetrical coil and in a case with subject motion. The fitted SVD method produces singularity-free images and recovers between 95-100% of the phase signal-to-noise ratio depending on the prescan data resolution. Using solid harmonic fitting to interpolate singular value decomposition derived receive sensitivities from existing prescans allows the fitted SVD method to be used on all acquisitions within a session without increasing exam duration. Our fitted SVD method is able to combine imaging datasets accurately without supervision during online reconstruction.

Single-step calculation of susceptibility through multiple orientation sampling

Quantitative susceptibility mapping (QSM) was developed to estimate the spatial distribution of magnetic susceptibility from MR signal phase acquired using a gradient echo (GRE) sequence. The field-to-susceptibility inversion in QSM is known to be ill-posed and needs numerical stabilization through either regularization or data oversampling. The calculation of susceptibility through the multiple orientation sampling (COSMOS) method uses phase data acquired at three or more head orientations to achieve a well-conditioned field-to-susceptibility inversion and is often considered the gold standard for in vivo QSM. However, the conventional COSMOS approach, here named multistep COSMOS (MSCOSMOS), solves the dipole inversion from the local field derived from raw GRE phase through multiple steps of phase preprocessing. Error propagations between these consecutive phase processing steps can thus affect the final susceptibility quantification. On the other hand, recently proposed single-step QSM (SSQSM) methods aim to solve an integrated inversion from unprocessed or total phase to mitigate such error propagations but have been limited to single orientation QSM. This study therefore aimed to test the feasibility of using single-step COSMOS (SSCOSMOS) to jointly perform background field removal and dipole inversion with multiple orientation sampling, which could serve as a better standard for gauging SSQSM methods. We incorporated multiple spherical mean value (SMV) kernels of various radii with the dipole inversion in SSCOSMOS. QSM reconstructions with SSCOSMOS and MSCOSMOS were compared using both simulations with a numerical head phantom and in vivo human brain data. SSCOSMOS permitted integrated background removal and dipole inversion without the need to adjust any regularization parameters. In addition, with sufficiently large SMV kernels, SSCOSMOS performed consistently better than MSCOSMOS in all the tested error metrics in our simulations, giving better susceptibility quantification and smaller reconstruction error. Consistent tissue susceptibility values were obtained between SSCOSMOS and MSCOSMOS.

Advanced patient-specific hyperthermia treatment planning

Hyperthermia treatment planning (HTP) is valuable to optimize tumor heating during thermal therapy delivery. Yet, clinical hyperthermia treatment plans lack quantitative accuracy due to uncertainties in tissue properties and modeling, and report tumor absorbed power and temperature distributions which cannot be linked directly to treatment outcome. Over the last decade, considerable progress has been made to address these inaccuracies and therefore improve the reliability of hyperthermia treatment planning. Patient-specific electrical tissue conductivity derived from MR measurements has been introduced to accurately model the power deposition in the patient. Thermodynamic fluid modeling has been developed to account for the convective heat transport in fluids such as urine in the bladder. Moreover, discrete vasculature trees have been included in thermal models to account for the impact of thermally significant large blood vessels. Computationally efficient optimization strategies based on SAR and temperature distributions have been established to calculate the phase-amplitude settings that provide the best tumor thermal dose while avoiding hot spots in normal tissue. Finally, biological modeling has been developed to quantify the hyperthermic radiosensitization effect in terms of equivalent radiation dose of the combined radiotherapy and hyperthermia treatment. In this paper, we review the present status of these developments and illustrate the most relevant advanced elements within a single treatment planning example of a cervical cancer patient. The resulting advanced HTP workflow paves the way for a clinically feasible and more reliable patient-specific hyperthermia treatment planning.

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.

Low conductivity on electrical properties tomography demonstrates unique tumor habitats indicating progression in glioblastoma

OBJECTIVES

Tissue conductivity measurements made with electrical properties tomography (EPT) can be used to define temporal changes in tissue habitats on longitudinal multiparametric MRI. We aimed to demonstrate the added insights for identifying tumor habitats obtained by including EPT with diffusion- and perfusion-weighted MRI, and to evaluate the use of these tumor habitats for determining tumor treatment response in post-treatment glioblastoma.

METHODS

Tumor habitats were developed from EPT, diffusion-weighted, and perfusion-weighted MRI in 60 patients with glioblastoma who underwent concurrent chemoradiotherapy. Voxels from EPT, apparent diffusion coefficient (ADC), and cerebral blood volume (CBV) maps were clustered into habitats, and each habitat was serially examined to assess its temporal change. The usefulness of temporal changes in tumor habitats for diagnosing tumor progression and treatment-related change was investigated using logistic regression. The performance of significant predictors was measured using the area under the curve (AUC) from receiver-operating-characteristics analysis with 1000-fold bootstrapping.

RESULTS

Five tumor habitats were identified, and of these, the hypervascular cellular habitat (odds ratio [OR] 5.45; 95% CI, 1.75-31.42; p = .02), hypovascular low conductivity habitat (OR 2.00; 95% CI, 1.45-3.05; p < .001), and hypovascular intermediate habitat (OR 1.57; 95% CI, 1.18-2.30; p = .006) were predictive of tumor progression. Low EPT and low CBV reflected a unique hypovascular low conductivity habitat that showed the highest diagnostic performance (AUC 0.86; 95% CI, 0.76-0.96). The combined habitats showed high performance (AUC 0.90; 95% CI, 0.82-0.98) in the differentiation of tumor progression from treatment-related change.

CONCLUSION

EPT reveals low conductivity habitats that can improve the diagnosis of tumor progression in post-treatment glioblastoma.

KEY POINTS

• Electrical properties tomography (EPT) demonstrated lower conductivity in tumor progression than in treatment-related change. • EPT allowed identification of a unique hypovascular low conductivity habitat when combined with cerebral blood volume mapping. • Tumor habitats with a hypovascular low conductivity habitat, hypervascular cellular habitat, and hypovascular intermediate habitat yielded high diagnostic performance for diagnosing tumor progression.

Electrical Properties Tomography: A Methodological Review

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

Brain Tissue Conductivity Measurements with MR-Electrical Properties Tomography: An In Vivo Study

First in vivo brain conductivity reconstructions using Helmholtz MR-Electrical Properties Tomography (MR-EPT) have been published. However, a large variation in the reconstructed conductivity values is reported and these values differ from ex vivo conductivity measurements. Given this lack of agreement, we performed an in vivo study on eight healthy subjects to provide reference in vivo brain conductivity values. MR-EPT reconstructions were performed at 3 T for eight healthy subjects. Mean conductivity and standard deviation values in the white matter, gray matter and cerebrospinal fluid (σWM, σGM, and σCSF) were computed for each subject before and after erosion of regions at tissue boundaries, which are affected by typical MR-EPT reconstruction errors. The obtained values were compared to the reported ex vivo literature values. To benchmark the accuracy of in vivo conductivity reconstructions, the same pipeline was applied to simulated data, which allow knowledge of ground truth conductivity. Provided sufficient boundary erosion, the in vivo σWM and σGM values obtained in this study agree for the first time with literature values measured ex vivo. This could not be verified for the CSF due to its limited spatial extension. Conductivity reconstructions from simulated data verified conductivity reconstructions from in vivo data and demonstrated the importance of discarding voxels at tissue boundaries. The presented σWM and σGM values can therefore be used for comparison in future studies employing different MR-EPT techniques.

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.

Demonstration and suppression of respiration-related artifacts in Bloch-Siegert shift-based B1+ maps of the human brain

Respiration-induced movement of the chest wall and internal organs causes temporal B₀ variations extending throughout the brain. This study demonstrates that these variations can cause significant artifacts in B1+ maps obtained at 7 T with the Bloch-Siegert shift (BSS) B1+ mapping technique. To suppress these artifacts, a navigator correction scheme was proposed. Two sets of experiments were performed. In the first set of experiments, phase shifts induced by respiration-related B₀ variations were assessed for five subjects at 7 T by using a gradient echo (GRE) sequence without phase-encoding. In the second set of experiments, B1+ maps were acquired using a GRE-based BSS pulse sequence with navigator echoes. For this set, the measurements were consecutively repeated 16 times for the same imaging slice. These measurements were averaged to obtain the reference B1+ map. Due to the periodicity of respiration-related phase shifts, their effect on the reference B1+ map was assumed to be negligible through averaging. The individual B1+ maps of the 16 repetitions were calculated with and without using the proposed navigator scheme. These maps were compared with the B1+ reference map. The peak-to-peak value of respiration-related phase shifts varied between subjects. Without navigator correction, the interquartile range of percentage error in B1+ varied between 4.0% and 8.3% among subjects. When the proposed navigator scheme was used, these numbers were reduced to 2.5% and 2.9%, indicating an improvement in the precision of GRE-based BSS B1+ mapping at high magnetic fields.

Current and Emerging Magnetic Resonance-Based Techniques for Breast Cancer

Breast cancer is the most commonly diagnosed cancer among women worldwide, and early detection remains a principal factor for improved patient outcomes and reduced mortality. Clinically, magnetic resonance imaging (MRI) techniques are routinely used in determining benign and malignant tumor phenotypes and for monitoring treatment outcomes. Static MRI techniques enable superior structural contrast between adipose and fibroglandular tissues, while dynamic MRI techniques can elucidate functional characteristics of malignant tumors. The preferred clinical procedure-dynamic contrast-enhanced MRI-illuminates the hypervascularity of breast tumors through a gadolinium-based contrast agent; however, accumulation of the potentially toxic contrast agent remains a major limitation of the technique, propelling MRI research toward finding an alternative, noninvasive method. Three such techniques are magnetic resonance spectroscopy, chemical exchange saturation transfer, and non-contrast diffusion weighted imaging. These methods shed light on underlying chemical composition, provide snapshots of tissue metabolism, and more pronouncedly characterize microstructural heterogeneity. This review article outlines the present state of clinical MRI for breast cancer and examines several research techniques that demonstrate capacity for clinical translation. Ultimately, multi-parametric MRI-incorporating one or more of these emerging methods-presently holds the best potential to afford improved specificity and deliver excellent accuracy to clinics for the prediction, detection, and monitoring of breast cancer.

Statistical analysis of the accuracy of water content-based electrical properties tomography

Water content-based electrical properties tomography (wEPT) can retrieve electrical properties (EPs) from water content maps, thereby eliminating the need for B₁ field measurement in the traditional magnetic resonance electrical properties tomography method. The wEPT is performed by conventional MR scanning, such as T₁ -weighted spin-echo imaging, and thus can be directly applied to clinical settings. However, the random noise propagation involved in wEPT causes inaccuracy in EP mapping. To guarantee the EP estimates desired for clinical practice, this study statically investigates the noise-specific uncertainty of wEPT through probability density function models. We calculated the probability distribution of EP maps with different noise levels and examined the effects of scan parameters on reconstruction accuracy with various flip angles (FAs) and repetition time (TR) settings. The theoretical derivation was validated by Monte Carlo simulations and human imaging experiment at 3 T. Results showed that a serious deviation could occur in tissues with large conductivity value at a low signal-to-noise ratio and quantitatively demonstrate that such deviation could be mitigated by increased FAs or TRs. This study provided useful information for the setup of scan parameters, evaluation of accuracy of the wEPT under specific SNR levels, and promote its clinical applications.

Deep learning-based reconstruction of in vivo pelvis conductivity with a 3D patch-based convolutional neural network trained on simulated MR data

PURPOSE

To demonstrate that mapping pelvis conductivity at 3T with deep learning (DL) is feasible.

METHODS

210 dielectric pelvic models were generated based on CT scans of 42 cervical cancer patients. For all dielectric models, electromagnetic and MR simulations with realistic accuracy and precision were performed to obtain B 1 + and transceive phase (ϕ^± ). Simulated B 1 + and ϕ^± served as input to a 3D patch-based convolutional neural network, which was trained in a supervised fashion to retrieve the conductivity. The same network architecture was retrained using only ϕ^± in input. Both network configurations were tested on simulated MR data and their conductivity reconstruction accuracy and precision were assessed. Furthermore, both network configurations were used to reconstruct conductivity maps from a healthy volunteer and two cervical cancer patients. DL-based conductivity was compared in vivo and in silico to Helmholtz-based (H-EPT) conductivity.

RESULTS

Conductivity maps obtained from both network configurations were comparable. Accuracy was assessed by mean error (ME) with respect to ground truth conductivity. On average, ME < 0.1 Sm^-1 for all tissues. Maximum MEs were 0.2 Sm^-1 for muscle and tumour, and 0.4 Sm^-1 for bladder. Precision was indicated with the difference between 90^th and 10^th conductivity percentiles, and was below 0.1 Sm^-1 for fat, bone and muscle, 0.2 Sm^-1 for tumour and 0.3 Sm^-1 for bladder. In vivo, DL-based conductivity had median values in agreement with H-EPT values, but a higher precision.

CONCLUSION

Anatomically detailed, noise-robust 3D conductivity maps with good sensitivity to tissue conductivity variations were reconstructed in the pelvis with DL.

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.

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.

A deep learning method for image-based subject-specific local SAR assessment

Purpose

Local specific absorption rate (SAR) cannot be measured and is usually evaluated by offline numerical simulations using generic body models that of course will differ from the patient's anatomy. An additional safety margin is needed to include this intersubject variability. In this work, we present a deep learning–based method for image‐based subject‐specific local SAR assessment. We propose to train a convolutional neural network to learn a “surrogate SAR model” to map the relation between subject‐specific B1+ maps and the corresponding local SAR.

Method

Our database of 23 subject‐specific models with an 8–transmit channel body array for prostate imaging at 7 T was used to build 5750 training samples. These synthetic complex B1+ maps and local SAR distributions were used to train a conditional generative adversarial network. Extra penalization for local SAR underestimation errors was included in the loss function. In silico and in vivo validation were performed.

Results

In silico cross‐validation shows a good qualitative and quantitative match between predicted and ground‐truth local SAR distributions. The peak local SAR estimation error distribution shows a mean overestimation error of 15% with 13% probability of underestimation. The higher accuracy of the proposed method allows the use of less conservative safety factors compared with standard procedures. In vivo validation shows that the method is applicable with realistic measurement data with impressively good qualitative and quantitative agreement to simulations.

Conclusion

The proposed deep learning method allows online image‐based subject‐specific local SAR assessment. It greatly reduces the uncertainty in current state‐of‐the‐art SAR assessment methods, reducing the time in the examination protocol by almost 25%.

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.

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.