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Diffusion-weighted double-echo steady-state (dwDESS) MRI with bipolar diffusion gradients is a promising candidate to obtain diffusion weighted images (DWI) free of geometric distortions and with low motion sensitivity. However, a wider clinical application of dwDESS is currently hindered as no method is reported to explicitly calculate the effective b-value of the obtained DWI from the diffusion-gradients applied in the sequence. To this end, a previously described signal model was adapted for dwDESS with bipolar diffusion gradients, which allows to estimate an effective b-value, dubbed b'. Evaluation in phantom examinations was performed on a clinical 1.5 T MR system. Experimental results were compared with theoretical predictions, including the apparent diffusion coefficient (ADC) based on b-values from a standard EPI-DWI sequence and ADC' based on the effective b' from the dwDESS sequence. The adapted signal model was able to describe the experimental results, and the obtained values of ADC' were in line with conventional ADC measurements.

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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.

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

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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.

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This chapter explains the magnetic resonance electrical impedance tomography (MREPT) technique used to image electrical properties at high frequencies. The chapter describes the MREPT data acquisition methods, current state-of-the-art image reconstruction algorithms, and experiments with phantoms, animals, and humans.

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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.

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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.

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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.

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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.

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To investigate deep learning electrical properties tomography (EPT) for application on different simulated and in-vivo datasets, including pathologies for brain conductivity reconstructions, 3D patch-based convolutional neural networks were trained to predict conductivity maps from B 1 transceive phase data. To compare the performance of DL-EPT networks on different datasets, three datasets were used throughout this work, one from simulations and two from in-vivo measurements from healthy volunteers and patients with brain lesions, respectively. At first, networks trained on simulations were tested on all datasets with different levels of homogeneous Gaussian noise introduced in training and testing. Secondly, to investigate potential robustness towards systematical differences between simulated and measured phase maps, in-vivo data with conductivity labels from conventional EPT were used for training. High quality conductivity reconstructions from networks trained on simulations with and without noise confirm the potential of deep learning for EPT. However, when this network is used for in-vivo reconstructions, measurement related artifacts affect the quality of conductivity maps. Training DL-EPT networks using conductivity labels from conventional EPT improves the quality of the results. Networks trained on realistic simulations yield reconstruction artifacts when applied to in-vivo data. Training with realistic phase data and conductivity labels from conventional EPT allows for reducing these artifacts.

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OBJECTIVES: To evaluate the diagnostic utility of electric properties tomography (EPT) in differentiating benign from malignant breast lesions in comparison with dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI). METHODS: In this institutional review board-approved retrospective study, 116 consecutive patients with 141 breast lesions (50 benign and 91 malignant) underwent 3-T MRI, including 3D turbo-spin echo (TSE) sequence and standard DCE-MRI scans between January 2014 and January 2017. The lesions were segmented semi-automatically using subtraction DCE-MR images, and they were registered to the phase images from 3D TSE. The mean conductivity of the lesion was obtained from phase-based reconstruction of lesions. From the DCE-MRI, initial enhancement rate (IER) and signal enhancement ratio (SER) were calculated from signal intensity (SI) as follows: IER = (SIearly - SIpre)/SIpre, SER = (SIearly - SIpre)/(SIdelayed - SIpre). The parameters from EPT and the DCE-MRI were compared between benign and malignant lesions. RESULTS: There was significant difference in mean conductivity (0.14 ± 1.77 vs 1.14 ± 1.36 S/m, p < 0.0001) and SER (0.77 ± 0.28 vs 1.04 ± 0.25, p < 0.0001) between benign and malignant lesions, but not in IER (p = 0.06). Receiver operating curve (ROC) analysis revealed that the area under the curve (AUC) of the mean conductivity and SER was 0.71 and 0.80, respectively, without significant difference (p = 0.15). CONCLUSIONS: The mean conductivity of EPT was significantly different between benign and malignant breast lesions as well as kinetic parameter or SER from DCE-MRI. KEY POINTS: • The conductivity of malignant lesions was higher than that of benign lesions. • EPT helps differentiatie benign from malignant lesions. • Diagnostic ability of EPT was not significantly different from that of DCE-MRI.

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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.

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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.

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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.

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OBJECTIVE: The purpose is to provide a comprehensive review of the electrical properties tomography (EPT) technique, which was introduced to image the electrical properties (EPs) of tissue noninvasively by exploiting the measured field data of MRI. METHODS: We reviewed the principle of EPT, reconstruction methods, biomedical applications such as tumor imaging, and existing challenges. As a key application of EPT, the estimation of specific absorption rate (SAR) due to MRI was discussed in the background of elevated risk of tissue heating at high field. RESULTS AND CONCLUSION: Since the originally proposed local, homogeneous Helmholtz equation-based reconstruction algorithm, advanced EPT algorithms have emerged to address the challenges of EPT, including reconstruction error near tissue boundaries, noise sensitivity, inaccurate phase estimation, and elimination of the unmeasurable component, along with demonstrations of in vivo experiments. EPT techniques have been applied to investigate EPs of both healthy and pathological tissues in vivo and factors contributing to various EP value, including sodium, water content, etc. More studies are anticipated to consolidate the current findings. EPT-based subject-specific SAR estimation has led to in vivo demonstration of its feasibility and prediction of temperature increase of phantom during MRI scans merely using measured data. SIGNIFICANCE: EPT has the advantage of high resolution and practical feasibility in a clinical setup for imaging the biomedically interesting EPs of tissue in the radiofrequency range. EPT-based SAR estimation is another promising topic for predicting tissue heating of individual subjects during a specific MRI scan.

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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.

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