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.

Low-frequency dominant electrical conductivity imaging of in vivo human brain using high-frequency conductivity at Larmor-frequency and spherical mean diffusivity without external injection current.

Diffusion weighted imaging based on random Brownian motion of water molecules within a voxel provides information on the micro-structure of biological tissues through water molecule diffusivity. As the electrical conductivity is primarily determined by the concentration and mobility of ionic charge carriers, the macroscopic electrical conductivity of biological tissues is also related to the diffusion of electrical ions. This paper aims to investigate the low-frequency electrical conductivity by relying on a pre-defined biological model that separates the brain into the intracellular (restricted) and extracellular (hindered) compartments. The proposed method uses B1 mapping technique, which provides a high-frequency conductivity distribution at Larmor frequency, and the spherical mean technique, which directly estimates the microscopic tissue structure based on the water molecule diffusivity and neurite orientation distribution. The total extracellular ion concentration, which is separated from the high-frequency conductivity, is recovered using the estimated diffusivity parameters and volume fraction in each compartment. We propose a method to reconstruct the low-frequency dominant conductivity tensor by taking into consideration the extracted extracellular diffusion tensor map and the reconstructed electrical parameters. To demonstrate the reliability of the proposed method, we conducted two phantom experiments. The first one used a cylindrical acrylic cage filled with an agar in the background region and four anomalies for the effect of ion concentration on the electrical conductivity. The other experiment, in which the effect of ion mobility on the conductivity was verified, used cell-like materials with thin insulating membranes suspended in an electrolyte. Animal and human brain experiments were conducted to visualize the low-frequency dominant conductivity tensor images. The proposed method using a conventional MRI scanner can predict the internal current density map in the brain without directly injected external currents.

Correlation of quantitative conductivity mapping and total tissue sodium concentration at 3T/4T.

PURPOSE: To investigate the correlation between electrical conductivity and sodium concentration, both measured in vivo, in the human brain. METHODS: Conductivity measurements were performed on samples with different sodium (Na+ ) and agarose concentrations using a dielectric probe, and the correlation between conductivity and Na+ content was evaluated. Subsequently, brain conductivity and total Na+ content maps were measured in 8 healthy subjects using phase-based MREPT and sodium MRI, respectively. After co-registration and spatial normalization to the 1 mm 152 MNI brain atlas, the relationship between conductivity and tissue sodium concentration (TSC) was examined within different brain regions. RESULTS: The conductivities of agarose gels increased linearly with NaCl concentration, while remaining almost independent of agarose content. When measured in healthy subjects, conductivities showed positive correlation with total tissue sodium concentration (R = 0.39, P < 0.005). The same trend was found in gray matter (R = 0.36, P < 0.005) and in white matter (R = 0.28, P < 0.05). CONCLUSION: Tissue conductivity shows a positive correlation with total sodium concentration. Conductivity might serve as a novel technique to visualize the total tissue electrolyte concentration, although refinements in the consideration of e.g., tissue water content, would be necessary to improve the quantitative value.

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

PURPOSE: To develop a novel regularized, model-based approach to phase-based conductivity mapping that uses structural information to improve the accuracy of conductivity maps. THEORY AND METHODS: The inverse of the three-dimensional Laplacian operator is used to model the relationship between measured phase maps and the object conductivity in a penalized weighted least-squares optimization problem. Spatial masks based on structural information are incorporated into the problem to preserve data near boundaries. The proposed Inverse Laplacian method was compared against a restricted Gaussian filter in simulation, phantom, and human experiments. RESULTS: The Inverse Laplacian method resulted in lower reconstruction bias and error due to noise in simulations than the Gaussian filter. The Inverse Laplacian method also produced conductivity maps closer to the measured values in a phantom and with reduced noise in the human brain, as compared to the Gaussian filter. CONCLUSION: The Inverse Laplacian method calculates conductivity maps with less noise and more accurate values near boundaries. Improving the accuracy of conductivity maps is integral for advancing the applications of conductivity mapping. Magn Reson Med 78:2011-2021, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

Variation in the dielectric properties of freshly excised colorectal cancerous tissues at different tumor stages.

The study was designed to identify differences in the dielectric properties of ex vivo colorectal cancerous tissues at different tumor stages. To date, 130 freshly excised colorectal cancerous specimens underwent measurement of both relative permittivity and conductivity on the serosal and mucosal surfaces of the carcinoma nidus, and the mucosa of the surgical resection margin ranging from 50 to 500 MHz at the Larmor frequencies. Tumor node metastasis staging was determined according to pathological reports for each patient. There were statistically significant differences in the relative permittivity of both colorectal cancerous serosa and mucosa among stages ≤I, II, III, and IV and between stages ≤II and ≥III (P < 0.05) at most frequencies under 300 MHz; statistically significant differences in conductivity were also observed for most of the measured frequencies (P < 0.05). The significant differences in dielectric characteristics among tumor stages, especially between early and advanced stages, have value for selecting appropriate surgical strategies. The presented ex vivo data provide important information for magnetic resonance electrical properties tomography in vivo system because the frequencies of 64 MHz (1.5T) and 128 MHz (3T) are usually used in clinical settings. Bioelectromagnetics. 38:522-532, 2017. © 2017 Wiley Periodicals, Inc.

Bias correction for phase-based cr-MREPT using low resolution B1+ magnitude.

ObjectiveFull-form Magnetic Resonance Electrical Properties Tomography (MREPT) requires bothB1+magnitude and phase information. SinceB1+phase can be obtained faster and with higher SNR compared toB1+magnitude, several phase-based methods have been developed for conductivity imaging. However, phase-based methods suffer from a concave bias due to the assumption that∇|B1+|is negligible in the ROI.ApproachIn this paper, we re-derive the central equation of phase-based cr-MREPT without assuming that∇|B1+|is negligible and thus propose a correction method directly integrated into the equation system.Main resultsProposed method successfully corrects the concave bias on both simulated and experimental data and significantly increases image quality.SignificanceThe proposed correction method depends on a very low-resolution|B1+|map, and therefore the imaging time does not increase significantly for obtainingB1+magnitude. Moreover, correction can be achieved using simulatedB1+magnitude, hence completely removing the additional imaging requirement.

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

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

Electrodeless conductivity tensor imaging (CTI) using MRI: basic theory and animal experiments.

The electrical conductivity is a passive material property primarily determined by concentrations of charge carriers and their mobility. The macroscopic conductivity of a biological tissue at low frequency may exhibit anisotropy related with its structural directionality. When expressed as a tensor and properly quantified, the conductivity tensor can provide diagnostic information of numerous diseases. Imaging conductivity distributions inside the human body requires probing it by externally injecting conduction currents or inducing eddy currents. At low frequency, the Faraday induction is negligible and it has been necessary in most practical cases to inject currents through surface electrodes. Here we report a novel method to reconstruct conductivity tensor images using an MRI scanner without current injection. This electrodeless method of conductivity tensor imaging (CTI) utilizes B1 mapping to recover a high-frequency isotropic conductivity image which is influenced by contents in both extracellular and intracellular spaces. Multi-b diffusion weighted imaging is then utilized to extract the effects of the extracellular space and incorporate its directional structural property. Implementing the novel CTI method in a clinical MRI scanner, we reconstructed in vivo conductivity tensor images of canine brains. Depending on the details of the implementation, it may produce conductivity contrast images for conductivity weighted imaging (CWI). Clinical applications of CTI and CWI may include imaging of tumor, ischemia, inflammation, cirrhosis, and other diseases. CTI can provide patient-specific models for source imaging, transcranial dc stimulation, deep brain stimulation, and electroporation.