Magnetic resonance current density imaging (MRCDI) provides a current density image by measuring the induced magnetic flux density within the subject with a magnetic resonance imaging (MRI) scanner. Magnetic resonance electrical impedance tomography (MREIT) has been focused on extracting some useful information of the current density and conductivity distribution in the subject Omega using measured B(z), one component of the magnetic flux density B. In this paper, we analyze the map Tau from current density vector field J to one component of magnetic flux density B(z) without any assumption on the conductivity. The map Tau provides an orthogonal decomposition J = J(P) + J(N) of the current J where J(N) belongs to the null space of the map Tau. We explicitly describe the projected current density J(P) from measured B(z). Based on the decomposition, we prove that B(z) data due to one injection current guarantee a unique determination of the isotropic conductivity under assumptions that the current is two-dimensional and the conductivity value on the surface is known. For a two-dimensional dominating current case, the projected current density J(P) provides a good approximation of the true current J without accumulating noise effects. Numerical simulations show that J(P) from measured B(z) is quite similar to the target J. Biological tissue phantom experiments compare J(P) with the reconstructed J via the reconstructed isotropic conductivity using the harmonic B(z) algorithm.

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. Keywords Conductivity tensor imaging (CTI) Á Diffusion weighted imaging Á Magnetic resonance electrical properties tomography Á Anisotropy & Eung Je Woo

Magnetic resonance electrical impedance tomography (MREIT) is an emerging method to visualize electrical conductivity and/or current density images at low frequencies (below 1 KHz). Injecting currents into an imaging object, one component of the induced magnetic flux density is acquired using an MRI scanner for isotropic conductivity image reconstructions. Diffusion tensor MRI (DT-MRI) measures the intrinsic three-dimensional diffusion property of water molecules within a tissue. It characterizes the anisotropic water transport by the effective diffusion tensor. Combining the DT-MRI and MREIT techniques, we propose a novel direct method for absolute conductivity tensor image reconstructions based on a linear relationship between the water diffusion tensor and the electrical conductivity tensor. We first recover the projected current density, which is the best approximation of the internal current density one can obtain from the measured single component of the induced magnetic flux density. This enables us to estimate a scale factor between the diffusion tensor and the conductivity tensor. Combining these values at all pixels with the acquired diffusion tensor map, we can quantitatively recover the anisotropic conductivity tensor map. From numerical simulations and experimental verifications using a biological tissue phantom, we found that the new method overcomes the limitations of each method and successfully reconstructs both the direction and magnitude of the conductivity tensor for both the anisotropic and isotropic regions.

Cross-sectional imaging of conductivity and permittivity distributions inside the human body has been actively investigated in impedance imaging areas such as electrical impedance tomography (EIT) and magnetic induction tomography (MIT). Since the conductivity and permittivity values exhibit frequencydependent changes, it is worthwhile to perform spectroscopic imaging from almost dc to hundreds of MHz. To probe the human body, we may inject

The aim of magnetic resonance electrical impedance tomography (MREIT) is to visualize the electrical properties, conductivity or current density of an object by injection of current. Recently, the prolonged data acquisition time when using the injected current nonlinear encoding (ICNE) method has been advantageous for measurement of magnetic flux density data, Bz, for MREIT in the signal-to-noise ratio (SNR). However, the ICNE method results in undesirable side artifacts, such as blurring, chemical shift and phase artifacts, due to the long data acquisition under an inhomogeneous static field. In this paper, we apply the ICNE method to a gradient and spin echo (GRASE) multi-echo train pulse sequence in order to provide the multiple k-space lines during a single RF pulse period. We analyze the SNR of the measured multiple B(z) data using the proposed ICNE-Multiecho MR pulse sequence. By determining a weighting factor for B(z) data in each of the echoes, an optimized inversion formula for the magnetic flux density data is proposed for the ICNE-Multiecho MR sequence. Using the ICNE-Multiecho method, the quality of the measured magnetic flux density is considerably increased by the injection of a long current through the echo train length and by optimization of the voxel-by-voxel noise level of the B(z) value. Agarose-gel phantom experiments have demonstrated fewer artifacts and a better SNR using the ICNE-Multiecho method. Experimenting with the brain of an anesthetized dog, we collected valuable echoes by taking into account the noise level of each of the echoes and determined B(z) data by determining optimized weighting factors for the multiply acquired magnetic flux density data.