• Magnetic Resonance Electrical Property Tomography (MREPT) aims to visualize both conductivity σ and permittivity ǫ distributions at the Larmor frequency (≈ 128 MHz for a 3 T MRI).

Conventional magnetic resonance electrical impedance tomography (MREIT) reconstruction methods require administration of two linearly independent currents via at least two electrode pairs. This requires long scanning times and inhibits coordination of MREIT measurements with electrical neuromodulation strategies. We sought to develop an isotropic conductivity reconstruction algorithm in MREIT based on a single current injection, both to decrease scanning time by a factor of two and enable MREIT measurements to be conveniently adapted to general transcranial- or implanted-electrode neurostimulation protocols. In this work, we propose and demonstrate an iterative algorithm that extends previously published MREIT work using two-current administration approaches. The proposed algorithm is a single-current adaptation of the harmonic B z algorithm. Forward modeling of electric potentials is used to capture changes of conductivity along current directions that would normally be invisible using data from a single-current administration. Computational and experimental results show that the reconstruction algorithm is capable of reconstructing isotropic conductivity images that agree well in terms of L 2 error and structural similarity with exact conductivity distributions or two-current-based MREIT reconstructions. We conclude that it is possible to reconstruct high quality electrical conductivity images using MREIT techniques and one current injection only.

No abstract

Magnetic resonance electrical impedance tomography (MREIT) aims to visualize a conductivity distribution inside the human body. In MREIT, we inject current to produce a current density J and magnetic flux density B inside the body, and we measure Bz, which is the z-component of B, using an MRI scanner with its main field in the z direction. Using fundamental relations between the measured Bz and the conductivity, we can reconstruct cross-sectional images of the internal conductivity distribution. In this paper, we adopt the harmonic Bz algorithm, which is based on the key observation that ∇ 2 Bz reveals changes in the log of the conductivity distribution along any equipotential curve on an imaging slice. When we apply the method to measured Bz data from animal or human subjects, however, there occur a few technical difficulties that are mainly related to measurement errors in Bz data, especially in a local region where MR signals are very small. This demands innovative data processing methods based on a rigorous mathematical analysis of such defective data. We carefully investigate sources of the error and its adverse effects on the image reconstruction process. We suggest a new error propagation blocking algorithm to prevent defective data at one local region from negatively influencing conductivity images of other regions. We experimentally examine the performance of the proposed method by comparing reconstructed images with and without applying the error propagation blocking algorithm. We found that the error blocking algorithm improves the accuracy of reconstructed conductivity images.

Electrodes are commonly used to inject current into the human body in various biomedical applications such as functional electrical stimulation, defibrillation, electrosurgery, RF ablation, impedance imaging, and so on. When a highly conducting electrode makes direct contact with biological tissues, the induced current density has strong singularity along the periphery of the electrode, which may cause painful sensation or burn. Especially in impedance imaging methods such as the magnetic resonance electrical impedance tomography, we should avoid such singularity since more uniform current density underneath a current-injection electrode is desirable. In this paper, we study an optimal geometry of a recessed electrode to produce a well-distributed current density on the contact area under the electrode. We investigate the geometry of the electrode surface to minimize the edge singularity and produce nearly uniform current density on the contact area. We propose a mathematical framework for the uniform current density electrode and its optimal geometry. The theoretical results are supported by numerical simulations.