Low frequency conductivity reconstruction based on a single current injection via MREIT

Abstract

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.

Convergence analysis of the harmonic $B_z$ algorithm with single injection current in MREIT

“…Single current harmonic B z algorithm for two-dimensional MREIT model, and convergence analysis. To reconstruct the conductivity distribution from a single B z dataset, or to solve the boundary value problem (2.18) stably using the given B z data, we previously proposed the single current harmonic B z algorithm in [32]. This algorithm can be divided into three steps.…”

“…In [32], we developed an iterative reconstruction algorithm, the single current harmonic B z algorithm, to reconstruct the conductivity from a single current administration. In this paper, we provided a strict mathematical analysis of the convergence behavior of the single current harmonic B z algorithm.…”

“…For these reasons, although we could accelerate the data acquisition through sub-sampling the time-consuming phase encoding process to improve the temporal resolution [29,30,31], the most efficient reconstruction algorithm is to exploit the B z set produced by only one injection current. This approach has been used in [11,32], to develop MREIT reconstruction methods that may be more suitable for practical clinical implementation.…”

“…In [32], we proposed a reconstruction algorithm, called the single current harmonic B z algorithm, to solve the two-dimensional first order linear hyperbolic PDE (1.1) with respect to ln σ to determine the conductivity using a single B z data set. In this novel algorithm, we take advantage of the forward model ∇ xy • J = 0 to track the change of conductivity along the direction of the current density.…”

“…In section 2, we briefly introduce the inverse problem model for MREIT with one-current injection, and then derive a 2-dimensional model for which we state the uniqueness of the conductivity reconstruction. In section 3, we review the single current harmonic B z algorithm proposed in [32] and establish our main result, the convergence analysis of this algorithm together with the error estimate, which gives a quantitative description of the inversion algorithm. In section 4, we validate the proposed theory for a two-dimensional toy model, the Shepp-Logan model and a more practical CT model.…”