Single-coil magnetic induction tomographic three-dimensional imaging

Abstract

Abstract. Previously, magnetic induction tomography (MIT) has been considered for noncontact imaging of human tissue electrical properties. Commonly, multiple coils are used, with any one serving as the source while others detect eddy currents generated in the specimen. Here, imaging of low conductivity objects is shown feasible with a single coil acting simultaneously as source and detector, provided that the coil is repeatedly relocated while collecting coil loss data. To enable such "scanning," an analytical coil loss formula is derived in the quasistatic limit for a single coil consisting of several concentric circular wire loops, all within a common plane. Conductivity may vary arbitrarily in space, whereas permittivity and permeability are treated as uniform. The analytical form is used to build an algorithm for imaging electrical conductivity in human tissues. A practical device operating at 12.5 MHz is described and used in a clinical trial that "scans" the region between the scapulae while collecting coil loss data. Inversion of data leads to electrical conductivity distribution images for the thoracic spinal column which are the first of their kind to correctly distinguish such basic features as size and depth of spinal canal, as well as size, depth, and spacing of transverse spinal processes. © The Authors. Published by SPIE under a Creative Commons Attribution 3.0 Unported License. Distribution or reproduction of this work in whole or in part requires full attribution of the original publication, including its DOI.

Validation of a Convolution Integral for Conductivity Imaging

“…Coil geometry and construction is identical to that described previously [9] -two planes of concentric circular loops, spaced 0.5 mm, prepared on a double-layer printed circuit board (PCB). Loop traces are 0.5 mm wide, built from 2 oz.…”

“…Equation (4) is a reasonable approximation for our coil's inductance provided that the distance between layers is very small compared with loop radii. Inductance for our coil was calculated to be 2.155 µH, which is used in all computations here and agrees with measurement to within 1% [9]. Coil loss, known to be weak and difficult to measure [11], is computed from a change in the real part of admittance, δY re , relative to the free space value, which subtracts the effect of any loss intrinsic to the coil.…”

“…There is a 1 mm buildup of PCB material on the side of the coil facing outward, so that there is at least a 1 mm separation between coil and target. Coil inductance, L, is calculated from Equations (5) and (6) of earlier work [9] -the latter repeated here in more general form in terms of loop self-inductance, L sj , and mutual inductances between loops, M jk :…”

“…The recently developed closed-form analytical expression [9] for inductive loss (or impedance change) may be written as a 3D convolution integral that convolves conductivity σ( r) with the kernel G( r c ). Given the rotation matrixR, vector r c =R T ( r − c) locates the field point in the coordinate system of the coil, and vector c locates the coil center relative to the lab frame origin:…”

“…Nevertheless, these closed-form expressions all have the difficulty that conductivity is treated as spatially invariant within the target geometries studied, making them unsuitable candidates for conductivity imaging. More recently [9], a closed-form expression relating impedance change, which we will call inductive loss since impedance change shows up as a dissipative resistive load in series with the coil, was developed that imposes no requirement on the electrical conductivity distribution. Though this makes it an attractive candidate for conductivity imaging, the expression was derived at the expense of treating permittivity and permeability as spatially uniform.…”