Validation of a Convolution Integral for Conductivity Imaging
Joe R. Feldkamp
Stephen Quirk
Magnetic induction tomography has been under consideration for imaging electrical conductivity distributions within the human body. Multi-coil systems are most commonly employed for this task, requiring a numerical solution of Maxwell's equations at each position of the coil array. An alternative uses a single coil placed near the conductive target while measuring coil self-impedance changes (``coil loss'') at a number of unique locations. Recently, a closed-form solution of Maxwell's equations, in the form of a 3D convolution integral, was found for a single coil consisting of concentric circular loops that relates impedance change to an arbitrary conductivity. Its development required spatially uniform permittivity and permeability, yet showed quantitative agreement with experiment. Here, we provide a much more critical test of the convolution integral in experiments that allow large permittivity changes over coil dimensions. Loss is measured while the coil is placed at known positions relative to plastic columns of variable diameter which are filled with salt solutions of varying conductivity. In all cases, coil loss varies linearly with conductivity and with zero intercept. Quantitative agreement is observed only when column diameter is greater than or equal to coil diameter. Because of linearity, the convolution integral is useful for image reconstruction, though contrast could be either reduced or enhanced in those circumstances when relative permittivity change exceeds ~70.
