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Theoretical limits to sensitivity and resolution in magneto-acousto-electrical tomography

2017-10-21
GHALICHI, Elyar
Gençer, Nevzat Güneri
In this study, the performance of magneto-acousto-electrical tomography (MAET) is investigated quantitatively by considering interrelations between its sensitivity, resolution and conductivity contrast. An analytical solution for the forward problem of MAET is derived for two-dimensional (2D) concentric bodies by the separation of variables method. The electric potential and the acoustic pressure are separated into their angular and radial components. The series coefficients for these solutions are obtained from their respective boundary conditions. The electric potential on the boundary is related to the acoustic boundary acceleration analytically. From this relation, a sensitivity expression is derived relating fractional change in conductivity contrast to fractional change in the measured electric potential. This expression is a function of the resolution and conductivity contrast of the imaging system. It also depends on the acoustic wave number and the dimensions of the body. The pair-wise relations between these parameters are presented. The sensitivity behavior of MAET is compared with applied current electrical impedance tomography and the improvements for small inhomogeneities are presented. For eccentric bodies, a modified expression for the sensitivity is obtained by conformal mapping. For arbitrary periodic boundary excitations, the sensitivity expressions for harmonic cases are combined to obtain a unified sensitivity expression.