Effects of electrode location error on boundary element impedance tomography solutions: CR bounds and simulation results

Electrical impedance tomography is an imaging modality that estimates the conductivity map inside a volume from electrical measurements on its surface. It is a badly posed inverse problem; one stabilization approach approximates the volume as having piecewise constant conductivity. One can then use the boundary element method, particularly advantageous if conductivity discontinuity boundaries, (internal organ boundaries), are first measured by anatomical imaging, and only conductivities are unknown. Even in this setting solutions are sensitive to modeling error, in particular mis-locating the electrodes used to inject current and measure voltage. We study this sensitivity by calculating the Cramer-Rao lower bound and through simulations. We explore three measurement methods in both static and dynamic imaging. Results show that sensitivity is particularly high for localized inhomogeneities, and on electrodes closest to them, that dynamic imaging is more robust than static, and that measuring voltages on all electrodes, including those injecting current, is especially important