Sensitivity Analysis for Optimizing Electrical Impedance Tomography Protocols

Electrical impedance tomography (EIT) is a noninvasive imaging method whereby electrical measurements on the boundary of a conductive medium (the data) are taken according to a prescribed protocol set and inverted to map the internal conductivity (the model). This paper introduces a sensitivity analysis method and corresponding inversion and protocol optimization that generalizes the criteria for tomographic inversion to minimize the model-space dimensionality and maximize data importance. Sensitivity vectors, defined as rows of the Jacobian matrix in the linearized forward problem, are used to map targeted conductivity features from model-space to data-space, and a volumetric outer-product of these vectors in model-space called the sensitivity parallelotope volume provides a figure-of-merit for data protocol optimization. Orthonormal basis functions that accurately constrain the model-space to features of interest can be defined from a priori information. By increasing the contact number to expand the number of possible measurements Dmax, and by reducing the model-space to a minimal number M0 of basis functions that describe only the features of interest, the M0 << Dmax sensitivity vectors of greatest length and maximal orthogonality that span this model-space can be identified. The reduction in model-space dimensionality accelerates the inversion by several orders of magnitude, and the enhanced sensitivity can tolerate noise levels up to 1,000 times larger than standard protocols.