Electrical Impedance Tomography (EIT) in 3D: Introducing the Sensitivity Method for Biomedical Imaging

Electrical impedance tomography (EIT) is a noninvasive imaging method whereby electrical measurements on the periphery of a conductor are inverted to map its internal conductivity. The method proposed here, called the sensitivity method, is anticipated to outperform prior EIT methods since the model-space dimensionality is minimized for increased feature specificity and data importance is maximized through optimal reduction of data-space thereby allowing computationally efficient, noise-tolerant 3D mapping, a longstanding goal of biomedical imaging. Sensitivity vectors, defined as rows of the Jacobian matrix of the linearized EIT forward problem, are combined in sets of greatest length and maximal orthogonality and their volumetric outer-product in model-space is introduced as a previously absent figure-of-merit for optimal data-space selection. By increasing the contact number to expand the maximum data-space dimensionality, and by reducing the model-space to describe only the features of interest, optimal data-spaces can be identified according to this figure of merit. The reduction in model-space dimensionality accelerates inversion by several orders of magnitude, while the enhanced sensitivity tolerates noise levels up to 1,000 times larger than datasets generated from standard data-spaces. Phantom models of 2D and 3D conducting volumes will be simulated and experimentally demonstrated.