A Nodal Jacobian Inverse Solver for Reduced Complexity Eit Reconstructions

Electrical impedance tomography (EIT) uses surface electrodes to make measurements from which an image of the conductivity distribution within some medium is calculated. Calculation of conductivity solutions requires inverting large linear systems that have to date restricted reconstructions to 2D or coarse 3D domains. This paper presents a Nodal Jacobian Inverse Solver that scales with the number of nodes in a finite element mesh rather than with the number of elements. For the example used in this paper the size of the linear system is reduced by a factor of 26. We validate the algorithm by comparing its performance to traditional 2D Elemental Jacobian algorithms. We then analyze its performance with a 21504 element 3D mesh that is too large to be solved with linear algebra systems based on 32 bit pointers (such as is available in current versions of Matlab). Finally, we demonstrate the applicability of the algorithm for clinical use by reconstructing experimentally measured human lung data.