Direct calculation of the electrode movement Jacobian for 3D EIT

Electrical Impedance Tomography (EIT) of media with deformable boundaries is very sensitive to electrode movement. This is especially important for EIT images of the thorax, which become distorted with breathing and posture change. Previously, we proposed a reconstruction method for imaging conductivity change and electrode movement based on an indirect perturbation Jacobian calculation, involving the re-computation of the forward solution. Although suitable for 2D and small 3D imaging, the reconstruction accuracy of this method gradually decreases, while the computation time grows rapidly for large 3D problems. We propose an efficient, novel method of calculating the Jacobian matrix directly from the Finite Element Method (FEM) system equations, without the re-calculation of the forward solution. The implemented algorithm is based on asymmetric rankone perturbations of the admittance matrix. We show that the measurement sensitivity calculations, due to the displacement of each electrode, reduce to operations on small submatrices of the FEM system matrix. The proposed algorithm is applied to simulated data using 3D FEM reconstruction models of various element densities. The computation speed and the reconstruction fidelity are compared between the proposed and previous methods. Keywords—electrical impedance tomography, electrode movement, inverse problems.