Saeed Babaeizadeh

Thesis title: 3-D Electrical Impedance Tomography for Domains with Piecewise Constant Conductivity

Date: Wednesday, January 25, 2006

Abstract:

Electrical Impedance Tomography (EIT), whose goal is to estimate the impedance map inside a volume from electrical measurements on its surface, has been a subject of much recent interest for biomedical applications, for example to construct an impedance model of the torso or head. This inverse problem is badly posed, but can be stabilized if the conductivity is treated as piecewise constant in the volume. In this thesis we treat several aspects of piecewise constant solutions to EIT. First we assume that the boundaries of the constant conductivity regions are known, e.g. via anatomical imaging. In this case methods such as Boundary Elements (BEM) and Finite Elements (FEM) can be used to effectively and robustly estimate the conductivities. We developed a three-dimensional BEM model for the forward EIT problem and three-dimensional inverse solutions for both BEM and FEM for this known-boundary problem. We also developed implementations of sophisticated electrode models for BEM, as well as explicit expressions for all the Jacobians involved. These methods were tested both via simulations using a realistic model of a human torso, and by means of an EIT phantom study carried out at Rensselaer Polytechnic Institue in an experimental tank, to verify the accuracy of both the BEM forward model and the inverse solutions. We achieved accurate estimates of the conductivities even with significant measurement noise over a range of SNR's for both simulations and phantom, even in the face of some inaccuracy in the assumed internal boundary locations.

Since small errors in locating the surface electrodes can significantly reduce the accuracy of EIT conductivity estimates, we also studied sensitivity to electrode mislocation of our known-geometry BEM-based inverse EIT solution, both through simulation and by calculating the Cramer-Rao Lower Bound on the estimate variance, for three common different current injections strategies, and for both static and dynamic imaging. We developed a method based on a likelihood ratio hypothesis test to use the statistical behavior of the residuals to identify potential electrode mislocation. Upon detection of electrode location error, we proposed two approaches to reduce the sensitivity of the reconstruction to this error, one based on separating the background conductivity retrieval from the reconstruction of internal object conductivities, and the other on Principal Component-based projection of the residuals.

We also investigated methods to employ BEM for EIT when the internal boundaries are not known, based on parameterization of the inhomogeneity surfaces using basis shape functions. The unknowns in the inverse problem are then the shape parameters and the conductivities. We employed two surface parameterization methods, one based on modified B-splines and the other on spherical harmonics. The performance of both methods was again tested using both simulations and phantom experiments.

Committee:
Prof. Dana Brooks (advisor)
Prof. Vinay Ingle
Prof. David Isaacson (RPI)
Prof. Eric Miller