Semester

Fall

Date of Graduation

2005

Document Type

Dissertation

Degree Type

PhD

College

Statler College of Engineering and Mineral Resources

Department

Lane Department of Computer Science and Electrical Engineering

Committee Chair

Bojan Cukic.

Abstract

It is well known that biological tissues possess impedance properties that might be useful in medical diagnostics and treatment. Electrical Impedance Tomography (EIT) images internal electrical properties by using numerical methods to solve Laplace's differential equation. The indirect reconstruction method (IRM), a common method in application, predicts internal electrical property distribution by iteratively computing a forward and inverse solution. This approach reduces the non-linear Laplace's equation into a poorly conditioned series of linear equations, which are solved simultaneously. This method suffers from high computational effort and is susceptible to prediction errors that stem from measurement noise.;As an alternative to Laplace's differential equation, this research applies the quasi-static approximation, Dirichlet boundary conditions and a rectangular shaped domain (with corresponding Green's function for Cartesian coordinates) to solve the integral form of Poisson's equation (Green's 2nd identity). The result is the charge-charge correlation method (CCCM), a well-conditioned relationship between static charge build-up at internal structures and induced domain boundary charge build-up (which corresponds to measured boundary current). The CCCM is applied in a reconstruction technique called Electrical Property Enhanced Tomography (EPET). While related to the existing impedance imaging methods, EPET does not attempt to create the image with the electrical data but rather adds electrical property information to an existing conventional imaging modality (CT or MI) and, in fact, requires the data from the other modality to locate the position of internal structures in the object. Predicted electrical properties are then superimposed over the a priori structural image to yield the electrical property distribution.;To test the feasibility of the CCCM, experiments using agar media placed in a saline bath were performed. The position, size and conductivity of the agar were varied and the CCCM applied to predict the conductivities from external boundary current measurements. Predicted conductivities yielded relative errors less than 10%, results that are equal to or better than the IRM. Additionally, CCCM was able to compute these results with a 104 improvement in speed over the IRM.

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