Effect of domain shape modeling and measurement errors on the 2-D D-bar method for EIT.

Area of Science:

• Computational mathematics
• Electrical impedance tomography
• Medical imaging

Background:

• The inverse conductivity problem seeks to determine internal electrical properties from surface measurements.
• Nachman's 2-D global uniqueness proof provides a theoretical foundation for solving this problem.
• Accurate modeling of complex geometries like the human chest is crucial for clinical applications.

Purpose of the Study:

• To implement and validate the D-bar algorithm for the inverse conductivity problem on a realistic chest-shaped domain.
• To assess the algorithm's performance using simulated data generated with the finite element method.
• To evaluate the robustness of the D-bar algorithm against common sources of error in electrical impedance tomography.

Main Methods:

• The D-bar algorithm, based on Nachman's uniqueness proof, was applied to a chest-shaped domain.
• Scattering transforms were computed using trigonometric and adjacent current patterns.
• The forward problem utilized the finite element method and the complete electrode model to simulate voltage measurements.

Main Results:

• The D-bar algorithm successfully reconstructed conductivity distributions on the chest-shaped domain.
• Simulated voltage measurements were obtained using the finite element method.
• The method demonstrated robustness when subjected to simulated errors in currents, voltages, electrode placement, and domain geometry.

Conclusions:

• The D-bar algorithm is an effective and robust method for solving the 2-D inverse conductivity problem.
• The implementation on a chest-shaped domain using the finite element method shows promise for medical imaging applications.
• The study confirms the practical applicability of the D-bar algorithm in the presence of realistic experimental uncertainties.