A Sensitivity-Based Algorithm Approach in Reconstructing Images in Electrical Impedance Tomography

Electrical impedance tomography (EIT) is a medical imaging technique used to reconstruct images inside the domain of interest. EIT collects data on the boundary of the domain to infer the conductivity distribution inside the domain. The conductivity distribution will then be used to produce a tomographic image of the inside of the domain. This paper aims to recover geometric properties of a spherical perturbation in the conductivity inside a domain using sensitivity values of the electric potential on the boundary of the domain. The continuum model for EIT is first considered, as it holds more boundary information compared to other models of EIT. A change on the conductivity inside the domain is applied, and the impact on the electric potential is studied. The inverse EIT problem is then solved by formulating relations between the sensitivity values on the boundary and the geometric properties of the spherical perturbation: the radius and the projection onto the boundary and depth of its center. A reconstruction method using these relations is proposed and the method is examined by performing numerical simulations on different domains to model the head and the thorax. Lastly, the proposed method is applied to the complete electrode model of the EIT problem to analyze the performance of the method when the boundary data is limited on the electrodes.