Electrical impedance tomography through constrained sequential linear programming: a topology optimization approach

Abstract

Electrical impedance tomography (EIT) is an imaging method that estimates conductivity distribution inside a body. In EIT, images are obtained by applying a sequence of low intensity electrical currents through electrodes attached to the body. Although in EIT there are serious difficulties to obtain a high-quality conductivity image, for medical applications this technology is safer and cheaper than other tomography techniques. The EIT deals with an inverse problem in which given the measured voltages on electrodes and a finite element (FE) model, it estimates the conductivity distribution, which are parameters of the FE model. In this work, the topology optimization method is applied as a reconstruction algorithm to obtain absolute images in EIT. It is an optimization method that has been applied successfully to structural mechanical applications and consists of systematically finding a conductivity distribution (or material distribution) in the domain that minimizes the difference between measured voltages and voltages calculated by using a computational model. This algorithm combines the finite element method and sequential linear programming (SLP) to solve the inverse problem of EIT. The SLP allows us to easily apply some regularization schemes based on included constraints in the topology optimization problem. Constraints based on image tuning control and weighted distance interpolation (WDI) are proposed, while a material model is applied to ensure the relaxation of the optimization problem. A new formulation to analytically perform the sensitivity analysis is proposed, using Maxwell's reciprocity theorem. To illustrate, the implemented algorithm is applied to obtain conductivity image distributions of some 2D examples using numerical and experimental data.