Topology Optimization Applied to Electrical Impedance Tomography

Abstract Electrical Impedance Tomography (EIT) is a imaging method that estimates conductivity distribution inside a body (domain). In this method, images are obtained by applying a sequence of low intensity electrical currents, through electrodes positioned around the body. Applications of EIT can be often found in geophysics sciences, non-destructive testing and medical applications. Although in EIT there are serious difficulties in obtaining a high-quality conductivity image its technology is safer and cheaper than other tomography techniques. The EIT deals with an inverse problem in which given the measured voltages on electrodes, it estimates the conductivity distribution by using an image reconstruction algorithm. In this work, Topology Optimization Method is applied as a reconstruction algorithm in EIT to obtain images of a foreign material or faults inside a body. This method combines the Finite Element Method and a Sequential Linear Programming (SLP) algorithm to solve the inverse problem of EIT. The SLP allows us to apply easily some regularization schemes based on included constraints in the topology optimization problem, which consists of finding systematically a material distribution (or conductivity distribution) in the domain that minimizes the difference between measured voltages and voltages calculated by using a computational model. A material model based on SIMP is applied to guarantee the relaxation of this optimization problem. The sensitivity analysis is obtained analytically through adjoint method. The implemented algorithm is applied to estimate conductivity distribution of some 2D and 3D examples by using numerical and experimental data, respectively.