A Discussion on the Algorithm Design of Electrical Impedance Tomography for Biomedical Applications

In this chapter, we present a discussion on the algorithm design of Electrical Impedance Tomography (EIT) for biomedical applications. Based on the Maxwell differential equations and the derived finite element (FE) linear equations, we first investigate the possibility to estimate the matrix that contains the impedance values based on Singular Value Decomposition (SVD) approximations. Secondly based on the biomedical properties we further explore the possibility to recover the impedance values uniquely by injecting various different types of currents with multi-frequency. Injecting various types of multi-frequency currents lead to a set of different measured voltages configurations, thus enhancing the possibility of uniquely recovering the impedance values in a stable way under the assumption that the biological cells respond to the different types of injecting currents in a different way. By converting the Maxwell differential equations into linear equations by Finite Element (FE) method, we are able to focus on the discussions based on the linear algebra method. We also explore some insights into the biological cells' electrical properties so that we can make use of the biological cell's electrical properties to make the numerical algorithm design more stable and robust.