A Comparison of Bound-Constrained and Positivity-Constrained Optimization Method to Estimate Head Tissue Conductivities by Scalp Voltage Information

Abstract

Electrical Impedance Tomography (EIT) is a noninvasive method used to estimate the conductivity of head tissues. Estimation based on the unconstrained Gauss-Newton (GN) method is conventional, but it may result in negative-value or extraordinary high-value estimates, which are unexpected. In this study, the bound-constrained method and the positivity-constrained optimization method were investigated and compared to the unconstrained optimization method. A two-dimensional model was created for conductivity estimation containing five head tissues, i.e., the scalp, the skull, the cerebrospinal fluid (CSF), grey matter (GM), and white matter (WM). The results showed that the accuracy, the robustness, and the estimation convergence of the estimation of this approach were significantly improved by constraining. All unexpected values also disappeared. The investigation proved that very high sensitivity of the skull region caused the unexpected outcome of the unconstrained cases. This high sensitivity can be significantly reduced by constraining. However, a degree of estimation nonlinearity can be increased by constraining as well, causing some estimation accuracies in the case of the positivity-constrained optimization method to be poor. Therefore, it is recommended to use only the bound-constrained optimization method.