In Vivo Estimation of Head Tissue Conductivities Using Bound Constrained Optimization

The conductivity of head tissues was noninvasively estimated using electrical impedance tomography technique. Instead of using conventional unconstrained optimization method to estimate the conductivities, a constrained method with the scaled-logistic function was employed to improve the very high sensitivity of the skull region resulting in accuracy and robustness improvement. Estimation of five conductivities i.e. scalp, skull, cerebrospinal fluid (CSF), grey matter (GM), and white matter (WM) conductivity was investigated by simulation on random and low-value initial guesses. Simulation results showed that the performance of the unconstrained method depended directly to the difference between the exact skull conductivity value and the initial guess value of the skull conductivity. However, the approached constrained method was independent of the guess selection. It can reduce the sensitivity of the skull region by 126 times and reduce the condition number of the sensitivity matrix by 13-17 times. The estimation resulted in only positive and in-range of reported conductivity values. The estimation error of the skull conductivity decreased by 15% and the robustness increased by 2 times. However, the estimation of the CSF, the WM, and the GM may be not reliable due to the very low sensitivity of these regions in both methods.