In vivo measurement of the brain and skull resistivities using an EIT-based method and realistic models for the head

In vivo measurements of equivalent resistivities of skull (ρ_skull) and brain (ρ_brain) are performed for six subjects using an electric impedance tomography (EIT)-based method and realistic models for the head. The classical boundary element method (BEM) formulation for EIT is very time consuming. However, the application of the Sherman-Morrison formula reduces the computation time by a factor of 5. Using an optimal point distribution in the BEM model to optimize its accuracy, decreasing systematic errors of numerical origin, is important because cost functions are shallow. Results demonstrate that ρ_skull/ρ_brain is more likely to be within 20 and 50 rather than equal to the commonly accepted value of 80. The variation in ρ_brain (average = 301 Ω · cm, SD = 13%) and ρ_skull (average = 12230 Ω · cm, SD = 18%) is decreased by half, when compared with the results using the sphere model, showing that the correction for geometry errors is essential to obtain realistic estimations. However, a factor of 2.4 may still exist between values of ρ_skull/ρ_brain corresponding to different subjects. Earlier results show the necessity of calibrating ρ_brain and ρ_skull by measuring them in vivo for each subject, in order to decrease errors associated with the electroencephalogram inverse problem. We show that the proposed method is suited to this goal.