CONICET | Buscador de Institutos y Recursos Humanos

1 IntroductionThe scalp and skull conductivity values (σ) are important for source localization in EEG and in EIT, and for dose estimation in TES. In parametric or bounded EIT (bEIT), a harmless electric current is applied on the scalp and the apparent scalp and skull conductivities are estimated by adjusting the model parameters to fit the scalp potential measurements. Currently, bEIT combined with state of the art electrical head models is a gold standard technique to estimate noninvasively subject specific scalp and skull conductivity values in-vivo using a simple EEG-like equipment. The wide range of the reported skull estimates (0.004-0.02 S/m) is most likely attributed to the inter-subject variability [4, 5], but also to the fact of different quality models and numerical methods used [6]. BEM like layered models overestimate the skull σ by 23% and neglecting the CSF layer introduces an additional 28% of overestimation [6]. We expand the results of [6] by increasing the subject number and analyzing an impact of the number of mesh elements, the marrow bone, and the skull holes. One of the four subjects is the well-known Atlas Man Collin 27, and two of the subjects are the Caucasian and Asian atlases used in the EGI source localization package GS 3:0.2 MethodsReference models for four adult male subjects labelled as S1, S2, (atlases in GS 3:0), S3, and AM (Colin27) were derived from 1mm MR and CT images. Segmentation and co-registration have been done using the EGI?s BrainK package [7]. bEIT data acquisition (approved by EGI?s IRB): the subjects wear a 128 (S1, S2, and AM) or 256 (S3) channel EGI geodesic net with gelled electrode-to-skin. 20μA current at 27 Hz was administered for 3 seconds in each of the 64 or 128 (S3) distinct current injection pairs.We constructed 4 types of FE tetrahedral meshes labelled M1, M2, M3 and M4 (see Fig. 1) using the iso2mesh package [8]. M1 is a high quality model with detailed skull, including minor foramina, small bones, and marrow bone as a separate tissue (built for all subjects). M2 is the same as M1, but considering the marrow and compact bones as only one tissue (built for all subjects). M3 has a closed skull, but keeping other skull geometrical details (built for S1 and AM). M4 was built from enclosed and non-intersecting surfaces, mimicking BEM models where skull surfaces needed several steps of smoothing (built for S1 and AM).Each forward problem (FP) was computed using linear FEM with the Galerking approach and considering the complete electrode model boundary conditions [9, 10]. We used the classic Newton's method to solve the inverse problem (IP) [10].3 Results:We built 6-8 million elements M1 and M2 for all subjects and 2 million elements M1 for S1 and S2, and estimated the scalp, skull and MB conductivities. For S1 and AM we also estimated the conductivities using M4, and for AM we added the estimations using M3. In all cases the estimations were done for each current injection pair individually. A 10-15% of the estimations corresponding to different injection pairs were discarded from the analysis because either the IP method failed to converge or the results were considered outliers. Fig. 2 shows a subset of the results.4 ConclusionsInfluence of the number of elements: for S1 and S2, it was low for the skull (4% difference) and negligible for the scalp. See box plots (BP) 3 and 4 for S2.MB: the compact bone σ reduced a 10-25% (compare BP 2-3, and BP 6-7). For precise bEIT compact bone σ estimations, the MB should be considered. Skull holes: comparing BP 7 (M2) and 8 (M3), the skull σ increases a 7%, but comparing BP 7 (M2) and 9 (M4), the effect of a BEM-like model is much larger: a 26% of skull σ overestimation. Note that the 0.07-0.08S/m overestimated value (as with BEM in [3]) is a typical reference. The smoothing the skull-CSF and skull-scalp interfaces increase the skull thickness (mostly at the bottom) resulting in a considerable amount of soft tissue mislabeled as the skull.

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