title: Using reciprocity for relating the simulation of transcranial current stimulation to the EEG forward problem.
abstract: To explore the relationship between transcranial current stimulation (tCS) and the electroencephalography (EEG) forward problem, we investigate and compare accuracy and efficiency of a reciprocal and a direct EEG forward approach for dipolar primary current sources both based on the finite element method (FEM), namely the adjoint approach (AA) and the partial integration approach in conjunction with a transfer matrix concept (PI). By analyzing numerical results, comparing to analytically derived EEG forward potentials and estimating computational complexity in spherical shell models, AA turns out to be essentially identical to PI. It is then proven that AA and PI are also algebraically identical even for general head models. This relation offers a direct link between the EEG forward problem and tCS. We then demonstrate how the quasi-analytical EEG forward solutions in sphere models can be used to validate the numerical accuracies of FEM-based tCS simulation approaches. These approaches differ with respect to the ease with which they can be employed for realistic head modeling based on MRI-derived segmentations. We show that while the accuracy of the most easy to realize approach based on regular hexahedral elements is already quite high, it can be significantly improved if a geometry-adaptation of the elements is employed in conjunction with an isoparametric FEM approach. While the latter approach does not involve any additional difficulties for the user, it reaches the high accuracies of surface-segmentation based tetrahedral FEM, which is considerably more difficult to implement and topologically less flexible in practice. Finally, in a highly realistic head volume conductor model and when compared to the regular alternative, the geometry-adapted hexahedral FEM is shown to result in significant changes in tCS current flow orientation and magnitude up to 45° and a factor of 1.66, respectively.
authors.affiliation: Institute for Biomagnetism and Biosignalanalysis, University of Münster, Münster, Germany.
authors.forename: S
authors.initials: S
authors.lastname: Wagner
authors.affiliation: Institute for Biomagnetism and Biosignalanalysis, University of Münster, Münster, Germany; Institute for Computational and Applied Mathematics, University of Münster, Münster, Germany; Centre for Medical Image Computing, University College London, WC1E 6BT London, UK.
authors.forename: F
authors.initials: F
authors.lastname: Lucka
authors.affiliation: Institute for Biomagnetism and Biosignalanalysis, University of Münster, Münster, Germany.
authors.forename: J
authors.initials: J
authors.lastname: Vorwerk
authors.affiliation: Experimental Psychology Lab, Center for Excellence Hearing4all, European Medical School, University of Oldenburg, Oldenburg, Germany.
authors.forename: C S
authors.initials: CS
authors.lastname: Herrmann
authors.affiliation: Department of Neurophysiology and Pathophysiology, University Medical Center Hamburg-Eppendorf, Hamburg, Germany.
authors.forename: G
authors.initials: G
authors.lastname: Nolte
authors.affiliation: Institute for Computational and Applied Mathematics, University of Münster, Münster, Germany; Cells in Motion Cluster of Excellence, University of Münster, Münster, Germany.
authors.forename: M
authors.initials: M
authors.lastname: Burger
authors.affiliation: Institute for Biomagnetism and Biosignalanalysis, University of Münster, Münster, Germany; Cells in Motion Cluster of Excellence, University of Münster, Münster, Germany. Electronic address: carsten.wolters@uni-muenster.de.
authors.forename: C H
authors.initials: CH
authors.lastname: Wolters
mesh_terms: D001921:Brain / Q000502:physiology*; D001931:Brain Mapping / Q000379:methods*; D003198:Computer Simulation; D004553:Electric Conductivity; D004569:Electroencephalography / Q000379:methods* / Q000592:standards; D005071:Evoked Potentials / Q000502:physiology*; D006257:Head / Q000502:physiology; D006801:Humans; D008959:Models, Neurological; D009415:Nerve Net / Q000502:physiology*; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D065908:Transcranial Direct Current Stimulation / Q000379:methods*
keywords: EEG forward problem; Evaluation in realistic head model; Finite element method; Reciprocity; Transcranial current stimulation; Validation in multilayer sphere model