Using reciprocity for relating the simulation of transcranial current stimulation to the EEG forward problem

• Published in: NeuroImage (Orlando, Fla.) Vol. 140; pp. 163 - 173
• Main Authors: Wagner, S., Lucka, F., Vorwerk, J., Herrmann, C.S., Nolte, G., Burger, M., Wolters, C.H.
• Format: Journal Article
• Language: English
• Published: United States Elsevier Inc 15-10-2016; Elsevier Limited
• Subjects: Alzheimer's disease; Brain - physiology; Brain Mapping - methods; Computer Simulation; EEG forward problem; Electric Conductivity; Electrodes; Electroencephalography - methods; Electroencephalography - standards; Evaluation in realistic head model; Evoked Potentials - physiology; Finite element method; Geometry; Head - physiology; Humans; Mathematical functions; Models, Neurological; Nerve Net - physiology; NMR; Nuclear magnetic resonance; Partial differential equations; Reciprocity; Reproducibility of Results; Sensitivity and Specificity; Studies; Transcranial current stimulation; Transcranial Direct Current Stimulation - methods; Validation in multilayer sphere model; Finite element method; Evaluation in realistic head model; EEG forward problem; Transcranial current stimulation; Reciprocity; Validation in multilayer sphere model
• ISSN: 1053-8119; 1095-9572
• DOI: 10.1016/j.neuroimage.2016.04.005

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.
•Comparison of a reciprocal and a direct finite element method EEG forward approach•Direct link between EEG forward problem and transcranial current stimulation (tCS)•Validation using tetrahedral, regular and geometry adapted hexahedral models•Significant changes in tCS current flow modeling in a realistic head model