A finite-element reciprocity solution for EEG forward modeling with realistic individual head models

Abstract

We present a finite element modeling (FEM) implementation for solving the forward problem in electroencephalography (EEG). The solution is based on Helmholtz's principle of reciprocity which allows for dramatically reduced computational time when constructing the leadfield matrix. The approach was validated using a 4-shell spherical model and shown to perform comparably with two current state-of-the-art alternatives (OpenMEEG for boundary element modeling and SimBio for finite element modeling).We applied the method to real human brain MRI data and created a model with five tissue types: white matter, grey matter, cerebrospinal fluid, skull, and scalp. By calculating conductivity tensors from diffusion-weighted MR images, we also demonstrate one of the main benefits of FEM: the ability to include anisotropic conductivities within the head model. Root-mean square deviation between the standard leadfield and the leadfield including white-matter anisotropy showed that ignoring the directional conductivity of white matter fiber tracts leads to orientation-specific errors in the forward model. Realistic head models are necessary for precise source localization in individuals. Our approach is fast, accurate, open-source and freely available online.

Head models of healthy and depressed adults for simulating the electric fields of non-invasive electric brain stimulation

“…At our data repository [27] we also provide the manually corrected segmentations for the different tissue types for those who would like to create high-quality meshes of their own using open-source software such as iso2mesh [39]. Finally, our meshes can be used for improving the anatomic precision of EEG source localization, using open-source tools [23].…”

“…Therefore, finite element models (FEM) derived from high resolution MR images have become more widespread because they are able to incorporate more tissue types, increasing the precision of EEG source localization. Our head models can be used for source localization using open-source software [23]. Thus, our head models can help researchers to optimize NIBS protocols and EEG source localization methods, and to test them on a larger sample (including both healthy and patient data).…”

Biophysical modeling of the neural origin of EEG and MEG signals

“…The model was constructed by taking advantage of the reciprocity theorem, stating that the position of the electrode and the dipolar source can be switched without affecting the measured potential [Rush and Driscoll, 1969]. This means, that virtually injecting current at the locations of the EEG electrodes and using the finite element method [Logg et al, 2012] to compute the resulting potential anywhere in the brain, gives the link between current dipoles in the brain and the resulting EEG signals [Malmivuo and Plonsey, 1995;Ziegler et al, 2014;Huang et al, 2016;Dmochowski et al, 2017]. This link was captured in a matrix known as the lead field L [Nunez and Srinivasan, 2006]:…”

“…The number of computing hours is, however, reduced by applying the reciprocity principle of Helmholtz. The reciprocity principle states, in short, that switching the location of a current source and a recording electrode will not affect the measured potential [Malmivuo and Plonsey, 1995;Ziegler et al, 2014;Huang et al, 2016;Dmochowski et al, 2017].…”

Evaluation of numerical techniques for solving the current injection problem in biological tissues

“…In particular, accurate solution of the current injection problem [5, 6, 4, 7] is crucial for both clinical pre-surgical planning [2], and therapeutic applications [8]. Current injection directly models TCS and also provides the basis for efficient reciprocity-based computation of EEG forward solutions [9]. …”