The symmetric BEM: bringing in more variables for better accuracy

International audienceElectrophysiological modeling of Magneto- and Electro-encephalography (MEG and EEG) rely on accurate forward solvers that relate source activities to sensor measurements. In comparing a Boundary Element (BEM) and a Finite Element Method (FEM) for forward electroencephalography, in our early numerical experiments, we found the FEM to have a better accuracy than the BEM. This triggered a quest to improve the accuracy of Boundary Element Methods and led us to study the extended Green representation theorem. A fundamental result in potential theory shows that, up to an additive constant, a harmonic function is determined within a domain from its value on the boundary (Dirichlet condition), or the value of its normal derivative (Neumann condition). The Green Representation Theorem has been used in forward EEG and MEG modeling, in deriving the Geselowitz BEM formulation, and the Isolated Problem Approach. The extended Green Representation Theorem provides a representation for the directional derivatives of a piecewise-harmonic function. By introducing the normal current as an additional variable in the forward problem, we derive a new Boundary Element Method, which leads to a symmetric matrix structure: we hence call it the Symmetric BEM. Accuracy comparisons demonstrate the superiority of the Symmetric BEM to the FEM and to the classical BEM

Fast Approximation of EEG Forward Problem and Application to Tissue Conductivity Estimation

Bioelectric source analysis in the human brain from scalp electroencephalography (EEG) signals is sensitive to the conductivity of the different head tissues. Conductivity values are subject dependent, so non-invasive methods for conductivity estimation are necessary to fine tune the EEG models. To do so, the EEG forward problem solution (so-called lead field matrix) must be computed for a large number of conductivity configurations. Computing one lead field requires a matrix inversion which is computationally intensive for realistic head models. Thus, the required time for computing a large number of lead fields can become impractical. In this work, we propose to approximate the lead field matrix for a set of conductivity configurations, using the exact solution only for a small set of basis points in the conductivity space. Our approach accelerates the computing time, while controlling the approximation error. Our method is tested for brain and skull conductivity estimation , with simulated and measured EEG data, corresponding to evoked somato-sensory potentials. This test demonstrates that the used approximation does not introduce any bias and runs significantly faster than if exact lead field were to be computed.Comment: Copyright (c) 2019 IEEE. Personal use of this material is permitted. However, permission to use this material for any other purposes must be obtained from the IEEE by sending a request to [email protected]

Domain-general Stroop Performance and Hemispheric Asymmetries: A Resting-state EEG Study

The ability to suppress irrelevant information while executing a task or interference resistance is a function of pFC that is critical for successful goal-directed human behavior. In the study of interference resistance and, more generally, executive functions, two key questions are still open: Does pFC contribute to cognitive control abilities through lateralized but domain-general mechanisms or through hemispheric specialization of domain-specific processes? And what are the underlying causes of interindividual differences in executive control performance? To shed light on these issues, here we employed an interindividual difference approach to investigate whether participants' hemispheric asymmetry in resting-state electrophysiological brain dynamics may reflect their variability in domain-general interference resistance. We recorded participants' resting-state electroencephalographic activity and performed spectral power analyses on the estimated cortical source activity. To measure participants' lateralized brain dynamics at rest, we computed the right-left hemispheric asymmetry score for the \u3b2/\u3b1 power ratio. To measure their domain-general interference resistance ability, verbal and spatial Stroop tasks were used. Robust correlations followed by intersection analyses showed that participants with stronger resting-state-related left-lateralized activity in different pFC regions, namely the mid-posterior superior frontal gyrus, middle and posterior middle frontal gyrus, and inferior frontal junction, were more able to inhibit irrelevant information in both domains. The present results confirm and extend previous findings showing that neurophysiological difference factors may explain interindividual differences in executive functioning. They also provide support for the hypothesis of a left pFC hemispheric specialization for domain-independent phasic cognitive control processes mediating Stroop performance

Domain decomposition for coupling finite and boundary element methods in EEG

International audienceThe forward problem in electroencephalography aims to simulate on the scalp the potential V of an electromagnetic field generated by a simulated source. It must fit precisely with the electromagnetic propagation in the patient head. Yet, the skull anisotropy happens to be highly anisotropic, and must then be modeled. Although boundary element methods cannot deal with anisotropy like finite element methods, the symmetric BEM offers a higher accuracy than FEM wherever the conductivity can be considered as constant (i.e. for the brain and the scalp). A domain decomposition (DD) framework allows to split the global system into several ones with smaller computational domains. Then, one method (BEM or FEM) can be used per volume. This work presents such a coupling formulation of a 3-DD method solving iteratively a BEM for the brain, a FEM for the skull layer, and finally a BEM for the scalp

Large brain effective network from EEG/MEG data and dMR information

International audienceOver the past 30 years, neuroimaging has become a predominant technique. One might envision that over the next years it will play a major role in disclosing the brain's functional interactions. In this work, we use information coming from diffusion magnetic resonance imaging (dMRI) to reconstruct effective brain network from two functional modalities: electroencephalography (EEG) and magnetoen-cephalography (MEG)