Electrical Neuroimaging with Irrotational Sources.

This paper discusses theoretical aspects of the modeling of the sources of the EEG (i.e., the bioelectromagnetic inverse problem or source localization problem). Using the Helmholtz decomposition (HD) of the current density vector (CDV) of the primary current into an irrotational (I) and a solenoidal (S) part we show that only the irrotational part can contribute to the EEG measurements. In particular we present for the first time the HD of a dipole and of a pure irrotational source. We show that, for both kinds of sources, I extends all over the space independently of whether the source is spatially concentrated (as the dipole) or not. However, the divergence remains confined to a region coinciding with the expected location of the sources, confirming that it is the divergence rather than the CDV that really defines the spatial extension of the generators, from where it follows that an irrotational source model (ELECTRA) is always physiologically meaningful as long as the divergence remains confined to the brain. Finally we show that the irrotational source model remains valid for the most general electrodynamics model of the EEG in inhomogeneous anisotropic dispersive media and thus far beyond the (quasi) static approximation.

Spatiotemporal scales and links between electrical neuroimaging modalities.

Recordings of brain electrophysiological activity provide the most direct reflect of neural function. Information contained in these signals varies as a function of the spatial scale at which recordings are done: from single cell recording to large scale macroscopic fields, e.g., scalp EEG. Microscopic and macroscopic measurements and models in Neuroscience are often in conflict. Solving this conflict might require the developments of a sort of bio-statistical physics, a framework for relating the microscopic properties of individual cells to the macroscopic or bulk properties of neural circuits. Such a framework can only emerge in Neuroscience from the systematic analysis and modeling of the diverse recording scales from simultaneous measurements. In this article we briefly review the different measurement scales and models in modern neuroscience to try to identify the sources of conflict that might ultimately help to create a unified theory of brain electromagnetic fields. We argue that seen the different recording scales, from the single cell to the large scale fields measured by the scalp electroencephalogram, as derived from a unique physical magnitude--the electric potential that is measured in all cases--might help to conciliate microscopic and macroscopic models of neural function as well as the animal and human neuroscience literature.

EEG/MEG source imaging: methods, challenges, and open issues.

We present the four key areas of research-preprocessing, the volume conductor, the forward problem, and the inverse problem-that affect the performance of EEG and MEG source imaging. In each key area we identify prominent approaches and methodologies that have open issues warranting further investigation within the community, challenges associated with certain techniques, and algorithms necessitating clarification of their implications. More than providing definitive answers we aim to identify important open issues in the quest of source localization.

Methods for determining frequency- and region-dependent relationships between estimated LFPs and BOLD responses in humans.

The relationship between electrophysiological and functional magnetic resonance imaging (fMRI) signals remains poorly understood. To date, studies have required invasive methods and have been limited to single functional regions and thus cannot account for possible variations across brain regions. Here we present a method that uses fMRI data and singe-trial electroencephalography (EEG) analyses to assess the spatial and spectral dependencies between the blood-oxygenation-level-dependent (BOLD) responses and the noninvasively estimated local field potentials (eLFPs) over a wide range of frequencies (0-256 Hz) throughout the entire brain volume. This method was applied in a study where human subjects completed separate fMRI and EEG sessions while performing a passive visual task. Intracranial LFPs were estimated from the scalp-recorded data using the ELECTRA source model. We compared statistical images from BOLD signals with statistical images of each frequency of the eLFPs. In agreement with previous studies in animals, we found a significant correspondence between LFP and BOLD statistical images in the gamma band (44-78 Hz) within primary visual cortices. In addition, significant correspondence was observed at low frequencies (<14 Hz) and also at very high frequencies (>100 Hz). Effects within extrastriate visual areas showed a different correspondence that not only included those frequency ranges observed in primary cortices but also additional frequencies. Results therefore suggest that the relationship between electrophysiological and hemodynamic signals thus might vary both as a function of frequency and anatomical region.

Bayesian models of mentalizing.

Surprisingly effortless is the human capacity known as "mentalizing", i.e., the ability to explain and predict the behavior of others by attributing to them independent mental states, such as beliefs, desires, emotions or intentions. This capacity is, among other factors, dependent on the correct anticipation of the dynamics of facially expressed emotions based on our beliefs and experience. Important information about the neural processes involved in mentalizing can be derived from dynamic recordings of neural activity such as the EEG. We here exemplify how the so-called Bayesian probabilistic models can help us to model the neural dynamic involved in the perception of clips that evolve from neutral to emotionally laden faces. Contrasting with conventional models, in Bayesian models, probabilities can be used to dynamically update beliefs based on new incoming information. Our results show that a reproducible model of the neural dynamic involved in the appraisal of facial expression can be derived from the grand mean ERP over five subjects. One of the two models used to predict the individual subject dynamic yield correct estimates for four of the five subjects analyzed. These results encourage the future use of Bayesian formalism to build more detailed models able to describe the single trial dynamic.

Electrical neuroimaging based on biophysical constraints.

This paper proposes and implements biophysical constraints to select a unique solution to the bioelectromagnetic inverse problem. It first shows that the brain's electric fields and potentials are predominantly due to ohmic currents. This serves to reformulate the inverse problem in terms of a restricted source model permitting noninvasive estimations of Local Field Potentials (LFPs) in depth from scalp-recorded data. Uniqueness in the solution is achieved by a physically derived regularization strategy that imposes a spatial structure on the solution based upon the physical laws that describe electromagnetic fields in biological media. The regularization strategy and the source model emulate the properties of brain activity's actual generators. This added information is independent of both the recorded data and head model and suffices for obtaining a unique solution compatible with and aimed at analyzing experimental data. The inverse solution's features are evaluated with event-related potentials (ERPs) from a healthy subject performing a visuo-motor task. Two aspects are addressed: the concordance between available neurophysiological evidence and inverse solution results, and the functional localization provided by fMRI data from the same subject under identical experimental conditions. The localization results are spatially and temporally concordant with experimental evidence, and the areas detected as functionally activated in both imaging modalities are similar, providing indices of localization accuracy. We conclude that biophysically driven inverse solutions offer a novel and reliable possibility for studying brain function with the temporal resolution required to advance our understanding of the brain's functional networks.