Background
The aim of electroencephalogram (EEG) source localization is to find the brain areas responsible for EEG waves of interest. It consists of solving forward and inverse problems. The forward problem is solved by starting from a given electrical source and calculating the potentials at the electrodes. These evaluations are necessary to solve the inverse problem which is defined as finding brain sources which are responsible for the measured potentials at the EEG electrodes.

/pdf/review-on-solving-the-forward-problem-in-eeg-source-analysis-4susg04pdg.pdf

Review on solving the forward problem in EEG source analysis

https://www.sci.utah.edu/publications/wolters06/Tissue_Cond_Anisotropy.pdf

Influence of tissue conductivity anisotropy on EEG/MEG field and return current computation in a realistic head model: A simulation and visualization study using high-resolution finite element modeling

Subject-specific four-layer boundary element method (BEM) electrical forward head models for four participants, generated from magnetic resonance (MR) head images using NFT ( www.sccn.ucsd.edu/wiki/NFT ), were used to simulate electroencephalographic (EEG) scalp potentials at 256 recorded electrode positions produced by single current dipoles of a 3-D grid in brain space. Locations of these dipoles were then estimated using gradient descent within five template head models fit to the electrode positions. These were: a spherical model, three-layer and four-layer BEM head models based on the Montreal Neurological Institute (MNI) template head image, and these BEM models warped to the recorded electrode positions. Smallest localization errors (4.1-6.2 mm, medians) were obtained using the electrode-position warped four-layer BEM models, with largest localization errors (~20 mm) for most basal brain locations. When we increased the brain-to-skull conductivity ratio assumed in the template model scalp projections from the simulated value (25:1) to a higher value (80:1) used in earlier studies, the estimated dipole locations moved outwards (12.4 mm, median). We also investigated the effects of errors in co-registering the electrode positions, of reducing electrode counts, and of adding a fifth, isotropic white matter layer to one individual head model. Results show that when individual subject MR head images are not available to construct subject-specific head models, accurate EEG source localization should employ a four- or five-layer BEM template head model incorporating an accurate skull conductivity estimate and warped to 64 or more accurately 3-D measured and co-registered electrode positions.

/pdf/effects-of-forward-model-errors-on-eeg-source-localization-16l8nj6x3y.pdf

Effects of Forward Model Errors on EEG Source Localization

Electromagnetic source characterisation requires accurate volume conductor models representing head geometry and the electrical conductivity field. Head tissue conductivity is often assumed from previous literature, however, despite extensive research, measurements are inconsistent. A meta-analysis of reported human head electrical conductivity values was therefore conducted to determine significant variation and subsequent influential factors. Of 3121 identified publications spanning three databases, 56 papers were included in data extraction. Conductivity values were categorised according to tissue type, and recorded alongside methodology, measurement condition, current frequency, tissue temperature, participant pathology and age. We found variation in electrical conductivity of the whole-skull, the spongiform layer of the skull, isotropic, perpendicularly- and parallelly-oriented white matter (WM) and the brain-to-skull-conductivity ratio (BSCR) could be significantly attributed to a combination of differences in methodology and demographics. This large variation should be acknowledged, and care should be taken when creating volume conductor models, ideally constructing them on an individual basis, rather than assuming them from the literature. When personalised models are unavailable, it is suggested weighted average means from the current meta-analysis are used. Assigning conductivity as: 0.41 S/m for the scalp, 0.02 S/m for the whole skull, or when better modelled as a three-layer skull 0.048 S/m for the spongiform layer, 0.007 S/m for the inner compact and 0.005 S/m for the outer compact, as well as 1.71 S/m for the CSF, 0.47 S/m for the grey matter, 0.22 S/m for WM and 50.4 for the BSCR.

/pdf/variation-in-reported-human-head-tissue-electrical-1vdua0jfdh.pdf

Variation in Reported Human Head Tissue Electrical Conductivity Values

https://www.sci.utah.edu/~wolters/PaperWolters/2009/RullmannEtAl_NeuroImage_2009.pdf

EEG source analysis of epileptiform activity using a 1 mm anisotropic hexahedra finite element head model.

We experimentally studied the role of the auditory information, and its potential implications to enhance the performance in hammer throwing. We stimulated our athletes auditory by using the rhythmic sound (produced by the impact between the hammer and the air) associated to the best personal throw. The results are coherent with literature claiming that auditory information is an essential factor to guide motor action in sport activities. In fact, all the tested athletes both metrically improved and standardized their performance. This kind of suggestions, merging from applied studies in sport activities, offers important indications to develop cognitive models about mental strategies in sport.

The Relevance of Auditory Information in Optimizing Hammer Throwers Performance

EEG-based source localization techniques use scalp-potential data to estimate the location of underlying neural activity. EEG source location reconstruction requires the assumption of a source model and the assumption of a conductive head model. Brain lesions can present conductivity values that are dramatically different from those of surrounding normal tissues and have to be included in head models for accurate neural source reconstruction. It is therefore necessary to analyze subjects' anatomic images (using MRI or computed tomography) to identify lesion type and to assign the appropriate conductivity value. Source localization accuracy may be influenced by uncertainties in tissue conductivity assignment during head model construction. The authors present a sensitivity study quantifying the effect of uncertainty in brain lesion conductivity assignment on EEG dipole source localization. They adopted an eccentric-spheres head model in which an eccentric bubble approximated the effects of actual brain lesions. After simulating EEG signal measurement in 64 different pathologic situations, an inverse dipole fitting procedure was carried out, assuming an incorrect lesion conductivity assignment ranging from a half to twice the real value. Incorrect lesion conductivity assignment led to markedly wrong source reconstruction for highly conductive lesions like liquid-filled ones (localization errors as much as 1.7 cm). Conversely, low sensitivity to uncertainties in conductivity assignment was found for lesions with low conductivity like calcified tumors. The authors propose a method based on residual error analysis to improve the lesion conductivity estimate. This procedure can identify lesion tissue conductivity with only a few percent error and guarantees source localization errors less than 5 mm.

Improving lesion conductivity estimate by means of EEG source localization sensitivity to model parameter.

Accurate head modeling is required to properly simulate bioelectric phenomena in 3-D as well as to estimate the 3-D bioelectric activity starting from superficial bioelectric measurements and 3-D imaging. Aiming to build an accurate and realistic representation of the volume conductor of the head, also the anisotropy of head tissues should be taken into account. In this paper we describe a new finite-difference method (FDM) formulation which accounts for anisotropy of the various head tissues. Our proposal, being based on FDM, derives the head model directly from patient's specific clinical images. We present here the details of the numerical formulation and the method validation by comparing our numerical proposal and known analytical results using a multi- shell anisotropic head model with skull anisotropy. Furthermore, we analyzed also different numerical grid refinement and EEG source characteristics. The comparison with previously developed FDM methods shows a good performance of the proposed method.

A FDM anisotropic formulation for EEG simulation.

Bioelectrical phenomena spread within the whole body (the conductor medium) independently of electrical source position within the body. However, under certain circumstances, it is possible to limit the volume within which the study can be done. Given its high resistivity, the skull limits the spread of bioelectrical currents due to brain sources and it leaves only few holes for current flow, namely the occipital hole and the openings for the optic nerves. This is a simulation study performed adopting realistic head models extended to different percentages of the whole head volume conductor to determine the possibility of limiting the model volume for bioelectric field analysis. A realistic head model extended to the chin was used as reference model to analyze three reduced model extensions: 80% of the volume of the reference model (including the neck upper part), 70% (including all the skull but not the neck) and 60% (cutting the head at cerebellum level). The lower limit of the reduced model was named "cut-plane". We simulated the head electrical potential generated by various dipole current sources within the brain, either far from or near the cut-plane and either orthogonal or parallel to it. The scalp potential distributions were compared between each reduced model and the reference model by means of relative-difference measure (RDM). The larger differences were found for sources near the cut-plane and for sources orthogonal to it. The differences increased non linearly with model volume reduction, dramatically augmenting as the skull was intercepted by the cut-plane. The same model performed differently according to source position relative to the particular head structure.

Head model extension for the study of bioelectric phenomena.

Inverse solution techniques based on electroencephalographic (EEG) measurements are a powerful mean of gaining knowledge about brain functioning, being used to estimate location, orientation and strength of neural electrical sources of brain activity. A model of the head, a model of the source and an electric-field computational method are necessary to describe the EEG problem mathematically. Volume conductor models commonly used to describe the EEG neglect the presence of brain lesions. We evaluated the need of considering brain lesions in head models for precise mapping of neural activity nearby the lesion, as it is requested for neurosurgical preoperative planning. A systematic evaluation of the effects of neglecting brain lesions in EEG dipole source localisation accuracy has been performed by computer simulations for different pathologic conditions, source types and source positions. Simulations of EEG measurements were carried out using a modified eccentric-spheres model of the head in which an eccentric bubble approximates effects of actual brain lesions. A three concentric spheres model has been used in the inverse dipole fitting procedure to quantify source localisation errors caused by ignoring the presence of lesions in the head model. 64 different situations have been analysed. Source reconstruction errors resulted negligible only for some relative positions of source, lesion and electrodes. The largest errors, up to 2.5 cm, have been found for a lesion placed between source and electrodes and for a source internal to the lesion (not circumscribed tumours). We conclude that source localisation process is largely affected by a nearby lesion and thus electrical mapping of brain activity must be performed embedding brain lesions in the head model.

Accuracy of EEG dipole source localisation in presence of brain lesions.

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