Insidious errors in dipole parameters due to shell model misspecification using multiple time-points

From evoked potentials to cortical currents: Resolving V1 and V2 components using retinotopy constrained source estimation without fMRI

Despite evoked potentials' (EP) ubiquity in research and clinical medicine, insights are limited to gross brain dynamics as it remains challenging to map surface potentials to their sources in specific cortical regions. Multiple sources cancellation due to cortical folding and cross-talk obscures close sources, e.g. between visual areas V1 and V2. Recently retinotopic functional magnetic resonance imaging (fMRI) responses were used to constrain source locations to assist separating close sources and to determine cortical current generators. However, an fMRI is largely infeasible for routine EP investigation. We developed a novel method that replaces the fMRI derived retinotopic layout (RL) by an approach where the retinotopy and current estimates are generated from EEG or MEG signals and a standard clinical T1-weighted anatomical MRI. Using the EEG-RL, sources were localized to within 2 mm of the fMRI-RL constrained localized sources. The EEG-RL also produced V1 and V2 current waveforms that closely matched the fMRI-RL's (n = 2) r(1,198)  = 0.99, P < 0.0001. Applying the method to subjects without fMRI (n = 4) demonstrates it generates waveforms that agree closely with the literature. Our advance allows investigators with their current EEG or MEG systems to create a library of brain models tuned to individual subjects' cortical folding in retinotopic maps, and should be applicable to auditory and somatosensory maps. The novel method developed expands EP's ability to study specific brain areas, revitalizing this well-worn technique. Hum Brain Mapp 37:1696-1709, 2016. © 2016 Wiley Periodicals, Inc.

Effects of forward model errors on EEG source localization

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.

Event-related potential activity in the basal ganglia differentiates rewards from nonrewards: temporospatial principal components analysis and source localization of the feedback negativity

Event-related potential studies of reward processing have consistently identified the feedback negativity (FN), an early neural response that differentiates feedback indicating unfavorable versus favorable outcomes. Several important questions remain, however, about the nature of this response. In this study, the FN was recorded in response to monetary gains and losses during a laboratory gambling task, and temporospatial principal components analysis was used to separate the FN from overlapping responses. The FN was identified as a positive deflection at frontocentral recording sites that was enhanced for rewards compared with nonrewards. Furthermore, source localization techniques identified the striatum as a likely neural generator. These data indicate that this apparent FN reflects increased striatal activation in response to favorable outcomes that is reduced or absent for unfavorable outcomes, thereby providing unique information about the timing and nature of basal ganglia activity related to reward processing.

Neuroelectromagnetic forward head modeling toolbox

This paper introduces a Neuroelectromagnetic Forward Head Modeling Toolbox (NFT) running under MATLAB (The Mathworks, Inc.) for generating realistic head models from available data (MRI and/or electrode locations) and for computing numerical solutions for the forward problem of electromagnetic source imaging. The NFT includes tools for segmenting scalp, skull, cerebrospinal fluid (CSF) and brain tissues from T1-weighted magnetic resonance (MR) images. The Boundary Element Method (BEM) is used for the numerical solution of the forward problem. After extracting segmented tissue volumes, surface BEM meshes can be generated. When a subject MR image is not available, a template head model can be warped to measured electrode locations to obtain an individualized head model. Toolbox functions may be called either from a graphic user interface compatible with EEGLAB (http://sccn.ucsd.edu/eeglab), or from the MATLAB command line. Function help messages and a user tutorial are included. The toolbox is freely available under the GNU Public License for noncommercial use and open source development.

The folding fingerprint of visual cortex reveals the timing of human V1 and V2

Primate neocortex contains over 30 visual areas. Recent techniques such as functional magnetic resonance imaging (fMRI) have successfully identified many of these areas in the human brain, but have been of limited value for revealing the temporal dynamics between visual areas. The electroencephalogram (EEG) provides information with high temporal precision, but has had limited success separating out the signals from individual neighboring cortical areas. Consequently, controversies exist over the temporal dynamics across cortical areas. In order to address this problem we developed a new method to identify the sources of the EEG. An individual's unique cortical pattern of sulci and gyri along with a visual area's functional retinotopic layout provides a folding fingerprint that predicts specific scalp topographies for stimuli presented in different parts of the visual field. Using this folding fingerprint with a 96 or 192 location stimulus severely constrains the solution space making it relatively easy to extract the temporal response of multiple visual areas to multiple stimulus locations. The large number of stimuli also provides a means to validate the waveforms by comparing across stimulus sets, an important feature not present in most EEG source identification procedures. Using this method our data reveal that both V1 and V2 waveforms have similar onset latencies, and their temporal dynamics provide new information regarding the response latencies of these areas in humans. Our method enables the previously unattainable separation of EEG responses from neighboring brain areas. While we applied the method to the first two cortical visual areas, V1 and V2, this method is also applicable to somatosensory areas that have defined mappings. This method provides a means to study the rapid information flow in the human brain to reveal top-down and bottom-up cognitive processes.

Localizing Sites of Activation in Primary Visual Cortex Using Visual-Evoked Potentials and Functional Magnetic Resonance Imaging

This study compared retinotopic map identification in primary visual cortex (V1) using: (i) functional magnetic resonance imaging (fMRI) and (ii) visual evoked potentials (VEPs) coupled with dipole source localization (DSL). A multielectrode array was used to record VEPs while subjects viewed a flickering dartboard pattern modulated by a 16-bit m-sequence. The stimulus preferentially activates V1. Using a common time function DSL algorithm, the primary source of each stimulus patch was found independent of the fMRI. The VEP/DSL and fMRI localization data for each subject were aligned by a rigid translation and rotation. The average distance between VEP and corresponding fMRI sources was 10.8 mm +/- 3.8 mm. To assess the significance of the results, fMRI and DSL solutions were scrambled so the comparisons were no longer for corresponding patches. The average distance between the noncorresponding data sets was 17.2 mm for 50 million scrambles. The probability of the scrambled data yielding a better fit than the real data was p < 10(-7). The combination of multielectrode recording, multiinput visual stimulation and common time function DSL analysis can provide a detailed retinotopic map of visual cortex that has high correspondence with independent fMRI localization analysis on the same subject.

Noninvasive identification of human central sulcus: a comparison of gyral morphology, functional MRI, dipole localization, and direct cortical mapping

The locations of the human primary hand cortical somatosensory and motor areas were estimated using structural and functional MRI, scalp-recorded somatosensory-evoked potential dipole localization, expert judgments based on cortical anatomy, and direct cortical stimulation and recording studies. The within-subject reliability of localization (across 3 separate days) was studied for eight normal subjects. Intraoperative validation was obtained from five neurosurgical patients. The mean discrepancy between the different noninvasive functional imaging methods ranged from 6 to 26 mm. Quantitative comparison of the noninvasive methods with direct intraoperative stimulation and recording studies did not reveal a significant mean difference in accuracy. However, the expert judgments of the location of the sensory hand areas were significantly more variable (maximum error, 39 mm) than the dipole or functional MRI techniques. It is concluded that because expert judgments are less reliable for identifying the cortical hand area, consideration of the findings of noninvasive functional MRI and dipole localization studies is desirable for preoperative surgical planning.

Spatio-temporal EEG source localization using simulated annealing

The estimation of multiple dipole parameters in spatio-temporal source modeling (STSM) of electroencephalographic (EEG) data is a difficult nonlinear optimization problem due to multiple local minima in the cost function. A straightforward iterative optimization approach to such a problem is very susceptible to being trapped in a local minimum, thereby resulting in incorrect estimates of the dipole parameters. In this paper, we present and evaluate a more robust optimization approach based on the simulated annealing algorithm. The complexity of this approach for the STSM problem was reduced by separating the dipole parameters into linear (moment) and nonlinear (location) components. The effectiveness of the proposed method and its superiority over the traditional nonlinear simplex technique in escaping local minima were tested and demonstrated through computer simulations. The annealing algorithm and its implementation for multidipole estimation are also discussed. We found the simulated annealing approach to be 7-31% more effective than the simplex method at converging to the true global minimum for a number of different kinds of three-dipole problems simulated in this work. In addition, the computational cost of the proposed approach was only marginally higher than its simplex counterpart. The annealing method also yielded similar solutions irrespective of the initial guesses used. The proposed simulated annealing method is an attractive alternative to the simplex method that is currently more common in dipole estimation applications.

Toward a dynamic topographic components model

Möcks' topographic component model (TCM) (Möcks, J. Topographic components model for event-related potentials and some biophysical considerations. IEEE Trans. Biomed. Eng., 1988a, 35: 482-484; Möcks, J. Decomposing event-related potentials: a new topographic components model. Biol. Psychol., 1988b, 26: 199-215) decomposes event-related potentials into components uniquely determined by their respective amplitude profiles across replicates, assuming a constant topography and wave shape for each component. To accommodate possible changes in the component expression across conditions, a dynamic version of TCM is investigated which further admits component modulation in time scale. Twenty test problems were synthesized, incorporating two arbitrary topographies each activated with its own arbitrary wave shape modified, across two conditions, in amplitude, onset and duration. Seventeen problems were perfectly solved, with substantial success on the remaining three, confirming that component jitter or stretching can even help component identification.

Principal component analysis of event-related potentials: misallocation of variance revisited

Misallocating variance, in event-related potential analysis, refers to attributing an experimental effect to components not actually affected. A vector interpretation of the relationship between mathematically derived and true underlying components shows that misallocation depends exclusively on incorrect identification of the affected component. Simulations, using seven imperfect rotations, confirmed all predictions from the vector interpretation concerning the presence, direction, and size of misallocated variance. Contrary to principal component analysis (PCA). Möcks's topographic component model (TCM) is not subject to rotation problems. These two methods were compared over 100 simulations in which the components had constant waveforms and topographics across participants. The group effect was always detected, but only PCA and not TCM showed significance on other components, except when their random weights happened to differ between groups.

The usefulness of the Laplacian in principal component analysis and dipole source localization

Evoked potentials are difficult to analyze because multiple sources are active simultaneously. Principal component analysis and dipole localization are two techniques that have been used to disentangle overlapping sources. Both of these techniques have problems. Principal component analysis suffers from a rotation ambiguity. Dipole localization suffers from biases when the model used to derive the sources from the scalp potentials is misspecified. Using computer simulations we demonstrate that by applying both of these techniques to the Laplacian of the voltages rather than to the raw voltages the problems associated with the two techniques are reduced. Computer programs for the analyses are presented in an Appendix.

Comparison of realistically shaped boundary-element and spherical head models in source localization of early somatosensory evoked potentials

Source localizations of early somatosensory evoked potentials and electrical potentials produced by dipoles in the region of the central sulcus were computed using realistically shaped boundary-element head models (BEM) and compared to localizations obtained using 3-shell spherical models. Realistically shaped 3-shell boundary-element-models were constructed on the basis of the individual anatomy obtained from 3D-MR-tomography in 6 subjects. Spherical head models were fitted to the actual locations of the electrodes and to the surface of the heads, respectively. Source locations calculated within the spherical head models differed by an average of 4 mm (range: 2 to 7 mm) with respect to the 3-shell BEM, taking into account the limited accuracy of this model. This mislocation was most prominently due to deeper source locations predicted using a spherical head model and caused by incorrect modelling of the geometry of the heads, although sources were located in a favourable region of the heads.

Improved method for computation of potentials in a realistic head shape model

The Lead Field Analysis (LFA) algorithm, a new computational technique for the calculation of potentials on the surface of a realistic head shaped volume conductor model based on the Boundary Element Method and the Reciprocity Theorem, is presented. The new algorithm, in comparison to the Standard Boundary Element Method, offers improved computational efficiency and lower storage requirements. It also yields more accurate surface potential results in the face of varying dipole source locations for a head shape Boundary Element model with a given number of nodes. Additionally, the algorithm results in quasi-analytic expressions of the derivatives of the surface potential with respect to the location of the sources, allowing the use of optimization techniques with better convergence properties. A set of simulations demonstrating the increased robustness of the LFA Algorithm in the face of varying dipole source parameters is also described.

Multiple-generator errors are unavoidable under model misspecification

Model misspecification poses a major problem for dipole source localization (DSL) because it causes insidious multiple-generator errors (MulGenErrs) to occur in the fitted dipole parameters. This paper describes how and why this occurs, based upon simple algebraic considerations. MulGenErrs must occur, to some degree, in any DSL analysis of real data because there is model misspecification and mathematically the equations used for the simultaneously active generators must be of a different form than the equations for each generator active alone.

DSL and MUSIC under model misspecification and noise-conditions

The concepts of both the traditional DSL (Dipole Source Localization) and MUSIC (MUltiple SIgnal Classification) are explained using simple vectors. DSL and MUSIC differ in the way the weighting functions are found. In both DSL and MUSIC, the fitted generator magnitudes are found by projecting the recorded potential map onto the fitted weighting functions, and the model transfers the weighting functions into generator locations/orientations. Both DSL and MUSIC will cause errors in the fitted dipole parameters when there is model misspecification, noise, or both. Therefore, an accurate head model is essential for either method to give reliable results.

Model misspecification detection by means of multiple generator errors, using the observed potential map

Due to model misspecification, currently-used Dipole Source Localization (DSL) methods may contain Multiple-Generator Errors (MulGenErrs) when fitting simultaneously-active dipoles. The size of the MulGenErr is a function of both the model used, and the dipole parameters, including the dipoles' waveforms (time-varying magnitudes). For a given fitting model, by examining the variation of the MulGenErrs (or the fit parameters) under different waveforms for the same generating-dipoles, the accuracy of the fitting model for this set of dipoles can be determined. This method of testing model misspecification can be applied to evoked potential maps even when the parameters of the generating-dipoles are unknown. The dipole parameters fitted in a model should only be accepted if the model can be shown to be sufficiently accurate.