Tuning Minimum-Norm regularization parameters for optimal MEG connectivity estimation.

The accurate characterization of cortical functional connectivity from Magnetoencephalography (MEG) data remains a challenging problem due to the subjective nature of the analysis, which requires several decisions at each step of the analysis pipeline, such as the choice of a source estimation algorithm, a connectivity metric and a cortical parcellation, to name but a few. Recent studies have emphasized the importance of selecting the regularization parameter in minimum norm estimates with caution, as variations in its value can result in significant differences in connectivity estimates. In particular, the amount of regularization that is optimal for MEG source estimation can actually be suboptimal for coherence-based MEG connectivity analysis. In this study, we expand upon previous work by examining a broader range of commonly used connectivity metrics, including the imaginary part of coherence, corrected imaginary part of Phase Locking Value, and weighted Phase Lag Index, within a larger and more realistic simulation scenario. Our results show that the best estimate of connectivity is achieved using a regularization parameter that is 1 or 2 orders of magnitude smaller than the one that yields the best source estimation. This remarkable difference may imply that previous work assessing source-space connectivity using minimum-norm may have benefited from using less regularization, as this may have helped reduce false positives. Importantly, we provide the code for MEG data simulation and analysis, offering the research community a valuable open source tool for informed selections of the regularization parameter when using minimum-norm for source space connectivity analyses.

An in-vivo validation of ESI methods with focal sources.

Electrophysiological source imaging (ESI) aims at reconstructing the precise origin of brain activity from measurements of the electric field on the scalp. Across laboratories/research centers/hospitals, ESI is performed with different methods, partly due to the ill-posedness of the underlying mathematical problem. However, it is difficult to find systematic comparisons involving a wide variety of methods. Further, existing comparisons rarely take into account the variability of the results with respect to the input parameters. Finally, comparisons are typically performed using either synthetic data, or in-vivo data where the ground-truth is only roughly known. We use an in-vivo high-density EEG dataset recorded during intracranial single pulse electrical stimulation, in which the true sources are substantially dipolar and their locations are precisely known. We compare ten different ESI methods, using their implementation in the MNE-Python package: MNE, dSPM, LORETA, sLORETA, eLORETA, LCMV beamformers, irMxNE, Gamma Map, SESAME and dipole fitting. We perform comparisons under multiple choices of input parameters, to assess the accuracy of the best reconstruction, as well as the impact of such parameters on the localization performance. Best reconstructions often fall within 1 cm from the true source, with most accurate methods hitting an average localization error of 1.2 cm and outperforming least accurate ones erring by 2.5 cm. As expected, dipolar and sparsity-promoting methods tend to outperform distributed methods. For several distributed methods, the best regularization parameter turned out to be the one in principle associated with low SNR, despite the high SNR of the available dataset. Depth weighting played no role for two out of the six methods implementing it. Sensitivity to input parameters varied widely between methods. While one would expect high variability being associated with low localization error at the best solution, this is not always the case, with some methods producing highly variable results and high localization error, and other methods producing stable results with low localization error. In particular, recent dipolar and sparsity-promoting methods provide significantly better results than older distributed methods. As we repeated the tests with "conventional" (32 channels) and dense (64, 128, 256 channels) EEG recordings, we observed little impact of the number of channels on localization accuracy; however, for distributed methods denser montages provide smaller spatial dispersion. Overall findings confirm that EEG is a reliable technique for localization of point sources and therefore reinforce the importance that ESI may have in the clinical context, especially when applied to identify the surgical target in potential candidates for epilepsy surgery.

Towards the Automatic Localization of the Irritative Zone Through Magnetic Source Imaging.

The present work aims at validating a Bayesian multi-dipole modeling algorithm (SESAME) in the clinical scenario consisting of localizing the generators of single interictal epileptiform discharges from resting state magnetoencephalographic recordings. We use the results of Equivalent Current Dipole fitting, performed by an expert user, as a benchmark, and compare the results of SESAME with those of two widely used source localization methods, RAP-MUSIC and wMNE. In addition, we investigate the relation between post-surgical outcome and concordance of the surgical plan with the cerebral lobes singled out by the methods. Unlike dipole fitting, the tested algorithms do not rely on any subjective channel selection and thus contribute towards making source localization more unbiased and automatic. We show that the two dipolar methods, SESAME and RAP-MUSIC, generally agree with dipole fitting in terms of identified cerebral lobes and that the results of the former are closer to the fitted equivalent current dipoles than those of the latter. In addition, for all the tested methods and particularly for SESAME, concordance with surgical plan is a good predictor of seizure freedom while discordance is not a good predictor of poor post-surgical outcome. The results suggest that the dipolar methods, especially SESAME, represent a reliable and more objective alternative to manual dipole fitting for clinical applications in the field of epilepsy surgery.

A Comparative Study of the Robustness of Frequency-Domain Connectivity Measures to Finite Data Length.

In this work we use numerical simulation to investigate how the temporal length of the data affects the reliability of the estimates of brain connectivity from EEG time-series. We assume that the neural sources follow a stable MultiVariate AutoRegressive model, and consider three connectivity metrics: imaginary part of coherency (IC), generalized partial directed coherence (gPDC) and frequency-domain granger causality (fGC). In order to assess the statistical significance of the estimated values, we use the surrogate data test by generating phase-randomized and autoregressive surrogate data. We first consider the ideal case where we know the source time courses exactly. Here we show how, expectedly, even exact knowledge of the source time courses is not sufficient to provide reliable estimates of the connectivity when the number of samples gets small; however, while gPDC and fGC tend to provide a larger number of false positives, the IC becomes less sensitive to the presence of connectivity. Then we proceed with more realistic simulations, where the source time courses are estimated using eLORETA, and the EEG signal is affected by biological noise of increasing intensity. Using the ideal case as a reference, we show that the impact of biological noise on IC estimates is qualitatively different from the impact on gPDC and fGC.

Expectation maximization and the retrieval of the atmospheric extinction coefficients by inversion of Raman lidar data.

We consider the problem of retrieving the aerosol extinction coefficient from Raman lidar measurements. This is an ill-posed inverse problem that needs regularization, and we propose to use the Expectation-Maximization (EM) algorithm to provide stable solutions. Indeed, EM is an iterative algorithm that imposes a positivity constraint on the solution, and provides regularization if iterations are stopped early enough. We describe the algorithm and propose a stopping criterion inspired by a statistical principle. We then discuss its properties concerning the spatial resolution. Finally, we validate the proposed approach by using both synthetic data and experimental measurements; we compare the reconstructions obtained by EM with those obtained by the Tikhonov method, by the Levenberg-Marquardt method, as well as those obtained by combining data smoothing and numerical derivation.

The SESAMEEG package: a probabilistic tool for source localization and uncertainty quantification in M/EEG.

Source localization from M/EEG data is a fundamental step in many analysis pipelines, including those aiming at clinical applications such as the pre-surgical evaluation in epilepsy. Among the many available source localization algorithms, SESAME (SEquential SemiAnalytic Montecarlo Estimator) is a Bayesian method that distinguishes itself for several good reasons: it is highly accurate in localizing focal sources with comparably little sensitivity to input parameters; it allows the quantification of the uncertainty of the reconstructed source(s); it accepts user-defined a priori high- and low-probability search regions in input; it can localize the generators of neural oscillations in the frequency domain. Both a Python and a MATLAB implementation of SESAME are available as open-source packages under the name of SESAMEEG and are well integrated with the main software packages used by the M/EEG community; moreover, the algorithm is part of the commercial software BESA Research (from version 7.0 onwards). While SESAMEEG is arguably simpler to use than other source modeling methods, it has a much richer output that deserves to be described thoroughly. In this article, after a gentle mathematical introduction to the algorithm, we provide a complete description of the available output and show several use cases on experimental M/EEG data.

EEG in extreme conditions: An advanced analysis pipeline for the human electroencephalographic signals recorded in space during the ALTEA experiment.

The Anomalous Long Term Effects in Astronauts (ALTEA) project originally aimed at disentangling the mechanisms behind astronauts' perception of light flashes. To this end, an experimental apparatus was set up in order to concurrently measure the tracks of cosmic radiation particles in the astronauts' head and the electroencephalographic (EEG) signals generated by their brain. So far, the ALTEA data set has never been analyzed with the broader intent to study possible interference between cosmic radiation and the brain, regardless of light flashes. The aim of this work is to define a pipeline to systematically pre-process the ALTEA EEG data. Compared to the analysis of standard EEG recording, this task is made more difficult by the presence of unconventional artifacts due to the extreme recording conditions that, in particular, require the EEG cap to be positioned next to another noisy electronic device, namely the particle detectors. Here we show how standard tools for the analysis of EEG data can be tuned to deal with these unconventional artifacts. After pre-processing the available data we were able to elucidate a shift of the center frequency of the α rhythm induced by visual stimulation, thus proving the effectiveness of the implemented pipeline. This work represents the first study presenting results of signal processing of ALTEA EEG time series. Further, it is the starting point of a future work aimed at analyzing the interaction between EEG and cosmic radiation.

Simultaneous human intracerebral stimulation and HD-EEG, ground-truth for source localization methods.

Precisely localizing the sources of brain activity as recorded by EEG is a fundamental procedure and a major challenge for both research and clinical practice. Even though many methods and algorithms have been proposed, their relative advantages and limitations are still not well established. Moreover, these methods involve tuning multiple parameters, for which no principled way of selection exists yet. These uncertainties are emphasized due to the lack of ground-truth for their validation and testing. Here we present the Localize-MI dataset, which constitutes the first open dataset that comprises EEG recorded electrical activity originating from precisely known locations inside the brain of living humans. High-density EEG was recorded as single-pulse biphasic currents were delivered at intensities ranging from 0.1 to 5 mA through stereotactically implanted electrodes in diverse brain regions during pre-surgical evaluation of patients with drug-resistant epilepsy. The uses of this dataset range from the estimation of in vivo tissue conductivity to the development, validation and testing of forward and inverse solution methods.

Dynamical MEG source modeling with multi-target Bayesian filtering.

We present a Bayesian filtering approach for automatic estimation of dynamical source models from magnetoencephalographic data. We apply multi-target Bayesian filtering and the theory of Random Finite Sets in an algorithm that recovers the life times, locations and strengths of a set of dipolar sources. The reconstructed dipoles are clustered in time and space to associate them with sources. We applied this new method to synthetic data sets and show here that it is able to automatically estimate the source structure in most cases more accurately than either traditional multi-dipole modeling or minimum current estimation performed by uninformed human operators. We also show that from real somatosensory evoked fields the method reconstructs a source constellation comparable to that obtained by multi-dipole modeling.

Bayesian multi-dipole modelling in the frequency domain.

BACKGROUND: Magneto- and Electro-encephalography record the electromagnetic field generated by neural currents with high temporal frequency and good spatial resolution, and are therefore well suited for source localization in the time and in the frequency domain. In particular, localization of the generators of neural oscillations is very important in the study of cognitive processes in the healthy and in the pathological brain. NEW METHOD: We introduce the use of a Bayesian multi-dipole localization method in the frequency domain. Given the Fourier Transform of the data at one or multiple frequencies and/or trials, the algorithm approximates numerically the posterior distribution with Monte Carlo techniques. RESULTS: We use synthetic data to show that the proposed method behaves well under a wide range of experimental conditions, including low signal-to-noise ratios and correlated sources. We use dipole clusters to mimic the effect of extended sources. In addition, we test the algorithm on real MEG data to confirm its feasibility. COMPARISON WITH EXISTING METHOD(S): Throughout the whole study, DICS (Dynamic Imaging of Coherent Sources) is used systematically as a benchmark. The two methods provide similar general pictures; the posterior distributions of the Bayesian approach contain much richer information at the price of a higher computational cost. CONCLUSIONS: The Bayesian method described in this paper represents a reliable approach for localization of multiple dipoles in the frequency domain.