Steven Le Cam

Applying ICA in EEG: Choice of the Window Length and of the Decorrelation Method

Blind Source Separation (BSS) approaches for multi-channel EEG processing are popular, and in particular Independent Component Analysis (ICA) algorithms have proven their ability for artefacts removal and source extraction for this very specific class of signals. However, the blind aspect of these techniques implies well-known drawbacks. As these methods are based on estimated statistics from the data and rely on an hypothesis of signal stationarity, the length of the window is crucial and has to be chosen carefully: large enough to get reliable estimation and short enough to respect the rather non-stationary nature of the EEG signals. In addition, another issue concerns the plausibility of the resulting separated sources. Indeed, some authors suggested that ICA algorithms give more physiologically plausible results than others. In this paper, we address both issues by comparing four popular ICA algorithms (namely FastICA, Extended InfoMax, JADER and AMICA). First of all, we propose a new criterion aiming to evaluate the quality of the decorrelation step of the ICA algorithms. This criterion leads to a heuristic rule of minimal sample size that guarantees statistically robust results. Next, we show that for this minimal sample size ensuring constant decorrelation quality we obtain quasi-constant ICA performances for some but not all tested algorithms. Extensive tests have been performed on simulated data (i.i.d. sub and super Gaussian sources mixed by random mixing matrices) and plausible data (macroscopic neural population models placed inside a three layers spherical head model). The results globally confirm the proposed rule for minimal data length and show that the use of sphering as decorrelation step might significantly change the global performances for some algorithms.

Dipolar source localization from intracerebral SEEG recordings

This paper aims at exploring the feasibility of a brain source localization method from intracerebral stereo-electroencephalography (SEEG) measurements. The SEEG setup consists in multi-contact electrodes inserted in the brain volume, each containing about 10 collinear measuring contacts. In clinical context, these signals are usually observed using a bipolar montage (potential differences between neighbouring contacts of a SEEG electrode). The propagation of distant activity is thus suppressed, resulting in the observation of local activities around the contacts. We propose in this paper to take benefit of the propagation information by considering the original SEEG recordings (common reference montage), with the objective to localize sources possibly distant from the electrode contacts, and whose activities are propagating through the volume. Our method is based on an equivalent dipole model for the source and homogeneous infinite models for the propagation environment. This simple approach shows satisfactory localization performance under appropriate conditions, described in this paper. The proposed method is validated on real SEEG signals for the localisation of an intra-cortical electrical stimulation (ICS) generator.

A Space-Time-Frequency Dictionary for Sparse Cortical Source Localization

Objective: Cortical source imaging aims at identifying activated cortical areas on the surface of the cortex from the raw electroencephalogram (EEG) data. This problem is ill posed, the number of channels being very low compared to the number of possible source positions. Methods: In some realistic physiological situations, the active areas are sparse in space and of short time durations, and the amount of spatio-temporal data to carry the inversion is then limited. In this study, we propose an original data driven space-time-frequency (STF) dictionary which takes into account simultaneously both spatial and time-frequency sparseness while preserving smoothness in the time frequency (i.e., nonstationary smooth time courses in sparse locations). Based on these assumptions, we take benefit of the matching pursuit (MP) framework for selecting the most relevant atoms in this highly redundant dictionary. Results: We apply two recent MP algorithms, single best replacement (SBR) and source deflated matching pursuit, and we compare the results using a spatial dictionary and the proposed STF dictionary to demonstrate the improvements of our multidimensional approach. We also provide comparison using well-established inversion methods, FOCUSS and RAP-MUSIC, analyzing performances under different degrees of nonstationarity and signal to noise ratio. Conclusion: Our STF dictionary combined with the SBR approach provides robust performances on realistic simulations. From a computational point of view, the algorithm is embedded in the wavelet domain, ensuring high efficiency in term of computation time. Significance: The proposed approach ensures fast and accurate sparse cortical localizations on highly nonstationary and noisy data.

Influence of the stereo-EEG sensors setup and of the averaging on the dipole localization problem.

While scalp EEG/MEG source imaging have been extensively studied in the last two decades, the case of source localization from invasive measurements has resulted in few works to date. Yet there is a lot to gain from stereo-electroencephalographic (SEEG) recordings, providing high signal to noise ratio measurements of the explored brain structures. The SEEG setup consists in multi-contact electrodes inserted in the brain volume, each containing a dozen of collinear measuring contacts. This particular setup raises the question of the conditioning of the inverse problem. In recent works, we have evaluated the feasibility to localize a single dominant equivalent dipole facing different sensors and noise configurations. We deepen here the analysis by evaluating the influence of the chosen subset of sensors and of the number of averaged time samples on the accuracy of the localization. We conduct experiments on simulated data as well as on real epileptic spikes, illustrating the trade off to be made between these two factors.

Hidden Markov chain modeling for epileptic networks identification

The partial epileptic seizures are often considered to be caused by a wrong balance between inhibitory and excitatory interneuron connections within a focal brain area. These abnormal balances are likely to result in loss of functional connectivities between remote brain structures, while functional connectivities within the incriminated zone are enhanced. The identification of the epileptic networks underlying these hypersynchronies are expected to contribute to a better understanding of the brain mechanisms responsible for the development of the seizures. In this objective, threshold strategies are commonly applied, based on synchrony measurements computed from recordings of the electrophysiologic brain activity. However, such methods are reported to be prone to errors and false alarms. In this paper, we propose a hidden Markov chain modeling of the synchrony states with the aim to develop a reliable machine learning methods for epileptic network inference. The method is applied on a real Stereo-EEG recording, demonstrating consistent results with the clinical evaluations and with the current knowledge on temporal lobe epilepsy.

Detection of Transient Signals in Lung Sounds: Local Approach Using a Markovian Tree with Frequency Selectivity

We deal in this paper with the extraction of multiresolution statistical signatures for the characterization of transient signals in strongly noisy contexts. These short-time signals have sharp and highly variable frequency components. The time/frequency window to choose for our analysis is then a major issue. We have chosen the Wavelet Packet Transform (WPT) due to its ability to provide multiple windows analysis with different time/frequency resolutions. We propose a new oriented Hidden Markov Tree (HMT) dedicated to the tree structure of the WPT, which offers promising statistical characterization of time/frequency variations in a signal, by exploiting several time/frequency resolutions. This model is exploited in a Bayesian context for the segmentation of signals containing transient components. The chosen data likelihood is a Generalized Gaussian Distributions (GGD), well suited for the modeling of Wavelet Packet Coefficients (WPC) distributions. We demonstrate the efficiency of our method on synthetic signals with several Signal to Noise Ratio (SNR). Our application domain is related to biomedical signals, and more specifically for the detection of uprising abnormalities in pulmonary sounds. This original method shows remarkable ability to detect such sounds, which are usually buried in the normal lung noise and are often very difficult to perceive with the human earing.

Assessing human brain impedance using simultaneous surface and intracerebral recordings.

Most of the literature on the brain impedance proposes a frequency-independent resistive model. Recently, this conclusion was tackled by a series of papers (Bédard et al., 2006; Bédard and Destexhe, 2009; Gomes et al., 2016), based on microscopic sale modeling and measurements. Our paper aims to investigate the impedance issue using simultaneous in vivo depth and surface signals recorded during intracerebral electrical stimulation of epileptic patients, involving a priori different tissues with different impedances. Our results confirm the conclusions from Logothethis et al. (2007): there is no evidence of frequency dependence of the brain tissue impedance (more precisely, there is no difference, in terms of frequency filtering, between the brain and the skull bone), at least at a macroscopic scale. In order to conciliate findings from both microscopic and macroscopic scales, we recall different neural/synaptic current generators models from the literature and we propose an original computational model, based on fractional dynamics.

SEEG dipole source localization based on an empirical Bayesian approach taking into account forward model uncertainties

Abstract Electromagnetic brain source localization consists in the inversion of a forward model based on a limited number of potential measurements. A wide range of methods has been developed to regularize this severely ill‐posed problem and to reduce the solution space, imposing spatial smoothness, anatomical constraint or sparsity of the activated source map. This last criteria, based on physiological assumptions stating that in some particular events (e.g., epileptic spikes, evoked potential) few focal area of the brain are simultaneously actives, has gained more and more interest. Bayesian approaches have the ability to provide sparse solutions under adequate parametrization, and bring a convenient framework for the introduction of priors in the form of probabilistic density functions. However the quality of the forward model is rarely questioned while this parameter has undoubtedly a great influence on the solution. Its construction suffers from numerous approximation and uncertainties, even when using realistic numerical models. In addition, it often encodes a coarse sampling of the continuous solution space due to the computational burden its inversion implies. In this work we propose an empirical Bayesian approach to take into account the uncertainties of the forward model by allowing constrained variations around a prior physical model, in the particular context of SEEG measurements. We demonstrate on simulations that the method enhance the accuracy of the source time‐course estimation as well as the sparsity of the resulting source map. Results on real signals prove the applicability of the method in real contexts. HighlightsOriginal approach for simultaneous brain source estimation and forward field optimization.A coarse One Sphere model is used to accurately inverse a realistic Finite Element model.Improvements of both source localization precision and time‐course estimation.Original use of intracerebral recordings (SEEG) for source localization.Validation on data set of intra‐cerebral stimulation and interictal epileptic spikes

Sparse cortical source localization using spatio-temporal atoms

This paper addresses the problem of sparse localization of cortical sources from scalp EEG recordings. Localization algorithms use propagation model under spatial and/or temporal constraints, but their performance highly depends on the data signal-to-noise ratio (SNR). In this work we propose a dictionary based sparse localization method which uses a data driven spatio-temporal dictionary to reconstruct the measurements using Single Best Replacement (SBR) and Continuation Single Best Replacement (CSBR) algorithms. We tested and compared our methods with the well-known MUSIC and RAP-MUSIC algorithms on simulated realistic data. Tests were carried out for different noise levels. The results show that our method has a strong advantage over MUSIC-type methods in case of synchronized sources.

Smoothness constraint for cortical dipolar sources estimation

In the last decade, a wide range of approaches have been proposed to estimate the activity of physiological sources from multi-channel electroencephalographic (EEG) data. Two utterly different directions can be distinguished: brain source imaging (BSI) and blind source separation (BSS). While the first approach is based on the inversion of a given forward model, the latter blindly decomposes the EEG mixing by optimization of a contrast function excluding any physiological priors on the problem. All these methods have proven their ability in reconstructing efficiently the source activities in some well adapted situations. Nevertheless, the synthesis of a reliable lead field model for BSI is computationally demanding, and the criterion to be optimized in BSS are often inadequate with regards to the physiology of the problem. In this paper, a compromise between these two methodological trends is introduced. A BSS method is described taking account of physiological knowledge on the projection of the sources on the scalp map in conjunction with strong priors on the localization of the recorded sources. This estimation method is demonstrated to lead to a generalization of the classical Hjorths laplacian montage, and provides satisfactory simulation results when the appropriate configurations on the sources are met.