Conjugate Gradient Method Applied to Cortical Imaging in EEG/ERP

International audienc

Dynamic Decomposition of Spatiotemporal Neural Signals

Neural signals are characterized by rich temporal and spatiotemporal dynamics that reflect the organization of cortical networks. Theoretical research has shown how neural networks can operate at different dynamic ranges that correspond to specific types of information processing. Here we present a data analysis framework that uses a linearized model of these dynamic states in order to decompose the measured neural signal into a series of components that capture both rhythmic and non-rhythmic neural activity. The method is based on stochastic differential equations and Gaussian process regression. Through computer simulations and analysis of magnetoencephalographic data, we demonstrate the efficacy of the method in identifying meaningful modulations of oscillatory signals corrupted by structured temporal and spatiotemporal noise. These results suggest that the method is particularly suitable for the analysis and interpretation of complex temporal and spatiotemporal neural signals

The Neuroelectromagnetic Inverse Problem and the Zero Dipole Localization Error

A tomography of neural sources could be constructed from EEG/MEG recordings once the neuroelectromagnetic inverse problem (NIP) is solved. Unfortunately the NIP lacks a unique solution and therefore additional constraints are needed to achieve uniqueness. Researchers are then confronted with the dilemma of choosing one solution on the basis of the advantages publicized by their authors. This study aims to help researchers to better guide their choices by clarifying what is hidden behind inverse solutions oversold by their apparently optimal properties to localize single sources. Here, we introduce an inverse solution (ANA) attaining perfect localization of single sources to illustrate how spurious sources emerge and destroy the reconstruction of simultaneously active sources. Although ANA is probably the simplest and robust alternative for data generated by a single dominant source plus noise, the main contribution of this manuscript is to show that zero localization error of single sources is a trivial and largely uninformative property unable to predict the performance of an inverse solution in presence of simultaneously active sources. We recommend as the most logical strategy for solving the NIP the incorporation of sound additional a priori information about neural generators that supplements the information contained in the data

Dynamic filtering of static dipoles in magnetoencephalography

We consider the problem of estimating neural activity from measurements of the magnetic fields recorded by magnetoencephalography. We exploit the temporal structure of the problem and model the neural current as a collection of evolving current dipoles, which appear and disappear, but whose locations are constant throughout their lifetime. This fully reflects the physiological interpretation of the model. In order to conduct inference under this proposed model, it was necessary to develop an algorithm based around state-of-the-art sequential Monte Carlo methods employing carefully designed importance distributions. Previous work employed a bootstrap filter and an artificial dynamic structure where dipoles performed a random walk in space, yielding nonphysical artefacts in the reconstructions; such artefacts are not observed when using the proposed model. The algorithm is validated with simulated data, in which it provided an average localisation error which is approximately half that of the bootstrap filter. An application to complex real data derived from a somatosensory experiment is presented. Assessment of model fit via marginal likelihood showed a clear preference for the proposed model and the associated reconstructions show better localisation

Dynamic inverse problem solution considering non-homogeneous source distribution with frequency spatio temporal constraints applied to brain activity reconstruction

Para reconstruir la actividad cerebral es necesario estimular la ubicación de las fuentes activas del cerebro. El método de localización de fuentes usando electroencefalogramas es usado para esta tarea por su alta resolución temporal. Este método de resolver un problema inverso mal planteado, el cual no tiene una solución única debido al que el números de variables desconocidas es mas grande que el numero de variables conocidas. por lo tanto el método presenta una baja resolución espacial..

Multimodal Integration: fMRI, MRI, EEG, MEG

This chapter provides a comprehensive survey of the motivations, assumptions and pitfalls associated with combining signals such as fMRI with EEG or MEG. Our initial focus in the chapter concerns mathematical approaches for solving the localization problem in EEG and MEG. Next we document the most recent and promising ways in which these signals can be combined with fMRI. Specically, we look at correlative analysis, decomposition techniques, equivalent dipole tting, distributed sources modeling, beamforming, and Bayesian methods. Due to difculties in assessing ground truth of a combined signal in any realistic experiment difculty further confounded by lack of accurate biophysical models of BOLD signal we are cautious to be optimistic about multimodal integration. Nonetheless, as we highlight and explore the technical and methodological difculties of fusing heterogeneous signals, it seems likely that correct fusion of multimodal data will allow previously inaccessible spatiotemporal structures to be visualized and formalized and thus eventually become a useful tool in brain imaging research

Sparse Bayesian Inference & Uncertainty Quantification for Inverse Imaging Problems

During the last two decades, sparsity has emerged as a key concept to solve linear and non-linear ill-posed inverse problems, in particular for severely ill-posed problems and applications with incomplete, sub-sampled data. At the same time, there is a growing demand to obtain quantitative instead of just qualitative inverse results together with a systematic assessment of their uncertainties (Uncertainty quantification, UQ). Bayesian inference seems like a suitable framework to combine sparsity and UQ but its application to large-scale inverse problems resulting from fine discretizations of PDE models leads to severe computational and conceptional challenges. In this talk, we will focus on two different Bayesian approaches to model sparsity as a-priori information: Via convex, but non-smooth prior energies such as total variation and Besov space priors and via non-convex but smooth priors arising from hierarchical Bayesian modeling. To illustrate our findings, we will rely on experimental data from challenging biomedical imaging applications such as EEG/MEG source localization and limited-angle CT. We want to share the experiences, results we obtained and the open questions we face from our perspective as researchers coming from a background in biomedical imaging rather than in statistics and hope to stimulate a fruitful discussion for both sides