Modeling the Connectivity of Neural Ensembles Underlying EEG/MEG
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1
Berlin Institute of Technology, Machine Learning Group, Germany
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2
The University of Tokyo, Department of Mathematical Informatics, Japan
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3
Fraunhofer Institute FIRST, IDA, Germany
The analysis of neural interaction (connectivity) plays a crucial role for understanding the brain's general functioning. Given multiple simultaneously-recorded time-series reflecting neural activity in different brain regions, a functional (task-related) connection between two regions is commonly inferred, if a significant time-lagged influence between the corresponding time-series is found. Different measures have been proposed for quantifying this influence (e.g., coherence, PSI, Granger causality, PDC, DTF).
EEG and MEG are well suited to study neural connectivity due to their noninvasiveness and high temporal resolution. But here, the problem of volume conduction arises, i.e., each EEG/MEG sensor captures a linear superposition of signals from all over the brain. This mixing introduces instantaneous correlations, which can cause the above-mentioned analyses to detect spurious connectivity between sensors.
We here propose a method that directly estimates the connectivity of hidden brain sources, which, in the case of EEG/MEG, represent the synchronous behaviour of large neural populations [1]. Our approach is straightforward: the measurements are modeled as a linear instantaneous mixture of sources, which follow a multivariate autoregressive (MVAR) model. We derive the joint likelihood for MVAR coefficients and (de)mixing matrix based on the assumption that the innovations driving the source MVAR process are super-Gaussian distributed and (spatially and temporally) independent. The model parameters can be optimized using maximum-likelihood, but we also consider a variant, in which off-diagonal parts of the MVAR-coefficient tensor are additionally penalized. This penalty acts as a regularizer, preventing the model to overfit the data. Furthermore, it will shrink some of the MVAR-coefficients to zero, thereby effectively pruning connections between sources. This leads to better interpretability of the data. By variation of the regularization parameter, our method is able to interpolate between a fully-correlated source model and a model which allows no crosstalk between sources.
Upon having fitted the model we are provided with a demixing matrix, by which time-courses of the estimated sources can be extracted from the EEG. The connectivity structure of the sources can be simply read off from the sparsity pattern of the estimated MVAR coefficients, but it is also possible to calculate any other type of connectivity measure on the source traces. Finally, the estimated inverse demixing matrix describes the spread of the sources onto the EEG channels. These spatial patterns can be subjected to source localization and thereby used to link the sources to actual locations in the brain.
We show in a simulation study that our method has excellent performance under several realistic noise conditions. Furthermore, we present a preliminary analysis of resting-state data (eyes closed), where our method finds a number of distinct interrelated components in the alpha-band range.
References
[1] Haufe et al., 2010. Modeling sparse connectivity between underlying brain sources for EEG/MEG. IEEE Trans Biomed Eng. In Press.
Keywords:
computational neuroscience
Conference:
Bernstein Conference on Computational Neuroscience, Berlin, Germany, 27 Sep - 1 Oct, 2010.
Presentation Type:
Presentation
Topic:
Bernstein Conference on Computational Neuroscience
Citation:
Haufe
S,
Tomioka
R,
Nolte
G,
Mueller
KR and
Kawanabe
M
(2010). Modeling the Connectivity of Neural Ensembles Underlying EEG/MEG.
Front. Comput. Neurosci.
Conference Abstract:
Bernstein Conference on Computational Neuroscience.
doi: 10.3389/conf.fncom.2010.51.00027
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Received:
20 Sep 2010;
Published Online:
23 Sep 2010.
*
Correspondence:
Dr. Stefan Haufe, Berlin Institute of Technology, Machine Learning Group, Berlin, Germany, haufe_work@mailbox.org