### Abstract

The fundamental problem faced by noninvasive neuroimaging techniques such as EEG/MEG^{1}1Electroencephalography(EEG); Magnetoencephalography (MEG). is to elucidate functionally important aspects of the microscopic neuronal network dynamics from macroscopic aggregate measurements. Due to the mixing of the activities of large neuronal populations in the observed macroscopic aggregate, recovering the underlying network that generates the signal in the absence of any additional information represents a considerable challenge. Recent MEG studies have shown that macroscopic measurements contain sufficient information to allow the differentiation between patterns of activity, which are likely to represent different stimulus-specific collective modes in the underlying network (Hadjipapas, A., Adjamian, P., Swettenham, J.B., Holliday, I.E., Barnes, G.R., 2007. Stimuli of varying spatial scale induce gamma activity with distinct temporal characteristics in human visual cortex. NeuroImage 35, 518-530). The next question arising in this context is whether aspects of collective network activity can be recovered from a macroscopic aggregate signal. We propose that this issue is most appropriately addressed if MEG/EEG signals are to be viewed as macroscopic aggregates arising from networks of coupled systems as opposed to aggregates across a mass of largely independent neural systems. We show that collective modes arising in a network of simulated coupled systems can be indeed recovered from the macroscopic aggregate. Moreover, we show that nonlinear state space methods yield a good approximation of the number of effective degrees of freedom in the network. Importantly, information about hidden variables, which do not directly contribute to the aggregate signal, can also be recovered. Finally, this theoretical framework can be applied to experimental MEG/EEG data in the future, enabling the inference of state dependent changes in the degree of local synchrony in the underlying network.

Original language | English |
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Pages (from-to) | 1290-1303 |

Number of pages | 14 |

Journal | NeuroImage |

Volume | 44 |

Issue number | 4 |

DOIs | |

Publication status | Published - 15 Feb 2009 |

### Keywords

- Coupled systems
- EEG/MEG theory
- Macroscopic aggregate
- Observability
- Singular spectrum analysis
- State space reconstruction
- Synchronization

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## Cite this

*NeuroImage*,

*44*(4), 1290-1303. https://doi.org/10.1016/j.neuroimage.2008.10.035