Comparison of Causality Network Estimation in the Sensor and Source Space: Simulation and Application on EEG.

Christos Koutlis,Dimitris Kugiumtzis,Vasilios K Kimiskidis

doi:10.3389/fnetp.2021.706487

Christos Koutlis, Dimitris Kugiumtzis + Show 1 more

Open Access

https://doi.org/10.3389/fnetp.2021.706487

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Abstract

The usage of methods for the estimation of the true underlying connectivity among the observed variables of a system is increasing, especially in the domain of neuroscience. Granger causality and similar concepts are employed for the estimation of the brain network from electroencephalogram (EEG) data. Also source localization techniques, such as the standardized low resolution electromagnetic tomography (sLORETA), are widely used for obtaining more reliable data in the source space. In this work, connectivity structures are estimated in the sensor and in the source space making use of the sLORETA transformation for simulated and for EEG data with episodes of spontaneous epileptiform discharges (ED). From the comparative simulation study on high-dimensional coupled stochastic and deterministic systems originating in the sensor space, we conclude that the structure of the estimated causality networks differs in the sensor space and in the source space. Moreover, different network types, such as random, small-world and scale-free, can be better discriminated on the basis of the data in the original sensor space than on the transformed data in the source space. Similarly, in EEG epochs containing epileptiform discharges, the discriminative ability of network topological indices was significantly better in the sensor compared to the source level. In conclusion, causality networks constructed at the sensor and source level, for both simulated and empirical data, exhibit significant structural differences. These observations indicate that further studies are warranted in order to clarify the exact relationship between data registered in the sensor and source space.

Highlights

There is an increasing interest in neuroscience in working on the true current distribution of the sources in the grey matter of the brain, termed source space, and not on the extracranial electroencephalograms (EEG) or magnetic encephalogram (MEG) recordings, termed sensor space (De Vico Fallani et al, 2010; Lehmann et al, 2014)
The level of preservation of the main network structure when estimated on the original data, called the sensor space, and data transformed to the so-called source space has been investigated
The transformation is performed using the software standardized low resolution electromagnetic tomography (sLORETA) and the causality effects among the system variables are estimated with a linear method (RCGCI) and a nonlinear information based method (PMIME)

Summary

Introduction

There is an increasing interest in neuroscience in working on the true current distribution of the sources in the grey matter of the brain, termed source space, and not on the extracranial electroencephalograms (EEG) or magnetic encephalogram (MEG) recordings, termed sensor space (De Vico Fallani et al, 2010; Lehmann et al, 2014). The overdetermined inverse models presuppose that a small number of points in the source space is capable of explaining the extracranial measurements sufficiently In this case, a unique solution, in terms of source location and current activity, is provided when the number of parameters to be estimated is less or equal to the number of sensor space channels. The underdetermined inverse models consider a dense three dimensional (3D) grid of points in the brain having fixed positions and being many more than the sensor space channels, which leads to infinite solutions, as stated first in (Helmholtz, 1853) The objective for these models is to determine a unique optimal source electric activity distribution over the grid of points

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