Constructing Surrogate Data to Control for Artifacts of Volume Conduction for Functional Connectivity Measures
The major problem in examining interactions between sources of brain activity from MEG and EEG data are the ‘artifacts of volume conduction’ denoting the fact that the sensors measure a largely unknown superposition of brain activities. In this work we suggest a method to test for artifacts of volume conductions. The test is absolutely general: it is applicable to both linear and nonlinear methods and both on the sensor and source level.
The idea of the method is to construct surrogate data which are statistically as close as possible to the original data but which are a superposition of independent sources. As a first step we decompose the data via Independent Component Analysis (ICA) resulting in signals which are as independent as possible. In a second step we destroy any remaining dependencies by shifting the n.th signal by a time (n-1)*T where T must be substantially larger than any autocorrelation time. Finally, these shifted signals are mixed again into sensors using the mixing matrix found by the ICA algorithm. Any interaction measure can now be calculated both for the original and the surrogate data. If a specific effect can be seen in both data sets we consider this effect as insufficient evidence for an observed brain interaction.
We applied this method to real and imaginary parts of coherency (real EEG data), 1:2 phase locking (real EEG data) and Granger causality (simulated data). We found that the real part of coherency is almost perfectly consistent with mixtures of independent sources while the imaginary part cannot be explained with the surrogate data at all. Results for phase locking can only be explained partly by volume conductions. For true directional interactions Granger causality is attenuated but not removed in the surrogate data as compared to the original data.
KeywordsFunctional connectivity measures Volume conduction Surrogate Data Coherency method Phase Locking Granger causality ICA
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