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J. W. Choi and K. H. Kim
It is warranted that the field spread effect is not completely removed in the source
space so that the FCA results should be carefully interpreted. The use of FC measures
which are inherently insensitive to the instantaneous mixing, such as imaginary part
of coherence (imagcoh), can be recommended to alleviate this problem [46].
Marzetti et al. [32] developed a method to decorrelate the reconstructed sources
using principal component analysis (PCA) [32]. Assuming orthogonality between
the estimated sources, further demixing is performed using an algorithm called minimum overlap component analysis. The locations of interacting sources are estimated
under minimum overlap constraint after identifying the spatial topography of interacting sources from the sensor-space cross-spectral density. Gomez-Herrero et al. [18]
presented a method for effective connectivity estimation based on the independent
component decomposition of the residuals of the MVAR model, which are probably due to the field spread [18]. The spatial topography of the interacting sources is
obtained from the ICA mixing matrix. More recently, Haufe [21] proposed a novel
measure of effective connectivity based on physiologically-motivated model of interacting sources and sparse connectivity graph [21]. A one-shot calculation method
for the blind source separation and inverse source reconstruction, which yields the
source time series, their spatial distribution, and the connectivity structure.
6.6 Determination of Significance
The calculated FC metrics may include false positives due to several confounding
effects such as residual artifacts, volume conduction, and common reference. Hence
it is important to determine statistical significance. As shown in Fig. 6.7a, null distribution of the FC can be generated from a surrogate data obtained by random shuffling
and used to determine significance, which is often defined by the upper 5 or 1% of
the null distribution.
Several methods can be used to generate the surrogate data from the experimental
data [15, 30, 54]. Random shuffling of the time samples of one of the two timeseries destroys the temporal structure. If all time samples are randomly shuffled and
the temporal structure is completely destroyed, the null distribution obtained from
the surrogate data may result in excessively high false positive rate, i.e., inflate the
statistical significance. This can be understood from the fact that the FC measure
calculated from any experimental data would be much higher than those calculated
from surrogate data, in which the temporal structure is completely destroyed. An
alternative is illustrated in Fig. 6.7b, which is called ‘time-shift’ method [15]. Here
one time-series is separated into two segments at a randomly chosen temporal point,
and then, a new surrogate time-series is generated by exchanging temporal positions
of those two segments.
Instead of the random shuffling in time domain, it can also be performed in the
frequency domain as shown in Fig. 6.7c [54]. Briefly, the procedure includes fast
Fourier transform (FFT), shuffling the phase of the signal in the frequency domain,
J. W. Choi and K. H. Kim
It is warranted that the field spread effect is not completely removed in the source
space so that the FCA results should be carefully interpreted. The use of FC measures
which are inherently insensitive to the instantaneous mixing, such as imaginary part
of coherence (imagcoh), can be recommended to alleviate this problem [46].
Marzetti et al. [32] developed a method to decorrelate the reconstructed sources
using principal component analysis (PCA) [32]. Assuming orthogonality between
the estimated sources, further demixing is performed using an algorithm called minimum overlap component analysis. The locations of interacting sources are estimated
under minimum overlap constraint after identifying the spatial topography of interacting sources from the sensor-space cross-spectral density. Gomez-Herrero et al. [18]
presented a method for effective connectivity estimation based on the independent
component decomposition of the residuals of the MVAR model, which are probably due to the field spread [18]. The spatial topography of the interacting sources is
obtained from the ICA mixing matrix. More recently, Haufe [21] proposed a novel
measure of effective connectivity based on physiologically-motivated model of interacting sources and sparse connectivity graph [21]. A one-shot calculation method
for the blind source separation and inverse source reconstruction, which yields the
source time series, their spatial distribution, and the connectivity structure.
6.6 Determination of Significance
The calculated FC metrics may include false positives due to several confounding
effects such as residual artifacts, volume conduction, and common reference. Hence
it is important to determine statistical significance. As shown in Fig. 6.7a, null distribution of the FC can be generated from a surrogate data obtained by random shuffling
and used to determine significance, which is often defined by the upper 5 or 1% of
the null distribution.
Several methods can be used to generate the surrogate data from the experimental
data [15, 30, 54]. Random shuffling of the time samples of one of the two timeseries destroys the temporal structure. If all time samples are randomly shuffled and
the temporal structure is completely destroyed, the null distribution obtained from
the surrogate data may result in excessively high false positive rate, i.e., inflate the
statistical significance. This can be understood from the fact that the FC measure
calculated from any experimental data would be much higher than those calculated
from surrogate data, in which the temporal structure is completely destroyed. An
alternative is illustrated in Fig. 6.7b, which is called ‘time-shift’ method [15]. Here
one time-series is separated into two segments at a randomly chosen temporal point,
and then, a new surrogate time-series is generated by exchanging temporal positions
of those two segments.
Instead of the random shuffling in time domain, it can also be performed in the
frequency domain as shown in Fig. 6.7c [54]. Briefly, the procedure includes fast
Fourier transform (FFT), shuffling the phase of the signal in the frequency domain,