Biomedical Engineering Reference
In-Depth Information
Chapter 7
Source-Space Connectivity Analysis Using
Imaginary Coherence
7.1 Introduction
There has been tremendous interest in estimating the functional connectivity of
neuronal activities across different brain regions using electromagnetic brain imag-
ing. Functional connectivity analysis has traditionally been implemented in the sensor
space, but lately, a number of studies have begun to use source-space analysis, in
which voxel time courses are first estimated by an inverse algorithm, and brain inter-
actions are then analyzed using those estimated voxel time courses [
1
-
3
]. Although a
certain degree of inaccuracy exists in the source estimation process, the source-space
analysis has the potential of providing more accurate information regarding which
brain regions are functionally coupled.
Source-space connectivity analysis computes a metric of brain interaction called
a connectivity metric, using the voxel time courses. Among existing connectivity
metrics, a representative metric is the coherence [
2
-
5
]. However, in the source-space
coherence analysis, a serious problem arises from spurious coherence caused by the
leakage of an inverse algorithm. Such leakages are more or less inevitable in all types
of inverse algorithms [
6
]. One representative ramification of this spurious coherence
is an artifactual large peak around the seed voxel, called seed blur, in the resulting
coherence image. To remove such spurious coherence, the use of the imaginary
part of coherence, which is called the imaginary coherence, has been proven to
be effective [
7
]. It should be mentioned that the use of imaginary coherence was
originally proposed by Nolte et al. [
8
] to remove the spurious coherence caused by
the volume conduction in EEG sensor-space analysis.
This chapter reviews the source-space imaginary coherence analysis and related
methods. We first provide a detailed theoretical analysis on how the use of imaginary
coherence leads to the removal of the spurious coherence caused by the algorithm
leakage. We then discuss several related methods of imaginary coherence, includ-
ing corrected imaginary coherence, canonical coherence, and envelope-to-envelope
correlation/coherence. We present numerical examples that confirm our arguments.
