Image Processing Reference
In-Depth Information
16.5.5
I
NTERPRETATION
OF
THE
R
ESULTS
16.5.5.1
Thresholding the Maps
The thresholding operation of each map is usually performed by scaling the
intensity values to the z score. Within each component map, the voxels that
contribute significantly to the map are those having a z score whose absolute value
is greater than a threshold. Voxels whose time series are modulated opposite to
the time course of the component show a negative z score. It is important to stress
that the z score has no statistical significance, but it is used only for descriptive
purposes. In order to make statistical inferences about these maps, some hypothesis
about the distribution of the noise or the signal is needed. In Reference 41 a
probabilistic ICA model that takes noise into account is introduced. The use of a
z score for inferential purposes is not recommended here because of the non-
Gaussian distribution of the intensity values in each map. A different z score
normalization is proposed, using the estimate of the voxel-wise noise standard
deviation, evaluated as residuals of the IC model. Each resulting map is then is
fitted with a Gaussian mixture model (GMM) by means of an expectation maxi-
mization algorithm. The Gaussian that identifies the background noise is typically
thought to coincide with the dominant mode of the histogram, and the probability
density function of the background noise can be evaluated, as well as the
probability that any voxel belongs to the background noise. The Gaussian
mixtures that do not belong to background noise can be used to estimate the
probability of the hypothesis of activation related to the relevant time course.
16.5.5.2
Task-Related Activations
McKeown [34] was the first to apply ICA to fMRI data. In this early applica-
tion, ICA was applied in the spatial domain. In the application of spatial ICA
to fMRI data, McKeown grouped the components found in different classes
based on the shapes of the associated time courses. Block-designed experi-
ments were analyzed in which two conditions, task and control, alternate in
time. Even if no information about the shape of the activation or its location
is used in the decomposition process, it can be used after the independent
components are estimated for classification purposes. Usually in order to detect
task-related components, the correlation coefficient between the time courses
of each component (in spatial ICA the columns of the mixing matrix
A
) and
a reference function depicting the task is evaluated [42]. The components
whose associated time courses highly correlate with the paradigm are consid-
ered task-related components or consistently task related (CTR), whereas
components whose activation is related only partly to the paradigm are called
transiently task related (TTR). These components were thought to be related
to a complex spatiotemporal structure of the activation. In fact, they may be
the decomposition results of different neural processes with overlapping areas
or related to transient neural processes such as arousal, habituation, or learning.
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