Fundamentals of Data Analysis Methods in Functional MRI - Advance Image Processing in Magnetic Resonance Imaging - page 483

activations. “Real” cortical activation is expected to cover clusters of adjacent
pixels; conversely, there is a low probability that a given number of pixels
exceeding a threshold will be contiguous simply by chance. This distinction
between signal (which tends to cluster) and noise (which does not tend to cluster)
may be exploited to reduce the false positive probability without decreasing the
statistical power [33-37]. A natural way to do this is to use the detection criteria
that rely on the use of a cluster-size threshold in conjunction with the intensity
threshold, i.e., voxels are considered as activated by the stimulus if the uncorrected
false positive rate is below the fixed threshold and the same condition is verified
for a minimum number of adjacent voxels.
When this is the case, to quantify the statistical significance of an activated
region, it becomes necessary to determine the probability with which clusters of
various sizes occur by chance and to determine the likelihood of detecting such
clusters when activation is really present [33]. Several authors approached this
problem assuming that the fMR images can be approximated by a continuous
random field, where the voxel values are considered to be the realizations of a
random field sampled on an equally spaced grid. With this approach, the signif-
icance of activated clusters is determined on the basis of explicit expressions for
the probability of excursion sets of random fields derived from the theory of
Gaussian fields [34-36]. Although elegant and quantitative, this approach has the
drawback of requiring fMR images to be smoothed with spatial Gaussian filters
with broad full widths at half maximum (FWHM, FWHM/pixel size 2). As

discussed earlier, this inevitably reduces the effective spatial resolution of images
and is especially undesirable for single-subject studies. Alternative approaches
are based on the generation of null-hypothesis probability distributions through
Monte Carlo simulations [33] or randomization tests [37]. Forman et al. [33]
provided probability distributions of cluster sizes as a function of the uncorrected
false positive rate and for different values of the Gaussian spatial smoothing filter.
These distributions, obtained with Monte Carlo simulations and verified with
fMRI studies, provide approximated values for false positive rates that are asso-
ciated with combinations of the uncorrected false positive rates and a minimum
cluster-size threshold. These methods require fewer assumptions but are more
time consuming.
A solution that mitigates the problem of multiple comparisons in fMRI is to
limit the number of statistical tests to those voxel time courses that are indexed
by a reconstructed cortical sheet (gray matter voxels) and to use surface-based
2-D cluster-size thresholds [38].
Recently, a new approach has been proposed by Genovese et al. [39] to deal
with the problem of the multiple comparisons in fMRI. The approach is based
on the control of the false discovery rate (FDR), i.e., of the proportion of false
positives (incorrect rejections of the null hypothesis) among those tests for which
the null hypothesis is rejected. One advantage of this approach is that it offers
an objective way to automatically select “adaptive” thresholds across subjects

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(for details see Reference 39 ).