HAL Id: cea-00333747
https://hal-cea.archives-ouvertes.fr/cea-00333747
Submitted on 24 Oct 2008
HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entic research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diusion de documents
scientiques de niveau recherche, publiés ou non,
émanant des établissements d’enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.
Structural analysis of fMRI data revisited: improving
the sensitivity and reliability of fMRI group studies.
Bertrand Thirion, Philippe Pinel, Alan Tucholka, Alexis Roche, Philippe
Ciuciu, Jean-François Mangin, Jean-Baptiste Poline
To cite this version:
Bertrand Thirion, Philippe Pinel, Alan Tucholka, Alexis Roche, Philippe Ciuciu, et al.. Structural
analysis of fMRI data revisited: improving the sensitivity and reliability of fMRI group studies..
IEEE Transactions on Medical Imaging, Institute of Electrical and Electronics Engineers, 2007, 26
(9), pp.1256-69. �10.1109/TMI.2007.903226�. �cea-00333747�
Structural Analysis of fMRI Data Revisited:
Improving the Sensitivity and Reliability of
fMRI Group Studies
Abstract
Group studies of functional MRI datasets are usually based on the computation of the mean signal across subjects
at each voxel (Random Effects Analyses), assuming that all subjects have been set in the same anatomical space
(normalization). Although this approach allows for a correct specificity (rate of false detections), it is not very
efficient, for three reasons: i) its underlying hypotheses, perfect coregistration of the individual datasets and normality
of the measured signal at the group level, are frequently violated ; ii) the group size is small in general, so that
asymptotic approximations on the parameters distributions do not hold ; iii) the large size of the images requires
some conservative strategies to control the false detection rate, at the risk of increasing the number of false negatives.
Given that it is still very challenging to build generative or parametric models of inter-subject variability, we rely
on a rule based, bottom-up approach: we present a set of procedures that detect structures of interest from each
subject’s data, then search for correspondences across subjects and outline the most reproducible activation regions
in the group studied. This framework enables a strict control on the number of false detections. It is shown here
that this analysis demonstrates increased validity and improves both the sensitivity and reliability of group analyses
compared with standard methods. Moreover, it directly provides information on the spatial position correspondence
or variability of the activated regions across subjects, which is difficult to obtain in standard voxel-based analyses.
Index Terms
functional MRI, Group analysis, spatial normalization, structural methods, watershed, belief propagation, replicator
dynamics, group comparison.
May 29, 2007 DRAFT
1
Structural Analysis of fMRI Data Revisited:
Improving the Sensitivity and Reliability of
fMRI Group Studies
I. INTRODUCTION
Functional neuroimaging aims at finding brain regions
specifically involved in the performance of cognitive
tasks. In particular, functional MRI (fMRI) is based
on the detection of task-related Blood Oxygen-Level
Dependent (BOLD) effect in the brain. The measurement
of this effect is performed by regression analysis of
four-dimensional datasets (three spatial dimensions plus
time) against pre-defined regressors that represent the
expected BOLD response to the stimulations across time;
this analysis framework is known as the General Linear
Model (GLM) [1]. Inference about putative regions of
activity is generally based on several subjects (∼10-
15 subjects typically), and the current standard proce-
dure consists in detecting voxels for which the average
task-related BOLD signal increase is significant across
subjects (random/mixed effects analyses, R/MFX) [1],
[2]. Such voxel-based inference schemes require the
images to be warped to a common space, which is
usually performed by coregistration of the anatomical,
then functional data with a template image [3]. In most
data analysis software packages, the reference image is
the average T1 image provided by the Montreal Neu-
rological Institute (MNI), which matches approximately
the Talairach coordinate system [4].
Voxel-based inference schemes are explicitly based
on the assumptions that i) the functional images are
properly co-registered, so that a location in the common
space corresponds to the same region in the brain of
each subject; ii) at a given spatial location in the ref-
erence space, the signal is normally distributed across
subjects, so that the RFX and MFX statistics are Student-
distributed under the null hypothesis that no activation
occurs. Both hypotheses might be wrong: the signal can
be inhomogeneous across subjects [5], so that normal-
ity assumptions are not met [6], and mis-registrations
remain after spatial normalization of the datasets. The
magnitude of such local shifts is probably 1cm in many
brain regions (this can be observed for functional regions
like the the motor cortex or the visual areas [7], [8]
or the position of anatomical landmarks [9]–[11]). In
addition, the number of subjects included in the analysis
is generally small, so that RFX analyses are known to
have a weak sensitivity.
In order to deal with the spatial mis-registration issues,
most neuroscientists are thus accustomed to smoothing
their datasets (8-12mm FWHM typically in group stud-
ies) to increase signal spatial overlap across subjects.
This leads to biased and less precise localization of acti-
vated regions and may in some cases reduce sensitivity.
The interpretation of the boundaries of supra-threshold
May 29, 2007 DRAFT
2
regions in group studies is not clear. Another approach
consists in computing local or global anatomical warps
that improve inter-subject co-registration [12]–[14]. But
such warps may require the additional use of anatomical
landmarks, and it is not clear that different brains can
be correctly warped onto each other. In particular, the
variability in the large scale sulco-gyral anatomy [15],
[16] might imply that no such correspondences exist.
Note also that Talairach atlas was designed for sub-
cortical structures.
In order to cope with non-normality of the signal
across subjects, robust inference schemes, based e.g. on
the sign test or Wilcoxon signed rank’s statistic [17] have
been designed. Moreover, permutation-based assessment
of the group signal statistics [18], [19] yields an unbiased
significance for the statistical maps across subjects, and
thus bypasses some approximations implied by the use
of random field theory [1].
However, performing a test on each and every voxel
has a statistical cost (multiple comparison correction of
the p-values), while many of these voxels are probably
of little relevance to the cognitive function under study.
An interesting alternative is thus to perform inference
at a higher level than the voxel level. In other words,
one can consider functional regions, or structures, that
are found active across subjects rather than active vox-
els. This point of view has been advocated by many
groups that would use functional localizer paradigms
to define brain regions before testing the activity of
these regions in other conditions [20]. In particular,
regions of interest are frequently defined anatomically in
order to ease functional studies [21]–[25]. However, such
regions are defined within a reference space (e.g. MNI
space), which raises the aforementioned issue of mis-
registrations; moreover, such approaches define regions
very coarsely [21], [25] (less than hundred regions for
the entire brain). It is thus necessary to propose data-
driven approaches.
In the literature, there is no generally accepted gen-
erative model of brain activity that could drive group
inference procedures. Although few attempts have been
proposed recently [26]–[28], such approaches are likely
to be confounded by the complexity of the data, the
unknown extent and nature of the activations networks
and the global cross-subjects variability. Therefore, a
more pragmatic solution consists in modelling some
structures of interest observed in the groups of subjects,
and then to compare them in order to infer a group-
level template of the observed data. Such approach
are rule-based rather than based on a generative model
of the data. Hereafter, such approaches will be called
structural.
Structural approaches have to address several impor-
tant questions:
• What are the structures of interest in each subject?
In the case of fMRI data, it is clear that the informa-
tion of interest is coded in the maxima of activity
maps, e.g. large supra-threshold clusters [18], [29],
scale-space blobs [30] or activity peaks [31]. Al-
ternatively, some alternative approaches start with
the prior definition of regions (parcels), based on
clustering of anatomical and/or functional datasets
[7]. Some of these approaches might be somewhat
coarse for a fine description of activated areas [7],
[29], [31]. In this work, we rely on watersheds
of supra-threshold areas, which is an intuitive and
classical technique in pattern recognition [32].
• How to associate such regions across subjects ? This
point may be more difficult, in particular because
there exists clearly no isomorphism between indi-
vidual active regions. While the position in a com-
mon space is an important information [29], [31],
May 29, 2007 DRAFT
3
there might be local variations that induce some
ambiguities. In such cases, the relative position of
neighboring regions might be of great importance
[7], [30]. In this work, we propose a relatively
simple scheme to take this information into account.
• How to validate the sets of regions that have been
associated across subjects ? In [30] a procedure that
takes into account the individual feature quality,
structural similarity between features and associ-
ation strength, has been proposed. However, its
complexity may be quite problematic for interpreta-
tion purposes. Here, we prefer to perform a spatial
density test on the candidate regions, which allows
a strict control on the specificity (type I error rate)
of the method.
Finally, another important point is that structural meth-
ods involve many parameters in the modelling steps, and
it is thus quite important to control the robustness of the
results with respect to mild variations in the parameter
setting.
In the present paper, we propose a framework that
solves the aforementioned issues sequentially; in brief
1) it extracts regions of interest (ROIs) in each subject’s
dataset, 2) tests which of these regions are reason-
ably close to other activated regions in other subject’s
datasets, 3) searches for probabilistic correspondences of
the regions across subjects so that the relative positions
of ROIs coincide, 4) builds clusters of inter-subject
corresponding regions. Such clusters will be termed
cliques in this paper. Group inference proceeds through
the definition of spatial confidence regions associated
with each clique, while each subject may or may not
have a region associated with a clique defined at the
group level. Thus, the method results consist in a group-
level model and individual instances of this model. This
gives some means to account for and characterize inter-
subject differences, a key issue in group studies [6], [33].
We describe the method in Section II, and some
artificial and real benchmark datasets in Section III.
Importantly, our approach allows for an explicit control
on specificity, which is shown in Section IV; in Section
V we illustrate the improvement in terms of sensitivity
and reliability of fMRI group analyses. Reliability is
assessed by jackknife subsampling in a population of 102
subjects, and we show that the results of the proposed
method are less dependent on the particular subgroup
of subjects under study than standard voxel-based tests.
Finally, we describe the results of the method when
applied to the whole group of 102 subjects. Technical
issues and implications for neuroimaging studies are
discussed in Section VI.
II. M
ETHODS
A. Notations
Let us assume that a group of S subjects take part
in an fMRI acquisition protocol while they undergo a
certain cognitive experiment. After some standard pre-
processing (distortion correction, correction of differ-
ences in slice timing, motion correction, normalization),
the dataset of each subject is analysed in the General
Linear Model (GLM) framework: for a given subject
s ∈ {1, .., S}, let Y
s
be the dataset written as matrix
(scans×voxel), and let X be the design matrix that
describes effects of interest and confounds; the GLM
proceeds by estimating the effect vectors β
s
such that
Y
s
= Xβ
s
+ ǫ
s
, ∀s ∈ {1, .., S}, (1)
where ǫ
s
represents the residual matrix. The estimation
is based on a maximum likelihood approach performed
in each voxel, where the noise is assumed to be an AR(1)
process [1], [2], [34]. Let c be the linear combination of
May 29, 2007 DRAFT
