Relating Functional Measures to Network
Descriptions in the Study of Brain Systems
Steven E. Petersen, PhD, Steven M. Nelson, PhD,
Kelly Anne Barnes, PhD, and Bradley L. Schlaggar, MD, PhD
Department of Neurology
Washington University in St. Louis School of Medicine
St. Louis, Missouri
© 2010 Petersen
Relating Functional Measures to Network Descriptions in the Study of Brain Systems
Introduction
Unlike in other networks, such as those seen in social
systems, the components of brain networks, i.e., their
nodes and edges, are not easily defined. As mentioned
in the chapter by Sporns, node and edge definition
is critical to understanding functional networks in
the brain. The teaching points of this chapter relate
to an integration of evoked functional responses, as
determined from task-related functional magnetic
resonance imaging (fMRI), and resting correlations
between brain regions, as defined with resting state
“functional connectivity” MRI (rs-fcMRI). By
integrating the two kinds of data across a number of
analyses, we make the following arguments:
• That candidate node definitions are aided greatly
by an integrated approach; and
• That the outcome of the more calibrated node
definition can provide deeper insights into
functional differentiation and interpretation.
To this end, a set of analyses focused on the left
lateral parietal cortex (LLPC) will be presented.
These studies will include several analyses of taskevoked fMRI activation studies and rs-fcMRI
studies. This combined approach results in a sixfold
parcellation of LLPC based on several factors: the
presence (or absence) of memory retrieval–related
activity, dissociations in the profile of task-evoked
time courses, and membership in large-scale resting
brain networks. This parcellation strategy should
serve as a roadmap for future investigations aimed
at understanding LLPC function. In addition, this
analysis strategy can be applied to other extents of
the cerebral cortex.
Why the LLPC?
In humans, parietal cortex has traditionally been
linked to processing mechanisms involving attention
(Corbetta et al., 1998; Rushworth et al., 2001;
Corbetta and Shulman, 2002; Yantis et al., 2002;
Dosenbach et al., 2006, 2007). Other accounts of
parietal cortex function, particularly focused on the
left hemisphere, have examined its role in reading
(Turkeltaub et al., 2002), as well as numerosity
judgments and arithmetic (Göbel and Rushworth,
2004; Hubbard et al., 2005).
More recently, a surge in research has been devoted
to understanding the contributions LLPC makes
to memory retrieval (Wagner et al., 2005). In
particular, a great deal of research has been aimed
at understanding how humans distinguish between
previously experienced information (“old”) and that
which is novel (“new”), a phenomenon known as
the “retrieval success effect” (Henson et al., 2000;
© 2010 Petersen
Konishi et al., 2000; McDermott et al., 2000; Wheeler
and Buckner, 2003). The most common regions
showing retrieval success effects are found in the
lateral parietal cortex (Simons, 2008), and although
this differential activation is typically bilateral, the
most robust effects include a large expanse of LLPC
(McDermott et al., 2009). A secondary finding across
these studies is the presence of a dorsal–ventral
distinction in LLPC. This distinction appears to
dissociate dorsal regions near intraparietal sulcus
(IPS) involved in familiarity judgments from more
ventral regions near the angular gyrus (AG) that
are involved in recollection (Henson et al., 1999;
Wheeler and Buckner, 2004).
Studies across domains have yielded a multitude
of processing descriptions, suggesting that distinct
regions in parietal cortex might subserve unique
functional contributions. The analyses presented
here attempt to provide a parcellation scheme
based on convergence across multiple data types.
In doing so, we highlight the utility of a large-scale
network perspective.
Preliminary Parsing of LLPC Region
Using rs-fcMRI Boundary Mapping
The first step in parsing the LLPC region is to use the
recently developed technique of rs-fcMRI boundary
mapping to identify “correlationally” distinct regions
in LLPC. rs-fcMRI boundary mapping is based
on the observation that rs-fcMRI can dissociate
regions within the cortex using edge-detection
algorithms (Cohen et al., 2008). The technique
developed in Cohen et al. (2008) compares wholebrain correlation maps of adjacent cortical seeds and
searches for these abrupt changes in maps that depict
boundaries between cortical regions.
For the purposes of this experiment, a 27 × 27
grid of small spherical foci (6 mm diameter) was
generated over the extent of LLPC (Fig. 1A)
using Caret software (Van Essen Laboratory,
Saint Louis, MO) (Van Essen et al., 2001;
http://brainmap.wustl.edu/caret). The grid extended
outside the traditional bounds of parietal cortex to
decrease the chance that any functional borders
near the anatomical boundaries of LLPC would
go undetected.
The resulting rs-fcMRI boundary map depicts the
likely boundary at any given focus in the patch
(Fig. 1B). “Hot” and “cool” colors indicate high
and low probabilities, respectively, of the existence
of a boundary. The apparent centers of the bounded
regions in LLPC were obtained by inverting the map
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Notes
28
Notes
Figure 1. rs-fcMRI data were used to generate probabilistic boundary maps in order to define regions in
LLPC. A, A square patch of 729 spherical foci (6 mm diameter, 27 × 27 grid, spaced 6 mm apart) was created
using Caret software (Van Essen et al., 2001) and is shown here on an inflated cortical surface rendering.
The surface is rotated to allow better visualization of LLPC. A (anterior), P (posterior), L (lateral), M (medial).
B, rs-fcMRI boundary map generated using Canny method indicates the likelihood of a border at each seed.
“Cooler” colors represent stable rs-fcMRI patterns, whereas “hotter” colors represent high border likelihood, i.e., rapidly changing rs-fcMRI patterns. C, Inverted rs-fcMRI boundary map demonstrates peaks of
stability from the previous map. Centers are shown as dark gray spheres (10 mm diameter) on the inflated
surface. The blue circle indicates ROIs located within LLPC. D, Unprojected data from previous panel C allowing better visualization of borders. Gray dots represent ROIs, and those circled in blue indicate regions
located within LLPC. For orientation purposes, the grid contains anatomical labels that roughly correspond
to these locations on the cortical surface. aIPS, anterior intraparietal sulcus; SMG, supramarginal gyrus; SPL,
superior parietal lobule; vIPS, ventral intraparietal sulcus.
so that hot colors indicate rs-fcMRI map consistency
between nearby seeds (Fig. 1C,D). Regions of interest
(ROIs) were defined as 10 mm diameter spheres
(gray) at peak locations of consistency using twodimensional peak-finding algorithms. This resulted
in 25 ROIs across the grid. Ten of the defined ROIs
were outside of the parietal cortex and were excluded
from further analyses, leaving 15 LLPC mapping
ROIs to become targets of additional investigation.
Preliminary Examination of the
Functional Responses of Each ROI
We next applied the 15 mapping ROIs to a number
of task-related fMRI studies that contained a
contrast of “old” versus “new” items and performed
a meta-analysis. Preliminary examination of
the functional responses of each ROI showed a
geographic distinction between retrieval-related and
-unrelated regions. Only the seven more posterior
© 2010 Petersen
Relating Functional Measures to Network Descriptions in the Study of Brain Systems
ROIs showed consistent retrieval success effects
(Fig. 2A, green circles), defining a strong functional
boundary between region sets. Among the retrieval
success regions, different time course relationships
appeared (Fig. 2B–D), perhaps suggesting that
further functional subdivision would be appropriate.
rs-fcMRI Relationships Between
Boundary Mapping ROIs and
Other Brain Regions
The boundary mapping definition of the LLPC
regions was driven by differences in whole-brain
rs-fcMRI relationships, which were overlapping yet
distinct. One avenue to address this ambiguity is to
interrogate these relationships among the specific
regions of LLPC. In other words, which regions
outside of LLPC are most strongly functionally
connected to each of the LLPC regions (the region’s
“neighborhood”)? And do regions in different
neighborhoods show distinct functional time courses?
If an LLPC region, such as the posterior inferior
parietal lobule (pIPL), possesses a task-evoked time
course reflecting some functional process, do other
regions in its neighborhood share similar functional
time courses? The following sections aim to answer
these questions by exploring the relationships of
LLPC regions to regions elsewhere in the brain.
The next step in our analysis was to define sets of
regions that are related to LLPC regions using rsfcMRI data. Although rs-fcMRI boundary mapping
and subsequent peak-finding algorithms can separate
adjacent cortex into distinct regions based on
underlying differences in rs-fcMRI correlation maps,
they do not reveal what underlying differences are
actually driving the spatial distinctions.
To explore these differences, we generated rs-fcMRI
“neighborhoods,” defined as the sets of regions most
highly correlated with each of the 15 LLPC ROIs.
Neighbors that appeared in more than one seed map
were consolidated to eliminate overlap, resulting
in 87 final neighbors that spanned the cortex and
cerebellum. The 87 neighbors and 15 LLPC ROIs
formed a collection of 102 ROIs, which could then
Figure 2. Regions showing retrieval success effects are located in posterior parietal cortex. A, ROIs circled in
green indicate those that showed retrieval success effects across the eight studies that comprised the metaanalysis, while ROIs circled in red did not. The thick black line indicates this distinction. ROIs are displayed
on inflated cortical surface renderings of the human brain using Caret software. B, C, D, Time courses from
regions showing retrieval success effects. Posterior middle IPS (pmIPS), pIPL, and AG time courses correspond
to B, C, and D, as labeled in A. P values indicate level of significance for hit > correct rejection (CR).
© 2010 Petersen
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Notes
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Notes
Figure 3. Modularity optimization performed separately on modules not showing retrieval success effects
(supramarginal gyrus [SMG] and superior parietal lobule [SPL]) and retrieval success modules (AG and IPS).
A, The SPL and SMG modules did not split into separate submodules, although regions within the supplementary motor area (SMA) and dorsal anterior cingulate cortex (dACC) separate from the two (SMA/dACC,
dark green). The SPL module is now labeled SPL/”frontal eye fields” (FEFs), and the SMG module is now
labeled SMG/Insula to more appropriately describe the distributed regions contained therein. B, The AG and
IPS modules each split into multiple separate submodules, four of which (AG/mPFC [red], pIPL/sFG [light
yellow], LIPS/dlPFC [light blue], and aIPL/aPFC [light green] contained regions within LLPC showing retrieval
success effects. Regions in the right IPS (RIPS) and right dlPFC (dlPFC, purple), cerebellum (light brown),
and superior occipital cortex (SOC, teal) were also found to be distinct from the other regions. Parameters
dictating the placement of nodes in network space are the same as in A. C, Modularity optimization assignments shown in LLPC. Lines drawn in LLPC delineate submodule assignments. Colors are as in A and B. D,
Modularity optimization shown on lateral and medial views of the cortex using Caret software. Cerebellum
(light brown in B) not shown. Colors are as in A and B.
be viewed as a network of 102 nodes related to each
other by rs-fcMRI correlations.
The next set of analyses aimed at understanding
this network, and in particular, whether distinct
groupings or “modules” existed within it that might
provide further distinctions between the LLPC
ROIs. Community-detection analyses can subdivide
networks into functionally related subsets of nodes
called “communities” or “modules.” For example,
a person’s social network might include a module
of coworkers, a module of relatives, and a module
of teammates, each of which is richly connected
internally but possesses few connections to
other modules.
To assess the underlying grouping of our LLPC
ROIs and their neighbors, we performed a two-step
community detection analysis using modularity
optimization (Newman, 2006) on the matrix of
pairwise rs-fcMRI correlations between the 102
ROIs. This resulted in a set of six communities, or
submodules, that were related to six separate sets of
beginning LLPC ROIs. Among other relationships,
© 2010 Petersen
Relating Functional Measures to Network Descriptions in the Study of Brain Systems
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Notes
Figure 4. Four rs-fcMRI–derived submodules show different task-evoked fMRI time course dynamics and retain retrieval success
effects independent of the LLPC ROIs. A, A region in AG is shown on a lateral view of the left hemisphere using Caret software.
Time courses (below) were extracted for hits and correct rejections across the eight studies that comprised the meta-analysis.
P values represent the significance of the difference between hits and CRs, determined by a response time X repeated across measures, ANOVA with two levels of response and seven levels of time. B, C, D, Same as in A but for pIPL (B), LIPS (C), and aIPL (D).
E, All ROIs in the AG/mPFC submodule (excluding AG) are shown on lateral and medial views of the cortex using Caret software.
Time course data were extracted as in A, but were averaged across all ROIs shown here. P values are the same as in A. F, G, H,
Same as in E but for pIPL/sFG (F), LIPS/dlPFC (G), and aIPL/aPFC (H).
each set of LLPC ROIs had separate relationships
to a different set of frontal regions (Fig. 3A–D, each
color representing a different submodule).
The rs-fcMRI–Defined Submodules
Are Reflected in Functional Time
Course Distinctions
The final analysis seeks, in part, to further corroborate
whether the previously described intermediate time
course in pIPL (Fig. 2C) is functionally distinct by
examining the time courses in regions within its
submodule. If they show a pattern similar to the
region in pIPL, and are distinct from the AG/medial
prefrontal cortex (mPFC) and left IPS (LIPS)/
dorsolateral prefrontal cortex (dlPFC) submodules,
this would indicate that the pIPL time course is
indeed not an artifact of spatial blurring in LLPC.
More generally, this analysis is meant to find out to
what degree the distinctions found using rs-fcMRI
are reflected in task-evoked signals, both within
LLPC and in related regions outside LLPC.
© 2010 Petersen
The characterization of submodules that consist of
regions outside of, but closely related to, each of the
LLPC ROIs now lets us assess task-evoked signals at
the submodule level. We extracted time courses for
hits and correct rejections (CRs) from the regions
comprising each of the four submodules. These
submodules contained an LLPC ROI exhibiting
retrieval success effects across the eight tasks we had
defined in an initial meta-analysis. It is important
to note that the following analyses were performed
on submodule ROIs in which the original time
courses from LLPC ROIs were excluded. As such,
any observed effects are necessarily independent
of the initial fMRI analysis, which examined only
LLPC ROIs.
The time course profiles between the submodules
AG/mPFC, pIPL/superior frontal gyrus (sFG)
and LIPS/dlPFC are distinct from one another
(Fig. 4E–H), mirroring both the apparent time course
distinctions of Figure 2 and the modularity analysis
that defined submodules (Fig. 3B). Additionally,
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Notes
Figure 5. LLPC boundary mapping has a similar topography
in children aged 7 to 10 years (A) and adults aged 23 to 28
years (B).
regions in the pIPL/sFG and anterior IPL (aIPL)/
anterior prefrontal cortex (aPFC) submodules were
dissociable throughout all levels of the rs-fcMRI
analyses. The overall take-home concept from this
section is that differences found in defined network
substructures, based on rs-fcMRI, are reflected in
specific aspects of the functional signals found
during task.
Similar Mapping Regions Are
Defined in Children, but With
Different Network Relationships
A common observation is that there are
developmental differences in the overall rs-fcMRI
network structure (Fair et al., 2009; Supekar et
al., 2009). It is unknown whether this difference
would extend to areal parcellation, as in Cohen’s
work (2008), given that animal models suggest
that cortical area parcellation is completed early
in development.
To address this question, we applied boundary
mapping methods for parcellating the LLPC using
rs-fcMRI data (Cohen et al., 2008; Nelson et al.,
2010) to 7- to 10-year-old children and 23- to
28-year-old adults. The topography of the LLPC
areal parcellation maps was qualitatively similar
across children and adults (see Fig. 5A,B), which
suggested that the locations of LLPC areas would
be similar across groups. We identified LLPC areas
in each group using peak finding algorithms applied
to the areal parcellation maps. We then applied a
modified approach using the Hungarian assignment
algorithm to objectively “match” LLPC areas across
groups based on their distance in stereotactic space.
The assignment algorithm revealed 10 LLPC areas
that were separated by less than 9 mm in stereotactic
space (average distance between labeled pairs
<5 mm).
We then examined whether the similar parcellation
maps resulted from similar patterns of functional
connectivity over age. We queried the matched
LLPC areas and discovered that children showed
stronger functional connectivity with anatomically
proximal regions (i.e., other regions in parietal
cortex), whereas adults showed stronger functional
connectivity with anatomically distant regions (i.e.,
regions outside parietal cortex). Thus, although
anatomically similar LLPC “areas” can be identified
in 7- to 10-year-old children as well as in adults,
the patterns of functional connectivity for LLPC
areas continue to change during development. Our
findings converge with previous rs-fcMRI work that
revealed that functional connectivity networks
change from a “local” to a “distributed” organization
during the course of childhood and adolescence (Fair
et al., 2007, 2009). However, our findings suggest
that the locations of cortical areal boundaries are
established in school-aged children.
Conclusions
We believe that this series of studies/analyses has
several important implications:
• Adopting a large-scale network perspective
is profoundly useful, even for making local
distinctions between neighboring regions of cortex;
• Patterns of resting correlation are closely related
to patterns of task-evoked activity, consistent
with a hypothesis that resting correlation results
from a strong statistical history of task-evoked
coactivation; and
• rs-fcMRI and a network perspective can be used to
elucidate both stable (e.g., the location of putative
area boundaries) and changeable (e.g., the patterns
of connectivity for cortical areas) properties of the
developing brain, making it a powerful method for
studying human development.
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