Cerebral Cortex Advance Access published April 5, 2013
Cerebral Cortex
doi:10.1093/cercor/bht075
Complexity in Relational Processing Predicts Changes in Functional Brain
Network Dynamics
Luca Cocchi1, Graeme S. Halford2,3, Andrew Zalesky4, Ian H. Harding4, Brentyn J. Ramm3, Tim Cutmore3, David H. K. Shum3
and Jason B. Mattingley1,2
1
Queensland Brain Institute and 2School of Psychology, The University of Queensland, Brisbane 4067, Australia, 3Behavioural
Basis of Health, Griffith Health Institute and School of Applied Psychology, Griffith University, Brisbane 4122, Australia and
4
Melbourne Neuropsychiatry Centre, The University of Melbourne, Melbourne 3053, Australia
*Address correspondence to Dr Luca Cocchi, Queensland Brain Institute, The University of Queensland, 4072 St Lucia, QLD, Australia.
Email: l.cocchi@uq.edu.au; lcocchi78@gmail.com
Keywords: Cognitive control, Reasoning, Connectivity, fMRI, Prefrontal
cortex
Introduction
In humans, higher order cognition such as deductive reasoning is crucial for adaptive and rational goal-directed behavior
(Johnson-Laird 2010). Given increasingly complex task
demands, cognitive abilities typically become more effortful
and can eventually break down, suggesting that task complexity places limits on higher order cognition and the regulation
of adaptive behavior (Halford et al. 2005). Investigations of
the brain underpinnings of such limits in processing complex
information are crucial for understanding the biological processes that underlie higher cognitive capacities in humans.
A critical component of cognitive reasoning is the ability to
ascertain relationships between contextual variables, and to
act in accordance with these relations to produce appropriate
responses (Bunge, Wallis et al. 2005). This concept has been
formalized in the “relational complexity metric,” which postulates that the cognitive load of deductive reasoning is related
to the number of variables that need to be linked into a representation of the problem’s solution (Halford, Wilson et al.
1998; Halford et al. 2007).
Several studies have shown that the prefrontal cortex plays
a central role in regulating the formation, maintenance, and
use of relations between variables (Christoff et al. 2001;
Kroger et al. 2002; Bunge, Wendelken et al. 2005; Badre et al.
2010; Golde et al. 2010; Crescentini et al. 2011; Krawczyk
et al. 2011; Watson and Chatterjee 2011). Evidence supports a
rostral-caudal gradient of function within the prefrontal
cortex, with more abstract and complex relations processed
by progressively more rostral regions (Koechlin and Summerfield 2007; Badre and D’Esposito 2009; Badre et al. 2010).
Results from functional magnetic resonance imaging (fMRI)
studies further suggest that these prefrontal regions may interact with posterior brain regions, including the superior parietal lobule and the occipital cortex, to integrate, maintain, and
implement relations during reasoning (Goel and Dolan 2001;
Kroger et al. 2002; Goel 2007; Golde et al. 2010; Wendelken
et al. 2011; Reverberi et al. 2012; Knowlton et al. 2012). More
broadly, the evidence for such segregated brain activity
during the processing of relations is consistent with recent
studies suggesting that trial-by-trial cognitive control engages
a large-scale functional brain network encompassing frontal
and parietal cortices (Dosenbach et al. 2006, 2007, 2008).
Here, we used a classic deductive reasoning paradigm, the
Wason Selection Task (Wason 1968), and novel fMRI analyses
to examine the influence of relational complexity on networkbased neural dynamics. In its general form, the Wason task
requires participants to determine whether a given rule can
be disconfirmed by a small subset of propositions. As it is
known that even highly educated individuals make characteristic errors of logic in this task (Wason 1971; Evans and Ball
2010), we initially trained our participants to help them avoid
these misconceptions and to minimize individual differences
in strategies. We manipulated relational complexity by parametrically varying the number of variables that needed to be
integrated to solve a given problem. Using this design, we
aimed to characterize any complexity-induced changes in
brain activity and modulatory coupling (i.e., connectivity)
among frontal and prefrontal regions (Christoff et al. 2001;
Kroger et al. 2002; Bunge, Wallis et al. 2005; Badre et al.
2010; Crescentini et al. 2011; Krawczyk et al. 2011). We examined complexity-induced changes in frontal dynamics in the
context of broader functional changes in a large-scale cognitive control network operating on a rapid (trial-by-trial) timescale, and encompassing fronto-parietal cortices. We also
examined whether functional changes in the fronto-parietal
network are dynamically related to changes in a cognitive
control system operating at a slower timescale (determined
by task set; Dosenbach et al. 2007, 2008). We predicted that
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The ability to link variables is critical to many high-order cognitive
functions, including reasoning. It has been proposed that limits in
relating variables depend critically on relational complexity, defined
formally as the number of variables to be related in solving a
problem. In humans, the prefrontal cortex is known to be important
for reasoning, but recent studies have suggested that such processes are likely to involve widespread functional brain networks.
To test this hypothesis, we used functional magnetic resonance
imaging and a classic measure of deductive reasoning to examine
changes in brain networks as a function of relational complexity.
As expected, behavioral performance declined as the number of
variables to be related increased. Likewise, increments in relational
complexity were associated with proportional enhancements in
brain activity and task-based connectivity within and between 2
cognitive control networks: A cingulo-opercular network for maintaining task set, and a fronto-parietal network for implementing
trial-by-trial control. Changes in effective connectivity as a function
of increased relational complexity suggested a key role for the left
dorsolateral prefrontal cortex in integrating and implementing task
set in a trial-by-trial manner. Our findings show that limits in relational processing are manifested in the brain as complexity-dependent modulations of large-scale networks.
functional interactions within and between these 2 major
control systems should play a central role in limiting the integration of complex relations during reasoning.
Materials and Methods
Participants
Twenty-three right-handed, adult participants (12 females) were recruited. One female participant was excluded from the analyses due
to excessive head motion (>2 mm) during the functional acquisition,
and 1 male participant was discarded due to technical failure in
acquiring behavioral data. Thus, data from 21 participants, aged from
21 to 39 years (mean ± SD = 28.6 ± 5.0 years), were included in the
analyses. All participants provided informed written consent to participate in the study, the procedures of which were approved by
The University of Queensland Human Research Ethics Committee.
The study was conducted in accordance with the Declaration of
Helsinki.
2 Brain Dynamics and Complexity
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Cocchi et al.
Figure 1. Schematic representation of the experimental paradigm. We developed
a modified version of the Wason Selection Task, in which participants engage in a
card-turning game with the goal of disconfirming a given rule (e.g., “If there is an A
on one side of the card, there is a 7 on the other”). Cards always had a digit on one
side and a letter on the other. (A) On each trial, participants were first shown a rule,
followed by a single card (e.g., 5) that might or might not be able to disconfirm the
rule. (B) Before starting the experiment, participants practiced the task with feedback
to ensure they understood the rules and to reduce errors and individual differences in
cognitive strategies. For the example shown here, if the face side contains any digit
but the one mentioned in the rule (i.e., a 7), then the rule is disconfirmed if A
appears on the reverse side. By contrast, if there is a 7 on the face, no letter on the
reverse side can disconfirm the rule. If there is an A on the face, any digit on the
reverse other than 7 can disconfirm the rule. If any letter but A appears on the face
no digit on the reverse side can disconfirm the rule.
7 on the reverse side of the card disconfirms the rule (e.g., a 5 on the
other side of the card would disconfirm the rule). Therefore, the
answer would be “yes.” This is trial type “A” in Figure 1B). By contrast, if a card shows an element that differs from the rule’s first
element (e.g., “C,” trial type “Not-A,” Fig. 1B), this cannot inform on
the validity of the rule because “C” and “5” do not disconfirm “If A
then 7.” Therefore, the answer is “no.” If a card shows an element
that matches the second element of the rule (trial type 7 in Fig. 1B),
this card can only “confirm” the rule (if the reverse side contains “A”)
but cannot disconfirm it (if the reverse side contains a letter other
than “A”). Therefore, the answer is “no.” Finally, a card showing an
element that is different from the rule’s second element (“Not-7” in
Fig. 1B) can disconfirm the rule (e.g., if the card shows a 5, then an A
on the other side would disconfirm the rule “If A then 7”). Therefore,
the answer would be “yes.” Participants practiced the task, with feedback, on a desktop computer. Results from the practice session confirmed that all participants performed the task above what would
generally be expected in such WST paradigms (Canessa et al. 2005).
Critically, a “different rule” was displayed prior to every card, so
that it was not possible for participants to reduce the task to a mere
matching of elements. For every problem, therefore, elements had to
be identified by mapping between card elements and rule elements,
based on the relation in the rule. Thus, for the new rule, “If 3 then Z,”
a “2” is a “Not-3” card, a “P” becomes a “Not-Z” card, and so on. The
relation between “3” and “Z” is mapped to the relation between (say)
“2” and “P,” and the status of card elements is defined by this relation
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Paradigm and Procedures
We optimized the conventional version of the Wason Selection Task
(WST) for functional magnetic resonance imaging (fMRI), and programmed the task using Presentation software (http://www.neurobs.
com/). The design of this modified reasoning task is depicted in
Figure 1A.
Each trial commenced with a central fixation cross (800 ms) followed by a short-blank interval (500 ms), before a logical rule establishing a relation between 2 alphanumeric variables (e.g., “If A then
7”) was presented for 3000 ms. Rules always consisted of a single
letter and a single digit (1–9), with letters and digits presented with
equal frequency as the first and second elements of the rule across
runs. A total of 180 different rules were presented throughout the
experiment. Following a randomly varied time period of 3000–5000
ms, a single digit (50% of the trials) or letter was displayed for 3000
ms. Participants were instructed to consider this character as one side
of a card and to indicate, as quickly and as accurately as possible, if
the card was potentially able to “disconfirm” the rule, assuming the
other side of the card could contain any possible letter (if the face
side contained a number) or digit (if the face side contained a letter;
see Fig. 1B). Critically, participants were instructed that the rule was
not bidirectional. Thus, for example, the rule “If A then 7” does not
imply “If 7 then A.”
Five unique task conditions were created by presenting card
elements that were 1) the same as the first element of the rule (e.g., A,
assuming the rule “If A then 7”); 2) different to the first element of
the rule (e.g., C); 3) the same as the second element of the rule (e.g.,
7); 4) different to the second element of the rule (e.g., 5); and 5) a
nonalphanumeric element that was completely unrelated to the rule,
serving as an active control condition (e.g., %). A null trial, in which a
white fixation cross was presented for the whole duration of the trial,
was also included as a passive control condition. These 6 trial types
were presented with equal frequency in pseudo-random order
across 5, 10-min runs, each consisting of 36 task trials (6 per
condition). The order of trials in each run was generated using the
fMRI sequence-optimizing algorithm optseq2 (http://surfer.nmr.mgh.
harvard.edu/optseq/).
Stimuli were projected onto a semitransparent viewing screen
located at the head end of the MR scanner using an LCD projector.
Participants viewed the projected stimuli via a mirror mounted on the
head coil. Participants were instructed to respond as quickly and as
accurately as possible within a 2000-ms window after the word
“Respond” appeared on the screen (Fig. 1A), so that no motor activity
was present during the card period. Responses were registered using
an MR-compatible optical fiber response box.
Prior to entering the MRI scanner, participants engaged in a training and practice session that lasted ∼30 min, to ensure that the logic
of the task was clearly understood and to minimize individual differences in strategy. Given our example rule (If A then 7), if the first
element of the rule (A) appeared on the card, any element other than
Magnetic Resonance Imaging
Acquisitions were conducted on a 3T Siemens Magnetom Trio magnetic resonance scanner (Erlangen, Germany) using a 32-channel
head coil. Functional sequences consisted of gradient-echo echoplanar images (GE-EPI; time to repetition, 2550 ms; time to echo, 32
ms; flip angle, 90°) within a field of view of 210 × 210 mm, an
in-plane resolution of 3.3 × 3.3 mm, and with a slice thickness of 3
mm (no gap). Thirty-seven interleaved axial slices were acquired to
cover the entire brain for all functional sequences. The first 2 images
were discarded to allow tissue magnetization to reach a steady state.
Data Analysis
Behavioral Analysis
Task accuracy and reaction time (RT) data did not follow a normal
distribution and were therefore analyzed using univariate nonparametric statistics (Friedman test) implemented in SPSS 19 (Chicago, IL,
USA).
fMRI
Preprocessing. Image preprocessing and analysis was performed in
SPM8 (Wellcome Department of Cognitive Neurology, London, UK).
Functional images were corrected for acquisition time (slice timing),
spatially realigned to the middle volume and spatially normalized to a
standard neuroanatomical space defined by the Montreal Neurological
Institute (MNI) EPI template. The normalized images were resampled
to 3-mm isotropic voxels and then smoothed with FWHM Gaussian
kernel of 8 mm. Time-series were high-pass filtered with a 128-s cut
off period to remove low-frequency noise and signal drifts, and were
additionally corrected for first-order (AR1) serial autocorrelations.
Statistics. Statistical analyses were performed by adopting the
general linear model (GLM) as implemented by SPM8 running in
Matlab (Natick, Massachusetts, USA). At the first level (within-subject
analysis), conditions of interest were modeled as boxcar functions
convolved with a canonical hemodynamic response function and its
temporal derivative. The model comprised regressors for the rule
presentation epochs (3 s), the card epoch (3 s) for each card type, and
null epochs of 3 s overlapping in time with the rule and card
presentation epochs. Given that errors were one of our predictors for
changes in brain activity and connectivity as a function of complexity,
the card regressors included both correct and incorrect trials. The
inclusion of all trials also guaranteed balanced within-subjects
contrasts between the different card conditions. Note that activity
associated with the rule period was not modeled separately for the
different card conditions, as rules were always of the same format and
complexity. Estimated motion parameters were also included in the
model as nuisance regressors. The resulting first-level contrast images
were carried over to second-level random-effects analyses.
Brain activity during the rule period. We first examined patterns
of brain activity associated with the formation and encoding of
trial-specific relations by comparing blood oxygen-level–dependent
(BOLD) changes during the null epochs with BOLD changes during
the rule epochs. For this analysis, the threshold for significance was
set to P < 0.05 corrected for multiple comparisons at the cluster level
[Familywise error (FWE) correction, cluster sizes estimated at
P = 0.001 uncorrected].
Brain activity during the card period. We next isolated the
average BOLD responses related to processing of the different card
conditions (P < 0.05 FWE corrected at cluster level, cluster size
estimated at P = 0.001 uncorrected). Neural activity during the null
epochs was compared with the average activity from the card epochs.
Post hoc analyses were undertaken to interrogate significant
activations arising from the different card conditions. Specifically,
task-related β-regression values were extracted from spheres having a
diameter of 5 mm and centered on the average local maxima of each
region of interest. Differences across card conditions were tested
using standard univariate statistics. To further explore changes in
brain activity in the regions of interest, we analyzed the evolution of
the BOLD signal as a function of time in each card condition (i.e.,
event-related BOLD time course). This latter analysis was performed
using algorithms implemented in the software rfxplot (Gläscher,
2009).
Effective connectivity changes associated with card
processing. Functional interactions supporting card processing
were investigated with psychophysiological interaction (PPI)
modeling (Friston et al. 1997; O’Reilly et al, 2012). PPI is a
well-established technique that can be used to determine whether the
connectivity between a pair of regions increases during a given
context or task. Here, we used PPI to examine such connectivity
during the processing of each card type. PPI analyses have typically
been implemented to assess which voxels in the brain show an
increase in context-specific connectivity with respect to a single
predefined seed region. Pairwise correlation is not a desirable
connectivity measure in this case because it does not disambiguate
context-specific connectivity from resting-state connectivity or
connectivity associated with a common neuromodulatory input. We
implemented a multiregional PPI to assess how the influence of each
brain region on all others was modulated during the processing of
each card type. Multiregional PPI is a simple generalization of the PPI
approach; rather than assessing the connectivity between a
single-seed region and all brain voxels, we defined multiple regions
and assessed the connectivity between each pair of regions. The 18
regions considered corresponded to the main clusters isolated by the
GLM analysis (i.e., the average card effect, FWE corrected at the voxel
Cerebral Cortex 3
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in at least some cases, as outlined below. To summarize, therefore,
while our training regime reduced errors and encouraged a consistent
cognitive strategy across participants, it did not obviate or circumvent
the relational processes that the task is designed to measure.
According to the relational complexity metric, the relative complexity of deductive reasoning elicited by each card can be quantified by
the number of variables that need to be linked in order to determine
whether the card can disconfirm the rule (Halford, Wilson et al. 1998;
Halford et al. 2007; Halford et al. 2010). The rule “If A then 7” relates
2 variables, the “antecedent” (A) and “consequent” (7). Each card also
contains 2 variables, corresponding to the element on the “face” side
(A, C, 5, 7 in this example) and the possible element on the “reverse”
side (with any alphanumeric character).
Alphanumeric characters on the card that match either element of
the rule (e.g., A or 7) provide an aid that reduces the cognitive load of
the reasoning required. The A card matches the antecedent of the
rule, and if the reverse side is Not-7 (e.g., 5), the rule is disconfirmed.
This is a binary relation, A and Not-7, which is of low complexity.
The 7 card matches the consequent of the rule, and if the face side is
Not-A, the rule is not disconfirmed. This also is a binary relation,
Not-A and 7, though the match to the consequent (7) would be less
accessible than the direct match between the A and the antecedent.
Consequently, the 7 card should be somewhat more difficult than the
A card. In contrast, the C card (also referred to as the Not-A card)
requires not only consideration of the 2 rule variables, but also identification of the face variable as a negative instance of the antecedent
variable. Processing the negation of the antecedent increases the complexity and is equivalent to the ternary relation (C, not-antecedent,
consequent). Finally, the 5 card (or Not-7) requires participants to
consider that the “reverse” element could be A, then to construct a
representation of the relation A and Not-7 negates “A implies 7.” The
5 does not match the A component of the rule, and the Not-7 does
not match the 7 component of the rule, so both internal representations must be generated, and then related to the antecedent and
consequent of the rule. This relation requires the internal representation of all 4 variables, which is at the limit of human relational
processing capacity (Halford et al. 2005). Thus, according to the relational complexity metric, the A and the 7 cards represent the lowest
level of relational complexity, the Not-A (C) card represents the next
highest level of complexity, and the Not-7 card represents the highest
complexity of all cards.
Figure 2. Behavioral data obtained during scanning for the 4 card types of the
modified WST. The A condition trials were the least complex and thus the easiest,
and the “Not-7” trials were most difficult. (A) Accuracy. (B) Reaction time (error bars
represent the within-subjects standard error of the mean).
We tested whether the extent of any card-dependent influence of
one region on another significantly differed across the 5 active card
conditions. A within-subjects analysis of variance (ANOVA) was used
to test this hypothesis for each of the 18 × 17 = 308 connections. The
network-based statistic (NBS; Zalesky et al. 2010; Cocchi et al. 2012a;
Zalesky et al. 2012) was used to correct for multiple comparisons.
The NBS ascribed a corrected P-value to each network of regions for
which inter-regional interactions differed across the 5 card conditions.
A primary F-statistic threshold of 3 was used for the NBS.
Results
Behavioral Measures
RTs were measured from the onset of the Respond display,
which followed the “Card” display (Fig. 1A). As depicted in
Figure 2, although overall accuracy levels were high, due to
the training and feedback provided prior to testing, participants showed a linear performance deterioration across the 5
conditions (X 2 = 25.85, df = 4, P < 0.01). Reduced performance
as a function of increased relational complexity was also confirmed by analyses of the RTs (X 2 = 21.96, df = 4, P < 0.01).
Thus, as predicted by the relational complexity hypothesis,
participants’ accuracy was reduced and RTs were prolonged
with increases in the relational complexity (i.e., number of
variables to consider in order to solve the problem) of the
card condition.
fMRI
Brain Activity During the Rule Period
During presentation of the rule in each trial, participants had
to form and encode a new set of trial-specific relations. Analyses of the fMRI data indicated that this ability involves a
diffuse set of brain regions encompassing dorsal cingulate
cortex, lateral frontal and prefrontal cortices, posterior parietal
cortices, anterior insula, and the striatum (Fig. 3 and Table 1).
Brain Activity During the Card Period
A significant effect of the different card conditions was shown
in a set of brain regions encompassing the superior parietal
cortex, the dorsal cingulate and supplementary motor cortices, the frontal cortex, the rostrolateral prefrontal cortex
(RLPFC), and the dorsolateral prefrontal cortex (DLPFC). In
addition, card processing engaged a large cluster encompassing the anterior insula, the striatum, and the thalamus (Fig. 4
and Table 2). The analysis of brain activity induced by each
Figure 3. Brain activity during rule processing. Processing of the rule was associated with significant activity in a diffuse set of regions encompassing the lateral prefrontal,
lateral frontal, parietal and occipital cortices, and the dorsal cingulate cortex (P < 0.05 FWE corrected at cluster level).
4 Brain Dynamics and Complexity
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level). For each participant and region, brain activity (first
eigenvariate) was extracted from a spherical seed region having a
diameter of 5 mm around the peak activation voxel, defined by a
positive average card effect minus the temporally corresponding
baseline (null trials).
The PPI signal was determined for each region by elementwise
multiplication of the region’s activity with the card versus baseline regressor. This PPI signal is therefore equal to the region’s activity
during times associated with processing of a specific card, but zero
for all other card processing conditions and −1 for the baseline. Note
that the hemodynamic response function (HRF) was first deconvolved
from the region’s activity before multiplication, and the final PPI term
was convolved with the HRF. These steps were performed using SPM
(spm_peb_ppi.m) for each region, card type, and participant. A GLM
was used to model card-dependent influences of any given region
upon another. The activity of the region being influenced (i.e., the
target, or afferent region) was the dependent variable, while the explanatory variable was the PPI term corresponding to the region exerting the influence (i.e., the source, or efferent region). In this way, a
region for which the PPI signal is a good predictor of its activity indicates a stronger influence on that region (by the region used to determine the PPI signal) during card processing but not at other times
during the acquisition. As is standard in PPI analyses, the card versus
baseline regressor, and the activity of the region used to determine
the PPI term (i.e., the main effects of the psychological and physiological factors), were included as nuisance covariates. This step was
taken to alleviate correlations due to shared task input.
Repeating this procedure for every pair of regions resulted in an
18 × 18 connectivity matrix for each individual and card type, where
each element (i,j) of the connectivity matrix stored the parameter
estimate (β) for the corresponding PPI term and quantified the carddependent influence that region i exerts on region j (i.e., effective
connectivity; see Friston 2011 for details on this specific measure of
effective connectivity).
Table 1.
Brain activity during the rule period
Anatomya
Rule minus null trials
Occipital cortex
Parietal cortex
Temporal cortex
Dorsal cingulate and supplementary
motor cortices
Anterior insula and caudate nucleus
Lateral frontal cortex
Lateral prefrontal cortex
Statisticsb
x
y
z
KE
Z
Pcorr
36
18
−18
−15
33
−27
−27
−45
3
−3
−3
9
−21
−12
−51
−30
33
−33
−70
−88
−82
−91
−61
−55
−51
−40
−85
8
−4
20
26
23
−1
−4
47
50
−20
−2
−14
1
46
43
40
1
37
52
64
37
4
10
46
52
37
25
5618
5.15
5.80
5.71
5.08
5.05
4.85
4.77
4.73
4.72
4.95
5.28
3.56
4.64
3.82
4.59
3.99
4.59
4.34
<0.001
314
107
294
101
83
<0.001
0.02
<0.001
0.02
0.04
Activity coordinates (x, y, z) are given in Montreal Neurological Institute (MNI) atlas space.
P-values are familywise error (FWE) corrected for multiple comparisons at cluster level.
b
card (minus the corresponding null trials) indicates that
similar clusters were activated in each card condition, with
the exception of rostrolateral prefrontal clusters that were
not significantly engaged by the control card (Table 2). As
depicted in Figure 4, card complexity was associated with an
increase in the BOLD signal in most of the clusters (representative regions shown). These observations were statistically
validated by within-subjects ANOVA on β-regression values
(P < 0.05 for all comparisons shown in Fig. 4, except for a
trend level for the left parietal cortex P = 0.07).
Note that comparable results were obtained from exploratory analyses that excluded data from incorrect trials.
Effective Connectivity Changes Associated with Card
Processing
Changes in (PPI) effective connectivity during card processing
were assessed among the cortical clusters isolated by the GLM
analysis described above (see Table 3 for details).
Results showed a significant change in connectivity as a
function of card complexity in a large-scale functional brain
network encompassing the RLPFC, DLPFC, lateral frontal
cortex, anterior cingulate cortex, the parietal and occipital cortices, and the anterior insular cortices (Fig. 5A). Connectivity
was generally lower during the processing of the control card
(active baseline) and the cards characterized by lower relational complexity (A and 7). In contrast, cards requiring
complex manipulation of relations (Not-A and Not-7) induced
consistently high functional coupling between connected
regions (see the histogram in Fig. 5A).
Changes in effective connectivity as a function of relational
complexity overlapped with the functional architecture of
both the fronto-parietal network (trial-by-trial control) and
the cingulo-opercular network (task set; Dosenbach et al.
2007, 2008; Dosenbach et al. 2010; also Power et al. 2011 and
Fair et al. 2009; see Supplementary Table S1 for a comparison
of the coordinates) (Fig. 5B). The requirement to consider
progressively larger numbers of variables was related to
Discussion
Our objective in the current study was to characterize changes
in whole-brain network dynamics as a function of relational
complexity. Here we defined complexity as the number of
variables that need to be linked with an existing set of
relations (task rules) to solve a deductive problem, as exemplified in the Wason Selection Task (Halford, Bain et al. 1998;
Halford et al. 2007). Before commencing the experiment,
training was provided to ensure that all participants understood the logic of the task and to minimize individual differences in cognitive strategies. Thus, changes in task
performance were specifically related to the number of variables that needed to be considered to access the problems’
solution and not to individual differences in the way that variables were manipulated (i.e., cognitive strategies).
We used fMRI and a novel analysis approach that permitted
quantification of changes in activity and (PPI) effective
connectivity among spatially segregated brain regions. Results
demonstrated that limits in processing relational complexity
are associated with increased regional activity within, and
functional interactions between, regions encompassing the
rapid (trial-by-trial) fronto-parietal and slower (task set)
cingulo-opercular control networks (Dosenbach et al. 2006,
2007, 2008, 2010). These findings provide a first comprehensive characterization of the dynamic brain processes that
impose functional limits on the human capacity to process
complex relations. More broadly, our results are consistent
with mounting evidence that intellectual performance is
related to dynamic reorganization of the functional interplay
within and between large-scale brain systems (van den
Heuvel et al. 2009; Leech et al. 2011; Fornito et al. 2012;
Stevens et al. 2012).
Cerebral Cortex 5
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a
increased connectivity within and between brain regions encompassing these 2 cognitive control systems. Taken together,
the findings suggest that the left DLPFC represents a key hub
for integrating information from the contralateral DLPFC, the
left frontolateral, as well as the occipital and parietal cortices
(Fig. 5B). Also, the left DLPFC appears a target region for
cingulo-opercular inputs from the dorsal anterior cingulate
cortex, the anterior insula and the right RLPFC. The right
RLPFC also showed complexity-induced changes in connectivity with the cuneus. Note that although the RLPFC is often
associated with the fronto-parietal network (e.g., Dosenbach
et al. 2010; Power et al. 2011; Sadaghiani et al. 2012),
previous findings have shown that this region supports the
maintenance and trial-by-trial implementation of subgoals
(Koechlin et al. 1999; Sakai and Passingham 2003; Gilbert
2011). Because of its hybrid functional role, the RLPFC is
likely to be a key hub for mediating fronto-parietal and
cingulo-opercular control functions. This proposition is highlighted in Figure 5B, which shows that the right RLPFC is
associated with both fronto-parietal and cingulo-opercular
networks. Finally, results showed that the left lateral prefrontal cortex and regions within the visual network strengthened
their modulation of the striatum as a function of increases in
card complexity.
A comparable functional brain network and effective connectivity pattern were found when we included only correct
trials in the analyses.
Downloaded from http://cercor.oxfordjournals.org/ by guest on April 7, 2013
Figure 4. Brain activity during card processing. After isolating the average effect of card processing on brain activity (P < 0.05 FWE corrected at cluster level), post hoc
analyses were performed on the card-specific beta series. Overall, results from the post hoc analyses showed that brain activity increased as a function of card complexity.
Statistically, this observation was confirmed for the majority of the regions. The BOLD time-series (scaled to zero at stimulus onset) shown in the right panels support this
conclusion (blue = control; yellow = A; orange = 7; red = Not-A; dark red = Not-7).
6 Brain Dynamics and Complexity
•
Cocchi et al.
Table 2.
Brain activity during the card period
Anatomya
Average card activity minus null trials
Parietal cortex
Insula
Dorsal anterior cingulate cortex
Motor and supplementary motor cortices
Striatum and thalamus
Cerebellum
Cuneus
Dorsolateral prefrontal cortex
Dorsal frontal cortex
Card Control minus null trials
Cerebellum
Occipital cortex
Insula
Striatum
Parietal cortex
Insula
Dorsal cingulate and supplementary motor cortices
Thalamus
Somatosensory cortex
Parietal cortex
Lateral prefrontal cortex
Lateral frontal cortex
Temporal lobe
Card A minus null trials
Insula
Parietal cortex
Striatum
Motor cortex
Dorsal cingulate and supplementary motor cortices
Somatosensory cortex
Striatum/Thalamus
Lateral prefrontal cortex
Striatum and anterior insular cortex
Occipital cortex and cerebellum
Parietal cortex
Rostrolateral prefrontal cortex
Lateral prefrontal cortex
Medial temporal cortex
x
y
z
KE
Z
Pcorr
−45
42
−30
−57
−39
36
−30
3
−33
−30
−18
−21
−15
21
3
−9
12
42
−39
36
−24
−30
33
−34
−55
−52
−43
8
14
17
8
−10
−16
−10
−1
−19
5
−52
−73
−70
26
23
50
44
56
−7
49
46
40
31
1
7
7
52
64
58
1
16
10
16
−14
10
13
31
31
1
−11
−8
64
12 636
6.84
5.25
5.83
5.68
5.80
5.87
5.79
5.58
5.32
5.96
5.83
6.65
5.68
5.19
6.16
5.51
4.95
4.82
4.32
4.22
4.41
4.08
3.83
<0.001
30
−9
15
39
21
−45
−39
−33
−54
−42
−39
3
5
−24
−18
−33
42
33
−30
−60
−54
54
−46
−73
−67
11
−1
−37
−31
−55
−46
−4
8
2
−1
−22
−10
−25
−55
47
35
2
−1
−22
−26
10
10
10
10
52
52
43
34
13
4
58
61
−2
7
73
46
34
25
25
43
−11
4105
<0.001
671
356
228
85
6.65
5.35
4.87
5.35
4.68
6.40
5.83
5.59
5.34
5.04
5.83
5.81
5.68
5.76
5.23
5.50
6.06
5.23
4.69
4.48
136
4.02
0.007
−39
−45
−39
−48
−24
−24
−30
−30
−3
0
9
−12
−51
−24
−24
39
21
39
30
−36
42
54
−24
36
−39
−35
−45
8
−34
−37
−46
−52
−7
−4
−16
−4
5
11
−10
−19
−16
−22
35
−1
11
−49
−49
−52
−40
44
50
47
26
−43
1
49
52
34
37
13
−5
58
58
49
43
73
19
1
−2
31
16
−2
−26
−26
43
49
−11
−2
28
28
−2
5659
6.15
6.09
5.79
5.50
5.28
5.74
5.58
5.58
5.54
5.49
5.34
5.11
5.52
5.18
5.12
5.03
5.85
5.30
5.82
5.62
5.39
4.31
4.86
4.13
4.78
4.58
4.28
< 0.001
62
61
4970
1154
2267
427
42
33
289
103
0.07 (<0.05 FDR)
0.07 (<0.05 FDR)
<0.001
<0.001
<0.001
0.001
0.04
<0.001
<0.001
<0.001
0.06 (FDR)
0.09 (FDR)
<0.001
0.01
(continued )
Cerebral Cortex 7
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Rostrolateral prefrontal cortex
Rostrolateral prefrontal cortex
Statisticsb
Table 2. Continued
Anatomya
Card 7 minus null trials
Insula
Parietal cortex
Striatum
Dorsal cingulate and supplementary motor cortices
Motor and somatosensory cortices
Cerebellum
Occipital cortex
Lateral prefrontal cortex
Rostrolateral prefrontal cortex
Lateral frontal cortex
Card Not-A minus null trials
Parietal and occipital cortices
Motor cortex
Dorsal cingulate and supplementary motor cortices
Cerebellum
Insula
Striatum and thalamus
Dorsolateral prefrontal cortex
Parietal cortex
Rostrolateral prefrontal cortex
Inferior temporal cortex
Card Not-7 minus null trials
Dorsal cingulate and supplementary motor cortices
Parietal cortex
Striatum
Insula
Cerebellum
Motor cortex
x
y
z
KE
Z
Pcorr
−39
−39
−45
−36
42
−24
−21
−21
18
−3
−3
−12
−30
−33
−27
−12
12
3
3
−25
−18
−24
−9
−47
−45
33
−36
36
5
−4
−34
−31
−55
14
−1
−7
2
−16
2
−7
−16
−10
−16
−10
−46
−55
−52
−19
−16
−22
−73
8
29
56
56
−7
4
10
49
52
49
4
13
16
13
55
52
55
55
67
73
76
−23
−5
−11
10
7
−2
10
19
37
−5
−2
64
12 498
6.58
5.86
6.54
6.18
5.51
6.43
6.19
6.14
5.65
6.32
5.87
5.76
6.32
5.09
5.67
5.49
6.60
5.94
5.88
6.28
6.25
5.76
5.54
5.52
2.8
3.44
2.35
4.13
<0.001
−45
−30
12
9
−33
0
−3
3
−39
−39
−42
39
33
−42
−18
−21
18
−18
18
−15
−15
45
−39
42
33
30
−39
−34
−52
−70
−73
−10
5
−14
−52
11
8
5
14
17
−4
−4
−10
2
−10
−4
−10
−19
23
23
−52
50
59
−46
49
40
43
46
64
55
40
−11
10
4
7
7
4
10
16
16
19
10
19
−2
10
31
31
43
1
1
−8
9307
6.77
5.86
5.52
5.27
6.55
6.54
6.11
6.14
5.94
5.94
5.92
5.64
5.33
5.16
5.85
5.72
5.72
5.67
5.62
5.49
5.45
5.21
4.07
6.11
4.65
4.48
4.09
<0.001
3
−3
9
−9
−45
−57
−27
−21
21
18
−42
−27
−39
30
30
−27
5
−33
8
14
20
−7
−34
−43
−55
−1
5
−1
5
14
8
14
17
20
−52
−10
52
43
37
73
46
31
40
16
16
13
10
7
1
7
4
−8
−14
64
11 634
82
619
183
92
6.63
6.31
6.03
5.31
6.46
5.58
5.58
6.24
5.79
5.52
6.23
6.06
6.01
5.92
5.82
5.78
5.01
5.79
0.02
<0.001
0.001
0.01
<0.001
(continued )
8 Brain Dynamics and Complexity
•
Cocchi et al.
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Thalamus
Statisticsb
Table 2. Continued
Anatomya
Dorsolateral prefrontal cortex
Thalamus
Occipital cortex
Rostrolateral prefrontal cortex
Parietal cortex
Statisticsb
x
y
42
45
−42
−18
−15
−12
36
42
26
23
20
−10
−19
−73
50
−52
z
KE
31
34
31
1
10
10
−2
43
589
Z
Pcorr
5.50
5.34
4.08
5.48
5.31
5.40
2.73
5.66
<0.001
a
Activity coordinates (x, y, z) are given in Montreal Neurological Institute (MNI) atlas space.
P-values are familywise error (FWE) corrected for multiple comparisons at cluster level.
FDR, false discovery rate.
b
Anatomya
Parietal cortex
Anterior insula
Dorsal anterior cingulate cortex
Striatum
Thalamus
Cuneus
Lateral frontal cortex
Lateral prefrontal cortex
Dorsolateral prefrontal cortex
Rostrolateral prefrontal cortex
Motor cortex
Cerebellum
x
y
z
−45
42
−30
36
3
21
−15
−9
12
−57
−36
36
−39
42
36
−28
−30
3
−34
−55
17
14
8
5
−19
−73
−70
8
47
47
23
26
50
50
−16
−52
46
46
7
7
52
16
10
10
13
22
28
34
31
31
1
−8
58
−14
card (given the rule “If A then 7”) might reflect a tendency to
favor confirming over disconfirming evidence, because 7 can
only confirm, and cannot disconfirm, the rule. Alternatively,
selection of the 7 might reflect ambiguity in interpretation of
the rule, because it is a valid response according to a 2D
(biconditional) interpretation of the rule. In our study, the
frequency with which participants selected the 7 card was
around 6% (see Fig. 2), much lower than has been found previously (Evans and Ball 2010). This suggests that participants
typically interpret the rule as a biconditional, and that we effectively suppressed this response through preliminary training. Pragmatic reasoning schemas (i.e., generalized sets of
rules defined in relation to classes of goals; Cheng and
Holyoak 1985) such as permission might also suppress this
response because permission more closely matches a conditional (Halford 1993). Ambiguity of the rule is implied by
selection of the 7 card, and is related to training and knowledge, whereas relational complexity effects are indicated by
failures to select the Not-7 card.
a
Coordinates (x, y, z) are given in Montreal Neurological Institute (MNI) atlas space.
Behavioral Performance
The participants performed well in all card conditions (>86%
correct overall), indicating that the training and heuristics provided prior to scanning were effective in helping to avoid the
high error rates typically reported for the conventional WST
(Wason and Shapiro 1971). Despite the relatively low number
of errors, however, the overall pattern of performance across
the 4 card conditions, in terms of error rates and RTs, mirrored the pattern yielded in typical versions of the WST.
Hence, when seeking to disconfirm the rule “If A then 7,” participants often correctly classified the A and 7 cards but did
not respond appropriately to the Not-A and Not-7 cards
(Canessa et al. 2005; Evans and Ball 2010). Taken with previous results on classic versions of the WST, our findings
suggest that the observed decline in performance as a function of card complexity is related to intrinsic limits in the
brain’s capacity to process relations among increasing
numbers of variables.
In our study, the cognitive processes entailed in selecting
each card were assessed separately. This approach yielded a
number of insights that are not possible with the classic
version of the Wason task, in which all 4 cards are considered
simultaneously (Wason 1968). Frequent selection of the 7
Brain Activity Supporting Rule Processing
Rule processing involved the generation of an internal relational representation using the elements presented in the rule
(e.g., A and 7). In line with existing knowledge on the cortical
regions that integrate and maintain abstract rules, rule encoding in the WST engaged a widespread set of brain areas encompassing prefrontal, frontolateral, and cingulate cortices
(Christoff et al. 2001, 2011 Kroger et al. 2002; Koechlin and
Summerfield 2007; Badre 2008, 2010). This diffuse set of
regional co-activations overlaps with 2 of the principal networks involved in cognitive control, namely the frontoparietal and cingulo-opercular systems (Dosenbach et al.
2006, 2008). The fronto-parietal network supports dynamic
(trial-by-trial) cognitive control and in our task is likely to be
engaged to update internal relational representations in
accordance with trial-specific rule elements. In contrast, the
cingulo-opercular system is thought to underpin awareness of
salient stimuli and the stable maintenance of task set (here
the given logic) throughout task execution (Dosenbach et al.
2006, 2007; Seeley et al. 2007).
In addition to widespread cortical activity, rule processing
was associated with significant striatal activity. The contribution
of the striatum to the acquisition of abstract rules is consistent
with previous studies showing that fronto-striatal networks are
central to the establishment of new relational representations
Cerebral Cortex 9
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Table 3.
Brain regions included to isolate changes in effective connectivity as a function of card
complexity
Downloaded from http://cercor.oxfordjournals.org/ by guest on April 7, 2013
Figure 5. Changes in effective brain connectivity as a function of card complexity. (A) Large-scale brain network showing global changes in connectivity for the different card
conditions. The network was isolated by conducting a psychophysiological interaction analysis (PPI) for every pair of regions of interest, resulting in an 18 × 18 connectivity
matrix for each individual and card type. The 18 regions represent the main clusters involved in card processing isolated using the general linear model framework (see Table 3
for details). In these matrices, elements (i,j) stored the parameter estimate (β) for the PPI term and quantified the card-dependent influence that region i exerts on region j (PPI
effective connectivity, see Materials and Methods). Matrices were used to test whether the extent of card-dependent influence from one region to another significantly differed
across card conditions. A within-subjects ANOVA was used to test this hypothesis. The NBS was used to correct for multiple comparisons. The x-axis in the bar chart depicts
the 5 card conditions, and the y-axis indicates the absolute median value of connectivity between each pairwise connection. (B) Schematic representation of large-scale brain
networks involved in limiting the processing of relational complexity: fronto-parietal (black), cingulo-opercular (light blue), and visual (green). DLPFC: dorsolateral prefrontal cortex;
dACC: dorsal anterior cingulate cortex; RLPFC: rostrolateral prefrontal cortex (note that this region is associated with both the fronto-parietal and cingulo-opercular networks; see
text for details); LFC, lateral frontal cortex; LPFC, lateral prefrontal cortex; aI/fO, anterior insula/frontal operculum.
in the prefrontal cortex (Asaad et al. 1998; Bunge, Wallis et al.
2005; Badre 2010; Badre et al. 2010). Taken together, our
results are in agreement with existing neurophysiological data
from human and nonhuman primates suggesting that the
acquisition of task-related relational knowledge is supported
by functional coupling between the striatum and the frontal
cortex.
10 Brain Dynamics and Complexity
•
Cocchi et al.
Critically, the rules used were always of the same general
form (e.g., “If A then 7”), and thus were identical in their
complexity. As a result, the observed differences in behavior
and brain activity arising from the different card conditions
cannot be attributed to differential processing of the rules,
but must instead be due to the unique integration of each
card element with trial-specific relational knowledge.
task set (Dosenbach et al. 2006,
2007). Similarly, as
mentioned above, the RLPFC has been implicated in the maintenance and trial-by-trial implementation of subgoals (Koechlin
et al. 1999; Gilbert 2011). As such, increased effective connectivity between regions of this network and the left DLPFC in
response to higher complexity cards is likely to reflect the
greater demand for implementing the acquired logic when
evaluating these cards, as compared to the easier implementation of only some of the steps of the logic when evaluating
the lower complexity cards (e.g., A directly matches A in the
rule and does not involve the implementation of all strategy
steps). This suggestion is in line with the recent proposition
that the anterior insula, along with the RLPFC, may represent a
critical hub for the active generation of appropriate responses
according to task goals (Bressler and Menon 2010; Menon and
Uddin 2010; Nelson et al. 2010). The anterior insula is also
thought to be critical in linking sympathetic arousal states with
cognitive control functions (Craig 2009; Bressler and Menon
2010; Cocchi et al. 2012b; Critchley and Harrison, 2013). Thus,
increased effective connectivity from the anterior insular cortices to the left DLPFC as a function of increased card complexity may be, at least to some extent, also related to increased
arousal.
Numerous hypotheses have been advanced to explain the
difficulty of the WST (Evans 2008). These include difficulty
with disconfirmation of hypotheses, pragmatic reasoning
schemas (Cheng and Holyoak 1985), Bayesian accounts based
on optimization of information gain (Oaksford and Chater
2007) and social contract theories based on modules such as
cheater-detection (Cosmides and Tooby 1992). Our finding
that the different card types in the WST entail specific local
activations and distinct levels of network connectivity has
important implications for these hypotheses. For example, a
strategy of matching elements (e.g., selecting the A and 7
cards for the rule “If A then 7”) might be chosen because it
reduces the complexity and the related metabolic cost to
achieve a goal (Bullmore and Sporns 2012). Indeed, matching
elements may be regarded as a default strategy to avoid the
higher metabolic demands of recognizing that Not-7 disconfirms the rule “If A then7.” Pragmatic reasoning schemas,
such as permission (Cheng and Holyoak 1985), might also
reduce cognitive complexity by providing previously known
confirming and disconfirming instances. For example, most
adults know that driving without permission in the form of a
license violates the traffic laws, and that accepting a benefit
without fulfilling preconditions violates a social contract. Previous investigations of the WST have shown relatively high
levels of correct responses when participants must decide on
a rule such as “a person must be 18 years of age to consume
alcohol” (Cheng and Holyoak 1985). This reduces cognitive
complexity because the disconfirming instance, drinking
while <18 years, is already known and does not need to be
computed. Finally, relational complexity has also been considered a viable alternative to optimization of information in
deductive reasoning (Halford 2009; Zielinski et al. 2010).
While the current study provides novel insights into the
brain networks that support, and possibly even limit, the processing of relational complexity, it is important to acknowledge potential methodological limitations. Recent studies
have shown that “micro” head movements may cause systematic changes in functional connectivity (Satterthwaite et al.
Cerebral Cortex 11
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Brain Dynamics Related to Limits in Integrating
Relational Complexity
Processing card elements characterized by different levels of
relational complexity modulated the dynamics of a large-scale
brain network that encompasses the fronto-parietal and
cingulo-opercular systems. Both segregated neural activity
and effective connectivity across the diffuse brain network
scaled as a function of card complexity, with higher values
elicited by cards characterized as having greater complexity
(i.e., Not-A and Not-7).
The relevance of frontal and prefrontal regions for relational mechanisms supporting the implementation of defined
cognitive strategies has been shown by a number of previous
fMRI studies. In particular, the DLPFC and the lateral frontal
cortices have been associated with the online generation,
evaluation, and active maintenance of task-relevant relational
representations (Diwadkar et al. 2000; Bunge, Wallis et al.
2005; Crescentini et al. 2011, 2012; Wendelken et al. 2011).
On the other hand, the RLPFC is thought to be critical for implementing trial-based goals (Rowe et al. 2007; Bengtsson
et al. 2009; Reverberi et al. 2011) and plays a key role in applying rules while simultaneously maintaining alternative
rules in an active state (Koechlin et al. 1999; Braver and
Bongiolatti 2002; Kroger et al. 2002). Similarly, this anterior
prefrontal region seems to support the simultaneous consideration, comparison, and integration of multiple relations
(Christoff et al. 2001; Kroger et al. 2002; Fangmeier et al.
2006; Bunge and Wendelken 2009; Rodriguez-Moreno and
Hirsch 2009; Green et al. 2010). Taken together, our findings
point toward a central role for the RLPFC in generating appropriate delayed responses according to task sets (Sakai and
Passingham 2003; Gilbert 2011). Not only are our results in
agreement with current views on the role of prefrontal
regions in relational processing, they also extend this understanding by suggesting that the pattern of effective connectivity from the left frontal, right DLPFC, and right rostrolateral
prefrontal cortices to the left DLPFC is directly associated with
limits in the efficient processing of relations to achieve behavioral goals.
In addition to characterizing the impact of frontal dynamics
on limits in relational processing, our results highlight that
such dynamics alone occur in the context of broader systemic
changes. Specifically, our findings showed that the implementation of cognitive control strategies to solve complex
relational problems involve the coordinated action of both
the fronto-parietal and cingulo-opercular control systems
(Dosenbach et al. 2006, 2007, 2008). Our analysis of effective connectivity also suggests that relational complexity
modulates afferent connections between visual regions involved in integrating card stimuli and the DLPFC and right
RLPFC. Overall, these changes in large-scale brain network
dynamics are likely to reflect the increased effort in actively
linking and maintaining online an increased number of variables according to the given logic.
Inputs to the left DLPFC from the right RLPFC, anterior
insula, and dorsal anterior cingulate cortex were low in cards
characterized by low complexity (i.e., A and 7) and high in
cards characterized by higher complexity (i.e., Not-A and
Not-7). The dorsal anterior cingulate and anterior insular cortices represent key neural hubs of the cingulo-opercular
network, which is implicated in maintaining and implementing
Concluding Remarks
We have shown that the number of variables that need to be
linked into a representation to solve a problem predict
performance in a complex-reasoning task. Limits in efficiently
relating variables according to task goals are reflected in
complexity-dependent network dynamics within and between 2
main control systems, namely, the fronto-parietal and cinguloopercular networks. Overall, our study highlights the need to
consider limits in high-order cognitive processes that require the
manipulation of relations as complexity-induced changes in
large-scale brain network dynamics beyond the frontal cortex.
Supplementary Material
Supplementary material can be found at: http://www.cercor.oxford
journals.org/.
Funding
This study was supported by a grant from the National and
International Research Alliance Program (NIRAP), Queensland State Government, Australia, and by a Griffith University
Infrastructure Research Grant. J.B.M. was supported by an
Australian Research Council (ARC) Laureate Fellowship
(FL110100103). A.Z. is grateful for the support provided by
Professor Trevor Kilpatrick as part of the inaugural Melbourne
Neuroscience Institute Fellowship. This work was also supported by an ARC Discovery Project awarded to A.Z.
[DP0986320].
Notes
The authors thank Oscar Jacoby for his assistance in developing some
of the analysis tools. Conflict of Interest: None declared.
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