BR A IN RE S E A RCH 1 3 42 ( 20 1 0 ) 6 3 –7 3
available at www.sciencedirect.com
www.elsevier.com/locate/brainres
Research Report
An fMRI investigation of cognitive stages in reasoning
by analogy
Daniel C. Krawczyk a,b,⁎, M. Michelle McClelland a , Colin M. Donovan a ,
Gail D. Tillman a , Mandy J. Maguire a
a
The University of Texas at Dallas, Dallas, TX, USA
University of Texas Southwestern Medical Center at Dallas, Dallas, TX, USA
b
A R T I C LE I N FO
AB S T R A C T
Article history:
We compared reasoning about four-term analogy problems in the format (A:B::C: D) to semantic
Accepted 18 April 2010
and perceptual control conditions that required matching without analogical mapping. We
Available online 25 April 2010
investigated distinct phases of the problem solving process divided into encoding, mapping/
inference, and response. Using fMRI, we assessed the brain activation relevant to each of these
Keywords:
phases with an emphasis on achieving a better understanding of analogical reasoning relative to
Reasoning
these other matching conditions. We predicted that the analogical condition would involve
Prefrontal Cortex
the most cognitive effort in the encoding and mapping/inference phases, while the control
Analogy
conditions were expected to engage greater prefrontal cortex (PFC) activation at the response
period. Results showed greater activation for the analogical condition relative to the control
conditions at the encoding phase in several predominantly left lateralized and medial areas of
the PFC. Similar results were observed for the mapping/inference phase, though this difference
was limited to the left PFC and rostral PFC. The response phase resulted in the fastest and most
accurate responses in the analogy condition relative to the control conditions. This was
accompanied by greater processing within the left lateral and the medial PFC for the control
conditions relative to the analogy condition, consistent with most of the cognitive processing of
the analogy condition having occurred in the prior task phases. Overall we demonstrate that the
left ventral and dorsal lateral, medial, and rostral PFC are important in both the encoding of
relational information, mapping and inference processes, and verification of semantic and
perceptual responses in four term analogical reasoning.
© 2010 Elsevier B.V. All rights reserved.
1.
Introduction
Analogical reasoning is considered to be a key aspect of human
thinking. Successful analogies require connecting information
about the relations among items to other relational information
that may come from an entirely separate domain. For example,
one's knowledge of the structure and function of a computer can
serve as a source analog that can be mapped and related to the
⁎ Corresponding author. Center for BrainHealth®, The University of Texas at Dallas, 2200 Mockingbird Lane, Dallas, TX 75235, USA. Fax: +1
972 883 2491.
E-mail address: [email protected] (D.C. Krawczyk).
Abbreviations: fMRI, functional Magnetic Resonance Imaging; PFC, Prefrontal Cortex; ROI, Region of Interest; RLPFC, Rostrolateral
Prefrontal Cortex; DLPFC, Dorsolateral Prefrontal Cortex; LIFG, Left Inferior Frontal Gyrus; LMFG, Left Middle Frontal Gyrus; BA, Brodmann
Area
0006-8993/$ – see front matter © 2010 Elsevier B.V. All rights reserved.
doi:10.1016/j.brainres.2010.04.039
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BR A IN RE S EA RCH 1 3 42 ( 20 1 0 ) 6 3 –73
often less well-understood domain of the human brain which
may serve as a target analog. From one's prior knowledge of the
source domain, novel inferences can be generated about the
target domain. This ability has achieved its highest level of
development in humans, as many studies of analogy and
relational thinking in other species indicate that they are limited
to using perceptual information for making matches (Oden et al.,
2001; Penn et al., 2008). Analogical reasoning ability also shows a
relatively predictable developmental timecourse with young
children exhibiting a tendency to make similarity judgments
based on perceptual features, while older children gradually
make greater use of abstract relational similarity among objects
and situations as they age (Gentner et al., 1995; Richland et al.,
2006). The emergence of analogical reasoning ability enables
sophisticated inferences characteristic of adult humans.
Analogical reasoning is composed of several component
processes. The nature of these processes vary to some degree
depending on the type of analogy under consideration (e.g.
analogies based on relations involving semantic knowledge
versus analogies based on perceptual relations), but in all cases a
source analog must be either encoded or retrieved from memory.
These representations will serve as templates to which target
analogs can be matched through the process of mapping
(Gentner, 1983; Gick and Holyoak, 1983; Krawczyk et al., 2004,
2005; Krawczyk, in press). Analogical mappings require finding
correspondences between the source and target analogs. These
correspondences can be concrete such as matching two
patterns together on the basis of shared perceptual features.
The correspondences can be highly abstract when the corresponding relations are purely semantic, such as an analogy
between a library and the internet, where there are very few
shared perceptual features. Key cognitive processes involved in
reasoning by analogy include attentional selection and screening (Krawczyk et al., 2008) and retrieval of information from long
term memory (Wharton et al., 1994, 1996), as well as maintenance and manipulation of information in working memory
(Waltz et al., 2000; Cho et al., 2007). The precise combination of
these cognitive processes is likely to depend upon factors
including the novelty, complexity, and type of similarities
involved in an analogy.
The neural basis of analogical reasoning has been a topic of
recent investigation with the majority of early studies focused
on determining the effects of brain damage on analogical
reasoning and finding functional imaging activation associated
with analogy tasks. Studies of dementia patients and transcranial magnetic stimulation (TMS) studies of healthy subjects have
consistently focused on the importance of the prefrontal cortex
(PFC) for successful analogical reasoning in perceptually-based
analogies (Boroojerdi et al., 2001; Morrison et al., 2004) and in
analogies based on semantic relations (Morrison et al., 2004;
Krawczyk et al., 2008). Initial functional imaging studies of
relational reasoning focused on investigating the neural processes involved in making analogical matches compared to
perceptual matches. Wharton et al. (2000) reported extensive left
PFC and parietal PET activation when perceptual analogical
matches were processed compared to non-relational feature
matches. In a related TMS study, stimulation of the left PFC was
reported to enhance analogical reasoning performance in this
task as indexed by faster response times (Boroojerdi et al., 2001).
Interestingly, right PFC stimulation did not show this enhance-
ment. Similar results have been reported in related studies of
visuo-spatial relational reasoning implicating PFC (Prabhakaran
et al., 1997) and more specifically the left rostrolateral PFC
(RLPFC) (Christoff et al., 2001; Kroger et al., 2002) in solving high
complexity problems in the Raven's Progressive Matrices task
(Raven, 1938). The importance of the lateral PFC and left RLPFC
for relational reasoning has been further established by
subsequent studies of visuo-spatial reasoning (Bunge et al.,
2009; Crone et al., 2009).
Recent functional neuroimaging studies have advanced
our understanding of analogical reasoning particularly in
analogies based on semantic relations. Most of these studies
have been conducted using four-term verbal analogies in
the format A:B :: C:D. Luo et al. (2003) compared activation for
four-term verbal analogies using Chinese characters with a
control condition consisting of semantic judgments that were
not analogically related. They reported activation bilaterally
within the inferior PFC and also in the left middle frontal
gyrus. Similar results were obtained by Green et al. (2006)
using a similar design with English word stimuli. In this study
the primary region of activation for analogical relative to
semantic processing was a localized region within the left
anterior PFC. In a followup study, this region was noted to be
responsive to semantic distance of the analogies based on
word association strengths (Green et al., 2009). This finding is
consistent with prior results reported by Bunge et al. (2005)
who presented subjects with four-term verbal analogies
finding that left anterior PFC was most responsive to
integration demands, while the left ventrolateral PFC was
more responsive to semantic retrieval. In all of these prior
studies the activation was measured over the full problem
solution period which typically included relational encoding,
mapping, and response. Using this type of design does not
permit determining whether regions have temporally separable roles in analogical reasoning based on their contribution to
different processing stages.
There has been little investigation into the functional
anatomy associated with analogical inference. One recent
study (Wendelken et al., 2008) was the first to report activation
differences between mapping alone and mapping with inference. This study utilized a similar format as a prior study (Bunge
et al., 2005) where all four terms in the analogy were presented
and subjects had to verify whether they formed an analogy but,
in addition, included a modified condition in which subjects
were required to complete the fourth term of the analogy
themselves. This comparison revealed greater activation of the
left RLPFC in problems that required mapping all four terms
relative to those where subjects had to infer the fourth term.
This finding suggests that the left RLPFC may have more of a
specialized role in analogical mapping, as the primary difference between conditions was that all four terms could be
aligned and compared in one condition and not the other. The
presentation of the first two terms of the analogy and the final
term or terms had been done independently; however, these
aspects of analogical processing were not modeled separately as
independent task phases.
A recent electrophysiology study found evidence of temporal separability in analogical reasoning about letter sequences
(Qiu et al., 2008). Unlike the majority of prior neuroimaging
studies, Qiu and colleagues used analogies between non-
BR A IN RE S E A RCH 1 3 42 ( 20 1 0 ) 6 3 –7 3
semantic letter sequences of the type developed for the copycat
model (Mitchell, 1993; Hofstadter, 1995). A prior fMRI study of this
style of letter string analogies revealed bilateral PFC and parietal
activation associated with letter string analogy solutions, as well
as left DLPFC activation specifically associated with analogical
solutions that were judged to be greater in the depth of their
relational structure (Geake and Hansen, 2005). The ERP task of
Qiu et al. (2008) separated the presentation of the first two terms
of the letter string analogies from the third term letter string.
This enabled the investigators to find ERP differences related to
schema induction with source localization indicating an anterior
medial PFC generator. Left PFC was implicated in the mapping
phase, which is broadly consistent with the prior findings that
left DLPFC is frequently active in analogy tasks and specifically
shows greater activation in association with greater analogical
depth in the letter string fMRI study (Geake and Hansen, 2005).
This study was limited by the spatial resolution of ERP and by the
fact that the letter sequences contained little semantic
information.
In the current study we investigated semantic four-term
analogical reasoning using an experimental design that
enabled neuroimaging assessments of different task phases
required to processes analogies. We included three phases: an
encoding period, a combined mapping and inference period
(note that there is minimal mapping possible with simple
four-term analogies), and a response period. Similar techniques have been successfully used previously to investigate the
neural basis of separate phases of working memory delay
tasks, which were a significant advance over prior block
design studies that had been limited to recording activation
from whole trials (Zarahn et al., 1997b). Such studies revealed
neural differences between encoding, delay, and response
periods (D'Esposito et al., 1999a,b,c; Rypma and D'Esposito,
1999; Narayanan et al., 2005). We anticipated that a similar
event-related approach could further our understanding of
analogical reasoning, which frequently requires a strong role
for working memory (Hummel and Holyoak, 1997, 2003; Waltz
et al., 2000; Cho et al., 2007). The inclusion of an inference
requirement is also a relatively new design feature, as this has
only been included in one prior study (Wendelken et al., 2008)
and in this case the inference phase was not separated from
the encoding of the first two terms. It remains unclear the
degree to which left PFC contributes to these two task phases.
The majority of studies have used verbal stimuli for semantic
analogy tasks. In most studies the main comparison of interest
has been isolating activation associated with analogically
related four-term problems from that involved in processing
semantically related, but non-analogous problems (Luo et al.,
2003; Bunge et al., 2005; Wendelken et al., 2008). In some cases,
comparisons have also been made to four unrelated terms
(Green et al., 2006, 2009). In the current study, we use picture
stimuli as they enable another important comparison of
analogical problems to perceptual comparison problems. In
prior analogical reasoning studies with dementia patients,
perceptual distraction was demonstrated to be an important
factor that limits performance of patients with frontal lobe
damage (Krawczyk et al., 2008). Additionally, perceptual distractors have been shown to disrupt analogical reasoning with
picture stimuli in young children (Rattermann and Gentner,
1998; Richland et al., 2006). Analogical reasoning resides at the
65
top of a processing hierarchy with semantic association and
perceptual similarity judgments below it. Using an analogy
requires both semantic processing and mapping, thus it is
greater in complexity than judging semantic relatedness, which
in turn is more complex than judging similarity of perceptual
features, a process common to all three forms of processing
relevant to the current study.
We predict that PFC regions will be most sensitive to
analogical processing. Specifically, left PFC regions are predicted to be most active at the encoding phase, as subjects
must judge the relationship between the A and B items and
maintain this relation in working memory. This prediction is
supported by prior findings indicating the left inferior frontal
gyrus (LIFG) which has been previously shown to be involved
in processing semantic associations (Bokde et al., 2001; Kan
and Thompson-Schill, 2004; Zhang et al., 2004; Yang et al.,
2009). The inference phase of the analogical condition is also
predicted to show greater activation of the left PFC and RLPFC
over the other conditions. This is based on the prior findings of
Qiu et al. (2008), as well as the frequent reporting of left RLPFC
in relational reasoning (Christoff et al., 2001; Kroger et al., 2002;
Crone et al., 2009) and mapping in semantic analogy problems
(Green et al., 2006; 2009; Bunge et al., 2005; Wright et al., 2007).
Finally, we predict that the response phase of the task may
show greater PFC activation for the perceptual condition over
the others due to the greater demand for perceptual comparisons present in this condition. The response phase may also
show greater differences between the semantic condition and
the two other conditions related to semantic search requirements being higher. The analogical condition should have
been primarily solved by the mapping/inference phase, thus
we predict that it will be associated with greater activation
earlier in the trials during the encoding and mapping/
inference task phases where the majority of relational
encoding, maintenance, mapping, and inference are expected
to occur.
2.
Results
2.1.
Behavioral results
Behavioral data from the response phase of the analogy task
showed a significant main effect of accuracy, F(2, 54) = 3.55,
p < 0.05. Post-hoc tests corrected for multiple comparisons
(p < 0.05) demonstrated that analogy problems were solved
with greater accuracy than the perceptual control problems
(Fig. 1). A main effect of response time was also present, F(2,
54) = 3.66, p < 0.05 with post-hoc tests indicating that analogy
problems were solved at a faster rate than both semantic and
perceptual control problems (refer to Fig. 1). All problem types
were solved with high levels of speed and accuracy. Analogies
may have been fastest and most accurate, as they could be
argued to involve the least uncertainty of judgment. While the
analogies could likely be judged outright to be correct or
incorrect, the other conditions both required judgments that
the item was sufficiently semantically or perceptually similar,
though these judgments are rarely completely reliable across
individuals. While there were only a small set of potential
matches for the analogy task, the semantic and perceptual
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BR A IN RE S EA RCH 1 3 42 ( 20 1 0 ) 6 3 –73
Fig. 1 – Behavioral data from the response period of the task. (A) Analogy problems were solved with significantly greater
accuracy than the perceptual control problems. (B) Analogy problems were solved more quickly than problems from either the
semantic or perceptual control conditions.
were relatively open-ended, so the final item in these control
conditions could have been within a range of items and still fit.
2.2.
Neuroimaging results
2.2.1.
Encoding phase
All ROIs were evaluated for differences among conditions at
the encoding phase using one-way within subjects ANOVAs.
Fig. 2 summarizes these findings. An ROI within the left
dorsolateral PFC (DLPFC) was significant F(2, 57) = 7.96,
p < 0.001. Post-hoc tests revealed that the analogical condition
was significantly more active than both the semantic and
perceptual control conditions consistent with a greater need
to attend to and remember the relation between A and B term
elements in the problems. Similar results were also observed
in the medial PFC F(2, 57) = 10.68, p < 0.001 and a posterior
medial PFC F(2, 57) = 10.68, p < 0.001. In both of these ROIs, the
analogical condition was significantly more active than both
the semantic and perceptual control conditions. The other left
PFC ROIs defined from the response phase showed this same
pattern of data within the LIFG F(2, 57) = 5.01, p < 0.01 and the
left middle frontal gyrus (LMFG) F(2, 57) = 6.10, p < 0.01. As in the
other three ROIs, the analogical condition showed significantly greater activation than both the semantic and perceptual
control conditions. In summary, ROIs within the medial PFC,
posterior medial PFC, left DLPFC, LIFG, and LMFG showed
greater activation selectively in the analogical condition
which required the greatest attention and memory for the A:
B relation.
2.2.2.
Mapping/inference phase
The mapping/inference phase data are presented in Fig. 2. In
this task phase the LIFG showed modulation by condition F(2,
57) = 3.00, p = 0.05. Post-hoc tests revealed that the analogical
condition was significantly more active than the perceptual
condition only. This supports a role for the LIFG in analogical
processing when semantic analysis is required compared to
feature-based perceptual analysis of candidate matches to
the item occupying the third term position within the
analogy.
2.2.3.
Response phase
There were several significant differences associated with the
response phase (refer to Fig. 2). The left DLPFC was significantly
modulated by condition F(2, 57) = 6.20, p < 0.01. with both the
semantic and perceptual conditions showing greater activation
relative to the analogical condition. A similar effect appeared in
the medial PFC F(2, 57)= 3.84, p < 0.05. Post-hoc tests revealed
that the perceptual condition and the semantic condition
showed greater activation than the analogical condition. In
the left MFG F(2, 57) = 5.31, p < 0.01, post-hoc tests indicated again
that the perceptual condition and semantic condition showed
greater activation than the analogy condition. All of these
comparisons are consistent with greater cognitive effort being
necessary to evaluate perceptual and semantic matches relative
to analogical matches.
2.2.4.
RLPFC analysis
In order to assess the activation of RLPFC regions in each
phase of the analogy task, we conducted a targeted search
within the anterior portions of the frontal lobes bilaterally by
exploring searching all regions anterior to MNI y = 40. The
results of this search are presented in Table 1. Note that no
RLPFC regions survived SVC FDR p < 0.05, but several peaks
survived at uncorrected p < 0.001 in the encoding and mapping/inference stages. These analyses revealed four peaks of
activation for the encoding period within the left RLPFC for the
analogy > perceptual comparison but none for the analogy > semantic comparison. Two clusters were observed within the
left hemisphere during the mapping and inference phase
within similar locations for the analogy > perceptual and the
analogy > semantic contrasts. Consistent with prior literature,
the anterior PFC showed greater activation for analogical
reasoning.
3.
Discussion
We investigated activation occurring across separate phases of
an analogy task with comparisons to semantic and perceptual control conditions. Overall, the results indicate strong
BR A IN RE S E A RCH 1 3 42 ( 20 1 0 ) 6 3 –7 3
Fig. 2 – Activation within six Regions of Interest (ROIs) across the task phases. (A) Modulation of activation was observed within the left DLPFC at the encoding period, where
analogy trials were associated with significantly greater activation, while at the response phase, analogy trials showed significantly less activation relative to the other
conditions. (B) The same pair of effects were observed in the medial PFC. (C) A posterior medial PFC region was modulated by analogy trials at the encoding period. (D) The LIFG
showed significant modulation by condition with analogy trials showing greater activation at both the encoding and the mapping/inference phases. (E) The left MFG exhibited
the same pattern observed in the left DLPFC and medial PFC. (F) No significant modulation by condition was observed within the right DLPFC.
67
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Table 1 – Small volume correction analysis.
Contrast
A > P, encoding
A > S, encoding
A > P, mapping/
inference
A > S, mapping/
inference
A > P, response
A > S, response
X
Y
Z
p value (uncor)
p (FDR)
−50
−42
−42
−44
None
−48
40
40
40
40
8
4
−4
−12
0.000
0.000
0.000
0.001
0.410
0.410
0.410
0.419
40
−4
0.000
0.443
−22
52
0
0.000
0.704
None
None
involvement of the PFC when relational information must be
evaluated and maintained for use in analogical mapping and
inference. Analogical mapping and inference modulated the
LIFG. Finally, we demonstrate that verification of analogical
responses demanded less activation within PFC regions relative
to semantic and perceptual processing. This is consistent with
the idea that use of semantic information to constrain analogical
inferences may lead to more efficient evaluation of solutions.
Overall, these results contribute to the analogical reasoning
literature by demonstrating the modulation of several PFC
regions in relational encoding, mapping and inference stages.
Behaviorally, the analogy condition was performed with
the highest accuracy and quickest response time. In this task
the accuracy and RT reflect the response phase primarily,
though these measures may have been strongly influenced by
the preceding phases. In most of our ROI comparisons of the
encoding period, we observed the greatest differences when
contrasting analogies against the perceptual control condition. This pattern of results supports our hypothesis that the
analogical reasoning conditions constrained processing to
enable clearer inferences which were able to be evaluated
quickly and more accurately.
3.1.
Encoding period of analogical reasoning
Analysis of the encoding phase suggests that it was a
cognitively rigorous phase in the analogical condition within
this task. PFC activation for the analogy condition was highest
in the encoding period relative to the other periods. This
indicates that much of the initial mental effort of analogical
reasoning involves discovering the relation between the first
two terms in the analogy and maintaining that relation, and
possibly other candidate relations, in order to apply them to
the next phase of the reasoning process. The relevant relation
between the first two items was frequently based on a high
association from word norms data, but in some cases subjects
may have maintained multiple possible relations, as the third
term of the problem was not yet known.
At the encoding period, the analogy condition showed
recruitment of a series of left frontal regions including DLPFC
and LIFG and LMFG. Such analogy-related activation in left PFC
resembles activation from prior studies that have assessed
visuo-spatial analogies (Wharton et al., 2000) and semantic
analogies in verbal form (Bunge et al., 2005; Wendelken et al.,
2008) and picture form (Wright et al., 2007). The finding that
left PFC regions are highly active at the encoding relative to the
other phases of the task indicates that semantic retrieval plays
a particularly important role in analogical processing. This
raises the possibility that left PFC activation that has been
associated with analogical reasoning other prior studies may
have been driven to a large degree by encoding of relations.
This study marks an initial attempt to segregate the cognitive
processes contributing to analogy using fMRI. The only other
extant study in the literature contributing to this goal was
reported by Qiu et al. (2008) using ERP. Like our fMRI study, the
results of Qiu and colleagues also supported a contribution of
the left PFC to analogical processing. They had concluded that
Brodmann Area (BA) 6 was the likely generator of their ERP
effect. We extend these findings to indicate that activation
differences support analogical encoding in a series of left
lateralized frontal regions (DLPFC, LIFG, LMFG) as well as a pair
of medial PFC regions (medial PFC and posterior medial PFC).
This medial PFC activation may also be consistent with the
findings of Qiu et al. (2008), as they reported a medial frontal
ERP generator associated with relational encoding (or schema
induction), but their source localization suggested BA10 as the
ERP generator, while our results showed modulation of more
posterior medial regions in addition to RLPFC based on our
SVC analysis of the anterior PFC.
Considerable attention has been given to the functions of the
RLPFC in prior imaging studies of analogical reasoning (Bunge
et al., 2005; Green et al., 2006, 2009; Wright et al., 2007; Wendelken
et al., 2008). While the RLPFC was not the most intensely
activated PFC region in our task, our targeted SVC analysis
revealed four foci of activation in the analogy > perceptual
contrast. The four active RLPFC regions in the present study
fell close to the coordinates previously reported by Bunge et al.
(2005) and Wendelken et al. (2008) in their verbal four term
analogy tasks. Notably the regions we observed were more
lateral to the left RLPFC region reported by Green et al. (2006,
2009) also using a verbal four term analogy task. There were no
active regions within the RLPFC for the comparison of analogy >semantic at the encoding period, suggesting that the RLPFC
is associated with semantic processing which is consistent with
the recent findings of Green et al. (2009), who found that
semantic distance was a factor affecting the more medial
RLPFC region that they had reported.
3.2.
Mapping and inference period of analogical reasoning
The mapping and inference phase would likely have required
several additional steps in the analogical condition over the
two control conditions. In all conditions, an inference was
required, but unlike the control conditions, only the analogy
condition required that the inference be based on the prior
relation that had been encoded between the first two terms.
Further, a relational match was needed in these problems,
relative to an open-ended perceptual or association-based
candidate match in the control conditions. The key task
difference may be that only the analogical condition relied
upon the prior information, while the control conditions
required association-based inference about the third term
independently.
The resulting brain activation from the mapping and inference period indicated that analogical mapping and inferences
BR A IN RE S E A RCH 1 3 42 ( 20 1 0 ) 6 3 –7 3
involved the LIFG to a greater degree than the perceptual
control condition (refer to Fig. 2), though the semantic control
condition was also lower in activation though non-significantly. This result suggests that left hemisphere processing is
dominant in analogical mapping and inference, consistent
with prior findings from Wharton et al. (2000) and Wendelken
et al. (2008). Analyses of the RLPFC activation revealed
continued activation of one of the regions that had been
observed in the encoding period (left RLPFC MNI coordinates
X = −48, Y = 40, Z = −4 ) for the analogy > perceptual comparison
indicating an extended role for the RLPFC in analogical
encoding, mapping, and inference. A more medial region of
RLPFC was found to be active for the analogy > semantic
condition. These results diverge somewhat from the findings
of Wendelken et al. (2008) in that they did not observe
significant RLPFC activation despite using an inference
condition in their four-term verbal task. They did not include
a perceptual control condition and this may be responsible for
this discrepancy. Our results are broadly consistent with the
ERP results of Qiu et al. (2008) who also reported left PFC ERP
modulation relevant to mapping in a letter-string analogy task
that lacked the semantic association requirements that we
had included.
3.3.
Response period of analogical reasoning
The response phase was predicted to be the least active phase
for the analogical reasoning task. If subjects had solved the
analogy successfully, they should only have had to check the
correctness of their inferred candidate fourth term. In cases
where a subject's inferred fourth term did not match the
provided fourth term, he or she would likely have been able to
evaluate the given response quickly in order to determine
whether it was also an appropriate match. Meanwhile in the
perceptual and semantic conditions, greater cognitive effort
would have likely been required much of the time due to the
fact that the semantic and perceptual inferences would have
been less likely to have matched the provided fourth term, as
these inferences were less constrained than the analogical
condition match.
ROI activation associated with the analogy relative to the
control conditions support the position that analogical
response verification was less effortful relative to the other
phases. If a successful analogical inference had been drawn at
the mapping and inference phase then little effort would have
been necessary to ensure that the provided fourth term was
either a match to their inferred fourth term or an unrelated,
incorrect object. Consistent with this position, the analogy
condition showed reductions in recruitment of three frontal
regions (left DLPFC, MFG, and medial PFC) when compared to
the perceptual and semantic control conditions. These findings indicate that the assessment of the fourth term of the
semantic and perceptual conditions may have involved
greater cognitive effort (consistent with the behavioral data)
requiring greater PFC activation. Interestingly, these two
control conditions showed patterns of PFC activation resembling the pattern exhibited at the encoding and mapping/
inference phases for the analogy condition. This suggests that
a series of left PFC regions may contribute strongly to
inference processing.
4.
69
Conclusions
In this study we demonstrate that four-term analogical
reasoning consists of a highly active encoding phase, both
cognitively and neurally, in which reasoners must detect
relevant candidate relations and maintain them for later
comparison when preparing to infer a novel fourth term. This
processing relies heavily upon several PFC regions including
the LIFG, LMFG, and the left DLPFC, with some activation
present within the RLPFC and more posterior medial regions of
the PFC. The mapping of items and the process of inferring
relevant final terms also engaged similar neural regions
centering upon the LIFG and RLPFC. Finally, response checking
appeared to demand less cognitive or neural processing for
verification of a correct analogical match. This is likely due to
the greater constraints that a prior relation provides relative to
the more open-ended association searches of the control
conditions. PFC regions responded more to the less-constrained semantic and perceptual control conditions in this
task phase.
In this study, we attempted to separate aspects of analogical processing at both cognitive and neural levels. There
remain several other factors that still remain unexplored in the
neural basis of analogical reasoning. An important goal for
future studies will be to further explore the timecourse of
different cognitive operations relevant to analogical and
other forms of problem solving. Such work may benefit
from employing innovative designs involving trial-jittering
(Henson, 2006) and the use of partial-trials (Miller et al., 2008;
Motes and Rypma, 2010) which may help to further isolate
unique aspects of temporal processing relevant to analogical
reasoning within semantic and other domains. Another
important goal for future research will be the use of experimental paradigms that move beyond four-term problems.
While there have been numerous four-term semantic tasks
and several simple geometric analogical tasks, only the studies
using letter-string analogies have diverged from the four-term
format. While four-term analogical reasoning remains a
manageable problem type for neuroscience investigation, we
are unable to capture many of the more spontaneous and
complex aspects that are critical to real world analogical
reasoning. It remains important to bear in mind the need for
appropriate control conditions as tasks increase in complexity.
Key aspects of analogy such as remote semantic processing,
insight, and greater relational complexity are important goals
for future work.
5.
Experimental procedures
5.1.
Subjects
Twenty volunteer subjects (11 females) from the University of
Texas Southwestern Medical Center at Dallas participated
after providing informed consent. Age ranged from 19 to 37
(M = 27.2, S.D. = 6.74). All subjects had normal or corrected
vision, were free of neurological disorders, and were not
taking any medications having a psychoactive, cardiovascular, or homeostatic effect.
70
BR A IN RE S EA RCH 1 3 42 ( 20 1 0 ) 6 3 –73
Fig. 3 – Examples of the analogy task and control conditions. (A) The analogy condition required subjects to view a pair of items
to determine their relationship at the First Relation phase. After a delay, subjects viewed a third item and had to infer a possible
fourth term that could be paired with the third item to complete the same relation as in the First Relation Phase. Lastly, the
inference phase required subjects to determine whether the fourth item was a fit to complete the problem. (B) The semantic
match condition required no relational encoding at the First Relation phase. This was followed by inference of a semantic
associate to the third item (without the need to map to the first relation) and finally, verification if the fourth item fit the third.
(C) The perceptual condition was identical to the semantic condition, except subjects had to infer a fourth item based on
perceptual similarity and to verify whether the provided fourth term fit the problem on that basis.
5.2.
Procedure
Twenty-four picture analogy problems were presented in the
format A:B as C:D. The final picture of the second relation (D from
the C:D relation) had three possible conditions: an Analogical
Condition, a Perceptual Condition, and a Semantic condition
(refer to Fig. 3). The First Relation presentation slide revealed
images A and B simultaneously (e.g. spyglass : ship) with a
vertical line between them for a duration of four seconds. A focal
point was then presented for four seconds. The C image
(periscope) was presented directly after the previous focal
point for a duration of six seconds followed by another four
BR A IN RE S E A RCH 1 3 42 ( 20 1 0 ) 6 3 –7 3
second focal point. The correct D image (submarine) or a false
item (selected to have no perceptual or semantic overlap with
the C term) was then presented for four seconds. At this time,
subjects judged the analogy to be True or False. This design
enabled subjects to generate an answer at the third phase (C),
referred to as the mapping/inference phase, while separating the
response phase (D). In all three conditions (Analogical, Perceptual, and Semantic) the A, B, and C items remained the same;
however, the D item varied depending on the condition. All
images were presented in grayscale on a white background. Each
condition was cued prior to the beginning of a set of 12 trials to
avoid confusion on the part of the participants. True and False
problems varied randomly within each trial block in all
conditions.
Subject responses were indicated by button press during the
D trial phase. Three button options were available; true, false,
and a third button to be used if the subject could not provide a
confident answer regarding the A:B relationship. The true and
false buttons were held in each hand with hand placement
counterbalanced for the experiment. The third button was
positioned centrally.
5.2.1.
Analogical Condition
For the Analogy condition, subjects were asked to initially
infer the relationship of the A and B terms and hold it in mind
at the encoding phase. When the C term appeared subjects
were to map it onto the A term and generate a possible D item
that could complete the analogy. Lastly, the answer choice D
was revealed. Once presented, the D image was judged to be a
true (e.g. periscope : submarine in Fig. 3) or a false completion
of the analogy.
5.2.2.
Semantic condition
In the Semantic condition, subjects were to simply view the A
and B terms initially. Subjects were instructed to generate a
possible D term that would be highly semantically related to the
C term during the period when the C term was presented. They
were told to evaluate the D answer based on whether it had
high semantic similarity to the C image. If the similarity was high
(e.g. soap : suds in Fig. 3) a ‘true’ judgment was to be made.
Semantically true D term stimuli were generated by finding
highly correlated words from The University of South Florida
Word Association Norms (Nelson et al., 2004). In contrast to the
analogy condition, there was no need to encode and maintain
the relation between the A and B items. A true or false decision
was chosen by considering only the semantic similarity of the C
and D images.
5.2.3.
Perceptual condition
For the Perceptual condition, subjects were asked to base their
true/false decision on the perceptual similarity of the C to the
D item. Subjects were not required to maintain the A to B
relationship but were instructed to try to imagine a fit for the D
term based on the perceptual properties of the C term (e.g.
football : lemon in Fig. 3). A true or false decision was chosen
by comparing the perceptual characteristics of the C and D
images. Subjects were given practice items to allow them to
understand what level of perceptual similarity a true item
would need to have. This was typically based on overall shape
and spatial orientation of the item being similar, while more
71
subtle variations may have been less similar. The perceptual
condition required simple similarity matches based on
features, thus it lacks semantic evaluation and analogical
mapping (as the A and B items were irrelevant to the
perceptual judgments).
5.3.
Functional MRI acquisition
Images were acquired in six runs using a 3 T Philips MRI
scanner with a gradient echoplanar sequence (TR = 2000 ms,
TE = 28 ms, flip angle = 20°) sensitive to BOLD contrast. Each
volume consisted of tilted axial slices (3 mm thick, 0.5 mm
slice gap) that provided nearly whole brain coverage. Anatomical T1-weighted images were acquired in the following
space: TR = 500 ms, TE = 10, slice thickness = 4 mm with no gap
at a 90° flip angle. Head motion was limited using foam head
padding.
5.4.
Functional MRI data analysis
Detailed descriptions of the procedure used for analyzing
activation within event-related trials have been published
previously (Zarahn et al., 1997a; Buckner et al., 1998); and are
summarized below. Activation of each phase of the trials was
assessed using multiple regression (Postle et al., 2000).
Preprocessing analyses were conducted using Statistical
Parametric Mapping Software (SPM 5; Wellcome Trust Centre
for Neuroimaging, http://www.fil.ion.ucl.ac.uk/spm) run in
Matlab 6.5 (http://www.mathworks.com). EPI images were
realigned to the first volume of acquisition and then smoothed
with a 6 mm 3D Gaussian kernel.
Four separate regressors, repeated for each of the three
conditions, were used to model each phase of the task: encoding,
mapping/inference, and a response regressor for both true and
false analogies. Separate regressors were used to model the three
phases of the task: one regressor was used to model the encoding
period (0–4 s into the trial), another regressor modeled the
inference period (9–14 s into the trial) and two separate response
period regressors (for matching versus non-matching problems)
(19–22 s into the trial). Each regressor was convolved with a
canonical hemodynamic response function (HRF) provided in
SPM5 and entered into the modified general linear model of
SPM5. A high-pass filter (cutoff 128 s) was applied to the data to
remove frequency effects. Data from all subjects were coregistered to the MNI template brain and normalized for group
analyses of the encoding, inference, and response period data.
To assess activation differences among the three conditions we used a Region of Interest (ROI) approach. This
involved initially defining active regions based on the
normalized group maps for each task phase. We considered
ROIs from all task phases, as we were interested in all PFC
regions relevant to the task. This was accomplished by
initially isolating regions active within the frontal lobes
using the WFU Pickatlas toolbox (http://www.fmri.wfubmc.
edu/) (Maldjian et al., 2003, 2004). ROIs were defined as any
voxel cluster containing 10 or more contiguous voxels and
falling within either PFC search mask at a False-Discovery
Rate (FDR) corrected threshold (p < 0.05 level). This procedure
yielded no significant frontal regions within the encoding
phase. The inference phase analysis yielded three frontal ROIs
72
BR A IN RE S EA RCH 1 3 42 ( 20 1 0 ) 6 3 –73
Table 2 – ROI coordinate table.
Definition phase:
Anatomical
region
Peak MNI
coordinate
Voxel
count
Left DLPFC
Medial PFC
Posterior medial PFC
−48 10 32
−6 26 48
−6 10 56
532
34
55
Right DLPFC
LIFG
Left MFG
50 18 −4
−48 14 −6
−54 10 38
1540
165
164
(Significance)
Mapping/Inference:
(FWE 0.05)
Response:
(FDR 0.05)
defined after applying a Family-Wise Error (FWE) correction
(p < 0.05), as two of the regions were merged at the FDR
threshold. The ROIs consisted of a left DLPFC region, a medial
PFC region, and a posterior medial PFC region. Three
additional frontal ROIs were defined based on a conjunction
search evaluating the inference phase across all three conditions. These consisted of two left frontal regions (LIFG and
LMFG) and one right DLPFC ROI. These ROIs were defined at a
correction level FDR (p < 0.05). Parameter estimates (β values)
were extracted from each ROI for each regressor of interest
(encoding, mapping/inference, response). The two response
regressors representing true and false problems were averaged to produce a grand mean for the response phase for this
analysis. The mean parameter estimates for each condition
were then subjected to one-way ANOVAs and differences
between conditions were verified using Bonferroni-corrected
post-hoc tests. Means were evaluated from all task phases in
each ROI. The ROIs are summarized in Table 2.
We conducted an additional analysis of the RLPFC, given
the high level of interest in the functions of this region. In
order to be comprehensive in exploring its role the stages of
analogical reasoning we included a small volume corrected
analysis within SPM in a search volume constrained to be in
the rostral PFC bilaterally anterior to MNI coordinate y = 40.
This is the most posterior coordinate reported (by Kroger et al.,
2002) in the recent literature investigating relational responding in RLPFC based on a survey of the literature in this area and
the methods of Wendelken et al. (2008).
Acknowledgments
We thank members of the Center for BrainHealth® at UT
Dallas and the Advanced Imaging Research Center at UT
Southwestern Medical Center for their helpful comments and
suggestions. We thank Rani Varghese for assistance with data
collection and Hanzhang Lu for assistance with technical
aspects of the neuroimaging protocol. We also acknowledge
the contributions of two anonymous reviewers whose suggestions strengthened and clarified this manuscript.
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