Functional heterogeneity of inferior parietal cortex during mathematical cognition assessed with cytoarchitectonic probability maps.

Abstract

Although the inferior parietal cortex (IPC) has been consistently implicated in mathematical cognition, the functional roles of its subdivisions are poorly understood. We address this problem using probabilistic cytoarchitectonic maps of IPC subdivisions intraparietal sulcus (IPS), angular gyrus (AG), and supramarginal gyrus. We quantified IPC responses relative to task difficulty and individual differences in task proficiency during mental arithmetic (MA) tasks performed with Arabic (MA-A) and Roman (MA-R) numerals. The 2 tasks showed similar levels of activation in 3 distinct IPS areas, hIP1, hIP2, and hIP3, suggesting their obligatory role in MA. Both AG areas, PGa and PGp, were strongly deactivated in both tasks, with stronger deactivations in posterior area PGp. Compared with the more difficult MA-R task, the MA-A task showed greater responses in both AG areas, but this effect was driven by less deactivation in the MA-A task. AG deactivations showed prominent overlap with lateral parietal nodes of the default mode network, suggesting a nonspecific role in MA. In both tasks, greater bilateral AG deactivation was associated with poorer performance. Our findings suggest a close link between IPC structure and function and they provide new evidence for behaviorally salient functional heterogeneity within the IPC during mathematical cognition.

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Cerebral Cortex December 2009;19:2930--2945
doi:10.1093/cercor/bhp063
Advance Access publication April 30, 2009
Functional Heterogeneity of Inferior
Parietal Cortex during Mathematical
Cognition Assessed with
Cytoarchitectonic Probability Maps
S. S. Wu1, T. T. Chang1,2, A. Majid1, S. Caspers3, S. B. Eickhoff3
and V. Menon1,4,5
1Department of Psychiatry and Behavioral Sciences, Stanford
University School of Medicine, Stanford, CA 94305,2Institute of
Neuroscience, National Yang-Ming University, Taipei 112,
Taiwan,3Research Centre Ju ¨ lich, Institute of Neurosciences
and Biophysics-Medicine, 52425 Ju ¨ lich, Germany,4Program in
Neuroscience and5Symbolic Systems Program, Stanford
University School of Medicine, Stanford, CA 94305
S. S. Wu and T. T. Chang contributed equally to the study
Although the inferior parietal cortex (IPC) has been consistently
implicated in mathematical cognition, the functional roles of its
subdivisions are poorly understood. We address this problem using
probabilisticcytoarchitectonicmapsofIPCsubdivisionsintraparietal
sulcus (IPS), angular gyrus (AG), and supramarginal gyrus. We
quantified IPC responses relative to task difficulty and individual
differences in task proficiency during mental arithmetic (MA) tasks
performed with Arabic (MA-A) and Roman (MA-R) numerals. The 2
tasksshowedsimilarlevelsofactivationin3distinctIPSareas,hIP1,
hIP2,andhIP3,suggestingtheirobligatoryroleinMA.BothAGareas,
PGa and PGp, were strongly deactivated in both tasks, with stronger
deactivationsinposteriorareaPGp.Comparedwiththemoredifficult
MA-R task, the MA-A task showed greater responses in both AG
areas, but this effect was driven by less deactivation in the MA-A
task. AG deactivations showed prominent overlap with lateral
parietalnodesofthedefaultmodenetwork,suggestinganonspecific
role in MA. In both tasks, greater bilateral AG deactivation was
associated with poorer performance. Our findings suggest a close
link between IPC structure and function and they provide new
evidence for behaviorally salient functional heterogeneity within the
IPC during mathematical cognition.
Keywords: angular gyrus, automaticity, intraparietal sulcus, mental
arithmetic, supramarginal gyrus
Introduction
The neural basis of mathematical cognition has been intensely
studiedinrecentyearsgivenitsimportanceasaskillweusenearly
every day. Brain imaging studies have consistently identified
a distributed set of brain regions that includes, most prominently,
the ventral visual areas, including the lingual and fusiform gyri,
inferior parietal cortex (IPC), and the ventrolateral prefrontal
cortex(PFC;Burbaudetal.1995;Dehaeneetal.1999;Delazeretal.
2006; Menon, Rivera, White, Eliez, et al. 2000; Menon, Rivera,
White, Glover, et al. 2000; Menon et al. 2002; Rickard et al. 2000;
Zago et al. 2001). Within this distributed network, the IPC is
thought to play a critical role in representing and manipulating
quantitativeinformation,whereasotherbrainregions,suchasthe
ventrolateral and dorsolateral PFC, are engaged in supportive
functions such as working memory, sequencing, controlled
retrieval, and decision making (Rueckert et al. 1996; Dehaene
et al. 1999; Kazui et al. 2000; Menon, Rivera, White, Glover, et al.
2000;Gruberetal.2001;Delazeretal.2003;Zagoetal.2008).The
IPC comprises multiple heteromodal regions that play an
important role in semantic, phonological, and visuospatial
representation of numerical information (Caspers et al. 2008).
IPCregionsalongthebanksoftheintraparietalsulcus(IPS)aswell
as the adjoining angular gyrus (AG) and supramarginal gyrus
(SMG) have all been implicated in tasks involving mathematical
problem solving. Little is known, however, about the differential
contributions of these regions, an issue that has been particularly
confounded by lack of knowledge about the precise anatomical
boundaries of the IPC.
Current efforts in understanding the role of the IPC in
mathematical cognition have focused on the IPS because of its
role in basic number identification and number comparison tasks
(Cohen et al. 2000; Duffau et al. 2002; Delazer et al. 2003; Cohen
Kadoshetal.2007;Piazzaetal.2007).Toalesserextent,theleftAG
has drawn interest, based on its purported role in rapid, verbally
mediated fact retrieval. In a meta-analysis of their data, Dehaene
et al. (2003)suggested thatthe numbermanipulation inthe IPS is
supplemented by the left AG when verbal manipulation of
numbers is needed and that attention to visuospatial representa-
tions on the mental number line is supported by the bilateral
posterior superior parietal lobule. Less attention has been paid to
the SMG, a brain region important for phonological rehearsal and
working memory functions that are evoked during mathematical
problem-solving tasks.
Several brain imaging studies have investigated the role of the
left and right IPC in mental arithmetic (MA) operations such as
single- and double-digit addition, subtraction, and multiplication
(Roland and Friberg 1985; Burbaud et al. 1995; Dehaene and
Cohen 1997; Menon, Rivera, White, Eliez, et al. 2000; Gruber
et al. 2001; Simon et al. 2002). IPC responses during the solution
of more abstract and complex mathematical problems, such as
calculus integrals, have also been investigated (Krueger et al.
2008). In both cases, the specific contribution of various
subdivisions of the IPC in mathematical problem solving is still
unclear. Findings to date have been contradictory with respect
to task-related dissociations in the IPC during computationally
demanding tasks compared with more automated tasks.
Whereas some brain imaging studies have reported greater
bilateral activation in the IPS during more computationally
demanding MA tasks, others have reported greater responses in
the left AG during more automated MA tasks (Grabner et al.
2007; Ischebeck et al. 2007). Importantly, at least one study has
reported relative decreases, or deactivation, in the left and right
AG and the SMG during a simple well-automated multiplication
task, compared with a magnitude judgment task (Rickard et al.
2000). To our knowledge, the study by Rickard and colleagues
was the first and only study that reported deactivation in both
the left and right AG and SMG during MA. Interestingly, this
study noted deactivation in every one of their participants, but
the precise localization of this deactivation was ambiguously
stated to be in a bilateral area centered between the SMG and
the AG. Besides the lack of precise localization of IPC responses,
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anothercentralissuehereisthattask-relateddifferencescanarise
from greater activation in the more automated task or greater
deactivation during the more computationally demanding task.
We address both these issues here at length. Recent studies have
highlightedprominentandconsistentdeactivationsofIPCregions
in and around the AG across a broad range of cognitive tasks
(Greicius et al. 2003; Mechelli et al. 2003; Humphries et al. 2007;
Schulman et al. 2003; Harrison et al. 2008; Sweet et al. 2008).
Moreover, there is growing evidence to suggest that the level of
deactivation decreases with increasing task difficulty (Greicius
et al. 2003; Schulman et al. 2003). These deactivations have
received less attention in the domain of MA problem solving,
and several researchers have, on the contrary, highlighted the
engagement, rather than disengagement of the AG in more
automated fact retrieval. To address this issue, we systematically
investigated both activation and deactivation in specific subdivi-
sions of the IPC as a function of task difficulty.
A major reason for the contradictory findings in the literature
has been the poor demarcation of the boundaries of regions that
constitute the IPC. There are 2 fundamental problems here; first,
the boundaries between the IPS and rest of the IPC are unknown.
Second, demarcation of the AG from the SMG is ambiguous as far
as macroanatomical features are concerned. Brodmann (1909)
differentiated the IPC into2 areas: the SMG (BA 40) on the rostral
aspects of the IPC and AG (BA 39) on the caudal aspects of the
IPC.AccordingtoBrodmann,theSMGandtheAGaredemarcated
bytheJensensulcus,butusingthissulcusasaborderbetweenBA
40 and BA 39 is problematic because of its highly irregular and
variable form. Even more problematic is the issue of demarcating
theAGandtheSMGfromtheIPS.Othermorerecentlydeveloped
parcellation schemes (Tzourio-Mazoyer et al. 2002; Desikan et al.
2006) commonly used in brain imaging studies also suffer from
similar deficiencies. Importantly, no existing methods offer
a scheme to parcellate the IPS. The dorsal and ventral aspects
of the IPS are often arbitrarily ascribed to the IPC or the superior
parietallobule.Forexample,somestudieshavetreatedtheventral
bankoftheIPSasapartoftheAG,whereasothershavereferredto
it as the IPS (Menon, Rivera, White, Glover, et al. 2000; Ischebeck
et al. 2006). Thus, the boundaries segregating the IPS from the
AG and the SMG are ill specified, leading to misrepresentation
of observed functional brain responses in these regions.
The recent availability of probabilistic cytoarchitectonic
maps has the potential to inform and significantly enhance
our understanding of the functional architecture of the IPC in
mathematical cognition. Cytoarchitectonic maps obtained from
postmortem brains suggest that the human IPC has a more
finely grained parcellation than previously suggested by the
classical Brodmann map. These maps provide objective a priori
regions of interest (ROI) that can be used to test anatomically
specific hypotheses about the localization of functional
activations (Caspers et al. 2008). Recent studies have suggested
that the borders of the IPS, SMG, and the AG cannot be reliably
detected using macroanatomic or gross anatomical features on
magnetic resonance images (MRIs) (Caspers et al. 2008).
Detailed analysis of cell types suggests that the IPS can be
subdivided into at least 3 regions, as shown in Figure 1. The
human intraparietal area 2 (hIP2) occupies the anterior, lateral
bank of the human IPS, and area hIP1 is located immediately
posterior and medial to hIP2 (Choi et al. 2006). These regions
correspond roughly to the monkey anterior intraparietal area,
whereas area hIP3 that occupies the posterior human IPS
corresponds approximately to monkey ventral intraparietal area
(Scheperjans, Eickhoff, et al. 2008; Scheperjans, Hermann, et al.
2008). Ventral to these IPS regions are 2 areas that cover the AG
and 5 that cover the SMG (Caspers et al. 2006). The AG consists
of the anterior and posterior areas PGa and PGp, respectively,
encompassing the caudal aspects of the IPC. In contrast,
3 larger, more dorsal regions— PFm, PF, PFt— and 2 smaller
ventral regions— PFcm and PFop— encompass the rostral
segments of the IPC along the rostral to caudal axis. Posteriorly,
region PFm of the SMG borders the AG region PGa (Caspers
et al. 2006, 2008). To account for variability in size and extent
of these areas across individuals, cytoarchitectonic probabilistic
maps have been calculated for each area in stereotaxic space
(Caspers et al. 2008; Scheperjans, Eickhoff, et al. 2008). These
probabilistic maps provide a robust anatomical reference for
more accurately characterizing structure--function relations in
the human IPC during mathematical problem solving.
Figure 1. Cytoarchitectonic maps of the IPC. Cytoarchitectonic maps of 3 IPS—hIP3, hIP1, and hIP2, 2 AG—PGp and PGa, and 5 SMG—PFm, PF, PFt, PFcm, and PFop areas of
the IPC used in the study, ordered along a posterior to anterior gradient (Caspers et al. 2006; Choi et al. 2006; Scheperjans, Hermann, et al. 2008). Surface renderings and coronal
sections are shown with the numbers at the bottom of each panel indicating the location of the slices (y-axis in MNI coordinates).
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In the present study, we compared brain responses to simple
MA tasks involving familiar and well-rehearsed Arabic numerals
to similar MA tasks performed with less familiar Roman
numerals. Previous brain imaging studies of mathematical
cognition have focused primarily on MA operations that are well
rehearsed and automated in adults. An important question
regarding the function of specific IPC regions relates tohow they
respond to different levels of task automaticity and individual
differences in task proficiency. To address this question, we
examined IPC responses during both automated and nonauto-
mated MA tasks. We use the notion of automaticity here in the
samesenseasLogan(1988).Inthisview,automatedprocessesare
more dependent on memory-based solutions and retrieval,
whereas nonautomated processes rely on algorithmic computa-
tions. It is currently not known exactly how IPS, AG, and SMG
responseschangewithtaskautomaticity,anissueweaddresshere
using cytoarchitectonically distinct maps of the IPC.
Behavioral studies have provided compelling evidence that
changing the surface format of numerals is an effective way to
alter the automaticity of mathematical information processing
(Perry 1952; McCarthy and Dillon 1973; Gonzalez and Kolers
1982; Campbell and Fugelsang 2001; Hiscock et al. 2001;
Venkatraman et al. 2006; Ansari 2007). For example, Campbell
and Fugelsang (2001) found that participants were slower and
less accurate at assessing 1-digit math problems that were
presented in written English format (e.g. three + four = eight)
than in a number format (e.g. 3 + 4 = 8). They proposed that the
decrease in performance arose from the more complex written
format using less efficient strategies and that participants relied
more on explicit calculation thandirect retrieval-based strategies
(Schunn et al. 1997). Several studies have also compared
processing of familiar Arabic numerals with the less familiar
Roman numerals (Perry 1952; McCarthy and Dillon 1973;
Gonzalez and Kolers 1982). These studies have consistently
found that mental addition with Roman numerals takes signif-
icantlylongerthanwithArabicnumerals.Inapacedserialaddition
task, participants had significantly higher accuracy and shorter
reaction times (RTs) when the stimuli were presented in Arabic,
compared with Roman, format (Hiscock et al. 2001). Taken
together, these studies suggest that automaticity of mathematical
information processing can be manipulated in a controlled
manner by merely altering the surface format of the numerals.
We used arithmetic verification tasks similar to those used in
previous studies (Menon, Rivera, White, Eliez, et al. 2000;
Menon, Rivera, White, Glover, et al. 2000), except that the
participants performed 2 versions of the task—MA with Arabic
(MA-A task) and MA with Roman numerals (MA-R task).
Although the format of the Arabic and Roman equations (e.g.
2 + 3 – 1 = 4 and II + III – I = IV) was similar, the Roman
numeral condition relied less on efficient and automatic
memory retrieval than the Arabic numeral equations (Campbell
and Fugelsang 2001; Hiscock et al. 2001). We used 3-operand,
rather than 2-operand, equations in order to keep the tasks
relatively simple while simultaneously providing sufficient
variability in performance to facilitate examination of the
relation between accuracy and brain response in the IPC
(Menon, Rivera, White, Glover, et al. 2000). Lassaline and Logan
(1993) have argued that transfer of memory-based automaticity
is narrow because learning tends to be item specific. This
suggests that participants typically cannot directly retrieve
facts from memory when presented with MA problems in the
Roman format. A key difference between the 2 tasks is that the
MA-R requires more controlled and effortful retrieval, whereas
the MA-A task involves more direct and effortless retrieval.
In summary, the main aims of our study were to 1) investigate
the differential involvement of the IPS, AG, and SMG during MA
using cytoarchitectonically defined subdivisions of the IPC, 2)
examine activation and deactivation of the IPS, AG, and SMG as
a function of task automaticity, 3) compare differential responses
of the IPC and the PFC in relation to task automaticity, and 4)
investigate the neural basis of individual differences in MA
performance as a function of task automaticity. We predicted
that participants would perform the MA-A task more accurately
and faster than the MA-R task, reflecting the higher task
automaticity with familiar mathematical symbols. In conjunction
withthesebehavioraldifferences,wehypothesizedthat1)theIPS
would showactivation inbothtasks, with lesser activation during
the more automated MA-A task, 2) the AG would show de-
activationinbothtasks,withgreaterdeactivationintheMA-Rtask,
3)deactivationsintheAGwouldoverlapstronglywiththedefault
mode network (DMN), a set of brain regions that typically show
domain general reductions in brain responses during difficult
cognitivetasks(Greiciusetal.2003),4)adissociationbetweenIPS
and PFC responses would be observed, with the PFC showing
greater between-task differences than the IPS, and 5) individual
differencesinMAtaskperformancewouldbedifferentiallyrelated
to activation in the IPS and deactivation in the AG.
Materials and Methods
Participants
Eighteen healthy adult participants (7 males and 11 females; ages18--31.5,
mean 22.28 years ± 3.95) participated in the study after giving written
informedconsent.Allprotocolswereapprovedbythehumanparticipants
Institutional Review Board at the Stanford University School of Medicine.
All participants were volunteers and were treated in accordance with the
APA ‘‘Ethical Principles of Psychologists and Code of Conduct.’’
fMRI Experiments
This study consisted of 2 identical MA experiments, one using Arabic
numerals and the other using Roman numerals. Arabic and Roman
problems were presented in separate blocks in order to prevent
subjects from switching across stimulus types and changing task
strategy between conditions. The order of experiments was random-
ized across participants.
MA with Arabic numerals (MA-A)
Participants were presented with 16 alternating experimental and
control epochs, each lasting 32 s. Each experimental (Calculation)
epoch consisted of eight 3-operand equations of the form a + b – c = d
(e.g. 5 + 4 – 2 = 7); only single-digit numerals from 1 to 9 were used.
Each equation was presented for 3.5 s followed by a blank screen for
0.5 s. Participants were instructed to respond by pressing one of
2 keys, based on whether they thought the equation was correct (e.g.
4 + 5 – 2 = 7) or incorrect (e.g. 4 + 5 – 2 = 8). Half of the equations
presented were correct, and the other half incorrect; the order of
correct and incorrect equations was randomized. Each control
(Identification) epoch consisted of eight 7-symbol strings (e.g. 4 @ 3
& 2 # 5). Each string was presented for 3.5 s followed by a blank screen
for 0.5 s. Participants were instructed to respond by pressing one of 2
keys, based on whether they thought the string contained the numeral
5. Half of the strings presented contained the numeral 5, the other half
did not; the order of presentation of these strings was randomized.
MA with Roman Numerals (MA-R)
This experiment was identical to the MA-A task, except that the
equations consisted of Roman numerals (e.g. VI + II – I = VII). During
the control epochs, participants were asked to determine whether the
string contained the Roman numeral V (e.g. IX @ VI & I % V).
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Stimulus presentation
The task was programmed using PsyScope (Cohen et al. 1993) on a
Macintosh (Cupertino, CA) computer. Scan and task onsets were syn-
chronized using a TTL pulse delivered to the scanner timing micropro-
cessor board from a ‘‘CMU Button Box’’ microprocessor (http://
poppy.psy.cmu.edu/psyscope) connected to the Macintosh. Stimuli were
presented visually at the center of a screen using a custom-built magnet-
compatible projection system (Resonance Technology, CA). An external
timer maintained an accuracy of stimulus presentation to 1 ms.
Behavioral Data Analysis
RT and the number of correct responses for experimental and control
epochs were computed. RT was analyzed using analysis of variance
(ANOVA) with 2 repeated measures: numeral type (Roman vs. Arabic)
and task condition (Calculation vs. Identification).
fMRI Data Acquisition
Images were acquired on a 3T GE Signa scanner using a standard GE
whole head coil (software Lx 8.3). Head movement was minimized
during scanning by a comfortable custom-built restraint. A total of 28
axial slices (4.5 mm thickness, 0.5 mm skip) parallel to the AC-PC line
and covering the whole brain were imaged with a temporal resolution
of 2 s using a T2*-weighted gradient echo spiral pulse sequence (Glover
and Lai 1998) with the following parameters: TR = 2000 ms, TE = 30
ms, flip angle = 70?, 1 interleave. The field of view was 20 cm, and the
matrix size was 64 3 64, providing an in-plane spatial resolution of
3.125 mm. To reduce blurring and signal loss arising from field
inhomogeneities, an automated high-order shimming method based on
spiral acquisitions was used before acquiring functional MRI scans (Kim
et al. 2002). A high-resolution T1-weighted spoiled grass gradient
recalled inversion recovery 3D MRI sequence was acquired to facilitate
anatomical localization of functional activity. The following parameters
were used: TI = 300 ms, TR = 8 ms; TE = 3.6 ms; flip angle = 15?; 22 cm
field of view; 124 slices in coronal plane; 256 3 192 matrix; 2 NEX,
acquired resolution = 1.5 3 0.9 3 1.1 mm. Structural and functional
images were acquired in the same scan session.
fMRI Data Analysis
The first 5 volumes were not analyzed to allow for signal equilibration
effects. Images were reconstructed, by inverse Fourier transform, for
each of the time points into 64 3 64 3 28 image matrices (voxel size
3.125 3 3.125 3 4.5 mm). A linear shim correction was applied
separately for each slice during reconstruction using a magnetic field
map acquired automatically by the pulse sequence at the beginning of
the scan (Glover and Lai 1998). Functional MRI data were preprocessed
using SPM5 (http://www.fil.ion.ucl.ac.uk/spm). Images were realigned
to correct for motion, corrected for errors in slice timing, spatially
transformed to standard stereotaxic space (based on the Montreal
Neurologic Institute coordinate system), resampled every 2 mm using
sinc interpolation and smoothed with a 4-mm full-width half-maximum
Gaussian kernel to decrease spatial noise prior to statistical analysis.
Statistical analysis was performed on individual and group data using
the general linear model and the theory of Gaussian random fields as
implemented inSPM5 (http://www.fil.ion.ucl.ac.uk/spm/software/
spm5/). Individual subject analyses were first performed by modeling
task-related and task-unrelated confounds. Low-frequency noise was
removed with a high-pass filter (0.5 cycles/min) applied to the fMRI
time series at each voxel. A temporal smoothing function (Gaussian
kernel corresponding to half-width of 4 s) was applied to the fMRI time
series to enhance the temporal signal-to-noise ratio. Regressors were
modeled with a boxcar function corresponding to the epochs during
which each condition was presented and convolved with a hemody-
namic response function. We then defined the effects of interest for
each participant with the relevant contrasts of the parameter estimates.
Group analysis was performed using a random effects model that
incorporated a 2-stage hierarchical procedure (Holmes and Friston
1998). For the first-level analysis, contrast images for each participant
and each effect of interest were generated as described above. For the
second-level analysis, these contrast images were analyzed using
a general linear model to determine voxel-wise group t-statistics. One
contrast image was generated per participant, for each effect of
interest. Two-tailed t-tests were used to determine group-level
activation for each effect. Finally, the t-statistics were normalized
transformed to Z scores, and significant clusters of activation were
determined using the joint expected probability distribution of height
and extent of Z scores (Poline et al. 1997), with height (Z > 2.33;
P < 0.01) and extent thresholds (P < 0.01).
The following between-task comparisons were then performed at
the group level using paired t-tests: 1) MA-A: Arabic Calculation – Arabic
Identification; (2) MA-R: Roman Calculation – Roman Identification; and
the following between-numeral comparisons: (3) MA-A – MA-R: (Arabic
Calculation – Arabic Identification) – (Roman Calculation – Roman
Identification); (4) MA-R
– MA-A: (Roman Calculation
Identification) – (Arabic Calculation – Arabic Identification). In the
latter 2 comparisons, which involve double subtractions, additional
analyses were conducted to distinguish between differences arising
from calculation task-related increases in activation, as opposed to
identification task-related decreases in activation (or ‘‘deactivation’’).
For each significant cluster that was detected in these comparisons (i.e.
comparisons 3 and 4), mean t-scores were first computed for the MA-A
(comparison 1) and MA-R (comparison 2) tasks. Clusters in compar-
isons 3 and 4 were then categorized as arising from deactivation if 1)
the mean t-score (averaged across all participants) was significantly
negative in comparisons 2 and 1, respectively; and 2) the mean t-score
was not significantly different from 0 in comparisons 1 and 2,
respectively. A parallel analysis was conducted using percent signal
change between the Calculation and Identification conditions. The
results in each case were similar to those obtained using t-scores, so
only the latter is reported here.
Regression analysis was used to examine the relation between MA
experimental task accuracy and activation in the MA-A and MA-R tasks.
Voxel-wise t-statistics maps were generated and significant clusters of
activation were determined using a voxel-wise statistical height
threshold of (Z > 2.33; P < 0.01), with corrections for multiple spatial
comparisons at the cluster level (P < 0.05). Both the magnitude and the
sign of the activations were examined in order to ascertain whether the
observed brain--behavior relations were related to task-related activa-
tion or deactivation. Activation foci were superimposed on high-
resolution T1-weighted images and their locations were interpreted
using known neuroanatomical landmarks (Mai et al. 2007).
– Roman
IPC ROI
ROI were based on the cytoarchitectonically distinct maps of 3 IPS
(hIP3,hIP1,andhIP2),2AG(PGpandPGa),and5SMG(PFm,PF,PFt,PFcm,
and PFop) regions, as described above (Fig. 1). In the order listed, these
ROI run successively along the caudal to rostral axis of the IPC. Detailed
information about the anatomical boundaries of these maps has been
published elsewhere (Caspers et al. 2006; Choi et al. 2006; Scheperjans,
Hermann, et al. 2008). Probability maps of each of these ROIs were
evaluated using the SPM Anatomy Toolbox (Eickhoff et al. 2005).
The Anatomy Toolbox allowed us to characterize and label functional
activations in relation to the probabilistic ROI. The spatial distribution
of regional activations was characterized by 3 metrics— the percentage
of an activation cluster that was in a specific ROI, the percentage of
a specific ROI that belonged to an activated cluster, and probability that
a peak in the cluster was assigned to an ROI (Eickhoff et al. 2005, 2007).
Because of the spatial overlap in the 7 probabilistic IPC ROI, we used
maximum probability maps, which yield nonoverlapping ROIs, to
uniquely characterize the magnitude of regional responses. This
approach yields regions that 1) reflect most adequately the underlying
anatomy and 2) show a high degree of sensitivity in statistical analysis of
functional activations (Eickhoff et al. 2007).
Results
Behavior
Accuracy and RTs for the MA-R and MA-A calculation and
identification trials are summarized in Figure 2. For RT, ANOVAs
revealed a significant 2-way interaction between condition
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(Calculation and Identification) and task (MA-A and MA-R);
F(1,17) = 13.582,P <0.005,partialg2= 0.444.RTsinbothMA-A
and MA-R conditions were significantly higher in Calculation
than Identification conditions (F (1,17) = 481.423, P < 0.001,
partial g2= 0.966). The mean RT for both conditions within the
MA-A taskwere lower than
(F (1,17) = 126.885, P <0.001, partial g2= 0.882).
For accuracy, an ANOVA revealed a significant 2-way in-
teraction between condition and task (F (1,17) = 33.437, P <
0.000,partialg2= 0.663).AverageaccuracyinbothMA-AandMA-
RtasksweresignificantlyhigherinIdentificationthanCalculation
(F (1,17) = 42.918, P < 0.001, partial g2= 0.716). The average
accuracy for both conditions within the MA-A task was
significantly greater than the average accuracy of the conditions
in MA-R (F (1,17) = 20.631, P <0.001, partial g2= 0.548).
themean RTfor MA-R
IPC Activation during the MA-A and MA-R Tasks
MA-A (Arabic Calculation versus Number Identification)
We detected significant activation (Calculation > Identification)
as well as deactivation (Identification > Calculation) within the
IPC,asshowninFigure3aandTable1.Notethatdeactivationhere
refers to greater activation during the low-level control (Identi-
fication) condition (see Discussion and Supplementary Fig. S3 for
aconsiderationofdeactivationwithrespecttoarestingbaseline).
All 3 IPS areas (hIP1, hIP2, and hIP3) showed strong activation
during the MA-A task, whereas the 2 AG areas (PGa and PGp)
showed strong deactivation (Fig. 4). In contrast, the 5 SMG areas
showed minimal activation. We then examined the spatial profile
ofactivationusingprobabilisticlabelingofIPCresponses(Fig.5a).
TheanalysisshowedthatposteriorIPSareahIP3hadthestrongest
and most spatially extensive activation, followed by area hIP1. In
contrast, about 50% of PGp was deactivated, followed by 30% of
PGa. The deactivations also extended anteriorly to cover 14% of
SMG area PFm (Table 2).
MA-R (Roman Calculation versus Number Identification)
We detected significant activation as well as deactivation within
the IPC, as shown in Figures 3b and 4b. As with the MA-A task, all
3 IPS ROI showed strong activation during the MA-A task,
whereas the 2 AG ROI showed strong deactivation (Fig. 4b).
Again, the SMG ROI showed minimal activation. Table 2 shows
the spatial distribution of activations and deactivations in each
of the IPC ROI. The relative pattern of activation and deac-
tivation in these ROI is almost identical to that in the MA-A task,
except that the deactivations were stronger and more spatially
extensive in regions PGp and PGa of the AG (Table 2, Fig. 4b).
Activation Outside the IPC during the MA-A and MA-R
Tasks
MA-A (Arabic Calculation versus Number Identification)
SignificantactivationwasalsoobservedintheleftinferiorPFC(BA
44, 47) and anterior insula (BA 48), left superior parietal lobule
andmidoccipitalgyrus(BA7,19),andrightmidoccipitalgyrus(BA
7, 40), right inferior temporal cortex (BA 37), the fusiform gyrus
(BA 19), and cerebellum (vermis, bilateral crus 1 and 2, lobules
VI, VIII,and right lobule 7b), as showninFigure3a (Schmahmann
et al. 1999). Extensive deactivation was also observed in the right
middletemporalgyrusandbilaterallyinthesuperiorfrontalgyrus
(Fig. 3a). A detailed listing of the brain areas that showed
activations and deactivations is shown in Table 1.
MA-R (Roman Calculation versus Number Identification)
Outside the IPC, significant activation was observed in the right
inferior and midoccipital gyri (BA 18, 19), the right inferior
temporal gyrus (BA 37), the right insula and adjoining orbito-
frontal cortex(BA 47/12), andcerebellum (vermis, bilateral crus
1 and 2, lobules IV, V, VI, and VIII). Extensive deactivation was
also observed in the right superior and middle temporal gyri and
in the left superior frontal gyrus (Fig. 3b, Table 1).
IPC Activation Differences between the MA-A and MA-R
Tasks
MA-A – MA-R
Weexaminedbrainregionsthatshowedgreateractivationinthe
MA-A,comparedwiththeMA-R,condition.AsshowninFigure6,
Figure 2. Accuracy and RT during the MA-A and MA-R tasks. (a) Accuracy and (b) RT during Calculation and Identification conditions in the MA-A and MA-R tasks. Accuracy
was significantly lower, and RTs were significantly greater, during the calculation condition of the MA-R task. A significant task by condition interaction was observed for both
accuracy and RT. Mean and standard error are shown.
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Table 1
Brain regions that showed significantly greater activation and deactivation during the MA-A and MA-R calculation, compared with number identification, tasks
ComparisonBrain region BACorrected P valueNo. of voxels Peak Z scorePeak MNI coordinates (mm)
xyz
MA-A
Calculation ? Identification
L inferior frontal gyrus, L insula
L superior parietal lobule L middle occipital gyrus
R inferior parietal lobule R middle occipital gyrus
44, 47, 48
7, 19
40, 7
\0.001
\0.001
\0.001
12 210
10 206
2458
5.12
6.03
5.32
?52
?22
34
14 30
42
44
?70
?52
Identification ? Calculation
L/R medial superior frontal gyrus
R middle temporal gyrus, R/L precuneus
L angular gyrus
10, 30
\0.001
\0.001
\0.001
15 247
20 467
1244
6.19
5.90
4.61
?2
56
?46
548
37, 21, 23
?58
?72
12
42 39
MA-R
Calculation ? Identification
R inferior parietal lobule, R middle occipital gyrus
R inferior temporal gyrus
R cerebellum (vermis 8, crus 2)
R inferior/middle occipital gyrus
40, 7
\0.001
\0.01
\0.001
\0.01
2734
361
28 755
321
4.99
5.18
6.03
3.71
36
54
?50
?54
?64
?88
42
37
47
?18
?302
18, 19 364
Identification ? Calculation
L superior frontal gyrus, R middle cingulate, R precuneus
L angular gyrus
R middle occipital gyrus, R superior/middle temporal gyrus
9, 23
\0.001
\0.001
\0.001
28 183
1223
1813
5.68
5.07
5.38
?14
?54
48
52 34
28
28
39
?66
?70 39, 22
Note: For each significant cluster, region of activation, significance level, number of activated voxels, maximum Z score, and location of peak in MNI coordinates are shown. Each cluster was significant
after correction for height (p \ 0.01) and spatial extent (p \ 0.01). BA, Brodmann area.
Figure 3. Brain activation and deactivation during the MA-A and MA-R calculation tasks. (a) Surface rendering and coronal sections of brain regions that showed significant
activation (Calculation[Identification) and deactivation (Identification[Calculation) in the MA-A calculation task. Activations are shown in red and deactivations are shown in
blue. (b) Activations and deactivations in the MA-R calculation task. Each cluster was significant after correction for height (p \ 0.01) and spatial extent (p \ 0.01).
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a direct comparison between the 2 tasks revealed statistically
significant differences in the left IPC and the adjoining
temporoparietal cortex. More detailed analysis of the spatial
distribution of the responses revealed that the differences were
primarily localized to the AG – PGa and PGp together accounted
for73%oftheactivationandonly1.8%oftheactivationextended
into SMG region PFm (Table 4). ROI analyses were conducted to
further examine both the direction and magnitude of responses
within the IPC cluster, in order to examine whether between-
taskdifferencesabovearosefromincreasesduringMA-A,orfrom
decreases during the MA-R task (deactivation). This analysis
revealed that activation in the AG cluster arose from greater
deactivation during the MA-R condition (Fig. 6).
MA-R – MA-A
We then examined whether any brain regions showed greater
activation in the MA-R, compared with the MA-A, tasks. No
differences were observed in any of the IPC regions, even at
a liberal threshold of P < 0.05, uncorrected.
Activation Differences Outside the IPC between the MA-A
and MA-R Tasks
MA-A – MA-R
Compared with the MA-R task, the MA-A task showed greater
responses bilaterally in the medial aspects of the superior
frontal gyrus (BA 10). Further analysis revealed that in this
cluster, between-task differences arose from greater deactiva-
tion during the MA-R task (Table 3).
MA-R – MA-A
Compared with the MA-A task, the MA-R showed greater
responses in 6 clusters within the PFC and the cerebellum
(Fig. 7 and Table 3). PFC regions that showed differences
included the left inferior frontal gyrus with adjoining anterior
insula (BA 44, 48), left inferior and middle frontal gyrus (BA 47,
11), left middle and superior frontal gyri (BA 9, 8), and right
inferior frontal gyrus and adjoining anterior insular (BA 47, 48)
and the bilateral presupplementary motor area (pre-SMA; BA 6).
Cerebellar regions that showed differences included the left
cerebellum lobule VIII and vermis 8.
We then examined whether the activation clusters noted in
the MA-R – MA-A comparison above arose from task-related
decreases during MA-A, or from task-related increases during
MA-R (deactivation). This analysis showed that activation in all
the 6 clusters arose from greater activation in the MA-R task
(Fig. 7).
Relation of AG Deactivation to the DMN
TheDMN(Greiciusetal.2003)consistsof2bilateralnodesinthe
IPC as well as the medialPFC and posteromedial cortex(Greicius
et al. 2003). These regions are typically deactivated during
cognitive tasks in a domain general manner, and furthermore,
themagnitudeofdeactivationnormallyincreasesinproportionto
Figure 4. Relative strength of activation and deactivation in each cytoarchitectonically defined IPC region during the MA-A and MA-R calculation tasks. (a) Activation and
deactivation in each cytoarchitectonically defined IPC ROI during the MA-A task. All 3 IPS areas (hIP3, hIP1, and hIP2) were activated, whereas AG regions (PGp and PGa) were
deactivated. SMG regions (PFm, PF, PFt, PFcm, and PFop) showed minimal activation. Hemispheric differences were observed in AG region PGa, and SMG regions PF and PFcm.
(b) A similar pattern of activation and deactivation was observed during the MA-R task. In this case, hemispheric differences were observed only in the SMG region PFcm.
*indicates regions that showed significant hemispheric differences, p \ 0.05 after FDR correction for multiple comparisons. Mean and standard error are shown.
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cognitiveload.Wefirstexaminedwhetherdeactivationsobserved
in the IPC during the 2 tasks overlapped with the DMN. We
observedstrongdeactivationintherightAGareaPGpinbothtasks
and more extensive bilateral overlap in the MA-R task (Supple-
mentary Fig. S1). We then examined whether the left AG region
thatshowedgreaterdeactivationintheMA-R,comparedwiththe
Table 2
Probabilistic labeling of IPC regions that showed significant activation and deactivation during the MA-A and MA-R calculation, compared with number identification, tasks
Comparison Assigned region% of region activated% of cluster in regionProbability of peak in
assigned region (%)
Peak MNI coordinates (mm)
xyz
MA-A
Calculation ? IdentificationR IPS (hIP3)
R IPS (hIP1)
L AG (PGp)
L AG (PGa)
L SMG (PFm)
L SMG (PF)
91.6
62.1
49.2
30.4
13.6
1.6
11.1
5.8
42.9
20.1
5.5
1.2
60
20
60
34
44
?52
?48
?72
44
44
42 Identification ? Calculation
?46
MA-R
Calculation ? Identification R IPS (hIP3)
R IPS (hIP1)
89.1
80.3
9.7
6.7
5036
?50 42
Identification ? CalculationL AG (PGp)
L AG (PGa)
L SMG (PFm)
L SMG (PF)
54.1
33.6
9.8
0.8
48.0
22.6
4.0
0.7
70
?48
?7036
Note: IPC regions that showed significantly greater activation (Calculation[Identification) during the MA-A, compared with the MA-R, task (Identification[Calculation). For each significant cluster, the
probabilistic region, percentage of activation in the region, percentage of cluster that was in the region, peak MNI coordinate, and the probability of the peak being in the region are shown. Each cluster
was significant after correction for height (p \ 0.01) and extent (p \ 0.01). Cytoarchitectonically defined probability maps were used to interpret the locations of the cluster and peaks within
subdivisions of the IPS, AG, and SMG.
Figure 5. Activation and deactivation in cytoarchitectonically defined IPC regions during the MA-A and MA-R calculation tasks. (a) Activations (Calculation[Identification) and
deactivations (Calculation\Identification) during the MA-A task, overlaid on cytoarchitectonic probability maps of the IPC. Task-related activations had the highest probability of
being localized to the posterior-most IPS region hIP3, whereas deactivations had the highest probability of being localized to posterior-most AG region PGp. (b) A similar profile
was observed in the MA-R task, except that deactivations were more extensive and stronger within AG regions PGp and PGa. Each cluster was significant after correction for
height (p \ 0.01) and spatial extent (p \ 0.01). Table 2 provides additional details of localization of activation and deactivation foci.
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MA-A, task overlapped anatomically with DMN. As shown in
Supplementary Figure S2, there was significant overlap between
AG regions deactivated during these tasks and the DMN.
Relation between Performance and Brain Activation
during the MA-A Task
We next examined the relationship between brain response
and accuracy during the MA-A task. We found that accuracy
during the MA-A task was associated with responses in the left
(r = 0.69, P < 0.01) and right (r = 0.74, P < 0.01) IPC. Proba-
bilistic labeling showed that both left and right IPC clusters
overlapped most strongly with the posterior AG area PGp
(Table 5 and Fig. 8). Furthermore, poorer accuracy was
predominantly associated with deactivation in the AG region
PGp (Fig. 8). No such relations were observed between brain
activation and RT.
Relation between Performance and Brain Activation
during the MA-R Task
Accuracy during the MA-R task was associated with reduced
deactivation in the left (r = 0.578, P < 0.05) and right IPC
(r = 0.718, P < 0.01). As shown in Figure 8 and Table 5, the
clusters were localized to AG area PGa in the left hemisphere,
extending anteriorly to SMG area PFm and dorsally to IPS
region hIP1. The profile was somewhat different in the right
hemisphere, with the cluster being localized more posteriorly
to AG area PGp and the superior parietal lobule. No such
relations were observed between brain activation and RT.
Discussion
Our findings provide new insights into the functional organi-
zation of the IPC during mathematical cognition. The newly
developed cytoarchitectonically distinct maps of the IPC
allowed us to localize brain responses to each task condition
with an anatomical precision that was not possible heretofore.
In particular, the demarcation of the IPS from the AG and the
SMG allowed us to examine the extent, level, and distribution
of brain responses in a reliable manner. This in turn allowed us
to examine the effects of task automaticity in relation to
individual subject differences in performance with a high level
Table 3
Brain regions that showed significant differences between the MA-A and MA-R calculation tasks
Comparison Brain regionBA Corrected P valueNo. of voxelsPeak Z Score Peak MNI coordinates (mm)
xyz
MA-A ? MA-R
L angular gyrus L temporoparietal cortex
L/R superior frontal gyrus
39, 19
\0.001
\0.01
373
238
3.87
3.32
?46
?4
?72
56
20
24 10
MA-R -- MA-A
L inferior frontal gyrus, L anterior Insula
L inferior/middle frontal gyrus
L middle/superior frontal gyrus
L/R presupplementary motor area
R inferior frontal gyrus R anterior insula
L cerebellum (lobule VIII/vermis 8)
44, 48
47, 11
9, 8
\0.001
\0.01
\0.01
\0.01
\0.01
\0.001
544
331
278
286
227
947
4.28
3.59
4.56
3.44
4.19
4.54
?54
?26
?22
?2
38
?24
10
32
8
?4
58
60
?6
?42
8
66
47, 4820
?58
Note: Brain regions that showed significantly greater activations in the MA-A, compared with the MA-R task and the MA-R, compared with the MA-A task. For each cluster, region of activation,
significance level, number of activated voxels, maximum Z score, and location of peak in MNI coordinates are shown. Each cluster was significant after correction for height (p \ 0.01) and spatial extent
(p \ 0.01).
Figure 6. Probabilistic labeling of IPC regions that showed significant differences in activation between the MA-A and MA-R calculation tasks. (Left) Task-related differences
arose from activation, rather than deactivation, with the MA-R showing greater negative activations than the MA-A task. These differences were localized to the left AG and the
posterior temporo-parietal cortex (TPC). **indicates that differences between the MA-A and MA-R task were significant at P \ 0.01. (Right) Probabilistic labeling of IPC
responses showing that deactivations had the highest probability of being localized to posterior-most angular gyrus region PGp. Each cluster was significant after correction for
height (p \ 0.01) and spatial extent (p \ 0.01). Table 4 provides additional details of localization of task-related differences.
Table 4
Probabilistic labeling of IPC regions that showed greater responses during the MA-A, compared
with the MA-R, calculation task
ComparisonAssigned
region
% of region
activated
% of cluster
in region
Probability of
peak in assigned
region (%)
Peak MNI
coordinates (mm)
xyz
MA-A ? MA-R
L AG (PGp)
L AG (PGa)
L SMG (PFm)
17.5
10.0
1.3
50.8
22.0
1.8
60
30
?46
?60
?72
?60
20
22
Note: IPC regions that showed significantly greater activations during the MA-A compared with
MA-R task. Each cluster was significant after correction for height (p \ 0.01) and spatial extent
(p \ 0.01). Other details as in Table 2. The MA-R task did not show significantly greater
activations in any IPC region.
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of precision and consistency. Our results point to important
functional heterogeneities in the IPC, and they suggest that
task automaticity modulates neural responses in the IPS, AG,
and SMG differently. Our findings emphasize that the contri-
butions of the IPC to mathematical cognition are not unitary.
We discuss the implications of our findings for understanding
the neural basis of mathematical cognition below.
Behavioral Differences
As predicted, we found that participants are less accurate
and slower at processing the less familiar Roman numerals
(Gonzalez and Kolers 1982; Hiscock et al. 2001). Accuracy
and RTs were significantly different during the Calculation and
Identification conditions in the MA-A and MA-R tasks. These
results suggest that participants were equally adept at
recognizing the 2 types of numerals, but were significantly
slower in performing MA with Roman numerals. These results
indicate that the MA-A task is performed in a significantly
more automated manner than the MA-R task, consistent with
the view that automatized processes are often marked by
significant ‘‘speed-up’’ in response times due to more efficient
memory retrieval (Logan 1988). Because the decision-making
aspects of the MA-A and MA-R tasks did not differ, differences
in RT likely reflect the effortful, directed, retrieval required
during the MA-R task. RT differences in the identification
condition suggest that Arabic numerals were recognized more
efficiently than Roman numerals. Taken together with brain
imaging results, the behavioral findings support the observation
that cognitive operations are not independent of the symbols
that initiate them (Gonzalez and Kolers 1982).
Differential IPC and PFC Responses in Relation to Task
Automaticity
Before discussing regional differences within the IPC, we first
focus on overall global differences in brain response in relation
to task automaticity. Although there was extensive overlap in
the IPC and PFC regions activated during the MA-A and MA-R
tasks, activations in these regions could be dissociated: there
was significantly greater activation of the PFC during the MA-R,
compared with the MA-A, task, whereas there was greater
‘‘activation’’ of the IPC during the MA-A, compared with the
MA-R, task. These results suggest that the IPC and PFC
contribute differently to automated versus nonautomated MA
tasks. Notably, activations of the right anterior insula in the PFC
and the lobule VIII and vermis 8 regions of the cerebellum
were observed only in the MA-R task.
During the MA-R task, greater activation was observed
bilaterally in the ventrolateral PFC as well as the pre-SMA and
the cerebellum. However, left hemisphere responses were
stronger and more extensive and overlapped with language and
syntactic processing regions in BA 44 and 47. These differences
may arise from the need to transform numerals in the Roman
Figure 7. Brain regions that showed significant differences in activation between the MA-R and MA-A calculation tasks. Six brain regions, all outside the IPC, showed
significantly greater activation in the MA-R, compared with the MA-A, task: 1) left inferior frontal cortex and adjoining anterior insula (IFC; BA 44, 48), 2) left inferior frontal gyrus
(BA 47), 3) middle and superior frontal gyri (BA 9, 8), 4) right inferior frontal cortex and adjoining insular cortex (BA 47, 48), 5) bilateral presupplementary motor area (pre-SMA;
BA 6), and 6) left cerebellum (lobule VIII). In each of these regions, both the MA-R and the MA-A tasks showed positive activations (Calculation[Identification), and task-related
differences arose from greater positive activations in the MA-R task. Each cluster was significant after correction for height (p \ 0.01) and spatial extent (p \ 0.01). Table 3
provides additional details of localization of activation foci.
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format into phonological representations that facilitate fact
retrieval and calculation. Lexical processing, translation of
symbols, and the articulatory rehearsal needed prior to fact
retrieval are also known to engage a frontocerebellar loop
(Desmond et al. 1997; Fiez and Raichle 1997; Chen and
Desmond 2005; Hayter et al. 2007), consistent with our finding
of coactivation of the ventrolateral PFC and cerebellar lobule
VIII. Interestingly, there were no differences in the mid-
dorsolateral PFC, a finding that may reflect greater demands on
retrieval and maintenance rather than active manipulation of
numerical quantity in working memory (D’Esposito et al. 2000;
Curtis and D’Esposito 2003; Derrfuss et al. 2004; Blumenfeld
and Ranganath 2006). Importantly, our ventrolateral PFC foci
overlap with prefrontal regions that have been implicated in
effortful retrieval during a complex series of mental calcu-
lations (Anderson and Qin 2008).
Additionally, the MA-R task elicited greater responses in
pre-SMA, a region that has been implicated in sequential
planning of information in working memory. This may reflect
preparation for motor output that accompanies multistage
numerical computations during the more complex 3-operand
condition. This region also showed greater responses in
a previous study where we examined differences between
processing of 3- and 2-operand MA trials (Menon, Rivera, White,
Glover, et al. 2000). In that study, the increase in pre-SMA
activation reflected the longer duration (about 850 ms) of the
motor preparatory activity in a 3-operand, compared with a
2-operand, condition. Electrophysiological recordings have
consistently implicated the SMA and pre-SMA during motor
preparation (Tanji and Mushiake 1996) and delay-related fMRI
responses have been reported during working memory tasks
(Petit et al. 1998).
Dissociating IPS, AG and SMG Contributions to MA
During both the MA-A and MA-R tasks, the IPS showed increased
activation during the Calculation compared with the Identifica-
tion conditions (Figs 4 and 5). Increases were observed in the
hIP3, hIP1, and hIP2, encompassing the posterior, middle, and
anterior IPS segments shown in Figure 1. Activations were
highest in the posterior-most area hIP3. In contrast, both the
posterior AG area PGp and the anterior AG area PGa showed
deactivation in both tasks, with stronger and more extensive
deactivation in area PGp. Deactivation here refers to greater
responses in the control number identification task compared
with the calculation task. The MA-A task did not show activation
above the control condition in either AG region, contrary to its
predicted role in automated fact retrieval. Signal changes in the
SMG were modest and nonsignificant in both tasks.
We then examined differences in activation of the IPS, AG,
and the SMG between the automated and nonautomated tasks.
We observed differences in the AG but not in the IPS or the SMG.
It is particularly noteworthy that between-task differences arose
from differences in deactivation rather than differences in
activation (Figs 4 and 5). In the left AG, the MA-R task showed
greater deactivation than the MA-A task, whereas the right AG
showed equal levels of deactivation. Other regions of the IPC,
including the left and right IPS areas hIP3, hIP1, and hIP2,
showed similar levels of activation in both tasks; these IPC
regions were not modulated by task automaticity.
One potential issue in interpreting these findings is that it
leaves unclear whether the deactivations observed in our study
may have arisen from greater activation of the AG during the
numberidentificationcondition.Inordertoaddressthisissue,we
analyzed a different fMRI dataset, acquired in a separate group of
21adultparticipants,withbothnumberidentificationandpassive
fixation ‘‘rest’’ baseline conditions. We found no deactivations in
the AG when we compared number identification to rest; in
contrast,asexpected,weobservedsignificantactivationintheleft
IPS, in the left and right striate, extrastriate, lingual, and fusiform
gyri, and the left sensorimotor cortex (Supplementary Fig. S3).
This analysis strongly suggest that the within-task deactivations
and between-task differences in deactivation reported here arise
fromdifferencesindeactivationduringtheMACalculationtaskas
opposed to activations during the Identification task.
Ourfindingshelptoclarifythefunctionaldistinctionbetween
key IPC regions that have been implicated in mathematical
cognition. Delazer et al. (2003) suggested that with MA training,
there is a shift from the bilateral IPS to the left AG, especially as
individualsbegintorelylessoncomputationandmoreheavilyon
retrieval. It is, however, not clear whether these changes are
relatedtodifferencesinactivationordeactivation.Between-task
comparisons indicated a positive difference in AG activation
during the more automated task, compared with the less
automated task, reflecting greater deactivation in the MA-R than
in the MA-A task. In view of these findings, it is possible that the
‘‘shift’’ to the AG observed in the Delazer et al. study may have
been due todecreased deactivation when the task became more
automated after training. This notion was confirmed by the
results of a subsequent study (Ischebeck et al. 2006), in which
the AG showed less negative responses after training on
multiplication problems. Similarly, Grabner et al. (2007) ob-
served AG deactivation during mental calculation in individuals
with poor mathematical abilities. However, to date, no study of
mathematical cognition to our knowledge has examined
whether task-related differences in specific IPS and AG regions
arise primarily from activation or from deactivation, thus leaving
unclear the precise functions subserved by the IPC. Importantly,
many existing studies leave open the possibility that some of the
IPC responses may reflect suppression from increased task
difficulty rather than processing specificity for MA, an issue we
address more directly in our study. Taken together, these
findings highlight the need for careful analysis of the magnitude
and sign of changes in activation in each specific MA task,
particularlywithrespecttotheAGbutalsotoalesserextentwith
theSMGwhosevarioussubdivisionsshowedacomplexprofileof
Table 5
Probabilistic labeling of IPC regions where activation or deactivation was significantly correlated
with accuracy during the MA-A and MA-R calculation tasks
Comparison Assigned
region
% of region
activated
% of cluster
in region
Probability of peak
in assigned region (%)
Peak MNI
coordinates (mm)
xyz
MA-A
L AG (PGp)
R AG (PGp)
6.2
20.1
28.4
56.5
60
80
?40
42
?80
?72
28
38
MA-R
L AG (PGa)
L SMG (PFm) 4.7
L IPS (hIP1)
L AG (PGp)
R AG (PGp)
22.548.2
6.1
4.1
3.7
44.0
20
20
?40
?44
?62
?60
38
30
3.4
1.3
18.3
60
?46
40
?66
?78
42
2860%
Note: IPC regions that showed significant correlations between activation and performance
accuracy during the MA-A and MA-R tasks. Each cluster was significant after correction for
height (p \ 0.01) and spatial extent (p \ 0.05). Other details as in Table 2.
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low-level activation and deactivation. Most importantly, these
findings point to functionally heterogeneous responses in
cytoarchitectonically distinct areas of the IPC.
Obligatory Involvement of IPS in Automated and
Nonautomated MA
All 3 segments of the IPS showed positive task-related
activations during both the MA-R and MA-A tasks, but these
activations did not differ between the 2 tasks. This suggests
that the IPS is fully recruited in each condition, in contrast to
the AG and the IFC. The invariant and obligatory nature of
activation in the IPS further confirms its critical role in
mathematical problem solving. The middle IPS area hIP1
overlaps with the horizontal IPS (hIPS), a region thought to
be important for representing and manipulating quantity
(Ansari 2008). This IPS region was activated strongly in both
Figure 8. Probabilistic labeling of IPC regions where brain responses were significantly correlated with accuracy on the MA-A and MA-R calculation tasks. (a) During the MA-A
task, accuracy was significantly correlated with brain responses in the left and right posterior AG area PGp. The dashed line demarcates activation from deactivation and helps
illustrate that performance was primarily related to deactivation, rather than activation. Furthermore, greater deactivation in focal clusters within the PGp was associated with
poorer performance. As noted in the text, the outlier did not affect the statistical significance of these findings. The bottom panels show probabilistic labeling of responses
overlaid on cytoarchitectonic maps of the IPC. (b) A similar pattern was observed in the MA-R task, except that responses were stronger in area PGp and accuracy was correlated
with responses in the anterior AG region PGa (see Table 5). Each cluster was significant after correction for height (p \ 0.01) and spatial extent (p \ 0.01).
Cerebral Cortex December 2009, V 19 N 12 2941

Page 13

the MA-A and the MA-R tasks, even though the stimuli were
visually well balanced in the MA and number identification
tasks. However, no differences were observed between the
MA-A and MA-R tasks. This suggests that although the hIPS
region is sensitive to MA operations, it is not differentially
modulated by task automaticity when basic number processing
is controlled for. The same basic pattern was observed in each
IPS region, even though the posterior-most area hIP3 had the
strongest activation among the 3 subdivisions. All 3 IPS areas,
hIP3, hIP1, and hIP2, therefore, appear to play an obligatory
role in MA tasks, irrespective of the level of automaticity.
Task-Dependent AG Deactivation and Its Relation to the
DMN
Our findings are inconsistent with simplistic notions of the left
AG as being primarily involved in verbally mediated fact
retrieval (Dehaene et al. 2003; Delazer et al. 2003). Although
retrieval was more automated in the MA-A, very little positive
activation was observed in this region in either task. Both the
Rickard et al.’s (2000) study that involved simple 2-operand
multiplication and our study, which involves 3-operand
calculation, showed deactivation in the AG. Part of the reason
for the divergence of these findings from studies such as
those reviewed by Dehaene et al. (2003) is that sufficient
attention has not been paid to deactivation when multiple task
conditions were compared. For instance, the left AG was
reported to show increased activation for multiplication
relative to subtraction (Chochon et al. 1999; Lee 2000), for
multiplication and division relative to a letter substitution
control (Gruber et al. 2001), and for exact calculation than
approximation (Dehaene et al. 1999). It is likely that these
activations may have arisen from greater deactivation in the
more difficult task. Our findings suggest that it is crucial to
assess the precise, quantitative, profile of responses if we are to
understand the nature of cognitive and brain mechanisms
responsible for memory retrieval and algorithmic computation.
It should also be noted that it was not just the left AG that
showed significant deactivation in our study. The right AG also
showed significant deactivation, but deactivation related differ-
ences between the MA-A and the MA-R tasks were more
significant on the left than the right.
The AG regions that showed task-related deactivation differ-
ences in our study overlapped with IPC regions that have
previously identified as being part of the DMN (Supplementary
Fig. S1). More detailed analyses conducted to examine extent of
the overlap showed that the parts of the AG that overlapped
with the DMN were significantly more deactivated during the
MA-R task than during the MA-A task. Other parts of the AG,
which did not overlap with the DMN, showed positive
activations in both the MA-A and MA-R tasks, but these
activations did not differ between tasks (Supplementary Fig. S2).
AG areas outside of the DMN, most notably in the lateral
temporallobes,werealsodeactivated, but thesedeactivationsdid
not differ between the MA-A and MA-R tasks. The DMN, and
therefore the AG regions that overlap with it, are typically
suppressed when the executive control network is recruited
during demanding cognitive tasks (Seeley et al. 2007; Sridharan
et al. 2008). In agreement with this observation, greater de-
activationintheAGregionwasaccompaniedbygreateractivation
inthebilateralPFCregionsduringtheMA-Rtask.Ourfindingsare
alsoconsistentwithpreviousobservationsthatsuppressionofthe
DMNincreaseswithtaskdifficulty(Schulmanetal.2003;Greicius
and Menon 2004). The lateral IPC has been shown to be
deactivatedacrossa broadrangeofcognitive tasks,but its precise
anatomicallocalizationhasnotbeenadequatelyclarified.Whether
these deactivations are primarily in the AG proper, rather than in
more dorsal or rostral regions bordering the IPS and the SMG, has
been unclear. Our analysis using the cytoarchitectonic maps
described above strongly suggests that these deactivations are
localizedtotheAG.Oneviewofthedeactivationsobservedinthe
IPC is that it helps to divert attentional resources to the PFC and
more dorsal IPC regions for processing task-relevant visual
information (Schulman et al. 2003; Greicius and Menon 2004;
Todd et al. 2005). For example, Schulman et al. (2003) asked
participants to search and detect stimulus targets embedded
amongst nontarget stimuli and found that, whereas the IPS was
activated both during search and target detection, the right AG
wasdeactivatedduringsearch(Schulmanetal.2003).Inaddition,
Toddetal.(2005)foundthatsuppressionoftheAGincreasedwith
visual short-term memory load. These findings suggest that
suppression of the right AG is necessary during demanding tasks,
especially during tasks in which attention is voluntarily directed.
Importantly, the 2 other major nodes of the DMN— the
posterior cingulate cortex and the ventromedial PFC—showed
no differences between the tasks. These regions are also
sensitive to task difficulty and typically are deactivated together
during more difficult cognitive tasks (Schulman et al. 2003;
Greicius and Menon 2004). Our findings therefore suggest that
deactivation in the AG can be decoupled from most of the
midline structures of the DMN. The reason for this functional
dissociation is not entirely clear at this time, but our findings
are consistent with the view that these nodes serve different
cognitive and mental functions even though they are generally
considered as operating within a ‘‘network’’. Based on tasks that
upregulate the DMN, it appears that posterior cingulate cortex
and the ventromedial PFC are more related to self-related and
autobiographical information processing (Greicius et al. 2003),
whereas the AG is sensitive to integration of long-range
semantic information (Humphries et al. 2007).
Task-Dependent Left AG Deactivation and Its Relation to
Verbal Processing
How then are we to understand the role of the left AG in
mathematical cognition? Although a role for the left AG in
verbally mediated retrieval of MA facts has been suggested by
several investigators, the nature of this involvement is un-
known. In this context, recent findings in the literature on left
AG involvement in verbal processing are quite revealing. The
left AG shows deactivation to nonwords compared with
a resting state baseline, with no difference observed between
words and the resting state baseline (Mechelli et al. 2003;
Rissman et al. 2003; Binder et al. 2005; Xiao et al. 2005). In an
important study of the topic, Humphries et al. (2007) found
that whereas the middle temporal gyrus and the inferior frontal
gyrus showed greater activation during congruent, random, and
pseudorandom sentences and word lists, the left AG showed
activation only when semantic information had to be integrated
over a 6--15 s time course. In all other conditions, the AG was
either at baseline or significantly deactivated. Only very
complex semantic processing elevates the AG above resting
baseline, words, pseudowords, and even simple sentences
suppress it. These findings led Humphries et al. (2007) to
suggest that one important function of the AG is integration of
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Page 14

semantic information into an ongoing context. The incoming
stimulus interrupts processing of the internal narrative, but the
level of semantic input to the AG is impoverished during low-
level semantic processing, resulting in a reduction in AG
activity compared with a low-level task or even the resting state
baseline. In other words, during low-level tasks, the AG is
engaged in internally generated cognitive processes that are
suspended during more complex cognitive tasks (Greicius et al.
2003; Greicius and Menon 2004). Whether similar effects might
be at play during demanding multistep problem solving, for
example, in tasks involving word problems (Thevenot and
Oakhill 2005) and elaborate verbal processes in calculation
(Ansari 2008), remains to be investigated with more appropri-
ate experimental designs.
An alternate view of the AG function centers on its role at
the interface of memory and attention. Studies of memory
retrieval in patients with lesions to the IPC suggest weakened
retrieval effects in the absence of cues and paucity in the
semantic contents of the retrieval (Cabeza et al. 2008). Clearly,
furtherstudiesareneededtotestthesehypothesesandexamine
the precise conditions in which semantic content of individual
stimulimodulateresponsesintheleftandtherightAG.Critically,
for us here, these notions of AG function point to a domain-
general, rather than a domain-specific, role in mathematical
cognition.
AG and IPS Relation to Individual Differences in
Performance
Analysis of brain--behavior relations provides further insights into
the role of the IPS and AG in mathematical cognition. In the AG,
deactivation was associated with reduced accuracy during both
tasks. This effect was most strongly observed in the posterior AG
areaPGpinbothhemispheres,althoughtheeffectswerestronger
intherighthemisphere.AsimilarpatternwasobservedintheMA-
R task, except that responses were stronger in area PGp and
accuracy was also correlated with responses in the anterior AG
region PGa. These results converge on our findings of between-
task differences in deactivation and further suggest that
disengagement of the AG is necessary for accurate task
performance.Ourresultsarealsoconsistentwiththeobservation
above that the AG is deactivated, or relatively suppressed, to
a greater extent during performance of the less automated MA-R
task. More importantly, these findings suggest that AG de-
activation is related to individual differences in performance
andthesubjectivedifficultyofperformingtheMAtasks.TheseAG
regions overlap with the DMN and provide new evidence that
suppression of the lateral parietal lobe nodes, but not the midline
structures of the DMN, such as the posterior cingulate cortex or
the ventromedial PFC, is crucial for accurate MA task perfor-
mance.Inthisregard,theobservedbrain--behaviorrelationsdiffer
in interesting ways from those in cognitive studies of other
domainssuchasattention(Pollietal.2005;Weissmanetal.2006).
Our findings are partly consistent with those of Grabner
et al. (2007), who found that left AG responses during
multiplication were correlated with measures of math compe-
tence acquired outside the scanner (Grabner et al. 2007). The
AG cluster observed by Grabner and colleagues is in close
proximity to the left PGa peak detected during the more
demanding MA-R task. However, our findings of brain--behavior
correlations were associated more with focal task-related
deactivation, rather than activation. Furthermore, deactivations
were observed in both hemispheres in our studies. There are 2
potential reasons for this discrepancy. One, our study used
task-specific measures of performance, rather than general
measures of math intelligence. Two, the use of just 2 fixation
blocks, placed at the beginning and end of the task, may also
have contributed to errors in estimating the profile of
activation and deactivation during the multiplication task in
the Grabner and colleagues’ study. Taken together, however,
these findings suggest that performance, task automaticity as
well as general domain competence—factors related to sub-
jective difficulty—all contribute to modulation of AG responses
during mathematical information processing tasks.
BeyondtheAG,activationsintheleftmid-IPSareahIP1andthe
adjoining SMG area PFm were also correlated with accuracy, but
only in the more difficult MA-R task. These results suggest that
modulation of responses in specific IPC regions depends on task
automaticity and performance and that IPC contributions to
increased performance and efficiency are heterogeneous not
only between the 2 lateral IPC regions but also within each
hemisphere.
Conclusions
Our study provides a unique understanding of the architecture
of the IPC in mathematical cognition. More importantly, our
findings also pinpoint the link between cytoarchitectonically
defined regions of the IPC and the functionally heterogeneous
contributions of the IPS and AG to mathematical cognition. The
findings reported here point to close links between structure
and function within the IPC and they provide new insights into
the differential contributions of specific regions of the IPC in
relation to automated and successful MA task performance. The
functional heterogeneities we found are important for un-
derstanding the role of the IPS, AG, and the SMG of the IPC in
mathematical cognition. Our study also suggest that failure to
take into account the complex profile of activation and
deactivation above baseline can lead to misleading conclusions
about the role of the IPC in this domain. The systems neu-
roscience view advanced here suggests that the AG regions
must be disengaged as part of a general cognitive mechanism
involved duringcomplex information
(Greicius and Menon 2004). In this context, we highlight
further studies needed to investigate the precise cognitive
operations subserved by both the activated and deactivated
regions of the IPC and how they influence calculation, fact
retrieval, learning, and development of domain proficiency.
processingtasks
Supplementary Material
Supplementary
oxfordjournals.org/
material canbefoundat:http://www.cercor.
Funding
National Institutes of Health (HD047520 and HD059205) and
the National Science Foundation (BCS/DRL-0750340).
Notes
We thank Sonia Crottaz-Herbette for assistance with data acquisition
and Valorie Salimpoor for assistance with data analysis. Conflict of
Interest: None declared.
Address correspondence to: V. Menon, PhD, Symbolic Systems
Program, Program in Neuroscience and Department of Psychiatry and
Cerebral Cortex December 2009, V 19 N 12 2943

Page 15

Behavioral Sciences, 780 Welch Rd, Room 201, Stanford University
School of Medicine, Stanford, CA 94305, USA. Email: menon@stanford.
edu.
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