Neuroanatomical substrates of arabic number processing, numerical comparison, and simple addition: a PET study

Positron emission tomography was used to localize the cerebral networks specifically involved in three basic numerical processes: arabic numeral processing, numerical magnitude comparison, and retrieval of simple addition facts. Relative cerebral blood flow changes were measured while normal volunteers were resting with eyes closed, making physical judgment on nonnumerical characters or arabic digits, comparing, or adding the same digits. Processing arabic digits bilaterally produced a large nonspecific activation of occipito-parietal areas, as well as a specific activation of the right anterior insula. Comparison and simple addition fact retrieval revealed a fronto-parietal network involving mainly the left intraparietal sulcus, the superior parietal lobule and the precentral gyrus. Comparison also activated, but to a lesser extent, the right superior parietal lobe, whereas addition also activated the orbito-frontal areas and the anterior insula in the right hemisphere. Implications for current anatomo-functional models of numerical cognition are drawn.     

Differential contributions of the left and right inferior parietal lobules to number processing

We measured cerebral activation with functional magnetic resonance imaging at 3 Tesla while eight healthy volunteers performed various number processing tasks known to be dissociable in brain-lesioned patients: naming, comparing, multiplying, or subtracting single digits. The results revealed the activation of a circuit comprising bilateral intraparietal, prefrontal, and anterior cingulate components. The extension and lateralization of this circuit was modulated by task demands. The intraparietal and prefrontal activation was more important in the right hemisphere during the comparison task and in the left hemisphere during the multiplication task and was intensely bilateral during the subtraction task. Thus, partially distinct cerebral circuits with the dorsal parietal pathway underlie distinct arithmetic operations.     

Functional dissociations between four basic arithmetic operations in the human posterior parietal cortex: a cytoarchitectonic mapping study

Although lesion studies over the past several decades have focused on functional dissociations in posterior parietal cortex (PPC) during arithmetic, no consistent view has emerged of its differential involvement in addition, subtraction, multiplication, and division. To circumvent problems with poor anatomical localization, we examined functional overlap and dissociations in cytoarchitectonically defined subdivisions of the intraparietal sulcus (IPS), superior parietal lobule (SPL) and angular gyrus (AG), across these four operations. Compared to a number identification control task, all operations except addition, showed a consistent profile of left posterior IPS activation and deactivation in the right posterior AG. Multiplication and subtraction differed significantly in right, but not left, IPS and AG activity, challenging the view that the left AG differentially subserves retrieval during multiplication. Although addition and multiplication both rely on retrieval, multiplication evoked significantly greater activation in right posterior IPS, as well as the prefrontal cortex, lingual and fusiform gyri, demonstrating that addition and multiplication engage different brain processes. Comparison of PPC responses to the two pairs of inverse operations: division versus multiplication and subtraction versus addition revealed greater activation of left lateral SPL during division, suggesting that processing inverse relations is operation specific. Our findings demonstrate that individual IPS, SPL and AG subdivisions are differentially modulated by the four arithmetic operations and they point to significant functional heterogeneity and individual differences in activation and deactivation within the PPC. Critically, these effects are related to retrieval, calculation and inversion, the three key cognitive processes that are differentially engaged by arithmetic operations. Our findings point to distribute representation of these processes in the human PPC and also help explain why lesion and previous imaging studies have yielded inconsistent findings.     

Are multiplication facts implemented by the left supramarginal and angular gyri?

A patient with presumed cerebral vasculitis showed preserved single digit multiplication facts and impaired single digit subtraction facts. Her ability to comprehend and manipulate numerical quantities was intact. Detailed analysis of her MRI-scan revealed a lesion involving the left parietal lobe including the supramarginal gyrus up to the intraparietal sulcus and extending posteriorly to involve part of the angular gyrus. This finding contradicts a previous report by Lee [Ann. Neurol. 48 (2000) 657] suggesting that these areas are critical for multiplication. In addition, this case contradicts the predicted association between subtraction and quantity manipulation, proposed by Dehaene's triple-code model [Cortex 33 (1997) 219].     

The functional architectures of addition and subtraction: Network discovery using fMRI and DCM

The neuronal mechanisms underlying arithmetic calculations are not well understood but the differences between mental addition and subtraction could be particularly revealing. Using fMRI and dynamic causal modeling (DCM), this study aimed to identify the distinct neuronal architectures engaged by the cognitive processes of simple addition and subtraction. Our results revealed significantly greater activation during subtraction in regions along the dorsal pathway, including the left inferior frontal gyrus (IFG), middle portion of dorsolateral prefrontal cortex (mDLPFC), and supplementary motor area (SMA), compared with addition. Subsequent analysis of the underlying changes in connectivity – with DCM – revealed a common circuit processing basic (numeric) attributes and the retrieval of arithmetic facts. However, DCM showed that addition was more likely to engage (numeric) retrieval‐based circuits in the left hemisphere, while subtraction tended to draw on (magnitude) processing in bilateral parietal cortex, especially the right intraparietal sulcus (IPS). Our findings endorse previous hypotheses about the differences in strategic implementation, dominant hemisphere, and the neuronal circuits underlying addition and subtraction. Moreover, for simple arithmetic, our connectivity results suggest that subtraction calls on more complex processing than addition: auxiliary phonological, visual, and motor processes, for representing numbers, were engaged by subtraction, relative to addition. Hum Brain Mapp 38:3210–3225, 2017. © 2017 Wiley Periodicals, Inc.     

Motor familiarity: brain activation when watching kinematic displays of one's own movements

The perception of action is influenced by the observer's familiarity with its movement. However, how does motor familiarity with own movement patterns modulate the visual perception of action effects? Cortical activation was examined with fMRI while 20 observers were watching videotaped point-light displays of markers on the shoulders, the right elbow, and wrist of an opposing table tennis player. The racket and ball were not displayed. Participants were asked to predict the invisible effect of the stroke, that is, the ball flight direction. Different table tennis models were used without the observers knowing and being informed in advance that some of the presented videos displayed their own movements from earlier training sessions. Prediction had to be made irrespective of the identity of the player represented by the four moving markers. Results showed that participants performed better when observing their “own” strokes. Using a region-of-interest approach, fMRI data showed that observing own videos was accompanied by stronger activation (compared to other videos) in the left angular gyrus of the inferior parietal lobe and the anterior rostral medial frontal cortex. Other videos elicited stronger activation than own videos in the left intraparietal sulcus and right supramarginal gyrus. We suggest that during action observation of motorically familiar movements, the compatibility between the observed action and the observers’ motor representation is already coded in the parietal angular gyrus—in addition to the paracingulate gyrus. The activation in angular gyrus is presumably part of an action-specific effect retrieval that accompanies actor-specific prefrontal processing. The intraparietal sulcus seems to be sensitive to incongruence between observed kinematics and internal model representations, and this also influences processing in the supramarginal gyrus.     

Distinct representations of subtraction and multiplication in the neural systems for numerosity and language

It has been proposed that recent cultural inventions such as symbolic arithmetic recycle evolutionary older neural mechanisms. A central assumption of this hypothesis is that the degree to which a preexisting mechanism is recycled depends on the degree of similarity between its initial function and the novel task. To test this assumption, we investigated whether the brain region involved in magnitude comparison in the intraparietal sulcus (IPS), localized by a numerosity comparison task, is recruited to a greater degree by arithmetic problems that involve number comparison (single-digit subtractions) than by problems that involve retrieving number facts from memory (single-digit multiplications). Our results confirmed that subtractions are associated with greater activity in the IPS than multiplications, whereas multiplications elicit greater activity than subtractions in regions involved in verbal processing including the middle temporal gyrus (MTG) and inferior frontal gyrus (IFG) that were localized by a phonological processing task. Pattern analyses further indicated that the neural mechanisms more active for subtraction than multiplication in the IPS overlap with those involved in numerosity comparison and that the strength of this overlap predicts interindividual performance in the subtraction task. These findings provide novel evidence that elementary arithmetic relies on the cooption of evolutionary older neural circuits.     

Coherent motion sensitivity predicts individual differences in subtraction

Recent findings suggest deficits in coherent motion sensitivity, an index of visual dorsal stream functioning, in children with poor mathematical skills or dyscalculia, a specific learning disability in mathematics. We extended these data using a longitudinal design to unravel whether visual dorsal stream functioning is able to predict individual differences in subsequent specific mathematical skills, i.e., single-digit subtraction and multiplication. We measured children's sensitivity to coherent motion in kindergarten (mean age: 5 years 8 months) and evaluated their subtraction and multiplication skills in third grade (mean age 8 years 3 months). Findings revealed an association between subtraction but not multiplication performance and coherent motion sensitivity. This association remained significant even when intellectual ability and reading ability were additionally controlled for. Subtractions are typically solved by means of quantity-based procedural strategies, which reliably recruit the intraparietal sulcus. Against the background of a neural overlap between the intraparietal sulcus and visual dorsal stream functioning, we hypothesize that low-level visuospatial mechanisms might set constraints on the development of quantity representations, which are used during calculation, particularly in subtraction.     

Functional neuroanatomy of mental rotation

Brain regions involved in mental rotation were determined by assessing increases in fMRI activation associated with increases in stimulus rotation during a mirror-normal parity-judgment task with letters and digits. A letter-digit category judgment task was used as a control for orientation-dependent neural processing unrelated to mental rotation per se. Compared to the category judgments, the parity judgments elicited increases in activation in both the dorsal and the ventral visual streams, as well as higher-order premotor areas, inferior frontal gyrus, and anterior insula. Only a subset of these areas, namely, the posterior part of the dorsal intraparietal sulcus, higher-order premotor regions, and the anterior insula showed increased activation as a function of stimulus orientation. Parity judgments elicited greater activation in the right than in the left ventral intraparietal sulcus, but there were no hemispheric differences in orientation-dependent activation, suggesting that neither hemisphere is dominant for mental rotation per se. Hemispheric asymmetries associated with parity-judgment tasks may reflect visuospatial processing other than mental rotation itself, which is subserved by a bilateral fronto-parietal network, rather than regions restricted to the posterior parietal.     

The neural substrate of gesture recognition

Previous studies have linked action recognition with a particular pool of neurons located in the ventral premotor cortex, the posterior parietal cortex and the superior temporal sulcus (the mirror neuron system). However, it is still unclear if transitive and intransitive gestures share the same neural substrates during action-recognition processes. In the present study, we used event-related functional magnetic resonance imaging (fMRI) to assess the cortical areas active during recognition of pantomimed transitive actions, intransitive gestures, and meaningless control actions. Perception of all types of gestures engaged the right pre-supplementary motor area (pre-SMA), and bilaterally in the posterior superior temporal cortex, the posterior parietal cortex, occipitotemporal regions and visual cortices. Activation of the posterior superior temporal sulcus/superior temporal gyrus region was found in both hemispheres during recognition of transitive and intransitive gestures, and in the right hemisphere during the control condition; the middle temporal gyrus showed activation in the left hemisphere when subjects recognized transitive and intransitive gestures; activation of the left inferior parietal lobe and intraparietal sulcus (IPS) was mainly observed in the left hemisphere during recognition of the three conditions. The most striking finding was the greater activation of the left inferior frontal gyrus (IFG) during recognition of intransitive actions. Results show that a similar neural substrate, albeit, with a distinct engagement underlies the cognitive processing of transitive and intransitive gestures recognition. These findings suggest that selective disruptions in these circuits may lead to distinct clinical deficits.     

Location of the human posterior eye field with functional magnetic resonance imaging.

The frontal eye field and parietal eye field are known to be involved during visually guided saccades. As the location of the human parietal eye field is not yet well known, functional MRI was used during such a saccade task to better localise this field. Besides activity in visual areas of the occipital cortex, bilateral activity was seen in the precentral sulcus, corresponding to the frontal eye field, and in the deep region of the intraparietal sulcus. It is suggested that this intraparietal area, bordering areas 39 and 40 of Brodmann, corresponds to the human parietal eye field.     

Event-related potentials of single-digit addition, subtraction, and multiplication

This study compared the event-related potentials elicited by single-digit addition, subtraction, and multiplication problems. With a delayed verification paradigm, 18 Chinese undergraduates were first asked to solve the arithmetic problems that were presented visually for 200 ms and, after 1.5 s, to judge whether a presented solution was correct or not. Results showed that, compared to addition and subtraction, multiplication elicited a greater N300 at the left frontal electrodes peaking around 320 ms (in the interval between 275 and 334 ms after the onset of the arithmetic problem). To control for the confounding effects of task difficulty and solution size, comparisons were further made between "large" addition problems (with sums between 11 and 17) and "small" multiplication problems (with products between 6 and 24). Similar results were obtained (i.e., a significant difference between addition and multiplication in the N300 component between 296 and 444 ms). Source analyses demonstrated that a single dipole in the left anterior brain areas could have contributed to the topographies of the difference waveforms ("multiplication-addition", "multiplication-subtraction", and "'small' multiplication-'large' addition"). These results are interpreted in terms of the greater reliance on phonological processing for the retrieval of multiplication facts than for the retrieval of addition and subtraction facts.     

Learning complex arithmetic--an fMRI study

Aim of the present functional magnet resonance imaging (fMRI) study was to detect modifications of cerebral activation patterns related to learning arithmetic. Thirteen right-handed subjects were extensively trained on a set of 18 complex multiplication problems. In the following fMRI session, trained and untrained problems (closely matched for difficulty) were presented in blocked order alternating with a number matching task and a fact retrieval task. Importantly, left hemispheric activations were dominant in the two contrasts between untrained and trained condition, suggesting that learning processes in arithmetic are predominantly supported by the left hemisphere. Contrasting untrained versus trained condition, the left intraparietal sulcus showed significant activations, as well as the inferior parietal lobule. A further significant activation was found in the left inferior frontal gyrus. This activation may be accounted for by higher working memory demands in the untrained as compared to the trained condition. Contrasting trained versus untrained condition a significant focus of activation was found in the left angular gyrus. Following the triple-code model [Science 284 (1999) 970], the shift of activation within the parietal lobe from the intraparietal sulcus to the left angular gyrus suggests a modification from quantity-based processing to more automatic retrieval. The present study shows that the left angular gyrus is not only involved in arithmetic tasks requiring simple fact retrieval, but may show significant activations as a result of relatively short training of complex calculation.     

Localization of executive functions in dual-task performance with fMRI

We report a study that investigated the neuroanatomical correlates of executive functions in dual-task performance with functional magnetic resonance imaging. Participants performed an auditory and a visual three-choice reaction task either separately as single tasks or concurrently as dual tasks. In the dual-task condition, two stimuli were presented in rapid succession to ensure interference between the component tasks (psychological refractory period). The behavioral data showed considerable performance decrements in the dual-task compared to the single-task condition. Dual-task-related activation was detected with two different neuroimaging methods. First, we determined dual-task-related activation according to the method of cognitive subtraction. For that purpose, activation in the dual-task was compared directly with activation in the single-task conditions. This analysis revealed that cortical areas along the inferior frontal sulcus (IFS), the middle frontal gyrus (MFG), and the intraparietal sulcus (IPS) are involved in dual-task performance. The results of the subtraction method were validated with the method of parametric manipulation. For this purpose, a second dual-task condition was introduced, where the difficulty of the dual-task coordination was increased compared with the first dual-task condition. As expected, behavioral dual-task performance decreased with increased dual-task difficulty. Furthermore, the increased dual-task difficulty led to an increase of activation in those cortical regions that proved to be dual-task related with the subtraction method, that is, the IFS, the MFG, and the IPS. These results support the conclusion that dorsolateral prefrontal and superior parietal cortices are involved in the coordination of concurrent and interfering task processing.     

Tactile discrimination of grating orientation: fMRI activation patterns

Grating orientation discrimination is employed widely to test tactile spatial acuity. We used functional magnetic resonance imaging (fMRI) to investigate the neural circuitry underlying performance of this task. Two studies were carried out. In the first study, an extensive set of parietal and frontal cortical areas was activated during covert task performance, relative to a rest baseline. The active regions included the postcentral sulcus bilaterally and foci in the left parietal operculum, left anterior intraparietal sulcus, and bilateral premotor and prefrontal cortex. The second study examined selective recruitment of cortical areas during discrimination of grating orientation (a task with a macrospatial component) compared to discrimination of grating spacing (a purely microspatial task). The foci activated on this contrast were in the left anterior intraparietal sulcus, right postcentral sulcus and gyrus, left parieto-occipital cortex, bilateral frontal eye fields, and bilateral ventral premotor cortex. These findings not only confirm and extend previous studies of the neural processing underlying grating orientation discrimination, but also demonstrate that a distributed network of putatively multisensory areas is involved.     

Effective connectivity of the multiplication network: A functional MRI and multivariate granger causality mapping study

Developmental neuropsychology and functional neuroimaging evidence indicates that simple and complex mental calculation is subserved by a fronto‐parietal network. However, the effective connectivity (connection direction and strength) among regions within the fronto‐parietal network is still unexplored. Combining event‐related fMRI and multivariate Granger Causality Mapping (GCM), we administered a multiplication verification task to healthy participants asking them to solve single and double‐digit multiplications. The goals of our study were first, to identify the effective connectivity of the multiplication network, and second, to compare the effective connectivity patterns between a low and a high arithmetical competence (AC) group. The manipulation of multiplication difficulty revealed a fronto‐parietal network encompassing bilateral intraparietal sulcus (IPS), left pre‐supplementary motor area (PreSMA), left precentral gyrus (PreCG), and right dorsolateral prefrontal cortex (DLPFC). The network was driven by an intraparietal IPS‐IPS circuit hosting a representation of numerical quantity intertwined with a fronto‐parietal DLPFC‐IPS circuit engaged in temporary storage and updating of arithmetic operations. Both circuits received additional inputs from the PreCG and PreSMA playing more of a supportive role in mental calculation. The high AC group compared to the low AC group displayed a greater activation in the right IPS and based its calculation more on a feedback driven intraparietal IPS‐IPS circuit, whereas the low competence group more on a feedback driven fronto‐parietal DLPFC‐IPS circuit. This study provides first evidence that multivariate GCM is a sensitive approach to investigate effective connectivity of mental processes involved in mental calculation and to compare group level performances for different populations. Hum Brain Mapp, 2010. © 2010 Wiley‐Liss, Inc.     

A functional MRI study of simple arithmetic--a comparison between children and adults

The purpose of this study was to examine brain areas involved in simple arithmetic, and to compare these areas between adults and children. Eight children (four girls and four boys; age, 9-14 years) and eight adults (four women and four men; age, 40-49 years) were subjected to this study. Functional magnetic resonance imaging (fMRI) was performed during mental calculation of addition, subtraction, and multiplication of single digits. In each group, the left middle frontal, bilateral inferior temporal and bilateral lateral occipital cortices were activated during each task. The adult group showed activation of the right frontal cortex during addition and multiplication tasks, but the children group did not. Activation of the intraparietal cortex was observed in the adult group during each task. Although, activation patterns were slightly different among tasks, as well as between groups, only a small number of areas showed statistically significant differences. The results indicate that cortical networks involved in simple arithmetic are similar among arithmetic operations, and may not show significant changes in the structure during the second decade of life.     

Involvement of the human frontal eye field and multiple parietal areas in covert visual selection during conjunction search

Searching for a target object in a cluttered visual scene requires active visual attention if the target differs from distractors not by elementary visual features but rather by a feature conjunction. We used functional magnetic resonance imaging (fMRI) in human subjects to investigate the functional neuroanatomy of attentional mechanisms employed during conjunction search. In the experimental condition, subjects searched for a target defined by a conjunction of colour and orientation. In the baseline condition, subjects searched for a uniquely coloured target, regardless of its orientation. Eye movement recordings outside the scanner verified subjects' ability to maintain fixation during search. Reaction times indicated that the experimental condition was attentionally more demanding than the baseline condition. Differential activations between conditions were therefore ascribed to top-down modulation of neural activity. The frontal eye field, the ventral precentral sulcus and the following posterior parietal regions were consistently activated: (i) the postcentral sulcus; (ii) the posterior; and (iii) the anterior part of the intraparietal sulcus; and (iv) the junction of the intraparietal with the transverse occipital sulcus. Parietal regions were spatially distinct and displayed differential amplitudes of signal increase with a maximal amplitude in the posterior intraparietal sulcus. Less consistent activation was found in the lateral fusiform gyrus. These results suggest an involvement of the human frontal eye field in covert visual selection of potential targets during search. These results also provide evidence for a subdivision of posterior parietal cortex in multiple areas participating in covert visual selection, with a major contribution of the posterior intraparietal sulcus.     

What have Klingon letters and faces in common? An fMRI study on content-specific working memory systems

Neuroimaging studies show that prefrontal, premotor, and parietal cortical regions are part of a working memory network that supports the active retention of information. In two experiments we used fMRI to examine whether prefrontal and posterior cortical areas are organized in a content-specific way for object and spatial working memory. Subjects performed a delayed matching-to-sample task modified to allow the examination of content-specific retention processes, independent of perceptual and decision-related processes. In Experiment 1, either unfamiliar geometrical objects (Klingon letters from an artificial alphabet unknown to the participants) or their spatial locations had to be memorized, whereas in Experiment 2, either unfamiliar faces or biological objects (butterflies) were actively memorized. All tasks activated a similar cortical network including posterior parietal (banks of the intraparietal sulcus), premotor (banks of the inferior precentral sulcus) and prefrontal regions (banks of the inferior frontal sulcus), and the presupplementary motor area (pre-SMA). For geometrical objects and faces for which strategic semantic processing can be assumed, this activation was larger in the left than in the right hemisphere, whereas a bilateral or right dominant distribution was obtained for butterflies and spatial locations. The present results do not support the process-specific or content-specific view of the role of the prefrontal cortex in working memory task. Rather, they suggest that the inferior prefrontal cortex houses nonmemonic strategic processing systems required for response selection and task management that can flexibly be used across a variety of tasks and informational domains.     

Neural substrates for forward and backward recitation of numbers and the alphabet: a close examination of the role of intraparietal sulcus and perisylvian areas

Despite numerous studies on the neural basis of numerical processing, few studies have examined the neural substrates of one of the most basic numerical processing-number sequence recitation. The present study used fMRI to investigate neural substrates of number sequence recitation, focusing on the intraparietal sulcus (IPS) and perisylvian areas. This study used a 2 (number versus alphabet) x 2 (forward versus backward recitation) design. 12 Chinese undergraduates were asked to recite overtly but gently numerical and alphabetical sequences forward and backward. Results showed that, for both numerical and alphabetic sequences, the left IPS was activated when performing backward recitation, but not when performing forward recitation. In terms of perisylvian areas, all four tasks elicited activation in bilateral superior temporal gyrus and inferior frontal gyrus, but forward recitation elicited greater activation in the left posterior superior temporal gyrus than did backward recitation, whereas backward recitation elicited greater activation in the left inferior frontal gyrus than did forward recitation. These results suggest that forward recitation of numbers and the alphabet is typically based on verbal processing of numbers implemented in the perisylvian area, whereas backward recitation would likely require additional neural resources in the IPS.