Causal evidence of the involvement of the number form area in the visual detection of numbers and letters

Functional and representational differences between bilateral inferior temporal numeral areas

The processing of numerals as visual objects is supported by an "Inferior Temporal Numeral Area" (ITNA) in the bilateral inferior temporal gyri (ITG). Extant findings suggest some degree of hemispheric asymmetry in how the bilateral ITNAs process numerals. Pollack and Price (2019) reported such a hemispheric asymmetry by which a region in the left ITG was sensitive to digits during a visual search for a digit among letters, and a homologous region in the right ITG that showed greater digit sensitivity in individuals with higher calculation skills. However, the ITG regions were localized with separate analyses without directly contrasting their digit sensitivities and relation to calculation skills. So, the extent of and reasons for these functional asymmetries remain unclear. Here we probe whether the functional and representational properties of the ITNAs are asymmetric by applying both univariate and multivariate region-of-interest analyses to Pollack and Price's (2019) data. Contrary to the implications of the original findings, digit sensitivity did not differ between ITNAs, and digit sensitivity in both left and right ITNAs was associated with calculation skills. Representational similarity analyses revealed that the overall representational geometries of digits in the ITNAs were also correlated, albeit weakly, but the representational contents of the ITNAs were largely inconclusive. Nonetheless, we found a right lateralization in engagement in alphanumeric categorization, and that the right ITNA showed greater discriminability between digits and letters. Greater right lateralization of digit sensitivity and digit discriminability in the left ITNA were also related to higher calculation skills. Our findings thus suggest that the ITNAs may not be functionally identical and should be directly contrasted in future work. Our study also highlights the importance of within-individual comparisons for understanding hemispheric asymmetries, and analyses of individual differences and multivariate features to uncover effects that would otherwise be obscured by averages.

Spatiotemporal dynamics of successive activations across the human brain during simple arithmetic processing

Previous neuroimaging studies have offered unique insights about the spatial organization of activations and deactivations across the brain, however these were not powered to explore the exact timing of events at the subsecond scale combined with precise anatomical source information at the level of individual brains. As a result, we know little about the order of engagement across different brain regions during a given cognitive task. Using experimental arithmetic tasks as a prototype for human-unique symbolic processing, we recorded directly across 10,076 brain sites in 85 human subjects (52% female) using intracranial electroencephalography (iEEG). Our data revealed a remarkably distributed change of activity in almost half of the sampled sites. Notably, an orderly successive activation of a set of brain regions - anatomically consistent across subjects-was observed in individual brains. Furthermore, the temporal order of activations across these sites was replicable across subjects and trials. Moreover, the degree of functional connectivity between the sites decreased as a function of temporal distance between regions, suggesting that information is partially leaked or transformed along the processing chain. Furthermore, in each activated region, distinct neuronal populations with opposite activity patterns during target and control conditions were juxtaposed in an anatomically orderly manner. Our study complements the prior imaging studies by providing hitherto unknown information about the timing of events in the brain during arithmetic processing. Such findings can be a basis for developing mechanistic computational models of human-specific cognitive symbolic systems.

Significance statement

Our study elucidates the spatiotemporal dynamics and anatomical specificity of brain activations across >10,000 sites during arithmetic tasks, as captured by intracranial EEG. We discovered an orderly, successive activation of brain regions, consistent across individuals, and a decrease in functional connectivity as a function of temporal distance between regions. Our findings provide unprecedented insights into the sequence of cognitive processing and regional interactions, offering a novel perspective for enhancing computational models of cognitive symbolic systems.

Syntactic theory of mathematical expressions

Mathematical expressions consist of recursive combinations of numbers, variables, and operators. According to theoretical linguists, the syntactic mechanisms of natural language also provide a basis for mathematics. To date, however, no theoretically rigorous investigation has been conducted to support such arguments. Therefore, this study uses a methodology based on theoretical linguistics to analyze the syntactic properties of mathematical expressions. Through a review of recent behavioral and neuroimaging studies on mathematical syntax, we report several inconsistencies with theoretical linguistics, such as the use of ternary structures. To address these, we propose that a syntactic category called Applicative plays a central role in analyzing mathematical expressions with seemingly ternary structures by combining binary structures. Besides basic arithmetic expressions, we also examine algebraic equations and complex expressions such as integral and differential calculi. This study is the first attempt at building a comprehensive framework for analyzing the syntactic structures of mathematical expressions.

The brain lateralization and development of math functions: progress since Sperry, 1974

In 1974, Roger Sperry, based on his seminal studies on the split-brain condition, concluded that math was almost exclusively sustained by the language dominant left hemisphere. The right hemisphere could perform additions up to sums less than 20, the only exception to a complete left hemisphere dominance. Studies on lateralized focal lesions came to a similar conclusion, except for written complex calculation, where spatial abilities are needed to display digits in the right location according to the specific requirements of calculation procedures. Fifty years later, the contribution of new theoretical and instrumental tools lead to a much more complex picture, whereby, while left hemisphere dominance for math in the right-handed is confirmed for most functions, several math related tasks seem to be carried out in the right hemisphere. The developmental trajectory in the lateralization of math functions has also been clarified. This corpus of knowledge is reviewed here. The right hemisphere does not simply offer its support when calculation requires generic space processing, but its role can be very specific. For example, the right parietal lobe seems to store the operation-specific spatial layout required for complex arithmetical procedures and areas like the right insula are necessary in parsing complex numbers containing zero. Evidence is found for a complex orchestration between the two hemispheres even for simple tasks: each hemisphere has its specific role, concurring to the correct result. As for development, data point to right dominance for basic numerical processes. The picture that emerges at school age is a bilateral pattern with a significantly greater involvement of the right-hemisphere, particularly in non-symbolic tasks. The intraparietal sulcus shows a left hemisphere preponderance in response to symbolic stimuli at this age.

Notational systems are distinct cognitive systems with different material prehistories

Notations are cognitive systems involving distinctive psychological functions, behaviors, and material forms. Seen through this lens, two main types - semasiography and visible language - are fundamentally differentiated by their material prehistories, emphasis on iconography, and the centrality of language's combinatorial faculty. These fundamental differences suggest that key qualities (iconicity, expressiveness, concision) are difficult to conjoin in a single system.

Beyond the Visual Word Form Area - a cognitive characterization of the left ventral occipitotemporal cortex

The left ventral occipitotemporal cortex has been traditionally viewed as a pathway for visual object recognition including written letters and words. Its crucial role in reading was strengthened by the studies on the functionally localized "Visual Word Form Area" responsible for processing word-like information. However, in the past 20 years, empirical studies have challenged the assumptions of this brain region as processing exclusively visual or even orthographic stimuli. In this review, we aimed to present the development of understanding of the left ventral occipitotemporal cortex from the visually based letter area to the modality-independent symbolic language related region. We discuss theoretical and empirical research that includes orthographic, phonological, and semantic properties of language. Existing results showed that involvement of the left ventral occipitotemporal cortex is not limited to unimodal activity but also includes multimodal processes. The idea of the integrative nature of this region is supported by the broad functional and structural connectivity with language-related and attentional brain networks. We conclude that although the function of the area is not yet fully understood in human cognition, its role goes beyond visual word form processing. The left ventral occipitotemporal cortex seems to be crucial for combining higher-level language information with abstract forms that convey meaning independently of modality.

Representations within the Intraparietal Sulcus Distinguish Numerical Tasks and Formats

How does our brain understand the number five when it is written as an Arabic numeral, and when presented as five fingers held up? Four facets have been implicated in adult numerical processing: semantic, visual, manual, and phonological/verbal. Here, we ask how the brain represents each, using a combination of tasks and stimuli. We collected fMRI data from adult participants while they completed our novel "four number code" paradigm. In this paradigm, participants viewed one of two stimulus types to tap into the visual and manual number codes, respectively. Concurrently, they completed one of two tasks to tap into the semantic and phonological/verbal number codes, respectively. Classification analyses revealed that neural codes representing distinctions between the number comparison and phonological tasks were generalizable across format (e.g., Arabic numerals to hands) within intraparietal sulcus (IPS), angular gyrus, and precentral gyrus. Neural codes representing distinctions between formats were generalizable across tasks within visual areas such as fusiform gyrus and calcarine sulcus, as well as within IPS. Our results identify the neural facets of numerical processing within a single paradigm and suggest that IPS is sensitive to distinctions between semantic and phonological/verbal, as well as visual and manual, facets of number representations.

Neural representations of the perception of handwritten digits and visual objects from a convolutional neural network compared to humans

We investigated neural representations for visual perception of 10 handwritten digits and six visual objects from a convolutional neural network (CNN) and humans using functional magnetic resonance imaging (fMRI). Once our CNN model was fine-tuned using a pre-trained VGG16 model to recognize the visual stimuli from the digit and object categories, representational similarity analysis (RSA) was conducted using neural activations from fMRI and feature representations from the CNN model across all 16 classes. The encoded neural representation of the CNN model exhibited the hierarchical topography mapping of the human visual system. The feature representations in the lower convolutional (Conv) layers showed greater similarity with the neural representations in the early visual areas and parietal cortices, including the posterior cingulate cortex. The feature representations in the higher Conv layers were encoded in the higher-order visual areas, including the ventral/medial/dorsal stream and middle temporal complex. The neural representations in the classification layers were observed mainly in the ventral stream visual cortex (including the inferior temporal cortex), superior parietal cortex, and prefrontal cortex. There was a surprising similarity between the neural representations from the CNN model and the neural representations for human visual perception in the context of the perception of digits versus objects, particularly in the primary visual and associated areas. This study also illustrates the uniqueness of human visual perception. Unlike the CNN model, the neural representation of digits and objects for humans is more widely distributed across the whole brain, including the frontal and temporal areas.

Cortical representations of numbers and nonsymbolic quantities expand and segregate in children from 5 to 8 years of age

Number symbols, such as Arabic numerals, are cultural inventions that have transformed human mathematical skills. Although their acquisition is at the core of early elementary education in children, it remains unknown how the neural representations of numerals emerge during that period. It is also unclear whether these relate to an ontogenetically earlier sense of approximate quantity. Here, we used multivariate fMRI adaptation coupled with within- and between-format machine learning to probe the cortical representations of Arabic numerals and approximate nonsymbolic quantity in 89 children either at the beginning (age 5) or four years into formal education (age 8). Although the cortical representations of both numerals and nonsymbolic quantities expanded from age 5 to age 8, these representations also segregated with learning and development. Specifically, a format-independent neural representation of quantity was found in the right parietal cortex, but only for 5-year-olds. These results are consistent with the so-called symbolic estrangement hypothesis, which argues that the relation between symbolic and nonsymbolic quantity weakens with exposure to formal mathematics in children.

Neurodevelopmental differences in task-evoked number network connectivity: Comparing symbolic and nonsymbolic number discrimination in children and adults

Numerical cognition can take place in multiple representational formats, such as Arabic digits (e.g., 1), verbal number words (e.g., "two"), and nonsymbolic (e.g., •••) numerical magnitude. Basic numerical discrimination abilities are key factors underlying the development of arithmetic abilities, acting as an important developmental precursor of adult-level numeracy. While prior research has begun to detail the neural correlates associated with basic numerical discrimination skills in different representational formats, the interactions between functional neural circuits are less understood. A growing body of evidence suggests that the functional networks recruited by number discrimination tasks differ between children and adults, which may provide valuable insights into the development of numerical cognition. To this end, we posed two questions: how do the interactions between functional circuits associated with number processing differ in children and adults? Are differences in functional network connectivity modulated by numerical representational codes? A theoretically motivated 22 ROI analysis indicated significant functional connectivity differences between children and adults across all three codes. Adults demonstrated sparser and more consistent connectivity patterns across codes, indicative of developmental domain-specialization for number processing. Although neural activity in children and adults is similar, the functional connectivity supporting number processing appears subject to substantial developmental maturation effects.

Investigating the association between variability in sulcal pattern and academic achievement

Investigating how the brain may constrain academic achievement is not only relevant to understanding brain structure but also to providing insight into the origins of individual differences in these academic abilities. In this pre-registered study, we investigated whether the variability of sulcal patterns, a qualitative feature of the brain determined in-utero and not affected by brain maturation and learning, accounted for individual differences in reading and mathematics. Participants were 97 typically developing 10-year-olds. We examined (a) the association between the sulcal pattern of the IntraParietal Sulcus (IPS) and mathematical ability; (b) the association between the sulcal pattern of the Occipito Temporal Sulcus (OTS) and reading ability; and (c) the overlap and specificity of sulcal morphology of IPS and OTS and their associations with mathematics and reading. Despite its large sample, the present study was unable to replicate a previously observed relationship between the IPS sulcal pattern and mathematical ability and a previously observed association between the left posterior OTS sulcal pattern and reading. We found a weak association between right IPS sulcal morphology and symbolic number abilities and a weak association between left posterior OTS and reading. However, both these associations were the opposite of previous reports. We found no evidence for a possible overlap or specificity in the effect of sulcal morphology on mathematics and reading. Possible explanations for this weak association between sulcal morphology and academic achievement and suggestions for future research are discussed.

Impaired Arithmetic Fact Retrieval in an Adult with Developmental Dyscalculia: Evidence from Behavioral and Functional Brain Imaging Data

Developmental dyscalculia (DD) is a developmental disorder characterized by arithmetic difficulties. Recently, it has been suggested that the neural networks supporting procedure-based calculation (e.g., in subtraction) and left-hemispheric verbal arithmetic fact retrieval (e.g., in multiplication) are partially distinct. Here we compared the neurofunctional correlates of subtraction and multiplication in a 19-year-old student (RM) with DD to 18 age-matched controls. Behaviorally, RM performed significantly worse than controls in multiplication, while subtraction was unaffected. Neurofunctional differences were most pronounced regarding multiplication: RM showed significantly stronger activation than controls not only in left angular gyrus but also in a fronto-parietal network (including left intraparietal sulcus and inferior frontal gyrus) typically activated during procedure-based calculation. Region-of-interest analyses indicated group differences in multiplication only, which, however, did not survive correction for multiple comparisons. Our results are consistent with dissociable and processing-specific, but not operation-specific neurofunctional networks. Procedure-based calculation is not only associated with subtraction but also with (untrained) multiplication facts. Only after rote learning, facts can be retrieved quasi automatically from memory. We suggest that this learning process and the associated shift in activation patterns has not fully occurred in RM, as reflected in her need to resort to procedure-based strategies to solve multiplication facts.

Causal dynamics and information flow in parietal-temporal-hippocampal circuits during mental arithmetic revealed by high-temporal resolution human intracranial EEG

Mental arithmetic involves distributed brain regions spanning parietal and temporal cortices, yet little is known about the neural dynamics of causal functional circuits that link them. Here we use high-temporal resolution (1000 Hz sampling rate) intracranial EEG from 35 participants, 362 electrodes, and 1727 electrode pairs, to investigate dynamic causal circuits linking posterior parietal cortex (PPC) with ventral temporal-occipital cortex and hippocampal regions which constitute the perceptual, visuospatial, and mnemonic building blocks of mental arithmetic. Nonlinear phase transfer entropy measures capable of capturing information flow identified dorsal PPC as a causal inflow hub during mental arithmetic, with strong causal influences from fusiform gyrus in ventral temporal-occipital cortex as well as the hippocampus. Net causal inflow into dorsal PPC was significantly higher during mental arithmetic, compared to both resting-state and verbal memory recall. Our analysis also revealed functional heterogeneity of casual signaling in the PPC, with greater net causal inflow into the dorsal PCC, compared to ventral PPC. Additionally, the strength of causal influences was significantly higher on dorsal, compared to ventral, PPC from the hippocampus, and ventral temporal-occipital cortex during mental arithmetic, when compared to both resting-state and verbal memory recall. Our findings provide novel insights into dynamic neural circuits and hubs underlying numerical problem solving and reveal neurophysiological circuit mechanisms by which both the visual number form processing and declarative memory systems dynamically engage the PPC during mental arithmetic.

Developmental changes in neural lateralization for visual-spatial function: Evidence from a line-bisection task

Studies of hemispheric specialization have traditionally cast the left hemisphere as specialized for language and the right hemisphere for spatial function. Much of the supporting evidence for this separation of function comes from studies of healthy adults and those who have sustained lesions to the right or left hemisphere. However, we know little about the developmental origins of lateralization. Recent evidence suggests that the young brain represents language bilaterally, with 4-6-year-olds activating the left-hemisphere regions known to support language in adults as well as homotopic regions in the right hemisphere. This bilateral pattern changes over development, converging on left-hemispheric activation in late childhood. In the present study, we ask whether this same developmental trajectory is observed in a spatial task that is strongly right-lateralized in adults-the line bisection (or "Landmark") task. We examined fMRI activation among children ages 5-11 years as they were asked to judge which end of a bisected vertical line was longer. We found that young children showed bilateral activation, with activation in the same areas of the right hemisphere as has been shown among adults, as well as in the left hemisphere homotopic regions. By age 10, activation was right-lateralized. This strongly resembles the developmental trajectory for language, moving from bilateral to lateralized activation. We discuss potential underlying mechanisms and suggest that understanding the development of lateralization for a range of cognitive functions can play a crucial role in understanding general principles of how and why the brain comes to lateralize certain functions.

Sulcation of the intraparietal sulcus is related to symbolic but not non-symbolic number skills

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The horizontal segment of intraparietal sulcus (HIPS) is one of the key functional regions for processing numbers.

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Sulcal morphology is a qualitative feature of the brain determined in-utero and not affected by brain maturation and learning.

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The HIPS sulcal pattern explains part of the variance in participant’s symbolic number comparison and math fluency abilities.

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Participant’s non-symbolic number comparison abilities was not explained by HIPS sulcal pattern.

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This association between HIPS sulcal pattern and symbolic number abilities was stable from childhood to young adulthood.

Understanding the constraints, including biological ones, that may influence mathematical development is of great importance because math ability is a key predictor of career success, income and even psychological well-being. While research in developmental cognitive neuroscience of mathematics has extensively studied the key functional regions for processing numbers, particularly the horizontal segment of intraparietal sulcus (HIPS), few studies have investigated the effects of early cerebral constraints on later mathematical abilities. In this pre-registered study, we investigated whether variability of the sulcal pattern of the HIPS, a qualitative feature of the brain determined in-utero and not affected by brain maturation and learning, accounts for individual difference in symbolic and non-symbolic number abilities. Seventy-seven typically developing school-aged children and 21 young adults participated in our study. We found that the HIPS sulcal pattern, (a) explains part of the variance in participant’s symbolic number comparison and math fluency abilities, and (b) that this association between HIPS sulcal pattern and symbolic number abilities was found to be stable from childhood to young adulthood. However, (c) we did not find an association between participant’s non-symbolic number abilities and HIPS sulcal morphology. Our findings suggest that early cerebral constraints may influence individual difference in math abilities, in addition to the well-established neuroplastic factors.

Children With Dyscalculia Show Hippocampal Hyperactivity During Symbolic Number Perception

Dyscalculia is a learning disability affecting the acquisition of arithmetical skills in children with normal intelligence and age-appropriate education. Two hypotheses attempt to explain the main cause of dyscalculia. The first hypothesis suggests that a problem with the core mechanisms of perceiving (non-symbolic) quantities is the cause of dyscalculia (core deficit hypothesis), while the alternative hypothesis suggests that dyscalculics have problems only with the processing of numerical symbols (access deficit hypothesis). In the present study, the symbolic and non-symbolic numerosity processing of typically developing children and children with dyscalculia were examined with functional magnetic resonance imaging (fMRI). Control (n = 15, mean age: 11.26) and dyscalculia (n = 12, mean age: 11.25) groups were determined using a wide-scale screening process. Participants performed a quantity comparison paradigm in the fMRI with two number conditions (dot and symbol comparison) and two difficulty levels (0.5 and 0.7 ratio). The results showed that the bilateral intraparietal sulcus (IPS), left dorsolateral prefrontal cortex (DLPFC) and left fusiform gyrus (so-called “number form area”) were activated for number perception as well as bilateral occipital and supplementary motor areas. The task difficulty engaged bilateral insular cortex, anterior cingulate cortex, IPS, and DLPFC activation. The dyscalculia group showed more activation in the left orbitofrontal cortex, left medial prefrontal cortex, and right anterior cingulate cortex than the control group. The dyscalculia group showed left hippocampus activation specifically for the symbolic condition. Increased left hippocampal and left-lateralized frontal network activation suggest increased executive and memory-based compensation mechanisms during symbolic processing for dyscalculics. Overall, our findings support the access deficit hypothesis as a neural basis for dyscalculia.

White matter fascicles and cortical microstructure predict reading-related responses in human ventral temporal cortex

Reading-related responses in the lateral ventral temporal cortex (VTC) show a consistent spatial layout across individuals, which is puzzling, since reading skills are acquired during childhood. Here, we tested the hypothesis that white matter fascicles and gray matter microstructure predict the location of reading-related responses in lateral VTC. We obtained functional (fMRI), diffusion (dMRI), and quantitative (qMRI) magnetic resonance imaging data in 30 adults. fMRI was used to map reading-related responses by contrasting responses in a reading task with those in adding and color tasks; dMRI was used to identify the brain's fascicles and to map their endpoint densities in lateral VTC; qMRI was used to measure proton relaxation time (T1), which depends on cortical tissue microstructure. We fit linear models that predict reading-related responses in lateral VTC from endpoint density and T1 and used leave-one-subject-out cross-validation to assess prediction accuracy. Using a subset of our participants (N=10, feature selection set), we find that i) endpoint densities of the arcuate fasciculus (AF), inferior longitudinal fasciculus (ILF), and vertical occipital fasciculus (VOF) are significant predictors of reading-related responses, and ii) cortical T1 of lateral VTC further improves the predictions of the fascicle model. In the remaining participants (N=20, validation set), we show that a linear model that includes T1, AF, ILF and VOF significantly predicts i) the map of reading-related responses across lateral VTC and ii) the location of the visual word form area, a region critical for reading. Overall, our data-driven approach reveals that the AF, ILF, VOF and cortical microstructure have a consistent spatial relationship with an individual's reading-related responses in lateral VTC.

Network topology of symbolic and nonsymbolic number comparison

Studies of brain activity during number processing suggest symbolic and nonsymbolic numerical stimuli (e.g., Arabic digits and dot arrays) engage both shared and distinct neural mechanisms. However, the extent to which number format influences large-scale functional network organization is unknown. In this study, using 7 Tesla MRI, we adopted a network neuroscience approach to characterize the whole-brain functional architecture supporting symbolic and nonsymbolic number comparison in 33 adults. Results showed the degree of global modularity was similar for both formats. The symbolic format, however, elicited stronger community membership among auditory regions, whereas for nonsymbolic, stronger membership was observed within and between cingulo-opercular/salience network and basal ganglia communities. The right posterior inferior temporal gyrus, left intraparietal sulcus, and two regions in the right ventromedial occipital cortex demonstrated robust differences between formats in terms of their community membership, supporting prior findings that these areas are differentially engaged based on number format. Furthermore, a unified fronto-parietal/dorsal attention community in the nonsymbolic condition was fractionated into two components in the symbolic condition. Taken together, these results reveal a pattern of overlapping and distinct network architectures for symbolic and nonsymbolic number processing.

Developmental alterations of the numerical processing networks in the brain

Neuroimaging studies revealed that number perception is mainly located in parietal cortex. Although controversial, it was suggested that number is processed in the frontal lobe in childhood and in the parietal cortex in adulthood. The purpose of this study is to investigate developmental differences in the neural correlates of number representation with fMRI. Sixteen healthy young adults (age:21.69 ± 0.79) and 15 healthy children (age:11.87 ± 0.52) performed a numerosity comparison paradigm which consists of two numerical conditions with two difficulty levels. Adults showed broad parietal cortex activation, as well as activation in the inferior parietal lobes, dorsolateral and medial prefrontal cortex, anterior and posterior cingulate cortex, and peristriate cortex (PC) during number processing. Children showed activations in the intraparietal sulcus and PC. Group differences were observed in the posterior insula, fusiform gyrus, and PC whose coordinates correspond to the number form area (NFA). Region of interest analysis was performed for these clusters to get the time series of hemodynamic responses which were estimated with a finite impulse response function. In contrast to the prominent frontoparietal shift theory, no age-related differences were observed in the frontoparietal regions. Overall, the presented study suggests developmental changes in the brain's number processing revolving around the NFA.

Pure alexia with intact perception of complex visual stimuli: a case study

After a stroke involving the left occipitotemporal cortex our patient shows a word-length effect and has problems to identify letters or numbers in strings of symbols. But he is normal in identifying isolated letters and in non-verbally categorizing even complex images such as faces or natural scenes. His cortical lesion is stretching from the visual word form area (VWFA) anteriorly causing additional problems to name visual stimuli and to match acoustic stimuli with images. We conclude that our patient suffers from pure alexia without deficits to identify even complex visual stimuli. Our results directly contradict several explanations for letter-by-letter reading.

Separate lanes for adding and reading in the white matter highways of the human brain

Math and reading involve distributed brain networks and have both shared (e.g. encoding of visual stimuli) and dissociated (e.g. quantity processing) cognitive components. Yet, to date, the shared vs. dissociated gray and white matter substrates of the math and reading networks are unknown. Here, we define these networks and evaluate the structural properties of their fascicles using functional MRI, diffusion MRI, and quantitative MRI. Our results reveal that there are distinct gray matter regions which are preferentially engaged in either math (adding) or reading, and that the superior longitudinal and arcuate fascicles are shared across the math and reading networks. Strikingly, within these fascicles, reading- and math-related tracts are segregated into parallel sub-bundles and show structural differences related to myelination. These findings open a new avenue of research that examines the contribution of sub-bundles within fascicles to specific behaviors.

Visual form perception is fundamental for both reading comprehension and arithmetic computation

Visual perception has been found to be a critical factor for reading comprehension and arithmetic computation in separate lines of research with different measures of visual form perception. The current study of 1099 Chinese elementary school students investigated whether the same visual form perception (assessed by a geometric figure matching task) underlies both reading comprehension and arithmetic computation. The results showed that visual form perception had close relations with both reading comprehension and arithmetic computation, even after controlling for age, gender, and cognitive factors such as processing speed, attention, working memory, visuo-spatial processing, and general intelligence. Results also showed that numerosity comparison's relations with reading comprehension and arithmetic computation were fully accounted for by visual form perception. These results suggest that reading comprehension and arithmetic computation might share a similar visual form processing mechanism.

Connectivity of the Human Number Form Area Reveals Development of a Cortical Network for Mathematics

The adult brain contains cortical areas thought to be specialized for the analysis of numbers (the putative number form area, NFA) and letters (the visual word form area, VWFA). Although functional development of the VWFA has been investigated, it is largely unknown when and how the NFA becomes specialized and connected to the rest of the brain. One hypothesis is that NFA and VWFA derive their special functions through differential connectivity, but the development of this differential connectivity has not been shown. Here, we mapped the resting state connectivity of NFA and VWFA to the rest of the brain in a large sample (n = 437) of individuals (age 3.2-21 years). We show that within NFA-math network and within VWFA-reading network the strength of connectivity increases with age. The right NFA is significantly connected to the right intraparietal cortex already at the earliest age tested (age 3), before formal mathematical education has begun. This connection might support or enable an early understanding of magnitude or numerosity In contrast, the functional connectivity from NFA to the left anterior intraparietal cortex and to the right dorsolateral prefrontal cortex is not different from the functional connectivity of VWFA to these regions until around 12-14 years of age. The increase in connectivity to these regions was associated with a gradual increase in mathematical ability in an independent sample. In contrast, VWFA connects significantly to Broca's region around age 6, and this connectivity is correlated with reading ability. These results show how the differential connectivity of the networks for mathematics and reading slowly emerges through years of training and education.

Neurocognitive mechanisms of digit processing and their relationship with mathematics competence

The dominant model of number processing suggests the existence of a Number Form Area (NFA) in the inferior temporal gyrus (ITG) that supports the processing of Arabic digits as visual symbols of number. However, studies have produced inconsistent evidence for the presence and laterality of digit-specific ITG activity. Furthermore, whether any such activity relates to mathematical competence is unknown. This study investigated these two issues using functional magnetic resonance imaging. Thirty-two adults performed digit and letter detection tasks and reading and mathematics tests. During digit detection, participants determined whether digits were present in a string of letters (e.g., AH3NR versus AHTNR). During letter detection, participants determined whether letters were present in a string of digits (e.g., 93R78 versus 93478). Results showed four clusters in frontal, occipital, and temporal regions for digit detection, including a left ITG cluster. Five clusters in frontal, parietal, occipital, and temporal regions were associated with letter detection, including a left ITG cluster. Digit and letter-related ITG clusters were spatially distinct; however, a direct contrast of digit and letter processing did not reveal greater activity in the left ITG for digit detection. Whole brain correlations showed greater digit-related activity in the right ITG for participants with higher calculation skills, but there was no correlation between letter activity and calculation skills. Together, our results suggest functional localization, but not specialization, for digits in the left ITG and provide the first evidence of a relationship between calculation skills and digit processing in the right ITG.

Word deafness with preserved number word perception

We describe the performance of an aphasic individual, K.A., who showed a selective impairment affecting his ability to perceive spoken language, while largely sparing his ability to perceive written language and to produce spoken language. His spoken perception impairment left him unable to distinguish words or nonwords that differed on a single phoneme and he was no better than chance at auditory lexical decision or single spoken word and single picture matching with phonological foils. Strikingly, despite this profound impairment, K.A. showed a selective sparing in his ability to perceive number words, which he was able to repeat and comprehend largely without error. This case adds to a growing literature demonstrating modality-specific dissociations between number word and non-number word processing. Because of the locus of K.A.'s speech perception deficit for non-number words, we argue that this distinction between number word and non-number word processing arises at a sublexical level of representations in speech perception, in a parallel fashion to what has previously been argued for in the organization of the sublexical level of representation for speech production.

Meta-analytic evidence for a core problem solving network across multiple representational domains

Problem solving is a complex skill engaging multi-stepped reasoning processes to find unknown solutions. The breadth of real-world contexts requiring problem solving is mirrored by a similarly broad, yet unfocused neuroimaging literature, and the domain-general or context-specific brain networks associated with problem solving are not well understood. To more fully characterize those brain networks, we performed activation likelihood estimation meta-analysis on 280 neuroimaging problem solving experiments reporting 3166 foci from 1919 individuals across 131 papers. The general map of problem solving revealed broad fronto-cingulo-parietal convergence, regions similarly identified when considering separate mathematical, verbal, and visuospatial problem solving domain-specific analyses. Conjunction analysis revealed a common network supporting problem solving across diverse contexts, and difference maps distinguished functionally-selective sub-networks specific to task type. Our results suggest cooperation between representationally specialized sub-network and whole-brain systems provide a neural basis for problem solving, with the core network contributing general purpose resources to perform cognitive operations and manage problem demand. Further characterization of cross-network dynamics could inform neuroeducational studies on problem solving skill development.

Examining the Triple Code Model in numerical cognition: An fMRI study

The Triple Code Model (TCM) of numerical cognition argues for the existence of three representational codes for number: Arabic digits, verbal number words, and analog nonsymbolic magnitude representations, each subserved by functionally dissociated neural substrates. Despite the popularity of the TCM, no study to date has explored all three numerical codes within one fMRI paradigm. We administered three tasks, associated with each of the aforementioned numerical codes, in order to explore the neural correlates of numerosity processing in a sample of adults (N = 46). Independent task-control contrast analyses revealed task-dependent activity in partial support of the model, but also highlight the inherent complexity of a distributed and overlapping fronto-parietal network involved in all numerical codes. The results indicate that the TCM correctly predicts the existence of some functionally dissociated neural substrates, but requires an update that accounts for interactions with attentional processes. Parametric contrasts corresponding to differences in task difficulty revealed specific neural correlates of the distance effect, where closely spaced numbers become more difficult to discriminate than numbers spaced further apart. A conjunction analysis illustrated overlapping neural correlates across all tasks, in line with recent proposals for a fronto-parietal network of number processing. We additionally provide tentative results suggesting the involvement of format-independent numerosity-sensitive retinotopic maps in the early visual stream, extending previous findings of nonsymbolic stimulus selectivity. We discuss the functional roles of the components associated with the model, as well as the purported fronto-parietal network, and offer arguments in favor of revising the TCM.

Gray Bananas and a Red Letter A - From Synesthetic Sensation to Memory Colors

Grapheme-color synesthesia is a condition in which objectively achromatic graphemes induce concurrent color experiences. While it was long thought that the colors emerge during perception, there is growing support for the view that colors are integral to synesthetes' cognitive representations of graphemes. In this work, we review evidence for two opposing theories positing either a perceptual or cognitive origin of concurrent colors: the cross-activation theory and the conceptual-mediation model. The review covers results on inducer and concurrent color processing as well as findings concerning the brain structure and grapheme-color mappings in synesthetes and trained mappings in nonsynesthetes. The results support different aspects of both theories. Finally, we discuss how research on memory colors could provide a new perspective in the debate about the level of processing at which the synesthetic colors occur.

A preference for mathematical processing outweighs the selectivity for Arabic numbers in the inferior temporal gyrus

A region in the posterior inferior temporal gyrus (ITG), referred to as the number form area (NFA, here ITG-numbers) has been implicated in the visual processing of Arabic numbers. However, it is unknown if this region is specifically involved in the visual encoding of Arabic numbers per se or in mathematical processing more broadly. Using functional magnetic resonance imaging (fMRI) during experiments that systematically vary tasks and stimuli, we find that mathematical processing, not preference to Arabic numbers, consistently drives both mean and distributed responses in the posterior ITG. While we replicated findings of higher responses in ITG-numbers to numbers than other visual stimuli during a 1-back task, this preference to numbers was abolished when participants engaged in mathematical processing. In contrast, an ITG region (ITG-math) that showed higher responses during an adding task vs. other tasks maintained this preference for mathematical processing across a wide range of stimuli including numbers, number/letter morphs, hands, and dice. Analysis of distributed responses across an anatomically-defined posterior ITG expanse further revealed that mathematical task but not Arabic number form can be successfully and consistently decoded from these distributed responses. Together, our findings suggest that the function of neuronal regions in the posterior ITG goes beyond the specific visual processing of Arabic numbers. We hypothesize that they ascribe numerical content to the visual input, irrespective of the format of the stimulus.

Neuroanatomical basis of number synaesthesias: A voxel-based morphometry study

In synaesthesia, a specific sensory dimension leads to an involuntary sensation in another sensory dimension not commonly associated with it; for example, synaesthetes may experience a specific colour when listening or thinking of numbers or letters. Large-scale behavioural studies provide a rich description of different synaesthesia phenotypes, and a great amount of research has been oriented to uncovering whether a single or multiple brain mechanisms underlie these various synaesthesia phenotypes. Interestingly, most of the synaesthetic inducers are conceptual stimuli such as numbers, letters, and months. However, the impact of these concepts on the synaesthetic brain remains largely unexplored. Numbers appear as the most typical inducer in two common types of synaesthesia: grapheme-colour and sequence-space. Numbers are symbols that denote quantity information and their processing recruits a specific neural network. Therefore, numbers may play an important role in the brain mechanisms underlying some types of synaesthesia. We used voxel-based morphometry (VBM) to compare grey matter (GM) volume in synaesthetes and controls. Relative to controls, synaesthetes showed increase in GM in the right amygdala and in the left cerebellum. Within the synaestheste group, comparing synaesthetes who reported numbers as the inducer with synaesthetes who reported other stimuli as the inducer revealed increase in GM in the left angular gyrus, which is associated with the verbal aspect of number processing. These results reveal neuroanatomical differences between synaesthetes and controls, and show the impact of the type of inducer in the synaesthetic brain. We discuss these findings in line with current neurobiological models of synaesthesia.

Slower saccadic reading in Parkinson's disease

Idiopathic Parkinson's Disease (PD) is characterized by degeneration of dopaminergic and other neurons, leading to motor and non-motor deficits. Abnormal eye movements in PD, including fixations, saccades, and convergence, are well described. However, saccadic reading, which requires serial and alternating saccades and fixations, is not well studied, despite its obvious impact on the quality of life. In this study, we assessed saccadic reading using variations of the King-Devick (KD) test, a rapid single digit number naming test, as a way to assess the ability to make serial left-to-right ocular motor movements necessary for reading. We recruited 42 treated PD patients and 80 age-matched controls and compared their reading times with a variety of measures, including age, duration of disease, Unified Parkinson's Disease Rating Scale (UPDRS), the National Eye Institute 25-Item Visual Functioning Questionnaire 25 (VFQ-25), and Montreal Cognitive assessment (MoCA) test. The subjects performed 4 trials of reading 120 single digit numbers aloud as fast as possible without making errors. In each trial, they read 3 pages (KD1, KD2, and KD3), and each page contained 40 numbers per page in 8 lines with 5 numbers/line. We found that PD patients read about 20% slower than controls on all tests (KD1, 2, and 3 tests) (p < 0.02), and both groups read irregularly spaced numbers slower than regularly spaced numbers. Having lines between numbers to guide reading (KD1 tests) did not impact reading time in both PD and controls, but increased visual crowding as a result of decreased spacing between numbers (KD3 tests) was associated with significantly slower reading times in both PD and control groups. Our study revealed that saccadic reading is slower in PD, but controls and PD patients are both impacted by visuospatial planning challenges posed by increased visual crowding and irregularity of number spacing. Reading time did not correlate with UPDRS or MoCA scores in PD patients but significantly correlated with age, duration of disease, and VFQ-25 scores. The presence of convergence insufficiency did not significantly correlate with reading time in PD patients, although on average there was slower reading time in those with convergence insufficiency by 8 s (p = 0.2613). We propose that a simple reading task using 120 single-digit numbers can be used as a screening tool in the clinical setting to assess functional ocular motor difficulties in Parkinson's disease that can have a profound impact on quality of life.

Evaluation of the Triple Code Model of numerical processing-Reviewing past neuroimaging and clinical findings

This review reconciles past findings on numerical processing with key assumptions of the most predominant model of arithmetic in the literature, the Triple Code Model (TCM). This is implemented by reporting diverse findings in the literature ranging from behavioral studies on basic arithmetic operations over neuroimaging studies on numerical processing to developmental studies concerned with arithmetic acquisition, with a special focus on developmental dyscalculia (DD). We evaluate whether these studies corroborate the model and discuss possible reasons for contradictory findings. A separate section is dedicated to the transfer of TCM to arithmetic development and to alternative accounts focusing on developmental questions of numerical processing. We conclude with recommendations for future directions of arithmetic research, raising questions that require answers in models of healthy as well as abnormal mathematical development.

WHAT THIS PAPER ADDS

This review assesses the leading model in the field of arithmetic processing (Triple Code Model) by presenting knowledge from interdisciplinary research. It assesses the observed contradictory findings and integrates the resulting opposing viewpoints. The focus is on the development of arithmetic expertise as well as abnormal mathematical development. The original aspect of this article is that it points to a gap in research on these topics and provides possible solutions for future models.

Differential contributions to the interception of occluded ballistic trajectories by the temporoparietal junction, area hMT/V5+, and the intraparietal cortex

The ability to catch objects when transiently occluded from view suggests their motion can be extrapolated. Intraparietal cortex (IPS) plays a major role in this process along with other brain structures, depending on the task. For example, interception of objects under Earth's gravity effects may depend on time-to-contact predictions derived from integration of visual signals processed by hMT/V5+ with a priori knowledge of gravity residing in the temporoparietal junction (TPJ). To investigate this issue further, we disrupted TPJ, hMT/V5+, and IPS activities with transcranial magnetic stimulation (TMS) while subjects intercepted computer-simulated projectile trajectories perturbed randomly with either hypo- or hypergravity effects. In experiment 1, trajectories were occluded either 750 or 1,250 ms before landing. Three subject groups underwent triple-pulse TMS (tpTMS, 3 pulses at 10 Hz) on one target area (TPJ | hMT/V5+ | IPS) and on the vertex (control site), timed at either trajectory perturbation or occlusion. In experiment 2, trajectories were entirely visible and participants received tpTMS on TPJ and hMT/V5+ with same timing as experiment 1 tpTMS of TPJ, hMT/V5+, and IPS affected differently the interceptive timing. TPJ stimulation affected preferentially responses to 1-g motion, hMT/V5+ all response types, and IPS stimulation induced opposite effects on 0-g and 2-g responses, being ineffective on 1-g responses. Only IPS stimulation was effective when applied after target disappearance, implying this area might elaborate memory representations of occluded target motion. Results are compatible with the idea that IPS, TPJ, and hMT/V5+ contribute to distinct aspects of visual motion extrapolation, perhaps through parallel processing.NEW & NOTEWORTHY Visual extrapolation represents a potential neural solution to afford motor interactions with the environment in the face of missing information. We investigated relative contributions by temporoparietal junction (TPJ), hMT/V5+, and intraparietal cortex (IPS), cortical areas potentially involved in these processes. Parallel organization of visual extrapolation processes emerged with respect to the target's motion causal nature: TPJ was primarily involved for visual motion congruent with gravity effects, IPS for arbitrary visual motion, whereas hMT/V5+ contributed at earlier processing stages.

Development of children's identity and position processing for letter, digit, and symbol strings: A cross-sectional study of the primary school years

Letter recognition and digit recognition are critical skills for literate adults, yet few studies have considered the development of these skills in children. We conducted a nine-alternative forced-choice (9AFC) partial report task with strings of letters and digits, with typographical symbols (e.g., $, @) as a control, to investigate the development of identity and position processing in children. This task allows for the delineation of identity processing (as overall accuracy) and position coding (as the proportion of position errors). Our participants were students in Grade 1 to Grade 6, allowing us to track the development of these abilities across the primary school years. Our data suggest that although digit processing and letter processing end up with many similarities in adult readers, the developmental trajectories for identity and position processing for the two character types differ. Symbol processing showed little developmental change in terms of identity or position accuracy. We discuss the implications of our results for theories of identity and position coding: modified receptive field, multiple-route model, and lexical tuning. Despite moderate success for some theories, considerable theoretical work is required to explain the developmental trajectories of letter processing and digit processing, which might not be as closely tied in child readers as they are in adult readers.

Numbers and functional lateralization: A visual half-field and dichotic listening study in proficient bilinguals

Potential links between language and numbers and the laterality of symbolic number representations in the brain are still debated. Furthermore, reports on bilingual individuals indicate that the language-number interrelationships might be quite complex. Therefore, we carried out a visual half-field (VHF) and dichotic listening (DL) study with action words and different forms of symbolic numbers used as stimuli to test the laterality of word and number processing in single-, dual-language and mixed -task and language- contexts. Experiment 1 (VHF) showed a significant right visual field/left hemispheric advantage in response accuracy for action word, as compared to any form of symbolic number processing. Experiment 2 (DL) revealed a substantially reversed effect - a significant right ear/left hemisphere advantage for arithmetic operations as compared to action word processing, and in response times in single- and dual-language contexts for number vs. action words. All these effects were language independent. Notably, for within-task response accuracy compared across modalities significant differences were found in all studied contexts. Thus, our results go counter to findings showing that action-relevant concepts and words, as well as number words are represented/processed primarily in the left hemisphere. Instead, we found that in the auditory context, following substantial engagement of working memory (here: by arithmetic operations), there is a subsequent functional reorganization of processing single stimuli, whether verbs or numbers. This reorganization - their weakened laterality - at least for response accuracy is not exclusive to processing of numbers, but the number of items to be processed. For response times, except for unpredictable tasks in mixed contexts, the "number problem" is more apparent. These outcomes are highly relevant to difficulties that simultaneous translators encounter when dealing with lengthy auditory material in which single items such as number words (and possibly other types of key words) need to be emphasized. Our results may also shed a new light on the "mathematical savant problem".

The SNARC effect in two dimensions: Evidence for a frontoparallel mental number plane

The existence of an association between numbers and space is known for a long time. The most prominent demonstration of this relationship is the spatial numerical association of response codes (SNARC) effect, describing the fact that participants' reaction times are shorter with the left hand for small numbers and with the right hand for large numbers, when being asked to judge the parity of a number (Dehaene et al., J. Exp. Psychol., 122, 371-396, 1993). The SNARC effect is commonly seen as support for the concept of a mental number line, i.e. a mentally conceived line where small numbers are represented more on the left and large numbers are represented more on the right. The SNARC effect has been demonstrated for all three cardinal axes and recently a transverse SNARC plane has been reported (Chen et al., Exp. Brain Res., 233(5), 1519-1528, 2015). Here, by employing saccadic responses induced by auditory or visual stimuli, we measured the SNARC effect within the same subjects along the horizontal (HM) and vertical meridian (VM) and along the two interspersed diagonals. We found a SNARC effect along HM and VM, which allowed predicting the occurrence of a SNARC effect along the two diagonals by means of linear regression. Importantly, significant differences in SNARC strength were found between modalities. Our results suggest the existence of a frontoparallel mental number plane, where small numbers are represented left and down, while large numbers are represented right and up. Together with the recently described transverse mental number plane our findings provide further evidence for the existence of a three-dimensional mental number space.