Individual differences in left parietal white matter predict math scores on the Preliminary Scholastic Aptitude Test

The inferior fronto-occipital fasciculus correlates with early precursors of mathematics and reading before the start of formal schooling

Diffusion-weighted imaging studies in preschoolers have almost exclusively been done in the field of reading. As a result, virtually nothing is known about white matter tracts associated with individual differences in mathematics at this age. Studying the preschoolers' brain is crucial because it allows us to identify individual differences in brain anatomy without influences of formal mathematics and reading instruction. To fill this gap, we investigated for the first time before the start of formal school entry the associations between white matter tracts and precursors of mathematics and reading simultaneously. We also investigated whether these associations were specific to mathematics and to reading, or not. We focused on four bilateral white matter tracts (arcuate fasciculus (direct, anterior), inferior fronto-occipital fasciculus, inferior longitudinal fasciculus), which have been previously correlated with mathematical performance in older children and with reading performance in children of a similar age as the current study. Participants were 56 5-year-old children (Mage = 67 months; SD = 1.8), none of which received formal instruction. Our results showed an association between the bilateral inferior fronto-occipital fasciculus and precursors of mathematics (numerical ordering, numeral knowledge) and reading (phonological awareness, letter knowledge). Follow-up regression analyses revealed that the associations found with the inferior fronto-occipital fasciculus were neither specific to mathematics nor specific to reading. These findings suggest that, already before the start of formal schooling, the inferior fronto-occipital fasciculus might be related to the neural overlap between mathematics and reading. This overlap potentially reflects one of their many shared mechanisms, such as the reliance on phonological codes or the processing of visual symbols, and these mechanisms should be exploited in future studies.

Positive or negative environmental modulations on human brain development: the morpho-functional outcomes of music training or stress

In the last couple of decades, the study of human living brain has benefitted of neuroimaging and non-invasive electrophysiological techniques, which are particularly valuable during development. A number of studies allowed to trace the usual stages leading from pregnancy to adult age, and relate them to functional and behavioral measurements. It was also possible to explore the effects of some interventions, behavioral or not, showing that the commonly followed pathway to adulthood may be steered by external interventions. These events may result in behavioral modifications but also in structural changes, in some cases limiting plasticity or extending/modifying critical periods. In this review, we outline the healthy human brain development in the absence of major issues or diseases. Then, the effects of negative (different stressors) and positive (music training) environmental stimuli on brain and behavioral development is depicted. Hence, it may be concluded that the typical development follows a course strictly dependent from environmental inputs, and that external intervention can be designed to positively counteract negative influences, particularly at young ages. We also focus on the social aspect of development, which starts in utero and continues after birth by building social relationships. This poses a great responsibility in handling children education and healthcare politics, pointing to social accountability for the responsible development of each child.

Changes in the superior longitudinal fasciculus and anterior thalamic radiation in the left brain are associated with developmental dyscalculia

Developmental dyscalculia is a neurodevelopmental disorder specific to arithmetic learning even with normal intelligence and age-appropriate education. Difficulties often persist from childhood through adulthood lowering the individual's quality of life. However, the neural correlates of developmental dyscalculia are poorly understood. This study aimed to identify brain structural connectivity alterations in developmental dyscalculia. All participants were recruited from a large scale, non-referred population sample in a longitudinal design. We studied 10 children with developmental dyscalculia (11.3 ± 0.7 years) and 16 typically developing peers (11.2 ± 0.6 years) using diffusion-weighted magnetic resonance imaging. We assessed white matter microstructure with tract-based spatial statistics in regions-of-interest tracts that had previously been related to math ability in children. Then we used global probabilistic tractography for the first time to measure and compare tract length between developmental dyscalculia and typically developing groups. The high angular resolution diffusion-weighted magnetic resonance imaging and crossing-fiber probabilistic tractography allowed us to evaluate the length of the pathways compared to previous studies. The major findings of our study were reduced white matter coherence and shorter tract length of the left superior longitudinal/arcuate fasciculus and left anterior thalamic radiation in the developmental dyscalculia group. Furthermore, the lower white matter coherence and shorter pathways tended to be associated with the lower math performance. These results from the regional analyses indicate that learning, memory and language-related pathways in the left hemisphere might be related to developmental dyscalculia in children.

Cognition's dependence on functional network integrity with age is conditional on structural network integrity

Maintaining good cognitive function is crucial for well-being across the lifespan. We proposed that the degree of cognitive maintenance is determined by the functional interactions within and between large-scale brain networks. Such connectivity can be represented by the white matter architecture of structural brain networks that shape intrinsic neuronal activity into integrated and distributed functional networks. We explored how the function-structure connectivity convergence, and the divergence of functional connectivity from structural connectivity, contribute to the maintenance of cognitive function across the adult lifespan. Multivariate analyses were used to investigate the relationship between function-structure connectivity convergence and divergence with multivariate cognitive profiles, respectively. Cognitive function was increasingly dependent on function-structure connectivity convergence as age increased. The dependency of cognitive function on connectivity was particularly strong for high-order cortical networks and subcortical networks. The results suggest that brain functional network integrity sustains cognitive functions in old age, as a function of the integrity of the brain's structural connectivity.

Identifying the Neural Bases of Math Competence Based on Structural and Functional Properties of the Human Brain

Human populations show large individual differences in math performance and math learning abilities. Early math skill acquisition is critical for providing the foundation for higher quantitative skill acquisition and succeeding in modern society. However, the neural bases underlying individual differences in math competence remain unclear. Modern neuroimaging techniques allow us to not only identify distinct local cortical regions but also investigate large-scale neural networks underlying math competence both structurally and functionally. To gain insights into the neural bases of math competence, this review provides an overview of the structural and functional neural markers for math competence in both typical and atypical populations of children and adults. Although including discussion of arithmetic skills in children, this review primarily focuses on the neural markers associated with complex math skills. Basic number comprehension and number comparison skills are outside the scope of this review. By synthesizing current research findings, we conclude that neural markers related to math competence are not confined to one particular region; rather, they are characterized by a distributed and interconnected network of regions across the brain, primarily focused on frontal and parietal cortices. Given that human brain is a complex network organized to minimize the cost of information processing, an efficient brain is capable of integrating information from different regions and coordinating the activity of various brain regions in a manner that maximizes the overall efficiency of the network to achieve the goal. We end by proposing that frontoparietal network efficiency is critical for math competence, which enables the recruitment of task-relevant neural resources and the engagement of distributed neural circuits in a goal-oriented manner. Thus, it will be important for future studies to not only examine brain activation patterns of discrete regions but also examine distributed network patterns across the brain, both structurally and functionally.

Dysfunctions associated with the intraparietal sulcus and a distributed network in individuals with math learning difficulties: An ALE meta-analysis

Math learning difficulty (MLD) is a learning disorder characterized by persistent impairments in the understanding and application of numbers independent of intelligence or schooling. The current study aims to review existing neuroimaging studies to characterize the neurobiological basis in MLD for their quantity and arithmetic dysfunctions. We identified a total of 24 studies with 728 participants through the literature. Using the activation likelihood estimate (ALE) method, we found that the most consistent neurobiological dysfunction in MLD was observed in the right intraparietal sulcus (IPS) with distinct patterns of the anterior and posterior aspects. Meanwhile, neurobiological dysfunctions were also observed in a distributed network including the fusiform gyrus, inferior temporal gyrus, insula, prefrontal cortex, anterior cingulate cortex, and claustrum. Our results suggest a core dysfunction in the right anterior IPS and left fusiform gyrus with atypically upregulated functions in brain regions for attention, working memory, visual processing, and motivation, serving as the neurobiological basis of MLD.

White matter microstructure of superior longitudinal fasciculus II is associated with intelligence and treatment response of negative symptoms in patients with schizophrenia

Although the potential role of superior longitudinal fasciculus (SLF) in intellectual deficits and treatment response (TR) in patients with schizophrenia (SZ) has been previously described, little is known about the white-matter (WM) integrity of SLF subcomponents (SLF I, II, III, and arcuate fasciculus) and their particular relationships with the clinical presentations of the illness. This study examined the associations between fractional anisotropy (FA) of SLF subcomponents and intelligence level and 6-month treatment response (TR) of negative symptoms (NS) in patients with SZ. At baseline, 101 patients with SZ and 101 healthy controls (HCs) underwent structural magnetic resonance imaging. Voxel-wise group comparison analysis showed significant SLF FA reductions in patients with SZ compared with HCs. Voxel-wise correlation analyses revealed significant positive correlations of FAs of right SLF II with Korean–Wechsler Adult Intelligence Scale at baseline and the percentage reduction of negative syndrome subscale of the Positive and Negative Syndrome Scales at 6 months. These findings suggest that aberrance in WM microstructure in SLF II may be associated with intellectual deficits in patients with SZ and TR of NS, which may support the potential role of SLF II as a novel neuroimaging biomarker for clinical outcomes of the illness.

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.

Brain Mapping of Behavioral Domains Using Multi-Scale Networks and Canonical Correlation Analysis

Simultaneous mapping of multiple behavioral domains into brain networks remains a major challenge. Here, we shed some light on this problem by employing a combination of machine learning, structural and functional brain networks at different spatial resolutions (also known as scales), together with performance scores across multiple neurobehavioral domains, including sensation, motor skills, and cognition. Provided by the Human Connectome Project, we make use of three cohorts: 640 participants for model training, 160 subjects for validation, and 200 subjects for model performance testing thus enhancing prediction generalization. Our modeling consists of two main stages, namely dimensionality reduction in brain network features at multiple scales, followed by canonical correlation analysis, which determines an optimal linear combination of connectivity features to predict multiple behavioral performance scores. To assess the differences in the predictive power of each modality, we separately applied three different strategies: structural unimodal, functional unimodal, and multimodal, that is, structural in combination with functional features of the brain network. Our results show that the multimodal association outperforms any of the unimodal analyses. Then, to answer which human brain structures were most involved in predicting multiple behavioral scores, we simulated different synthetic scenarios in which in each case we completely deleted a brain structure or a complete resting state network, and recalculated performance in its absence. In deletions, we found critical structures to affect performance when predicting single behavioral domains, but this occurred in a lesser manner for prediction of multi-domain behavior. Overall, our results confirm that although there are synergistic contributions between brain structure and function that enhance behavioral prediction, brain networks may also be mutually redundant in predicting multidomain behavior, such that even after deletion of a structure, the connectivity of the others can compensate for its lack in predicting behavior.

Development of brain white matter and math computation ability in children born very preterm and full-term

Children born very preterm (VPT; <32 weeks' gestation) have alterations in brain white matter and poorer math ability than full-term (FT) peers. Diffusion-weighted magnetic resonance imaging studies suggest a link between white matter microstructure and math in VPT and FT children, although longitudinal studies using advanced modelling are lacking. In a prospective longitudinal cohort of VPT and FT children we used Fixel-Based Analysis to investigate associations between maturation of white matter fibre density (FD), fibre-bundle cross-section (FC), and combined fibre density and cross-section (FDC) and math computation ability at 7 (n = 136 VPT; n = 32 FT) and 13 (n = 130 VPT; n = 44 FT) years, as well as between change in white matter and math computation ability from 7 to 13 years (n = 103 VPT; n = 21 FT). In both VPT and FT children, higher FD, FC and FDC in visual, sensorimotor and cortico-thalamic/thalamo-cortical white matter tracts were associated with better math computation ability at 7 and 13 years. Longitudinally, accelerated maturation of the posterior body of the corpus callosum (FDC) was associated with greater math computation development. White matter-math associations were similar for VPT and FT children. In conclusion, white matter maturation is associated with math computation ability across late childhood, irrespective of birth group.

Developmental brain dynamics of numerical and arithmetic abilities

The development of numerical and arithmetic abilities constitutes a crucial cornerstone in our modern and educated societies. Difficulties to acquire these central skills can lead to severe consequences for an individual's well-being and nation's economy. In the present review, we describe our current broad understanding of the functional and structural brain organization that supports the development of numbers and arithmetic. The existing evidence points towards a complex interaction among multiple domain-specific (e.g., representation of quantities and number symbols) and domain-general (e.g., working memory, visual-spatial abilities) cognitive processes, as well as a dynamic integration of several brain regions into functional networks that support these processes. These networks are mainly, but not exclusively, located in regions of the frontal and parietal cortex, and the functional and structural dynamics of these networks differ as a function of age and performance level. Distinctive brain activation patterns have also been shown for children with dyscalculia, a specific learning disability in the domain of mathematics. Although our knowledge about the developmental brain dynamics of number and arithmetic has greatly improved over the past years, many questions about the interaction and the causal involvement of the abovementioned functional brain networks remain. This review provides a broad and critical overview of the known developmental processes and what is yet to be discovered.

Emerging neurodevelopmental perspectives on mathematical learning

Strong foundational skills in mathematical problem solving, acquired in early childhood, are critical not only for success in the science, technology, engineering, and mathematical (STEM) fields but also for quantitative reasoning in everyday life. The acquisition of mathematical skills relies on protracted interactive specialization of functional brain networks across development. Using a systems neuroscience approach, this review synthesizes emerging perspectives on neurodevelopmental pathways of mathematical learning, highlighting the functional brain architecture that supports these processes and sources of heterogeneity in mathematical skill acquisition. We identify the core neural building blocks of numerical cognition, anchored in the posterior parietal and ventral temporal-occipital cortices, and describe how memory and cognitive control systems, anchored in the medial temporal lobe and prefrontal cortex, help scaffold mathematical skill development. We highlight how interactive specialization of functional circuits influences mathematical learning across different stages of development. Functional and structural brain integrity and plasticity associated with math learning can be examined using an individual differences approach to better understand sources of heterogeneity in learning, including cognitive, affective, motivational, and sociocultural factors. Our review emphasizes the dynamic role of neurodevelopmental processes in mathematical learning and cognitive development more generally.

Cognitive Correlates of Math Performance in School-Aged Children with Sickle Cell Disease and Silent Cerebral Infarcts

OBJECTIVE

Attention, processing speed, executive functioning, and math difficulties are common in youth with sickle cell disease (SCD) with silent cerebral infarcts (SCI). This study investigated the cognitive underpinnings of math difficulties in children with SCD and SCI.

METHOD

Youth (n = 68) with SCD and SCI completed measures of attention [Digit Span forward (DSF); Conners Continuous Performance Test-Third Edition/Kiddie Conners Continuous Performance Test-Second Edition (CPT-3/KCPT-2)]; working memory [Wechsler Intelligence Scales (WPPSI-IV, WISC-IV, WISC-V, WAIS-IV), Working Memory Index (WMI), Digit Span backwards (DSB)]; processing speed [WPPSI-IV, WISC-IV, WISC-V, WAIS-IV Processing Speed Index (PSI)]; math reasoning [Wechsler Individual Achievement Test-Third Edition (WIAT-III) Mathematics composite (MC)]; and math fluency [WIAT-III Math Fluency composite (MF)] as part of a clinical neuropsychological evaluation. Parent ratings of attention and executive functioning were obtained [Behavior Assessment System for Children-Third Edition (BASC-3), Behavior Rating Inventory of Executive Function (BRIEF)].

RESULTS

MC was positively correlated with WMI (r = 0.59, p = 0.00), PSI (r = 0.40, p < 0.001), DSF (r = 0.29, p = 0.03), DSB (r = 0.47, p < 0.001), and MF (r = 0.71, p < 0.001). Correlations between MC, sustained attention, and parent ratings were nonsignificant. The linear regression model using correlated variables was significant [F(4,51) = 8.29, R2 = 0.39, p < 0.001]. WMI was the only significant variable within the model (p = 0.02).

CONCLUSIONS

Working memory deficits account for significant variance in untimed mathematical performance in this population-consistent with other populations with white matter dysfunction. Interventions targeting both mathematics and working memory may be beneficial.

Spatial Ability in Children with Mathematics Learning Disorder (MLD) and Its Impact on Executive Functions

Mathematics Learning Disorder (MLD) has been found to be related to impairments in cognitive functions. Spatial ability (SA), which is made up of eight single but unified elements can be assumed to have a leading part in different areas of math skills. The first objective of this study was to explore differences in SA factors in 128 school children of third to sixth grade with and without MLD. The Flexibility of Closure, Closure Speed, Perceptual Speed, Visualization, Spatial Relation, Spatial Orientation, Spatial Temporal, and Wayfinding were measured through eight tasks. The second objective of the study was to explore the SA factors' ability to predict the performance of MLD participants in three executive functions. The results revealed that participants with MLD had poorer performance in all the SA tasks and it took longer to finish the visualization, spatial relation, and spatial orientation tasks compared to children with typical development (TD). Regression analysis indicated that some of the SA factors could predict working memory and cognitive flexibility, but they were unable to predict response inhibition. Regarding these results, applying SA factors in cognitive rehabilitation programs of children with MLD seems necessary.

Distinct functional and structural connections predict crystallised and fluid cognition in healthy adults

White matter pathways between neurons facilitate neuronal coactivation patterns in the brain. Insight into how these structural and functional connections underlie complex cognitive functions provides an important foundation with which to delineate disease‐related changes in cognitive functioning. Here, we integrate neuroimaging, connectomics, and machine learning approaches to explore how functional and structural brain connectivity relate to cognition. Specifically, we evaluate the extent to which functional and structural connectivity predict individual crystallised and fluid cognitive abilities in 415 unrelated healthy young adults (202 females) from the Human Connectome Project. We report three main findings. First, we demonstrate functional connectivity is more predictive of cognitive scores than structural connectivity, and, furthermore, integrating the two modalities does not increase explained variance. Second, we show the quality of cognitive prediction from connectome measures is influenced by the choice of grey matter parcellation, and, possibly, how that parcellation is derived. Third, we find that distinct functional and structural connections predict crystallised and fluid abilities. Taken together, our results suggest that functional and structural connectivity have unique relationships with crystallised and fluid cognition and, furthermore, studying both modalities provides a more comprehensive insight into the neural correlates of cognition.

Association between the superior longitudinal fasciculus and perceptual organization and working memory: A diffusion tensor imaging study

The superior longitudinal fasciculus (SLF) is a white matter structure that has long bidirectional projections among the prefrontal, temporal, occipital, and parietal cortices and extends over a wide area in a human brain. Recently, anatomical details of the SLF have been clarified using a diffusion tensor imaging (DTI) template of subjects from the Human Connectome Project. However, the neurobehavioral functions of the SLF have not been fully elucidated. It is speculated that the SLF contributes to a broad cognitive domain including visuospatial nonverbal cognitive ability and verbal memory ability because of its anatomical location; however, previous findings in imaging studies are inconsistent. Showing the contribution of the SLF to cognitive function may be important for improving our understanding of the functional role of white matter structures in the human brain. This study aimed to identify the relationship between DTI indices of the SLF and the Verbal Comprehension, Perceptual Organization, Working Memory and Processing Speed Indices of the Wechsler Adult Intelligence Scale-Third Edition using regression analysis, accounting for the effects of age, sex and scanner type in 583 healthy volunteers. We showed significant correlations between the fractional anisotropy of the left SLF and the Perceptual Organization Index (β = 0.21, p =  4.5×10^-4) and Working Memory Index (β = 0.19, p =  4.0×10^-4). These findings may have implications for the rehabilitation of cognitive function in patients with neurological disorders.

Association between white matter impairment and cognitive dysfunction in patients with ischemic Moyamoya disease

Background

Ischemic Moyamoya disease is one of the important causes of stroke, which leads to severe impairment in cognitive functions. This cognitive impairment occurs prior to stroke. However, the cognitive functions that are impaired and the mechanisms of these impairments have not been determined.

Methods

We analyzed 12 patients with Moyamoya disease and 12 controls. All participants underwent cognitive tests and magnetic resonance imaging (MRI) scans. The diffusion tensor imaging (DTI) data was processed using Tract-Based Spatial Statistics (TBSS). Significantly different white matter areas were correlated with different cognitive functions.

Results

There were significant differences in intelligence and subtraction between the patients and controls (p < 0.05). The parameters of DTI such as fractional anisotropy (FA), mean diffusivity (MD), axial diffusivity (AD), and radial diffusivity (RD) have different changes in anterior thalamic radiation, inferior fronto-occipital fasciculus (IFO), superior longitudinal fasciculus (SLF), uncinate fasciculus (UF), inferior longitudinal fasciculus, forceps minor, and other regions between the two groups.

Conclusion

Left UF and IFO may be the key brain regions affecting arithmetic function, while bilateral IFO has an effect on intelligence. RD and AD may be better indicators for early prediction of chronic white matter damage than FA, while MD tends to have a comprehensive indirect change. There is cognitive impairment in ischemic MMD, which is closely related to white matter impairment.

Trial registration

Clinical Trial Registration, Unique identifier: ChiCTR1900023610. Registered 4 June 2019 – Prospective study registered.

Learning-Challenged Youth Show an Abnormal Relationship Between Fronto-Parietal Myelination and Mathematical Ability

BACKGROUND AND PURPOSE

Differences in the microstructure of fronto-parietal white matter tracts have been associated with mathematical achievement. However, much of the supporting evidence relies on nonspecific diffusion-weighted magnetic resonance imaging, making it difficult to isolate the role of myelin in math ability.

METHODS

We used myelin water imaging to measure brain myelin. We related myelin water fraction (MWF) to Woodcock-Johnson III (WJ-III) basic math scores using region of interest (ROI) and tract-based spatial statistics (TBSS) analyses, in 14 typically developing and 36 learning challenged youth aged 9-17 years.

RESULTS

The ROI analysis found a positive relationship between fronto-parietal MWF and math in typically developing youth, but not in learning challenged youth. The relationship between fronto-parietal MWF and math observed in typically developing youth was fully mediated by age. No group differences in fronto-parietal MWF were found between typically developing and learning challenged youth. TBSS also found no group differences in MWF values. TBSS indicated math-MWF relationships extend beyond fronto-parietal tracts to descending and ascending projection tracts in typically developing youth. TBSS identified math-MWF relationships in the cerebral peduncles of learning challenged youth.

CONCLUSIONS

Our results suggest that in typically developing youth, brain myelination contributes to individual differences in basic math achievement. In contrast, youth with learning challenges appear to have less capacity to leverage myelin to improve math achievement.

Altered Functional Connectivity Observed at Rest in Children and Adolescents Prenatally Exposed to Alcohol

Studies of brain structure in fetal alcohol spectrum disorder (FASD) have shown the global and focal effects that prenatal alcohol exposure (PAE) has on the brain, suggesting but not measuring altered function in FASD. This study aimed to (1) identify resting-state functional networks in children and adolescents with FASD, (2) investigate functional connectivity differences compared with healthy controls, and (3) assess the links to cognitive deficits. Participants included 66 children/adolescents with FASD (aged 5.5-18.9 years) and 67 healthy controls (aged 5.8-18.5 years) scanned across four sites as part of the NeuroDevNet study. Six core functional networks with 27 regions of interest (ROIs) were examined using seed-based and ROI-to-ROI analyses. Average seed-based connectivity maps showed significant spatial overlap of positively correlated regions for all six core networks between FASD and controls, but there was less overlap for negatively correlated regions. ROI-to-ROI matrices demonstrated lower internetwork connectivity between regions primarily associated with the salience network (anterior cingulate cortex and bilateral insula), frontal-parietal network (bilateral posterior parietal cortex), and language network (right posterior superior temporal gyrus). Post hoc correlations of the FASD participants without medication revealed a relationship between functional connectivity and performance on two cognitive tests associated with mathematics ability and attention. Even though participants with PAE exhibit very similar intranetwork functional connectivity patterns as controls, their lower internetwork functional connectivity suggests underlying deficits in the functional network brain architecture that may be related to cognitive impairment.

The brain-structural correlates of mathematical expertise

Studies in several domains of expertise have established that experience-dependent plasticity brings about both functional and anatomical changes. However, little is known about how such changes come to shape the brain in the case of expertise acquired by professional mathematicians. Here, we aimed to identify cognitive and brain-structural (grey and white matter) characteristics of mathematicians as compared to non-mathematicians. Mathematicians and non-mathematician academics from the University of Oxford underwent structural and diffusion MRI scans, and were tested on a cognitive battery assessing working memory, attention, IQ, numerical and social skills. At the behavioural level, mathematical expertise was associated with better performance in domain-general and domain-specific dimensions. At the grey matter level, in a whole-brain analysis, behavioural performance correlated with grey matter density in left superior frontal gyrus – positively for mathematicians but negatively for non-mathematicians; in a region of interest analysis, we found in mathematicians higher grey matter density in the right superior parietal lobule, but lower grey matter density in the right intraparietal sulcus and in the left inferior frontal gyrus. In terms of white matter, there were no significant group differences in fractional anisotropy or mean diffusivity. These results reveal new insights into the relationship between mathematical expertise and grey matter metrics in brain regions previously implicated in numerical cognition, as well as in regions that have so far received less attention in this field. Further studies, based on longitudinal designs and cognitive training, could examine the conjecture that such cross-sectional findings arise from a bidirectional link between experience and structural brain changes that is itself subject to change across the lifespan.

Unique Mapping of Structural and Functional Connectivity on Cognition

The unique mapping of structural brain connectivity (SC) and functional brain connectivity (FC) on cognition is currently not well understood. It is not clear whether cognition is mapped via a global connectome pattern or instead is underpinned by several sets of distributed connectivity patterns. Moreover, we also do not know whether the spatial distributions of SC and FC that underlie cognition are overlapping or distinct. Here, we study the relationship between SC and FC and an array of psychological tasks in 609 subjects (males, 269; females, 340) from the Human Connectome Project. We identified several sets of connections that each uniquely map onto cognitive function. We found a small number of distributed SCs and a larger set of corticocortical and corticosubcortical FCs that express this association. Importantly, the SC and FC each show unique and distinct patterns of variance across subjects as they relate to cognition. The results suggest that a complete understanding of connectome underpinnings of cognition calls for a combination of the two modalities.SIGNIFICANCE STATEMENT Structural connectivity (SC), the physical white-matter inter-regional pathways in the brain, and functional connectivity (FC), the temporal coactivations between the activity of the brain regions, have each been studied extensively. Little is known, however, about the distribution of variance in connections as they relate to cognition. Here, in a large sample of subjects (N = 609), we showed that two sets of brain-behavior patterns capture the correlations between SC and FC with a wide range of cognitive tasks, respectively. These brain-behavior patterns reveal distinct sets of connections within the SC and the FC network and provide new evidence that SC and FC each provide unique information for cognition.

Rapid and widespread white matter plasticity during an intensive reading intervention

White matter tissue properties are known to correlate with performance across domains ranging from reading to math, to executive function. Here, we use a longitudinal intervention design to examine experience-dependent growth in reading skills and white matter in grade school-aged, struggling readers. Diffusion MRI data were collected at regular intervals during an 8-week, intensive reading intervention. These measurements reveal large-scale changes throughout a collection of white matter tracts, in concert with growth in reading skill. Additionally, we identify tracts whose properties predict reading skill but remain fixed throughout the intervention, suggesting that some anatomical properties stably predict the ease with which a child learns to read, while others dynamically reflect the effects of experience. These results underscore the importance of considering recent experience when interpreting cross-sectional anatomy–behavior correlations. Widespread changes throughout the white matter may be a hallmark of rapid plasticity associated with an intensive learning experience.

White matter properties correlate with cognitive performance in a number of domains. Here the authors show that altering a child’s educational environment though a targeted intervention program induces rapid, large-scale changes in the white matter, and that these changes track the learning process.

Arithmetic in the developing brain: A review of brain imaging studies

Brain imaging studies on academic achievement offer an exciting window on experience-dependent cortical plasticity, as they allow us to understand how developing brains change when children acquire culturally transmitted skills. This contribution focuses on the learning of arithmetic, which is quintessential to mathematical development. The nascent body of brain imaging studies reveals that arithmetic recruits a large set of interconnected areas, including prefrontal, posterior parietal, occipito-temporal and hippocampal areas. This network undergoes developmental changes in its function, connectivity and structure, which are not yet fully understood. This network only partially overlaps with what has been found in adults, and clear differences are observed in the recruitment of the hippocampus, which are related to the development of arithmetic fact retrieval. Despite these emerging trends, the literature remains scattered, particularly in the context of atypical development. Acknowledging the distributed nature of the arithmetic network, future studies should focus on connectivity and analytic approaches that investigate patterns of brain activity, coupled with a careful design of the arithmetic tasks and assessments of arithmetic strategies. Such studies will produce a more comprehensive understanding of how the arithmetical brain unfolds, how it changes over time, and how it is impaired in atypical development.

Children's academic attainment is linked to the global organization of the white matter connectome

Literacy and numeracy are important skills that are typically learned during childhood, a time that coincides with considerable shifts in large-scale brain organization. However, most studies emphasize focal brain contributions to literacy and numeracy development by employing case-control designs and voxel-by-voxel statistical comparisons. This approach has been valuable, but may underestimate the contribution of overall brain network organization. The current study includes children (N = 133 children; 86 male; mean age = 9.42, SD = 1.715; age range = 5.92-13.75y) with a broad range of abilities, and uses whole-brain structural connectomics based on diffusion-weighted MRI data. The results indicate that academic attainment is associated with differences in structural brain organization, something not seen when focusing on the integrity of specific regions. Furthermore, simulated disruption of highly-connected brain regions known as hubs suggests that the role of these regions for maintaining the architecture of the network may be more important than specific aspects of processing. Our findings indicate that distributed brain systems contribute to the etiology of difficulties with academic learning, which cannot be captured using a more traditional voxel-wise statistical approach.

No evidence for systematic white matter correlates of dyslexia and dyscalculia

Learning disabilities such as dyslexia, dyscalculia and their comorbid manifestation are prevalent, affecting as much as 15% of the population. Structural neuroimaging studies have indicated that these disorders can be related to differences in white matter integrity, although findings remain disparate. In this study, we used a unique design composed of individuals with dyslexia, dyscalculia, both disorders and controls, to systematically explore differences in fractional anisotropy across groups using diffusion tensor imaging. Specifically, we focused on the corona radiata and the arcuate fasciculus, two tracts associated with reading and mathematics in a number of previous studies. Using Bayesian hypothesis testing, we show that the present data favor the null model of no differences between groups for these particular tracts—a finding that seems to go against the current view but might be representative of the disparities within this field of research. Together, these findings suggest that structural differences associated with dyslexia and dyscalculia might not be as reliable as previously thought, with potential ramifications in terms of remediation.

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Previous literature indicates important discrepancies in structural differences associated with dyslexia and dyscalculia

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We explore the relationship between these disorders and fractional anisotropy, a measure of white matter integrity

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We show support for the null model in the corona radiata and the arcuate fasciculus

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This suggests that structural differences associated with these disorders are not as reliable as previously thought

Learning Morse Code Alters Microstructural Properties in the Inferior Longitudinal Fasciculus: A DTI Study

Learning relies on neuroplasticity, which has mainly been studied in gray matter (GM). However, there is mounting evidence indicating a critical role of white matter changes involved in learning processes. One of the most important learning processes in human development is language acquisition. However, due to the length of this learning process, it has been notoriously difficult to investigate the underlying neuroplastic changes. Here, we report a novel learning paradigm to assess the role of white matter plasticity for language acquisition. By acoustically presenting Morse Code (MC) using an in house developed audio book as a model for language-type learning, we generated a well-controlled learning environment that allows for the detection of subtle white matter changes related to language type learning in a much shorter time frame than usual language acquisition. In total 12 letters of the MC alphabet were learned within six learning session, which allowed study participants to perform a word recognition MC decoding task. In this study, we found that learning MC was associated with significant microstructural changes in the left inferior longitudinal fasciculus (ILF). The fractional anisotropy (FA) of this associative fiber bundle connecting the occipital and posterior temporal cortex with the temporal pole as well as the hippocampus and amygdala was increased. Furthermore, white matter plasticity was associated with task performance of MC decoding, indicating that the structural changes were related to learning efficiency. In conclusion, our findings demonstrate an important role of white matter neuroplasticity for acquiring a new language skill.

White matter connectivity and Internet gaming disorder

Internet use and on-line game play stimulate corticostriatal-limbic circuitry in both healthy subjects and subjects with Internet gaming disorder (IGD). We hypothesized that increased fractional anisotropy (FA) with decreased radial diffusivity (RD) would be observed in IGD subjects, compared with healthy control subjects, and that these white matter indices would be associated with clinical variables including duration of illness and executive function. We screened 181 male patients in order to recruit a large number (n = 58) of IGD subjects without psychiatric co-morbidity as well as 26 male healthy comparison subjects. Multiple diffusion-weighted images were acquired using a 3.0 Tesla magnetic resonance imaging scanner. Tract-based spatial statistics was applied to compare group differences in diffusion tensor imaging (DTI) metrics between IGD and healthy comparison subjects. IGD subjects had increased FA values within forceps minor, right anterior thalamic radiation, right corticospinal tract, right inferior longitudinal fasciculus, right cingulum to hippocampus and right inferior fronto-occipital fasciculus (IFOF) as well as parallel decreases in RD value within forceps minor, right anterior thalamic radiation and IFOF relative to healthy control subjects. In addition, the duration of illness in IGD subjects was positively correlated with the FA values (integrity of white matter fibers) and negatively correlated with RD scores (diffusivity of axonal density) of whole brain white matter. In IGD subjects without psychiatric co-morbidity, our DTI results suggest that increased myelination (increased FA and decreased RD values) in right-sided frontal fiber tracts may be the result of extended game play.

Brain Structural Integrity and Intrinsic Functional Connectivity Forecast 6 Year Longitudinal Growth in Children's Numerical Abilities

Early numerical proficiency lays the foundation for acquiring quantitative skills essential in today's technological society. Identification of cognitive and brain markers associated with long-term growth of children's basic numerical computation abilities is therefore of utmost importance. Previous attempts to relate brain structure and function to numerical competency have focused on behavioral measures from a single time point. Thus, little is known about the brain predictors of individual differences in growth trajectories of numerical abilities. Using a longitudinal design, with multimodal imaging and machine-learning algorithms, we investigated whether brain structure and intrinsic connectivity in early childhood are predictive of 6 year outcomes in numerical abilities spanning childhood and adolescence. Gray matter volume at age 8 in distributed brain regions, including the ventrotemporal occipital cortex (VTOC), the posterior parietal cortex, and the prefrontal cortex, predicted longitudinal gains in numerical, but not reading, abilities. Remarkably, intrinsic connectivity analysis revealed that the strength of functional coupling among these regions also predicted gains in numerical abilities, providing novel evidence for a network of brain regions that works in concert to promote numerical skill acquisition. VTOC connectivity with posterior parietal, anterior temporal, and dorsolateral prefrontal cortices emerged as the most extensive network predicting individual gains in numerical abilities. Crucially, behavioral measures of mathematics, IQ, working memory, and reading did not predict children's gains in numerical abilities. Our study identifies, for the first time, functional circuits in the human brain that scaffold the development of numerical skills, and highlights potential biomarkers for identifying children at risk for learning difficulties.

SIGNIFICANCE STATEMENT

Children show substantial individual differences in math abilities and ease of math learning. Early numerical abilities provide the foundation for future academic and professional success in an increasingly technological society. Understanding the early identification of poor math skills has therefore taken on great significance. This work provides important new insights into brain structure and connectivity measures that can predict longitudinal growth of children's math skills over a 6 year period, and may eventually aid in the early identification of children who might benefit from targeted interventions.

Abacus Training Affects Math and Task Switching Abilities and Modulates Their Relationships in Chinese Children

Our previous work demonstrated that abacus-based mental calculation (AMC), a traditional Chinese calculation method, could help children improve their math abilities (e.g. basic arithmetical ability) and executive function (e.g. working memory). This study further examined the effects of long-term AMC training on math ability in visual-spatial domain and the task switching component of executive function. More importantly, this study investigated whether AMC training modulated the relationship between math abilities and task switching. The participants were seventy 7-year-old children who were randomly assigned into AMC and control groups at primary school entry. Children in AMC group received 2-hour AMC training every week since primary school entry. On the contrary, children in the control group had never received any AMC training. Math and task switching abilities were measured one year and three years respectively after AMC training began. The results showed that AMC children performed better than their peers on math abilities in arithmetical and visual-spatial domains. In addition, AMC group responded faster than control group in the switching task, while no group difference was found in switch cost. Most interestingly, group difference was present in the relationships between math abilities and switch cost. These results implied the effect of AMC training on math abilities as well as its relationship with executive function.

A review on functional and structural brain connectivity in numerical cognition

Only recently has the complex anatomo-functional system underlying numerical cognition become accessible to evaluation in the living brain. We identified 27 studies investigating brain connectivity in numerical cognition. Despite considerable heterogeneity regarding methodological approaches, populations investigated, and assessment procedures implemented, the results provided largely converging evidence regarding the underlying brain connectivity involved in numerical cognition. Analyses of both functional/effective as well as structural connectivity have consistently corroborated the assumption that numerical cognition is subserved by a fronto-parietal network including (intra)parietal as well as (pre)frontal cortex sites. Evaluation of structural connectivity has indicated the involvement of fronto-parietal association fibers encompassing the superior longitudinal fasciculus dorsally and the external capsule/extreme capsule system ventrally. Additionally, commissural fibers seem to connect the bilateral intraparietal sulci when number magnitude information is processed. Finally, the identification of projection fibers such as the superior corona radiata indicates connections between cortex and basal ganglia as well as the thalamus in numerical cognition. Studies on functional/effective connectivity further indicated a specific role of the hippocampus. These specifications of brain connectivity augment the triple-code model of number processing and calculation with respect to how gray matter areas associated with specific number-related representations may work together.

Plasticity of left perisylvian white-matter tracts is associated with individual differences in math learning

Plasticity of white matter tracts is thought to be essential for cognitive development and academic skill acquisition in children. However, a dearth of high-quality diffusion tensor imaging (DTI) data measuring longitudinal changes with learning, as well as methodological difficulties in multi-time point tract identification have limited our ability to investigate plasticity of specific white matter tracts. Here, we examine learning-related changes of white matter tracts innervating inferior parietal, prefrontal and temporal regions following an intense 2-month math tutoring program. DTI data were acquired from 18 third grade children, both before and after tutoring. A novel fiber tracking algorithm based on a White Matter Query Language (WMQL) was used to identify three sections of the superior longitudinal fasciculus (SLF) linking frontal and parietal (SLF-FP), parietal and temporal (SLF-PT) and frontal and temporal (SLF-FT) cortices, from which we created child-specific probabilistic maps. The SLF-FP, SLF-FT, and SLF-PT tracts identified with the WMQL method were highly reliable across the two time points and showed close correspondence to tracts previously described in adults. Notably, individual differences in behavioral gains after 2 months of tutoring were specifically correlated with plasticity in the left SLF-FT tract. Our results extend previous findings of individual differences in white matter integrity, and provide important new insights into white matter plasticity related to math learning in childhood. More generally, our quantitative approach will be useful for future studies examining longitudinal changes in white matter integrity associated with cognitive skill development.

Single-digit arithmetic processing-anatomical evidence from statistical voxel-based lesion analysis

Different specific mechanisms have been suggested for solving single-digit arithmetic operations. However, the neural correlates underlying basic arithmetic (multiplication, addition, subtraction) are still under debate. In the present study, we systematically assessed single-digit arithmetic in a group of acute stroke patients (n = 45) with circumscribed left- or right-hemispheric brain lesions. Lesion sites significantly related to impaired performance were found only in the left-hemisphere damaged (LHD) group. Deficits in multiplication and addition were related to subcortical/white matter brain regions differing from those for subtraction tasks, corroborating the notion of distinct processing pathways for different arithmetic tasks. Additionally, our results further point to the importance of investigating fiber pathways in numerical cognition.

Left fronto-parietal white matter correlates with individual differences in children's ability to solve additions and multiplications: a tractography study

Functional neuroimaging data have pointed to the activation of a fronto-parietal network during calculation tasks, the activity of which is modulated by arithmetic operation and arithmetical competence. As the cortical brain regions of this network are distant, it is crucial to investigate the white matter connections between them and to examine how these connections are related to different arithmetic operations and individual differences in arithmetical competence. By using diffusion tensor imaging (DTI) tractography in eighteen 12-year-olds, we tested whether white matter pathways connecting these distant regions were related to children's arithmetical competence and how this association was modulated by operation. For each child, we delineated the three subcomponents of the arcuate fasciculus, a bundle of pathways linking frontal and temporo-parietal regions that are commonly active during calculation tasks. Fractional anisotropy in the left anterior portion of the arcuate fasciculus was positively correlated with addition and multiplication, but not with subtraction and division, suggesting a specific role of this left anterior segment in the solution of those problems that are expected to be solved with fact retrieval. The observed correlation was not explained by age, intelligence and working memory. Follow-up control analyses using different types of reading measures revealed that the observed correlation only disappeared when measures that draw heavily on phonological processing, such as non-word reading, were controlled for, suggesting that the association between the left arcuate fasciculus-anterior and addition/multiplication reflects the involvement of phonological processing. These results are the first to demonstrate that individual differences in fronto-parietal white matter are associated with arithmetical competence in typically developing children of a very narrow age range and indicate that this association is modulated by arithmetic operation.

Individual structural differences in left inferior parietal area are associated with schoolchildrens' arithmetic scores

Arithmetic skill is of critical importance for academic achievement, professional success and everyday life, and childhood is the key period to acquire this skill. Neuroimaging studies have identified that left parietal regions are a key neural substrate for representing arithmetic skill. Although the relationship between functional brain activity in left parietal regions and arithmetic skill has been studied in detail, it remains unclear about the relationship between arithmetic achievement and structural properties in left inferior parietal area in schoolchildren. The current study employed a combination of voxel-based morphometry (VBM) for high-resolution T1-weighted images and fiber tracking on diffusion tensor imaging (DTI) to examine the relationship between structural properties in the inferior parietal area and arithmetic achievement in 10-year-old schoolchildren. VBM of the T1-weighted images revealed that individual differences in arithmetic scores were significantly and positively correlated with the gray matter (GM) volume in the left intraparietal sulcus (IPS). Fiber tracking analysis revealed that the forceps major, left superior longitudinal fasciculus (SLF), bilateral inferior longitudinal fasciculus (ILF) and inferior fronto-occipital fasciculus (IFOF) were the primary pathways connecting the left IPS with other brain areas. Furthermore, the regression analysis of the probabilistic pathways revealed a significant and positive correlation between the fractional anisotropy (FA) values in the left SLF, ILF and bilateral IFOF and arithmetic scores. The brain structure-behavior correlation analyses indicated that the GM volumes in the left IPS and the FA values in the tract pathways connecting left IPS were both related to children's arithmetic achievement. The present findings provide evidence that individual structural differences in the left IPS are associated with arithmetic scores in schoolchildren.

Brain structure, number magnitude processing, and math proficiency in 6- to 7-year-old children born prematurely: a voxel-based morphometry study

The aim of the present voxel-based morphometry study was to examine the link between brain structure and number skills in a group of 6-7-year-old children born prematurely, which are considered to be an at-risk population for mathematical learning disabilities. Therefore, gray and white matter density values were extracted from brain areas previously reported to be relevant for number processing in developing brain systems and, thereafter, correlated with response time results tapping semantic number knowledge [i.e. numerical distance effect (NDE) derived from a number comparison task] as well as with general math proficiency (as indexed by a standardized calculation test). Behavioral results disclosed a significant NDE, thus indicating well-established number magnitude representations for one-digit numerals in our study group. Significant positive correlations between gray matter and NDE emerged in parietal regions (including the right anterior inferior and the left superior parietal lobe) and in the right superior temporal gyrus. Moreover, white matter and NDE were negatively correlated in the right anterior inferior parietal lobe and the right inferior frontal gyrus. Overall, our results are novel insofar as they show that in 6-7-year-old children born prematurely, individual differences in gray and white matter structures are associated with numerical skills. Importantly, in our study group the observed link between brain structure and behavioral performance emerges only regarding an experimental task tapping semantic number knowledge, whereas general math proficiency does not seem to be related to individual differences in brain structure in our study group.

White matter microstructure correlates of mathematical giftedness and intelligence quotient

Recent functional neuroimaging studies have shown differences in brain activation between mathematically gifted adolescents and controls. The aim of this study was to investigate the relationship between mathematical giftedness, intelligent quotient (IQ), and the microstructure of white matter tracts in a sample composed of math-gifted adolescents and aged-matched controls. Math-gifted subjects were selected through a national program based on detecting enhanced visuospatial abilities and creative thinking. We used diffusion tensor imaging to assess white matter microstructure in neuroanatomical connectivity. The processing included voxel-wise and region of interest-based analyses of the fractional anisotropy (FA), a parameter which is purportedly related to white matter microstructure. In a whole-sample analysis, IQ showed a significant positive correlation with FA, mainly in the corpus callosum, supporting the idea that efficient information transfer between hemispheres is crucial for higher intellectual capabilities. In addition, math-gifted adolescents showed increased FA (adjusted for IQ) in white matter tracts connecting frontal lobes with basal ganglia and parietal regions. The enhanced anatomical connectivity observed in the forceps minor and splenium may underlie the greater fluid reasoning, visuospatial working memory, and creative capabilities of these children.

The neural bases of the multiplication problem-size effect across countries

Multiplication problems involving large numbers (e.g., 9 × 8) are more difficult to solve than problems involving small numbers (e.g., 2 × 3). Behavioral research indicates that this problem-size effect might be due to different factors across countries and educational systems. However, there is no neuroimaging evidence supporting this hypothesis. Here, we compared the neural correlates of the multiplication problem-size effect in adults educated in China and the United States. We found a greater neural problem-size effect in Chinese than American participants in bilateral superior temporal regions associated with phonological processing. However, we found a greater neural problem-size effect in American than Chinese participants in right intra-parietal sulcus (IPS) associated with calculation procedures. Therefore, while the multiplication problem-size effect might be a verbal retrieval effect in Chinese as compared to American participants, it may instead stem from the use of calculation procedures in American as compared to Chinese participants. Our results indicate that differences in educational practices might affect the neural bases of symbolic arithmetic.