Processing pathways in mental arithmetic--evidence from probabilistic fiber tracking

Probing Our Built-in Calculator: A Systematic Narrative Review of Noninvasive Brain Stimulation Studies on Arithmetic Operation-Related Brain Areas

This systematic review presented a comprehensive survey of studies that applied transcranial magnetic stimulation and transcranial electrical stimulation to parietal and nonparietal areas to examine the neural basis of symbolic arithmetic processing. All findings were compiled with regard to the three assumptions of the triple-code model (TCM) of number processing. Thirty-seven eligible manuscripts were identified for review (33 with healthy participants and 4 with patients). Their results are broadly consistent with the first assumption of the TCM that intraparietal sulcus both hold a magnitude code and engage in operations requiring numerical manipulations such as subtraction. However, largely heterogeneous results conflicted with the second assumption of the TCM that the left angular gyrus subserves arithmetic fact retrieval, such as the retrieval of rote-learned multiplication results. Support is also limited for the third assumption of the TCM, namely, that the posterior superior parietal lobule engages in spatial operations on the mental number line. Furthermore, results from the stimulation of brain areas outside of those postulated by the TCM show that the bilateral supramarginal gyrus is involved in online calculation and retrieval, the left temporal cortex in retrieval, and the bilateral dorsolateral prefrontal cortex and cerebellum in online calculation of cognitively demanding arithmetic problems. The overall results indicate that multiple cortical areas subserve arithmetic skills.

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.

Disconnection in a left-hemispheric temporo-parietal network impairs multiplication fact retrieval

Arithmetic fact retrieval has been suggested to recruit a left-lateralized network comprising perisylvian language areas, parietal areas such as the angular gyrus (AG), and non-neocortical structures such as the hippocampus. However, the underlying white matter connectivity of these areas has not been evaluated systematically so far. Using simple multiplication problems, we evaluated how disconnections in parietal brain areas affected arithmetic fact retrieval following stroke. We derived disconnectivity measures by jointly considering data from n = 73 patients with acute unilateral lesions in either hemisphere and a white-matter tractography atlas (HCP-842) using the Lesion Quantification Toolbox (LQT). Whole-brain voxel-based analysis indicated a left-hemispheric cluster of white matter fibers connecting the AG and superior temporal areas to be associated with a fact retrieval deficit. Subsequent analyses of direct gray-to-gray matter disconnections revealed that disconnections of additional left-hemispheric areas (e.g., between the superior temporal gyrus and parietal areas) were significantly associated with the observed fact retrieval deficit. Results imply that disconnections of parietal areas (i.e., the AG) with language-related areas (i.e., superior and middle temporal gyri) seem specifically detrimental to arithmetic fact retrieval. This suggests that arithmetic fact retrieval recruits a widespread left-hemispheric network and emphasizes the relevance of white matter connectivity for number processing.

The two-network framework of number processing: a step towards a better understanding of the neural origins of developmental dyscalculia

Developmental dyscalculia is a specific learning disorder that persists over lifetime and can have an enormous impact on personal, health-related, and professional aspects of life. Despite its central importance, the origin both at the cognitive and neural level is not yet well understood. Several classification schemas of dyscalculia have been proposed, sometimes together with an associated deficit at the neural level. However, these explanations are (a) not providing an exhaustive framework that is at levels with the observed complexity of developmental dyscalculia at the behavioral level and (b) are largely mono-causal approaches focusing on gray matter deficits. We suggest that number processing is instead the result of context-dependent interaction of two anatomically largely separate, distributed but overlapping networks that function/cooperate in a closely integrated fashion. The proposed two-network framework (TNF) is the result of a series of studies in adults on the neural correlates underlying magnitude processing and arithmetic fact retrieval, which comprised neurofunctional imaging of various numerical tasks, the application of probabilistic fiber tracking to obtain well-defined connections, and the validation and modification of these results using disconnectome mapping in acute stroke patients. Emerged from data in adults, it represents the endpoint of the acquisition and use of mathematical competencies in adults. Yet, we argue that its main characteristics should already emerge earlier during development. Based on this TNF, we develop a classification schema of phenomenological subtypes and their underlying neural origin that we evaluate against existing propositions and the available empirical data.

Structural and functional connectivity of the inferior temporal numeral area

A growing body of evidence suggests that in adults, there is a spatially consistent "inferior temporal numeral area" (ITNA) in the occipitotemporal cortex that appears to preferentially process Arabic digits relative to non-numerical symbols and objects. However, very little is known about why the ITNA is spatially segregated from regions that process other orthographic stimuli such as letters, and why it is spatially consistent across individuals. In the present study, we used diffusion-weighted imaging and functional magnetic resonance imaging to contrast structural and functional connectivity between left and right hemisphere ITNAs and a left hemisphere letter-preferring region. We found that the left ITNA had stronger structural and functional connectivity than the letter region to inferior parietal regions involved in numerical magnitude representation and arithmetic. Between hemispheres, the left ITNA showed stronger structural connectivity with the left inferior frontal gyrus (Broca's area), while the right ITNA showed stronger structural connectivity to the ipsilateral inferior parietal cortex and stronger functional coupling with the bilateral IPS. Based on their relative connectivity, our results suggest that the left ITNA may be more readily involved in mapping digits to verbal number representations, while the right ITNA may support the mapping of digits to quantity representations.

Systematic Fusion of Multi-Source Cognitive Networks With Graph Learning - A Study on Fronto-Parietal Network

Cognitive tasks induce fluctuations in the functional connectivity between brain regions which constitute cognitive networks in the human brain. Although several cognitive networks have been identified, consensus still cannot be achieved on the precise borders and distribution of involved brain regions for each network, due to the multifarious use of diverse brain atlases in different studies. To address the problem, the current study proposed a novel approach to generate a fused cognitive network with the optimal performance in discriminating cognitive states by using graph learning, following the synthesization of one cognitive network defined by different brain atlases, and the construction of a hierarchical framework comprised of one main version and other supplementary versions of the specific cognitive network. As a result, the proposed method demonstrated better results compared with other machine learning methods for recognizing cognitive states, which was revealed by analyzing an fMRI dataset related to the mental arithmetic task. Our findings suggest that the fused cognitive network provides the potential to develop new mind decoding approaches.

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.

Finger-Based Numerical Training Increases Sensorimotor Activation for Arithmetic in Children—An fNIRS Study

Most children use their fingers when learning to count and calculate. These sensorimotor experiences were argued to underlie reported behavioral associations of finger gnosis and counting with mathematical skills. On the neural level, associations were assumed to originate from overlapping neural representations of fingers and numbers. This study explored whether finger-based training in children would lead to specific neural activation in the sensorimotor cortex, associated with finger movements, as well as the parietal cortex, associated with number processing, during mental arithmetic. Following finger-based training during the first year of school, trained children showed finger-related arithmetic effects accompanied by activation in the sensorimotor cortex potentially associated with implicit finger movements. This indicates embodied finger-based numerical representations after training. Results for differences in neural activation between trained children and a control group in the IPS were less conclusive. This study provides the first evidence for training-induced sensorimotor plasticity in brain development potentially driven by the explicit use of fingers for initial arithmetic, supporting an embodied perspective on the representation of numbers.

Parietal and hippocampal hyper-connectivity is associated with low math achievement in adolescence - A preliminary study

Mathematical cognition requires coordinated activity across multiple brain regions, leading to the emergence of resting-state functional connectivity as a method for studying the neural basis of differences in mathematical achievement. Hyper-connectivity of the intraparietal sulcus (IPS), a key locus of mathematical and numerical processing, has been associated with poor mathematical skills in childhood, whereas greater connectivity has been related to better performance in adulthood. No studies to date have considered its role in adolescence. Further, hippocampal connectivity can predict mathematical learning, yet no studies have considered its contributions to contemporaneous measures of math achievement. Here, we used seed-based resting-state fMRI analyses to examine IPS and hippocampal intrinsic functional connectivity relations to math achievement in a group of 31 adolescents (mean age = 16.42 years, range 15-17), whose math performance spanned the 1% to 99% percentile. After controlling for IQ, IPS connectivity was negatively related to math achievement, akin to findings in children. However, the specific temporo-occipital regions were more akin to the posterior loci implicated in adults. Hippocampal connectivity with frontal regions was also negatively correlated with concurrent math measures, which contrasts with results from learning studies. Finally, hyper-connectivity was not a global feature of low math performance, as math performance did not modulate connectivity of Heschl's gyrus, a control seed not involved in math cognition. Our results provide preliminary evidence that adolescence is a transitional stage in which patterns found in childhood and adulthood can be observed; most notably, hyper-connectivity continues to be related to low math ability into this period.

Facing successfully high mental workload and stressors: An fMRI study

The present fMRI study aimed at highlighting patterns of brain activations and autonomic activity when confronted with high mental workload and the threat of auditory stressors. Twenty participants performed a complex cognitive task in either safe or aversive conditions. Our results showed that increased mental workload induced recruitment of the lateral frontoparietal executive control network (ECN), along with disengagement of medial prefrontal and posterior cingulate regions of the default mode network (DMN). Mental workload also elicited an increase in heart rate and pupil diameter. Task performance did not decrease under the threat of stressors, most likely due to efficient inhibition of auditory regions, as reflected by a large decrement of activity in the superior temporal gyri. The threat of stressors was also accompanied with deactivations of limbic regions of the salience network (SN), possibly reflecting emotional regulation mechanisms through control from dorsal medial prefrontal and parietal regions, as indicated by functional connectivity analyses. Meanwhile, the threat of stressors induced enhanced ECN activity, likely for improved attentional and cognitive processes toward the task, as suggested by increased lateral prefrontal and parietal activations. These fMRI results suggest that measuring the balance between ECN, SN, and DMN recruitment could be used for objective mental state assessment. In this sense, an extra recruitment of task‐related regions and a high ratio of lateral versus medial prefrontal activity may represent a relevant marker of increased but efficient mental effort, while the opposite may indicate a disengagement from the task due to mental overload and/or stressors.

ADGRL3, FGF1 and DRD4: Linkage and Association with Working Memory and Perceptual Organization Candidate Endophenotypes in ADHD

Attention deficit hyperactivity disorder (ADHD) is a highly heritable neurobehavioral disorder that affects children worldwide, with detrimental long-term consequences in affected individuals. ADHD-affected patients display visual-motor and visuospatial abilities and skills that depart from those exhibited by non-affected individuals and struggle with perceptual organization, which might partially explain impulsive responses. Endophenotypes (quantifiable or dimensional constructs that are closely related to the root cause of the disease) might provide a more powerful and objective framework for dissecting the underlying neurobiology of ADHD than that of categories offered by the syndromic classification. In here, we explore the potential presence of the linkage and association of single-nucleotide polymorphisms (SNPs), harbored in genes implicated in the etiology of ADHD (ADGRL3, DRD4, and FGF1), with cognitive endophenotypes related to working memory and perceptual organization in 113 nuclear families. These families were ascertained from a geographical area of the Caribbean coast, in the north of Colombia, where the community is characterized by its ethnic diversity and differential gene pool. We found a significant association and linkage of markers ADGRL3-rs1565902, DRD4-rs916457 and FGF1-rs2282794 to neuropsychological tasks outlining working memory and perceptual organization such as performance in the digits forward and backward, arithmetic, similarities, the completion of figures and the assembly of objects. Our results provide strong support to understand ADHD as a combination of working memory and perceptual organization deficits and highlight the importance of the genetic background shaping the neurobiology, clinical complexity, and physiopathology of ADHD. Further, this study supplements new information regarding an ethnically diverse community with a vast African American contribution, where ADHD studies are scarce.

Frontal Functional Network Disruption Associated with Amyotrophic Lateral Sclerosis: An fNIRS-Based Minimum Spanning Tree Analysis

Recent evidence increasingly associates network disruption in brain organization with multiple neurodegenerative diseases, including amyotrophic lateral sclerosis (ALS), a rare terminal disease. However, the comparability of brain network characteristics across different studies remains a challenge for conventional graph theoretical methods. One suggested method to address this issue is minimum spanning tree (MST) analysis, which provides a less biased comparison. Here, we assessed the novel application of MST network analysis to hemodynamic responses recorded by functional near-infrared spectroscopy (fNIRS) neuroimaging modality, during an activity-based paradigm to investigate hypothetical disruptions in frontal functional brain network topology as a marker of the executive dysfunction, one of the most prevalent cognitive deficit reported across ALS studies. We analyzed data recorded from nine participants with ALS and ten age-matched healthy controls by first estimating functional connectivity, using phase-locking value (PLV) analysis, and then constructing the corresponding individual and group MSTs. Our results showed significant between-group differences in several MST topological properties, including leaf fraction, maximum degree, diameter, eccentricity, and degree divergence. We further observed a global shift toward more centralized frontal network organizations in the ALS group, interpreted as a more random or dysregulated network in this cohort. Moreover, the similarity analysis demonstrated marginally significantly increased overlap in the individual MSTs from the control group, implying a reference network with lower topological variation in the healthy cohort. Our nodal analysis characterized the main local hubs in healthy controls as distributed more evenly over the frontal cortex, with slightly higher occurrence in the left prefrontal cortex (PFC), while in the ALS group, the most frequent hubs were asymmetrical, observed primarily in the right prefrontal cortex. Furthermore, it was demonstrated that the global PLV (gPLV) synchronization metric is associated with disease progression, and a few topological properties, including leaf fraction and tree hierarchy, are linked to disease duration. These results suggest that dysregulation, centralization, and asymmetry of the hemodynamic-based frontal functional network during activity are potential neuro-topological markers of ALS pathogenesis. Our findings can possibly support new bedside assessments of the functional status of ALS' brain network and could hypothetically extend to applications in other neurodegenerative diseases.

Hemispheric Lateralization of Arithmetic Facts and Magnitude Processing for Two-Digit Numbers

In the human brain, a (relative) functional asymmetry (i.e., laterality; functional and performance differences between the two cerebral hemispheres) exists for a variety of cognitive domains (e.g., language, visual-spatial processing, etc.). For numerical cognition, both bi-lateral and unilateral processing has been proposed with the retrieval of arithmetic facts postulated as being lateralized to the left hemisphere. In this study, we aimed at evaluating this claim by investigating whether processing of multiplicatively related triplets in a number bisection task (e.g., 12_16_20) in healthy participants (n = 23) shows a significant advantage when transmitted to the right hemisphere only as compared to transmission to the left hemisphere. As expected, a control task revealed that stimulus presentation to the left or both visual hemifields did not increase processing disadvantages of unit-decade incompatible number pairs in magnitude comparison. For the number bisection task, we replicated the multiplicativity effect. However, in contrast to the hypothesis deriving from the triple code model, we did not observe significant hemispheric processing asymmetries for multiplicative items. We suggest that participants resorted to keep number triplets in verbal working memory after perceiving them only very briefly for 150 ms. Rehearsal of the three numbers was probably slow and time-consuming so allowing for interhemispheric communication in the meantime. We suggest that an effect of lateralized presentation may only be expected for early effects when the task is sufficiently easy.

Dissociating Arithmetic Operations in the Parietal Cortex Using 1 Hz Repetitive Transcranial Magnetic Stimulation: The Importance of Strategy Use

The triple-code model (TCM) of number processing suggests the involvement of distinct parietal cortex areas in arithmetic operations: the bilateral horizontal segment of the intraparietal sulcus (hIPS) for arithmetic operations that require the manipulation of numerical quantities (e.g., subtraction) and the left angular gyrus (AG) for arithmetic operations that require the retrieval of answers from long-term memory (e.g., multiplication). Although neuropsychological, neuroimaging, and brain stimulation studies suggest the dissociation of these operations into distinct parietal cortex areas, the role of strategy (online calculation vs. retrieval) is not yet fully established. In the present study, we further explored the causal involvement of the left AG for multiplication and left hIPS for subtraction using a neuronavigated repetitive transcranial magnetic stimulation (rTMS) paradigm. Stimulation sites were determined based on an fMRI experiment using the same tasks. To account for the effect of strategy, participants were asked whether they used retrieval or calculation for each individual problem. We predicted that the stimulation of the left AG would selectively disrupt the retrieval of the solution to multiplication problems. On the other hand, stimulation of the left hIPS should selectively disrupt subtraction. Our results revealed that left AG stimulation was detrimental to the retrieval and online calculation of solutions for multiplication problems, as well as, the retrieval (but not online calculation) of the solutions to subtraction problems. In contrast, left hIPS stimulation had no detrimental effect on both operations regardless of strategy.

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.

Dissociation of visual extinction and neglect in the left hemisphere

Visual neglect and extinction are two distinct visuospatial attention deficits that frequently occur after right hemisphere cerebral stroke. However, their different lesion profiles remain a matter of debate. In the left hemisphere, a domain-general dual-loop model with distinct computational abilities onto which several cognitive functions may project, has been proposed: a dorsal stream for sensori-motor mapping in time and space and a ventral stream for comprehension and representation of concepts. We wondered whether such a distinction may apply to visual extinction and neglect in left hemisphere lesions. Of 165 prospectively studied patients with acute left hemispheric ischemic stroke with a single lesion on MRI, 122 had no visuospatial attention deficit, 10 had extinction, 31 neglect and 2 had both, visual extinction and neglect. Voxel-based-lesion-symptom mapping (VLSM, FDR<.05) showed a clear anatomical dissociation. Extinction occurred after damage to the parietal cortex (anterior bank of the intraparietal sulcus, inferior parietal lobe, and supramarginal gyrus), while visual neglect occurred after damage mainly to the temporal lobe (superior and middle temporal lobe, anterior temporal pole), inferior ventral premotor cortex, frontal operculum, angular gyrus, and insula. Direct comparison of both conditions linked extinction to intraparietal sulcus and supramarginal gyrus (FDR<.05). Thus, in the left hemisphere extinction seems to be related to dorsal stream lesions, whereas neglect maps more on the ventral stream. These data cannot be generalized to the right hemisphere. However, a domain-general point-of-view may stimulate discussion on visuospatial attention processing also in the right hemisphere.

Associations Between Individual Differences in Mathematical Competencies and Surface Anatomy of the Adult Brain

Previously conducted structural magnetic resonance imaging (MRI) studies on the neuroanatomical correlates of mathematical abilities and competencies have several methodological limitations. Besides small sample sizes, the majority of these studies have employed voxel-based morphometry (VBM)-a method that, although it is easy to implement, has some major drawbacks. Taking this into account, the current study is the first to investigate in a large sample of typically developed adults the associations between mathematical abilities and variations in brain surface structure by using surface-based morphometry (SBM). SBM is a method that also allows the investigation of brain morphometry by avoiding the pitfalls of VBM. Eighty-nine young adults were tested with a large battery of psychometric tests to measure mathematical competencies in four different areas: (1) simple arithmetic; (2) complex arithmetic; (3) higher-order mathematics; and (4) numerical intelligence. Also, we asked participants for their mathematics grades for their final school exams. Inside the MRI scanner, we collected high-resolution T1-weighted anatomical images from each subject. SBM analyses were performed with the computational anatomy toolbox (CAT12) and indices for cortical thickness, for cortical surface complexity, for gyrification, and sulcal depth were calculated. Further analyses revealed associations between: (1) the cortical surface complexity of the right superior temporal gyrus and numerical intelligence; (2) the depth of the right central sulcus and adults' ability to solve complex arithmetic problems; and (3) the depth of the left parieto-occipital sulcus and adults' higher-order mathematics competence. Interestingly, no relationships with previously reported brain regions were observed, thus, suggesting the importance of similar research to confirm the role of the brain regions found in this study.

Saccades under Mental Load in Infantile Nystagmus Syndrome and Controls

SIGNIFICANCE

This study compares saccades and visual task performance in patients with infantile nystagmus syndrome (INS) with that in normally sighted individuals under mental load. The results highlighted that to more completely evaluate INS therapies recognition time should also be measured with mental load, resembling real-world conditions.

PURPOSE

Patients with INS may complain of "being slow to see." Stress is reported to worsen nystagmus and to prolong visual recognition time. We hypothesized that the effects of mental load on timing indices of visual recognition, for example, saccade latency, target acquisition time, target viewing time, and subjects' reaction time, differ between the INS and control groups.

METHODS

Eye movements were recorded when participants (INS group, n = 15; controls, n = 25) reported the direction of tumbling-E targets presented randomly across ±25°. The task was repeated with both mental arithmetic and time restriction to impose high mental load, confirmed through subjective ratings and heart rate measurement.

RESULTS

Mental load increased saccade latency (mean, 32.69 milliseconds; 95% confidence interval [CI], 21.17 to 44.20 milliseconds; P < .001) and target acquisition time (57.00 milliseconds; 95% CI, 34 to 81 milliseconds; P < .001). Patients with INS showed longer saccade latency (39.79 milliseconds; 95% CI, 23.98 to 55.62 milliseconds; P < .001) and target acquisition time (134.00 milliseconds; 95% CI, 96 to 172 milliseconds; P < .001) compared with controls. The interaction between task and group was significant for saccade gain (0.11; 95% CI, 0.02 to 0.19; P = .015), target acquisition time (37.93 milliseconds; 95% CI, 36.91 to 38.96 milliseconds; P = .011), and subjects' reaction time (95.37 milliseconds; 95% CI, 65.91 to 124.84 milliseconds; P = .043). There was an inverse correlation between the changes in subjects' response errors and target viewing time with mental load only for controls (r = -0.484, P = .014). Total foveation exposure time and target viewing time remained unchanged.

CONCLUSIONS

Mental load worsens "being slow to see" in INS because of delayed target acquisition and possibly because efficiency of visual processing decreases more in patients with INS compared with controls. To investigate outcomes of INS therapies, visual recognition time should be also measured with mental load.

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.

White matter microstructure correlates with mathematics but not word reading performance in 13-year-old children born very preterm and full-term

Individuals born very preterm (VPT; <32 weeks' gestational age) are at increased risk of impaired mathematics and word reading performance, as well as widespread white matter microstructural alterations compared with individuals born full term (FT; ≥37 weeks' gestational age). To date, the link between academic performance and white matter microstructure is not well understood. This study aimed to investigate the associations between mathematics and reading performance with white matter microstructure in 114 VPT and 36 FT 13-year-old children. Additionally, we aimed to investigate whether the association of mathematics and reading performance with white matter microstructure in VPT children varied as a function of impairment. To do this, we used diffusion tensor imaging and advanced diffusion modelling techniques (Neurite Orientation Dispersion and Density Imaging and the Spherical Mean Technique), combined with a whole-brain analysis approach (Tract-Based Spatial Statistics). Mathematics performance across VPT and FT groups was positively associated with white matter microstructural measurements of fractional anisotropy and neurite density, and negatively associated with radial and mean diffusivities in widespread, bilateral regions. Furthermore, VPT children with a mathematics impairment (>1 standard deviation below FT mean) had significantly reduced neurite density compared with VPT children without an impairment. Reading performance was not significantly associated with any of the white matter microstructure parameters. Additionally, the associations between white matter microstructure and mathematics and reading performance did not differ significantly between VPT and FT groups. Our findings suggest that alterations in white matter microstructure, and more specifically lower neurite density, are associated with poorer mathematics performance in 13-year-old VPT and FT children. More research is required to understand the association between reading performance and white matter microstructure in 13-year-old children.

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Diffusion tensor and neurite density metrics were associated with mathematics.

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Associations were present in very preterm and full-term children.

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Associations were widespread throughout the white matter microstructure.

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Decreased neurite density was evident in children with a mathematics impairment.

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Limited evidence of associations between white matter microstructure and reading.

Interference during the retrieval of arithmetic and lexico-semantic knowledge modulates similar brain regions: Evidence from functional magnetic resonance imaging (fMRI)

Single-digit multiplications are mainly solved by memory retrieval. However, these problems are also prone to errors due to systematic interference (i.e., co-activation of interconnected but incorrect solutions). Semantic control processes are crucial to overcome this type of interference and to retrieve the correct information. Previous research suggests the importance of several brain regions such as the left inferior frontal cortex and the intraparietal sulcus (IPS) for semantic control. But, this evidence is mainly based on tasks measuring interference during the processing of lexico-semantic information (e.g., pictures or words). Here, we investigated whether semantic control during arithmetic problem solving (i.e., multiplication fact retrieval) draws upon similar or different brain mechanisms as in other semantic domains (i.e., lexico-semantic). The brain activity of 46 students was measured with fMRI while participants performed an operand-related-lure (OR) and a picture-word (PW) task. In the OR task participants had to verify the correctness of a given solution to a single-digit multiplication. Similarly, in the PW task, participants had to judge whether a presented word matches the concept displayed in a picture or not. Analyses showed that resolving interference in these two tasks modulates the activation of a widespread fronto-parietal network (e.g., left/right IFG, left insula lobe, left IPS). Importantly, conjunction analysis revealed a neural overlap in the left inferior frontal gyrus (IFG) pars triangularis and left IPS. Additional Bayesian analyses showed that regions that are thought to store lexico-semantic information (e.g., left middle temporal gyrus) did not show evidence for an arithmetic interference effect. Overall, our findings not only indicate that semantic control plays an important role in arithmetic problem solving but also that it is supported by common brain regions across semantic domains. Additionally, by conducting Bayesian analysis we confirmed the hypothesis that the semantic control network contributes differently to semantic tasks of various domains.

Mathematical expertise modulates the architecture of dorsal and cortico-thalamic white matter tracts

To what extent are levels of cognitive expertise reflected in differential structural connectivity of the brain? We addressed this question by analyzing the white matter brain structure of experts (mathematicians) versus non-experts (non-mathematicians) using probabilistic tractography. Having mathematicians and non-mathematicians as participant groups enabled us to directly compare profiles of structural connectivity arising from individual levels of expertise in mathematics. Tracking from functional seed regions activated during the processing of complex arithmetic formulas revealed an involvement of various fiber bundles such the inferior fronto-occipital fascicle, arcuate fasciculus/superior longitudinal fasciculus (AF/SLF), cross-hemispheric connections of frontal lobe areas through the corpus callosum and cortico-subcortical connectivity via the bilateral thalamic radiation. With the aim of investigating expertise-dependent structural connectivity, the streamline density was correlated with the level of expertise, defined by automaticity of processing complex mathematics. The results showed that structural integrity of the AF/SLF was higher in individuals with higher automaticity, while stronger cortico-thalamic connectivity was associated with lower levels of automaticity. Therefore, we suggest that expertise in the domain of mathematics is reflected in plastic changes of the brain's white matter structure, possibly reflecting a general principle of cognitive expertise.

Cognitive loading via mental arithmetic modulates effects of blink-related oscillations on precuneus and ventral attention network regions

Blink-related oscillations (BROs) have been linked with environmental monitoring processes associated with blinking, with cortical activations in the bilateral precuneus. Although BROs have been described under resting and passive fixation conditions, little is known about their characteristics under cognitive loading. To address this, we investigated BRO effects during both mental arithmetic (MA) and passive fixation (PF) tasks using magnetoencephalography (n =20), while maintaining the same sensory environment in both tasks. Our results confirmed the presence of BRO effects in both MA and PF tasks, with similar characteristics including blink-related increase in global field power and blink-related activation of the bilateral precuneus. In addition, cognitive loading due to MA also modulated BRO effects by decreasing BRO-induced cortical activations in key brain regions including the bilateral anterior precuneus. Interestingly, blinking during MA-but not PF-activated regions of the ventral attention network (i.e., right supramarginal gyrus and inferior frontal gyrus), suggesting possible recruitment of these areas for blink processing under cognitive loading conditions. Time-frequency analysis revealed a consistent pattern of BRO-related effects in the precuneus in both tasks, but with task-related functional segregation within the anterior and posterior subregions. Based on these findings, we postulate a potential neurocognitive mechanism for blink processing in the precuneus. This study is the first investigation of BRO effects under cognitive loading, and our results provide compelling new evidence for the important cognitive implications of blink-related processing in the human brain.

White matter neuro-plasticity in mental arithmetic: Changes in hippocampal connectivity following arithmetic drill training

Verbally-mediated arithmetic fact retrieval has been suggested to be subserved by a left-lateralized network including angular gyrus and hippocampus. However, the contribution of these areas to retrieval of arithmetic facts has been under debate lately, challenging the prominent role of the angular gyrus in arithmetic fact retrieval. In the present study, we evaluated changes in structural connectivity of left hippocampus and left angular gyrus in 32 participants following a short extensive drill training of complex multiplication. We observed a significant increase of structural connectivity in fibers encompassing the left hippocampus but not the left angular gyrus. As such, our findings substantiate that the left hippocampus plays a central role in arithmetic fact retrieval. While both structures, left angular gyrus and left hippocampus seem to be parts of the network processing arithmetic facts, hippocampus actually seems to subserve encoding and retrieval of arithmetic facts. In turn, the role of the left angular gyrus might rather be to mediate the fact retrieval network as to whether or not processes of fact retrieval are referred to.

The neural correlates of mental arithmetic in adolescents: a longitudinal fNIRS study

BACKGROUND

Arithmetic processing in adults is known to rely on a frontal-parietal network. However, neurocognitive research focusing on the neural and behavioral correlates of arithmetic development has been scarce, even though the acquisition of arithmetic skills is accompanied by changes within the fronto-parietal network of the developing brain. Furthermore, experimental procedures are typically adjusted to constraints of functional magnetic resonance imaging, which may not reflect natural settings in which children and adolescents actually perform arithmetic. Therefore, we investigated the longitudinal neurocognitive development of processes involved in performing the four basic arithmetic operations in 19 adolescents. By using functional near-infrared spectroscopy, we were able to use an ecologically valid task, i.e., a written production paradigm.

RESULTS

A common pattern of activation in the bilateral fronto-parietal network for arithmetic processing was found for all basic arithmetic operations. Moreover, evidence was obtained for decreasing activation during subtraction over the course of 1 year in middle and inferior frontal gyri, and increased activation during addition and multiplication in angular and middle temporal gyri. In the self-paced block design, parietal activation in multiplication and left angular and temporal activation in addition were observed to be higher for simple than for complex blocks, reflecting an inverse effect of arithmetic complexity.

CONCLUSIONS

In general, the findings suggest that the brain network for arithmetic processing is already established in 12-14 year-old adolescents, but still undergoes developmental changes.

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

Reduction but no shift in brain activation after arithmetic learning in children: A simultaneous fNIRS-EEG study

Neurocognitive studies of arithmetic learning in adults have revealed decreasing brain activation in the fronto-parietal network, along with increasing activation of specific cortical and subcortical areas during learning. Both changes are associated with a shift from procedural to retrieval strategies for problem-solving. Here we address the critical, open question of whether similar neurocognitive changes are also evident in children. In this study, 20 typically developing children were trained to solve simple and complex multiplication problems. The one-session and two-week training effects were monitored using simultaneous functional near-infrared spectroscopy (fNIRS) and electroencephalography (EEG). FNIRS measurement after one session of training on complex multiplication problems revealed decreased activation at the left angular gyrus (AG), right superior parietal lobule, and right intraparietal sulcus. Two weeks of training led to decreased activation at the left AG and right middle frontal gyrus. For both simple and complex problems, we observed increased alpha power in EEG measurements as children worked on trained versus untrained problems. In line with previous multiplication training studies in adults, reduced activation within the fronto-parietal network was observed after training. Contrary to adults, we found that strategy shifts via arithmetic learning were not contingent on the activation of the left AG in children.

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.

Mental arithmetic in the bilingual brain: Language matters

How do bilinguals solve arithmetic problems in each of their languages? We investigated this question by exploring the neural substrates of mental arithmetic in bilinguals. Critically, our population was composed of a homogeneous group of adults who were fluent in both of their instruction languages (i.e., German as first instruction language and French as second instruction language). Twenty bilinguals were scanned with fMRI (3T) while performing mental arithmetic. Both simple and complex problems were presented to disentangle memory retrieval occuring in very simple problems from arithmetic computation occuring in more complex problems. In simple additions, the left temporal regions were more activated in German than in French, whereas no brain regions showed additional activity in the reverse constrast. Complex additions revealed the reverse pattern, since the activations of regions for French surpassed the same computations in German and the extra regions were located predominantly in occipital regions. Our results thus highlight that highly proficient bilinguals rely on differential activation patterns to solve simple and complex additions in each of their languages, suggesting different solving procedures. The present study confirms the critical role of language in arithmetic problem solving and provides novel insights into how highly proficient bilinguals solve arithmetic problems.

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

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

Counteracting Implicit Conflicts by Electrical Inhibition of the Prefrontal Cortex

Cognitive conflicts and distractions by task-irrelevant information often counteract effective and goal-directed behaviors. In some cases, conflicting information can even emerge implicitly, without an overt distractor, by the automatic activation of mental representations. For instance, during number processing, magnitude information automatically elicits spatial associations resembling a mental number line. This spatial–numerical association of response codes (SNARC) effect can modulate cognitive-behavioral performance but is also highly flexible and context-dependent, which points toward a critical involvement of working memory functions. Transcranial direct current stimulation to the PFC, in turn, has been effective in modulating working memory-related cognitive performance. In a series of experiments, we here demonstrate that decreasing activity of the left PFC by cathodal transcranial direct current stimulation consistently and specifically eliminates implicit cognitive conflicts based on the SNARC effect, but explicit conflicts based on visuospatial distraction remain unaffected. This dissociation is polarity-specific and appears unrelated to functional magnitude processing as classified by regular numerical distance effects. These data demonstrate a causal involvement of the left PFC in implicit cognitive conflicts based on the automatic activation of spatial–numerical processing. Corroborating the critical interaction of brain stimulation and neurocognitive functions, our findings suggest that distraction from goal-directed behavior by automatic activation of implicit, task-irrelevant information can be blocked by the inhibition of prefrontal activity.

Decreased cerebellar-cerebral connectivity contributes to complex task performance

The cerebellum's role in nonmotor processes is now well accepted, but cerebellar interaction with cerebral targets is not well understood. Complex cognitive tasks activate cerebellar, parietal, and frontal regions, but the effective connectivity between these regions has never been tested. To this end, we used psycho-physiological interactions (PPI) analysis to test connectivity changes of cerebellar and parietal seed regions in complex (2-digit by 1-digit multiplication, e.g., 12 × 3) vs. simple (1-digit by 1-digit multiplication, e.g., 4 × 3) task conditions ("complex - simple"). For cerebellar seed regions (lobule VI, hemisphere and vermis), we found significantly decreased cerebellar-parietal, cerebellar-cingulate, and cerebellar-frontal connectivity in complex multiplication. For parietal seed regions (PFcm, PFop, PFm) we found significantly increased parietal-parietal and parietal-frontal connectivity in complex multiplication. These results suggest that decreased cerebellar-cerebral connectivity contributes to complex task performance. Interestingly, BOLD activity contrasts revealed partially overlapping parietal areas of increased BOLD activity but decreased cerebellar-parietal PPI connectivity.

Reconfiguration of parietal circuits with cognitive tutoring in elementary school children

Cognitive development is shaped by brain plasticity during childhood, yet little is known about changes in large-scale functional circuits associated with learning in academically relevant cognitive domains such as mathematics. Here, we investigate plasticity of intrinsic brain circuits associated with one-on-one math tutoring and its relation to individual differences in children's learning. We focused on functional circuits associated with the intraparietal sulcus (IPS) and angular gyrus (AG), cytoarchitectonically distinct subdivisions of the human parietal cortex with different roles in numerical cognition. Tutoring improved performance and strengthened IPS connectivity with the lateral prefrontal cortex, ventral temporal-occipital cortex, and hippocampus. Crucially, increased IPS connectivity was associated with individual performance gains, highlighting the behavioral significance of plasticity in IPS circuits. Tutoring-related changes in IPS connectivity were distinct from those of the adjacent AG, which did not predict performance gains. Our findings provide new insights into plasticity of functional brain circuits associated with the development of specialized cognitive skills in children.

Fact learning in complex arithmetic-the role of the angular gyrus revisited

In recent theoretical considerations as well as in neuroimaging findings the left angular gyrus (AG) has been associated with the retrieval of arithmetic facts. This interpretation was corroborated by higher AG activity when processing trained as compared with untrained multiplication problems. However, so far neural correlates of processing trained versus untrained problems were only compared after training. We employed an established learning paradigm (i.e., extensive training of multiplication problems) but measured brain activation before and afte training to evaluate neural correlates of arithmetic fact acquisition more specifically. When comparing activation patterns for trained and untrained problems of the post-training session, higher AG activation for trained problems was replicated. However, when activation for trained problems was compared to activation for the same problems in the pre-training session, no signal change in the AG was observed. Instead, our results point toward a central role of hippocampal, para-hippocampal, and retrosplenial structures in arithmetic fact retrieval. We suggest that the AG might not be associated with the actual retrieval of arithmetic facts, and outline an attentional account of the role of the AG in arithmetic fact retrieval that is compatible with recent attention to memory hypotheses. Hum Brain Mapp 37:3061-3079, 2016. © 2016 Wiley Periodicals, Inc.

Behavioural evidence for sex differences in the overlap between subtraction and multiplication

The present study aims to identify factors that may influence the dissociability of number magnitude processing and arithmetic fact retrieval at the behavioural level. To that end, we assessed both subtraction and multiplication performance in a within-subject approach and evaluated the interdependence of unit-decade integration measures on the one hand as well as sex differences in the interdependence of performance measures on the other hand. We found that subtraction items requiring borrowing (e.g. 53-29 = 24, 3 < 9) are more error prone than subtraction items not requiring borrowing (e.g. 59-23 = 34, 9 > 3), thereby demonstrating a borrowing effect, which has been suggested as a measure of unit-decade integration in subtraction. Furthermore, we observed that multiplication items with decade-consistent distractors (e.g. 6 × 4 = 28 instead of 24) are more error prone that multiplication items with decade-inconsistent distractors (e.g. 6 × 4 = 30 instead of 24), thereby demonstrating a decade-consistency effect, which has been suggested as a measure of unit-decade integration in simple multiplication. However, the borrowing effect in subtraction was not correlated with the effect of decade consistency in simple multiplication in either men or women. This indicates that unit-decade integration arises from different systems in subtraction and multiplication. Nevertheless, men outperformed women not only in subtraction, but also in multiplication. Furthermore, subtraction and multiplication performance on correct solution probes were correlated in women, but unrelated in men. Thus, the view of differential systems for number magnitude processing and arithmetic fact retrieval may not be universal across sexes.

Cardiovascular sympathetic arousal in response to different mental stressors

The altered regulation of autonomic response to mental stress can result in increased cardiovascular risk. The laboratory tests used to simulate the autonomic responses to real-life stressors do not necessarily induce generalized sympathetic activation; therefore, the assessment of regulatory outputs to different effector organs could be important. We aimed to study the cardiovascular sympathetic arousal in response to different mental stressors (Stroop test, mental arithmetic test) in 20 healthy students. The conceivable sympathetic vascular index--spectral power of low frequency band of systolic arterial pressure variability (LF-SAP) and novel potential cardio-sympathetic index--symbolic dynamics heart rate variability index 0V% were evaluated. The heart and vessels responded differently to mental stress--while Stroop test induced increase of both 0V% and LF-SAP indices suggesting complex sympathetic arousal, mental arithmetic test evoked only 0V% increase compared to baseline (p<0.01, p<0.001, p<0.01, respectively). Significantly greater reactivity of LF-SAP, 0V%, heart rate (HR) and mean arterial pressure (MAP) were found in response to Stroop test compared to mental arithmetic test potentially indicating the effect of different central processing (0V%, LF-SAP: p<0.001; HR, MAP: p<0.01). The different effectors' sympathetic responses to cognitive stressors could provide novel important information regarding potential pathomechanisms of stress-related diseases.

Improved Framework for Tractography Reconstruction of the Optic Radiation

The optic radiation (OR) is one of the major components of the visual system and a key structure at risk in white matter diseases such as multiple sclerosis (MS). However, it is challenging to perform track reconstruction of the OR using diffusion MRI due to a sharp change of direction in the Meyer's loop and the presence of kissing and crossing fibers along the pathway. As such, we aimed to provide a highly precise and reproducible framework for tracking the OR from thalamic and visual cortex masks. The framework combined the generation of probabilistic streamlines by high order fiber orientation distributions estimated with constrained spherical deconvolution and an automatic post-processing based on anatomical exclusion criteria (AEC) to compensate for the presence of anatomically implausible streamlines. Specifically, those ending in the contralateral hemisphere, cerebrospinal fluid or grey matter outside the visual cortex were automatically excluded. We applied the framework to two distinct high angular resolution diffusion-weighted imaging (HARDI) acquisition protocols on one cohort, comprised of ten healthy volunteers and five MS patients. The OR was successfully delineated in both HARDI acquisitions in the healthy volunteers and MS patients. Quantitative evaluation of the OR position was done by comparing the results with histological reference data. Compared with histological mask, the OR reconstruction into a template (OR-TCT) was highly precise (percentage of voxels within the OR-TCT correctly defined as OR), ranging from 0.71 to 0.83. The sensitivity (percentage of voxels in histological reference mask correctly defined as OR in OR-TCT) ranged from 0.65 to 0.81 and the accuracy (measured by F1 score) was 0.73 to 0.77 in healthy volunteers. When AEC was not applied the precision and accuracy decreased. The absolute agreement between both HARDI datasets measured by the intraclass correlation coefficient was 0.73. This improved framework allowed us to reconstruct the OR with high reliability and accuracy independently of the acquisition parameters. Moreover, the reconstruction was possible even in the presence of tissue damage due to MS. This framework could also be applied to other tracts with complex configuration.

A single dual-stream framework for syntactic computations in music and language

This study is the first to compare in the same subjects the specific spatial distribution and the functional and anatomical connectivity of the neuronal resources that activate and integrate syntactic representations during music and language processing. Combining functional magnetic resonance imaging with functional connectivity and diffusion tensor imaging-based probabilistic tractography, we examined the brain network involved in the recognition and integration of words and chords that were not hierarchically related to the preceding syntax; that is, those deviating from the universal principles of grammar and tonal relatedness. This kind of syntactic processing in both domains was found to rely on a shared network in the left hemisphere centered on the inferior part of the inferior frontal gyrus (IFG), including pars opercularis and pars triangularis, and on dorsal and ventral long association tracts connecting this brain area with temporo-parietal regions. Language processing utilized some adjacent left hemispheric IFG and middle temporal regions more than music processing, and music processing also involved right hemisphere regions not activated in language processing. Our data indicate that a dual-stream system with dorsal and ventral long association tracts centered on a functionally and structurally highly differentiated left IFG is pivotal for domain-general syntactic competence over a broad range of elements including words and chords.

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.