Overlapping but separate number representations in the intraparietal sulcus – probing format- and modality-independence in sighted Braille readers

The Triple-Code Model stipulates that numerical information from different formats and modalities converges on a common magnitude representation in the Intraparietal Sulcus (IPS). To what extent the representations of all numerosity forms overlap remains unsolved. It has been postulated that the representation of symbolic numerosities (for example, Arabic digits) is sparser and grounded in an existing representation that codes for non-symbolic numerosity information (i.e., sets of objects). Other theories argue that numerical symbols represent a separate number category that emerges only during education. Here, we tested a unique group of sighted tactile Braille readers with numerosities 2, 4, 6 and 8 in three number notations: Arabic digits, sets of dots, tactile Braille numbers. Using univariate methods, we showed a consistent overlap in activations evoked by these three number notations. This result shows that all three used notations are represented in the IPS, which may suggest at least a partial overlap between the representations of the three notations used in this experiment. Using MVPA, we found that only non-automatized number information (Braille and sets of dots) allowed successful number classification. However, the numerosity of one notation could not be predicted above chance from the brain activation patterns evoked by another notation (no cross-classification). These results show that the IPS may host independent number codes in overlapping cortical circuits. In addition, they suggest that the level of training in encoding a given type of number information is an important factor that determines the amount of exploitable information and needs to be controlled for in order to identify the neural code underlying numerical information per se.

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.

Representations within the Intraparietal Sulcus Distinguish Numerical Tasks and Formats

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

Network topology of symbolic and nonsymbolic number comparison

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

Shared Numerosity Representations Across Formats and Tasks Revealed with 7 Tesla fMRI: Decoding, Generalization, and Individual Differences in Behavior

Debate continues on whether encoding of symbolic number is grounded in nonsymbolic numerical magnitudes. Nevertheless, fluency of perceiving both number formats, and translating between them, predicts math skills across the life span. Therefore, this study asked if numbers share cortical activation patterns across formats and tasks, and whether neural response to number predicts math-related behaviors. We analyzed patterns of neural activation using 7 Tesla functional magnetic resonance imaging in a sample of 39 healthy adults. Discrimination was successful between numerosities 2, 4, 6, and 8 dots and generalized to activation patterns of the same numerosities represented as Arabic digits in the bilateral parietal lobes and left inferior frontal gyrus (IFG) (and vice versa). This indicates that numerosity-specific neural resources are shared between formats. Generalization was also successful across tasks where participants either identified or compared numerosities in bilateral parietal lobes and IFG. Individual differences in decoding did not relate to performance on a number comparison task completed outside of the scanner, but generalization between formats and across tasks negatively related to math achievement in the parietal lobes. Together, these findings suggest that individual differences in representational specificity within format and task contexts relate to mathematical expertise.

Numerical working memory alters alpha-beta oscillations and connectivity in the parietal cortices

Although the neural bases of numerical processing and memory have been extensively studied, much remains to be elucidated concerning the spectral and temporal dynamics surrounding these important cognitive processes. To further this understanding, we employed a novel numerical working memory paradigm in 28 young, healthy adults who underwent magnetoencephalography (MEG). The resulting data were examined in the time-frequency domain prior to image reconstruction using a beamformer. Whole-brain, spectrally-constrained coherence was also employed to determine network connectivity. In response to the numerical task, participants exhibited robust alpha/beta oscillations in the bilateral parietal cortices. Whole-brain statistical comparisons examining the effect of numerical manipulation during memory-item maintenance revealed a difference centered in the right superior parietal cortex, such that oscillatory responses during numerical manipulation were significantly stronger than when no manipulation was necessary. Additionally, there was significantly reduced cortico-cortical coherence between the right and left superior parietal regions during the manipulation compared to the maintenance trials, indicating that these regions were functioning more independently when the numerical information had to be actively processed. In sum, these results support previous studies that have implicated the importance of parietal regions in numerical processing, but also provide new knowledge on the spectral, temporal, and network dynamics that serve this critical cognitive function during active working memory maintenance.

A shared code for Braille and Arabic digits revealed by cross-modal priming in sighted Braille readers

Quantities can be represented by different formats (e.g. symbolic or non-symbolic) and conveyed via different modalities (e.g. tactile or visual). Despite different priming curves: V-shape and step-shape for place and summation coded representation, respectively, the occurrence of priming effect supports the notion of different format overlap on the same mental number line. However, little is known about tactile-visual overlap of symbolic numerosities i.e. Braille numbers to Arabic digits on the magnitude number representation. Here, in a priming experiment, we tested a unique group of sighted Braille readers to investigate whether tactile Braille digits would activate a place-coding type of mental number representation (V-shape), analogous to other symbolic formats. The primes were either tactile Braille digits presented on a Braille display or number words presented on a computer screen. The targets were visually presented Arabic digits, and subjects performed a naming task. Our results reveal a V-shape priming function for both prime formats: tactile Braille and written words representing numbers, with strongest priming for primes of identical value (e.g. "four" and "4"), and a symmetrical decrease of priming strength for neighboring numbers, which indicates that the observed priming is due to identity priming. We thus argue that the magnitude information is processed according to a shared phonological code, independent of the input modality.

The interplay between non-symbolic number and its continuous visual properties revisited: Effects of mixing trials of different types

In the last few years, the existence of a pure number sense has been challenged. Recent studies suggest that numerosity processing is influenced not only by the number of elements in a display but also by continuous magnitudes, such as the size of the elements. The aim of our study was to replicate and extend the findings by Gebuis and Reynvoet, who systematically manipulated different continuous magnitudes either congruently or incongruently with discrete numerosity. We were particularly interested in finding the same pattern of congruency effects and assess its stability and robustness as this pattern indicates a complex influence of continuous magnitudes on numerosity judgements. We did so by showing stimuli of different conditions either in separate blocks or mixed together while participants solved a dot comparison task. Our results are in line with the notion that discrete number and continuous magnitudes are integrated in numerosity judgements by means of a weighing process. Moreover, our findings suggest that this integration is modified by the mode of presentation (blocked vs. mixed).

Visual cognition in non-amnestic Alzheimer's disease: Relations to tau, amyloid, and cortical atrophy

Heterogeneity within the Alzheimer's disease (AD) syndromic spectrum is typically classified in a domain-specific manner (e.g., language vs. visual cognitive function). The central aim of this study was to investigate whether impairment in visual cognitive tasks thought to be subserved by posterior cortical dysfunction in non-amnestic AD presentations is associated with tau, amyloid, or neurodegeneration in those regions using 18F-AV-1451 and 11C-PiB positron emission tomography (PET) and magnetic resonance imaging (MRI). Sixteen amyloid-positive patients who met criteria for either Posterior Cortical Atrophy (PCA; n = 10) or logopenic variant Primary Progressive Aphasia (lvPPA; n = 6) were studied. All participants underwent a structured clinical assessment, neuropsychological battery, structural MRI, amyloid PET, and tau PET. The neuropsychological battery included two visual cognitive tests: VOSP Number Location and Benton Facial Recognition. Surface-based whole-cortical general linear models were used to first explore the similarities and differences between these biomarkers in the two patient groups, and then to assess their regional associations with visual cognitive test performance. The results show that these two variants of AD have both dissociable and overlapping areas of tau and atrophy, but amyloid is distributed with a stereotyped localization in both variants. Performance on both visual cognitive tests were associated with tau and atrophy in the right lateral and medial occipital association cortex, superior parietal cortex, and posterior ventral occipitotemporal cortex. No cortical associations were observed with amyloid PET. We further demonstrate that cortical atrophy has a partially mediating effect on the association between tau pathology and visual cognitive task performance. Our findings show that non-amnestic variants of AD have partially dissociable spatial patterns of tau and atrophy that localize as expected based on symptoms, but similar patterns of amyloid. Further, we demonstrate that impairments of visual cognitive dysfunction are strongly associated with tau in visual cortical regions and mediated in part by atrophy.

Spatial-numerical associations: Shared symbolic and non-symbolic numerical representations

During the last decades, there have been a large number of studies into the number-related abilities of humans. As a result, we know that humans and non-human animals have a system known as the approximate number system that allows them to distinguish between collections based on their number of items, separately from any counting procedures. Dehaene and others have argued for a model on which this system uses representations for numbers that are spatial in nature and are shared by our symbolic and non-symbolic processing of numbers. However, there is a conflicting theoretical perspective in which there are no representations of numbers underlying the approximate number system, but only quantity-related representations. This perspective would then suggest that there are no shared representations between symbolic and non-symbolic processing. We review the evidence on spatial biases resulting from the activation of numerical representations, for both non-symbolic and symbolic tests. These biases may help decide between the theoretical differences; shared representations are expected to lead to similar biases regardless of the format, whereas different representations more naturally explain differences in biases, and thus behaviour. The evidence is not yet decisive, as the behavioural evidence is split: we expect bisection tasks to eventually favour shared representations, whereas studies on the spatial-numerical association of response codes (SNARC) effect currently favour different representations. We discuss how this impasse may be resolved, in particular, by combining these behavioural studies with relevant neuroimaging data. If this approach is carried forward, then it may help decide which of these two theoretical perspectives on number representations is correct.

Content-specific codes of parametric auditory working memory in humans

Brain activity in frontal regions has been found to represent frequency information with a parametric code during working memory delay phases. The mental representation of frequencies has furthermore been shown to be modality independent in non-human primate electrophysiology and human EEG studies, suggesting frontal regions encoding quantitative information in a supramodal manner. A recent fMRI study using multivariate pattern analysis (MVPA) supports an overlapping multimodal network for the maintenance of visual and tactile frequency information over frontal and parietal brain regions. The present study extends the investigation of working memory representation of frequency information to the auditory domain. To this aim, we used MVPA on fMRI data recorded during an auditory frequency maintenance task. A support vector regression analysis revealed working memory information in auditory association areas and, consistent with earlier findings of parametric working memory, in a frontoparietal network. A direct comparison to an analogous dataset of vibrotactile parametric working memory revealed an overlap of information coding in prefrontal regions, particularly in the right inferior frontal gyrus. Therefore, our findings indicate that the prefrontal cortex represents frequency-specific working memory content irrespective of the modality as has been now also revealed for the auditory modality.

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.

Neural activation patterns and connectivity in visual attention during Number and Non-number processing: An ERP study using the Ishihara pseudoisochromatic plates

Visual cognitive function is important to build up executive function in daily life. Perception of visual Number form (e.g., Arabic digit) and numerosity (magnitude of the Number) is of interest to cognitive neuroscientists. Neural correlates and the functional measurement of Number representations are complex occurrences when their semantic categories are assimilated with other concepts of shape and colour. Colour perception can be processed further to modulate visual cognition. The Ishihara pseudoisochromatic plates are one of the best and most common screening tools for basic red-green colour vision testing. However, there is a lack of study of visual cognitive function assessment using these pseudoisochromatic plates. We recruited 25 healthy normal trichromat volunteers and extended these studies using a 128-sensor net to record event-related EEG. Subjects were asked to respond by pressing Numbered buttons when they saw the Number and Non-number plates of the Ishihara colour vision test. Amplitudes and latencies of N100 and P300 event related potential (ERP) components were analysed from 19 electrode sites in the international 10-20 system. A brain topographic map, cortical activation patterns and Granger causation (effective connectivity) were analysed from 128 electrode sites. No major significant differences between N100 ERP components in either stimulus indicate early selective attention processing was similar for Number and Non-number plate stimuli, but Non-number plate stimuli evoked significantly higher amplitudes, longer latencies of the P300 ERP component with a slower reaction time compared to Number plate stimuli imply the allocation of attentional load was more in Non-number plate processing. A different pattern of asymmetric scalp voltage map was noticed for P300 components with a higher intensity in the left hemisphere for Number plate tasks and higher intensity in the right hemisphere for Non-number plate tasks. Asymmetric cortical activation and connectivity patterns revealed that Number recognition occurred in the occipital and left frontal areas where as the consequence was limited to the occipital area during the Non-number plate processing. Finally, the results displayed that the visual recognition of Numbers dissociates from the recognition of Non-numbers at the level of defined neural networks. Number recognition was not only a process of visual perception and attention, but it was also related to a higher level of cognitive function, that of language.