Left parietal TMS disturbs priming between symbolic and non-symbolic number representations

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

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

Role of the intraparietal sulcus (IPS) in anxiety and cognition: Opportunities for intervention for anxiety-related disorders

Our objective was to review the literature on the parietal cortex and intraparietal sulcus (IPS) in anxiety-related disorders, as well as opportunities for using neuromodulation to target this region and reduce anxiety. We provide an overview of prior research demonstrating: 1) the importance of the IPS in attention, vigilance, and anxious arousal, 2) the potential for neuromodulation of the IPS to reduce unnecessary attention toward threat and anxious arousal as demonstrated in healthy samples; and 3) limited data on the potential for neuromodulation of the IPS to reduce hyper-attention toward threat and anxious arousal among clinical samples with anxiety-related disorders. Future research should evaluate the efficacy of IPS neuromodulation in fully powered clinical trials, as well as the value in augmenting evidence-based treatments for anxiety with IPS neuromodulation.

Early neural markers for individual difference in mathematical achievement determined from rational number processing

The neural markers for individual differences in mathematical achievement have been studied extensively using magnetic resonance imaging; however, high temporal resolution electrophysiological evidence for individual differences in mathematical achievement require further elucidation. This study evaluated the event-related potential (ERP) when 48 college students with high or low mathematical achievement (HA vs. LA) matched non-symbolic and symbolic rational numbers. Behavioral results indicated that HA students had better performance in the discretized non-symbolic matching, although the two groups showed similar performances in the continuous matching. ERP data revealed that even before non-symbolic stimulus presentation, HA students had greater Bereitschaftspotential (BP) amplitudes over posterior central electrodes. After the presentation of non-symbolic numbers, HA students had larger N1 amplitudes at 160 ms post-stimulus, over left-lateralized parieto-occipital electrodes. After the presentation of symbolic numbers, HA students displayed more profound P1 amplitudes at 100 ms post-stimulus, over left parietal electrodes. Furthermore, larger BP and N1 amplitudes were associated with the shorter reaction times, and larger P1 amplitudes corresponded to lower error rates. The BP effect could indicate preparation processing, and early left-lateralized N1 and P1 effects could reflect the non-symbolic and symbolic number processing along the dorsal neural pathways. These results suggest that the left-lateralized P1 and N1 components elicited by matching non-symbolic and symbolic rational numbers can be considered as neurocognitive markers for individual differences in mathematical achievement.

Automatic integration of numerical formats examined with frequency-tagged EEG

How humans integrate and abstract numerical information across different formats is one of the most debated questions in human cognition. We addressed the neuronal signatures of the numerical integration using an EEG technique tagged at the frequency of visual stimulation. In an oddball design, participants were stimulated with standard sequences of numbers (< 5) depicted in single (digits, dots, number words) or mixed notation (dots-digits, number words-dots, digits-number words), presented at 10 Hz. Periodically, a deviant stimulus (> 5) was inserted at 1.25 Hz. We observed significant oddball amplitudes for all single notations, showing for the first time using this EEG technique, that the magnitude information is spontaneously and unintentionally abstracted, irrespectively of the numerical format. Significant amplitudes were also observed for digits-number words and number words-dots, but not for digits-dots, suggesting an automatic integration across some numerical formats. These results imply that direct and indirect neuro-cognitive links exist across the different numerical formats.

Frequency-based Dissociation of Symbolic and Nonsymbolic Numerical Processing during Numerical Comparison

Recent evidence suggests that during numerical calculation, symbolic and nonsymbolic processing are functionally distinct operations. Nevertheless, both roughly recruit the same brain areas (spatially overlapping networks in the parietal cortex) and happen at the same time (roughly 250 msec poststimulus onset). We tested the hypothesis that symbolic and nonsymbolic processing are segregated by means of functionally relevant networks in different frequency ranges: high gamma (above 50 Hz) for symbolic processing and lower beta (12–17 Hz) for nonsymbolic processing. EEG signals were quantified as participants compared either symbolic numbers or nonsymbolic quantities. Larger EEG gamma-band power was observed for more difficult symbolic comparisons (ratio of 0.8 between the two numbers) than for easier comparisons (ratio of 0.2) over frontocentral regions. Similarly, beta-band power was larger for more difficult nonsymbolic comparisons than for easier ones over parietal areas. These results confirm the existence of a functional dissociation in EEG oscillatory dynamics during numerical processing that is compatible with the notion of distinct linguistic processing of symbolic numbers and approximation of nonsymbolic numerical information.

Anodal High-definition Transcranial Direct Current Stimulation over the Posterior Parietal Cortex Modulates Approximate Mental Arithmetic

The representation and processing of numerosity is a crucial cognitive capacity. Converging evidence points to the posterior parietal cortex (PPC) as primary "number" region. However, the exact role of the left and right PPC for different types of numerical and arithmetic tasks remains controversial. In this study, we used high-definition transcranial direct current stimulation (HD-tDCS) to further investigate the causal involvement of the PPC during approximative, nonsymbolic mental arithmetic. Eighteen healthy participants received three sessions of anodal HD-tDCS at 1-week intervals in counterbalanced order: left PPC, right PPC, and sham stimulation. Results showed an improved performance during online parietal HD-tDCS (vs. sham) for subtraction problems. Specifically, the general tendency to underestimate the results of subtraction problems (i.e., the "operational momentum effect") was reduced during online parietal HD-tDCS. There was no difference between left and right stimulation. This study thus provides new evidence for a causal involvement of the left and right PPC for approximate nonsymbolic arithmetic and advances the promising use of noninvasive brain stimulation in increasing cognitive functions.

Effects of online repetitive transcranial magnetic stimulation (rTMS) on cognitive processing: A meta-analysis and recommendations for future studies

Online repetitive transcranial magnetic stimulation (rTMS), applied while subjects are performing a task, is widely used to disrupt brain regions underlying cognition. However, online rTMS has also induced "paradoxical enhancement". Given the rapid proliferation of this approach, it is crucial to develop a better understanding of how online stimulation influences cognition, and the optimal parameters to achieve desired effects. To accomplish this goal, a quantitative meta-analysis was performed with random-effects models fitted to reaction time (RT) and accuracy data. The final dataset included 126 studies published between 1998 and 2016, with 244 total effects for reaction times, and 202 for accuracy. Meta-analytically, rTMS at 10 Hz and 20 Hz disrupted accuracy for attention, executive, language, memory, motor, and perception domains, while no effects were found with 1 Hz or 5 Hz. Stimulation applied at and 10 and 20 Hz slowed down RTs in attention and perception tasks. No performance enhancement was found. Meta-regression analysis showed that fMRI-guided targeting and short inter-trial intervals are associated with increased disruptive effects with rTMS.

Symbolic estrangement or symbolic integration of numerals with quantities: Methodological pitfalls and a possible solution

Previous studies, which examined whether symbolic and non-symbolic quantity representations are processed by two independent systems or by one common system, reached contradicting findings, possibly due to methodological differences. Indeed, some researchers advocate the two systems approach, based on the presence of notation-specific switch cost in conditions where adults have to compare pairs of symbolic and non-symbolic quantities, in combination with the absence of such a cost in conditions containing quantities of the same notation. However, other researchers used matching instructions, and reported a facilitation in the mixed notation conditions, suggesting that the two systems are automatically integrated. In the current study, we conducted three experiments, in which we examined the existence of two separate quantity systems, but we used various experimental manipulations (e.g., task instructions, presentation order) to unravel the previous inconsistent findings. In Experiment 1, we investigated the role of task instructions by presenting participants with pure and mixed notation trials with both comparison and matching tasks. In Experiment 2, we tested the role of blocked and randomized presentation order for the pure and mixed trials. Our data showed that cost for switching between the symbolic and non-symbolic quantities is present, but is prone to a certain methodological drawback: when the differences between the processing times for two sequentially presented stimuli of different notations are not taken into account, this masks the cost for switching between the two systems. To overcome this problem, in Experiment 3 we used an audio-visual paradigm. Overall, our results provide further evidence for the existence of distinct quantity representations, independently of task instructions or presentation order. Additionally, considering this methodological pitfall we argue that the audio-visual paradigm is better suited when investigating the integration between symbolic and non- symbolic quantities.

Different Neural Mechanisms for the Comparison and Priming Distance Effects: An fMRI Study

Using functional magnetic resonance imaging, the present study examined whether the comparison distance effect (CDE) and the priming distance effect (PDE) in number processing had the same underlying neural mechanisms. 24 healthy participants completed a number comparison task and a number priming task in the scanner. Imaging data were examined for brain regions selected based on a meta-analysis of previous studies of number processing. Results revealed robust CDE and PDE at both behavioral and neural levels. The CDE had a significant hemodynamic signature in the right parietal cortex but not in the left parietal cortex, although a direct test of this hemispheric laterality did not reach statistical significance. In contrast, the PDE showed significant left-hemisphere laterality with a significant hemodynamic signature in the left parietal cortex but not in the right parietal cortex. These results suggested that the CDE and PDE had different underlying neural mechanisms.

The Symbol Grounding Problem Revisited: A Thorough Evaluation of the ANS Mapping Account and the Proposal of an Alternative Account Based on Symbol-Symbol Associations

Recently, a lot of studies in the domain of numerical cognition have been published demonstrating a robust association between numerical symbol processing and individual differences in mathematics achievement. Because numerical symbols are so important for mathematics achievement, many researchers want to provide an answer on the ‘symbol grounding problem,’ i.e., how does a symbol acquires its numerical meaning? The most popular account, the approximate number system (ANS) mapping account, assumes that a symbol acquires its numerical meaning by being mapped on a non-verbal and ANS. Here, we critically evaluate four arguments that are supposed to support this account, i.e., (1) there is an evolutionary system for approximate number processing, (2) non-symbolic and symbolic number processing show the same behavioral effects, (3) non-symbolic and symbolic numbers activate the same brain regions which are also involved in more advanced calculation and (4) non-symbolic comparison is related to the performance on symbolic mathematics achievement tasks. Based on this evaluation, we conclude that all of these arguments and consequently also the mapping account are questionable. Next we explored less popular alternative, where small numerical symbols are initially mapped on a precise representation and then, in combination with increasing knowledge of the counting list result in an independent and exact symbolic system based on order relations between symbols. We evaluate this account by reviewing evidence on order judgment tasks following the same four arguments. Although further research is necessary, the available evidence so far suggests that this symbol–symbol association account should be considered as a worthy alternative of how symbols acquire their meaning.

Adults' arithmetic builds on fast and automatic processing of arabic digits: evidence from an audiovisual matching paradigm

Several studies have shown that performance on symbolic number tasks is related to individual differences in arithmetic. However, it is not clear which process is responsible for this association, i.e. fast, automatic processing of symbols per se or access to the underlying non-symbolic representation of the symbols. To dissociate between both options, adult participants performed an audiovisual matching paradigm. Auditory presented number words needed to be matched with either Arabic digits or dot patterns. The results revealed that a distance effect was present in the dots-number word matching task and absent in the digit-number word matching task. Crucially, only performance in the digit task contributed to the variance in arithmetical abilities. This led us to conclude that adults' arithmetic builds on the ability to quickly and automatically process Arabic digits, without the underlying non-symbolic magnitude representation being activated.