Transcranial direct current stimulation (tDCS) reveals a dissociation between SNARC and MARC effects: Implication for the polarity correspondence account

High-definition turns timing-dependent: Different behavioural consequences during and following cathodal high-definition transcranial direct current stimulation (HD tDCS) in a magnitude classification task

Neuromodulation with transcranial direct current stimulation (tDCS) can transiently alter neural activity, but its spatial precision is low. High-definition (HD) tDCS was introduced to increase spatial precision by placing additional electrodes over the scalp. Initial evaluations of HD tDCS indicated polarity-specific neurophysiological effects-similar to conventional tDCS albeit with greater spatial precision. Here, we compared the effects of cathodal tDCS or HD tDCS in a 4 × 1 configuration over prefrontal cortex (PFC) regions on behavioural outcomes in a magnitude classification task. We report results on overall performance, on the numerical distance effect as a measure of numerical processing, and on the spatial-numerical associations of response codes (SNARC) effect, which was previously affected by prefrontal tDCS. Healthy volunteers (n = 68) received sham or cathodal HD tDCS at 1 mA over the left dorsolateral prefrontal cortex (DLPFC) or the left inferior frontal gyrus (IFG). Results were compared to an identical protocol with conventional cathodal tDCS to the left PFC versus sham (n = 64). Mixed effects models showed performance gains relative to sham tDCS in all conditions after tDCS (i.e. 'offline'), whereas montages over PFC and DLPFC already showed performance gains during tDCS (i.e. 'online'). In contrast to conventional tDCS, HD tDCS did not reduce the SNARC effect. Neither condition affected numerical processing, as expected. The results suggest that HD tDCS with cathodal polarity might require further adjustments (i.e. regarding tDCS intensity) for effective modulations of cognitive-behavioural performance, which could be achieved by individualised current density in electric field modelling.

Regional specificity of cathodal transcranial direct current stimulation effects on spatial-numerical associations: Comparison of four stimulation sites

Neuromodulation with transcranial direct current stimulation (tDCS) is an increasingly popular research tool to experimentally manipulate cortical areas and probe their causal involvements in behavior, but its replicability and regional specificity are not clear. This registered report investigated cathodal tDCS effects on spatial-numerical associations (i.e., the SNARC effect), the numerical distance effect (NDE), and inhibitory control (i.e., stop-signal reaction time; SSRT). Healthy adults (N = 160) were randomly assigned to one of five groups to receive sham tDCS or 1 mA cathodal tDCS to one of four stimulation sites (left/right prefrontal cortex [PFC], left/right posterior parietal cortex) with extracephalic return. We replicated that cathodal tDCS over the left PFC reduced the SNARC effect compared to sham tDCS and to tDCS over the left parietal cortex. However, neither NDE nor SSRT were modulated in the main analyses. Post hoc contrasts and exploratory analyses showed that cathodal tDCS over the right PFC had a time-dependent effect by delayed practice-related improvements in SSRT. Math anxiety moderated changes in the NDE in the groups receiving tDCS to the right parietal cortex. With few exceptions, the replicability and regional specificity of tDCS effects on behavior were weak and partially moderated by individual differences. Future research needs to characterize the parameter settings for effective neuromodulation.

tDCS effects in basic symbolic number magnitude processing are not significantly lateralized

Functional lateralization was previously established for various cognitive domains-but not for number processing. Although numbers are considered to be bilaterally represented in the intraparietal sulcus (IPS), there are some indications of different functional roles of the left vs. right IPS in processing number pairs with small vs. large distance, respectively. This raises the question whether number size plays a distinct role in the lateralization within the IPS. In our preregistered study, we applied anodal transcranial direct current stimulation (tDCS) over the left vs. right IPS to investigate the effect of stimulation as compared to sham on small vs. large distance, in both single-digit and two-digit number comparison. We expected that anodal tDCS over the left IPS facilitates number comparison with small distance, while anodal tDCS over the right IPS facilitates number comparison with large distance. Results indicated no effect of stimulation; however, exploratory analyses revealed that tDCS over the right IPS slowed down single-digit number processing after controlling for the training effect. In conclusion, number magnitude processing might be bilaterally represented in the IPS, however, our exploratory analyses emphasise the need for further investigation on functional lateralization of number processing.

The role of cognitive control in the SNARC effect: A review

The spatial-numerical association of response codes (SNARC) effect, in which people respond to small numbers faster with the left hand and to large numbers faster with the right hand, is a popular topic in cognitive psychology. Some well-known theoretical accounts explaining this effect include the mental number line model, polarity correspondence principle, dual-route model, and working memory account. However, these fail to explain the finding that the size of the SNARC effect is modulated by cognitive control. Here, we propose a new account-a cognitive control-based view of the SNARC effect. This view argues that the SNARC effect is fundamentally determined by cognitive control in resolving conflicts during stimulus-response mapping. Several subcomponents of cognitive control, such as working memory, mental or task set shifting, inhibition control, and conflict adaptation, can easily modulate the SNARC effect. The cognitive control-based view can account for the flexible SNARC effect observed in diverse task situations while providing new insight into its mechanism.

Is 'heavy' up or down? Testing the vertical spatial representation of weight

Smaller numbers are typically responded to faster with a bottom than a top key, whereas the opposite occurs for larger numbers (a vertical spatial-numerical association of response codes: i.e. the vertical SNARC effect). Here, in four experiments, we explored whether a vertical spatial-magnitude association can emerge for lighter vs. heavier items. Participants were presented with a central target stimulus that could be a word describing a material (e.g. 'paper', 'iron': Experiment 1), a numerical quantity of weight (e.g. '1 g', '1 kg': Experiment 2) or a picture associated with a real object that participants weighed before the experiment (Experiments 3a/3b). Participants were asked to respond either to the weight (Experiments 1-3a) or to the size (i.e. weight was task-irrelevant; Experiment 3b) of the stimuli by pressing vertically placed keys. In Experiments 1 and 2, faster responses emerged for the lighter-bottom/heavier-top mapping-in line with a standard SNARC-like effect-whereas in Experiment 3a the opposite mapping emerged (lighter-top/heavier-bottom). No evidence of an implicit weight-space association emerged in Experiment 3b. Overall, these results provide evidence indicating a possible context-dependent vertical spatial representation of weight.

Regional specificity of cathodal transcranial direct current stimulation (tDCS) effects on spatial-numerical associations: Comparison of four stimulation sites

Based on a theory of impulsive and reflective human behavior, we test the effects of transcranial direct current stimulation (tDCS) targeting either prefrontal or parietal cortex in either hemisphere. In a confirmatory registered report, cathodal tDCS is administered to conceptually reproduce tDCS modulations of implicit spatial-numerical associations, numerical distance effects, and response inhibition. Those cognitive operations are hypothesized to draw on left prefrontal, parietal, and right prefrontal activations, respectively, thereby susceptible to inhibitory, cathodal tDCS across those regions. Vice versa, the mutual regional and behavioral specificity of tDCS effects on these behavioral indices is examined and expected to produce double dissociations. In a mixed within-subjects (baseline, during tDCS, post-tDCS) and between-subjects (target electrode: left/right prefrontal cortex/posterior parietal cortex, or sham tDCS) design, we collect (a) confirmatory data on the robustness of cathodal tDCS effects on three behavioral effects and (b) differential data on the specificity of regional targets in male and female human participants. Results will provide crucial tests of theories of cortical organization implied by implicit associations and explicit regulation, which can direct future brain stimulation studies.

Order versus chaos: The impact of structure on number-space associations

The Spatial-Numerical Association of Response Codes (SNARC) effect has been observed with different stimuli, beside Arabic numerals, such as written/spoken number words, sequences of acoustic stimuli, and groups of elements. Here we investigated how the enumeration of sets of elements can be affected by the spatial configuration of the displayed stimuli with regard to the emergence of the SNARC effect. To this aim, we asked participants to perform a magnitude comparison task with structured (i.e., dice-like) and unstructured (i.e., random) patterns of rectangles. With this manipulation, we sought to explore the presence of the SNARC effect in relation to the structure of the displayed visual stimuli. The results showed that the spatial arrangement of rectangles does not impact visual enumeration processes leading to the SNARC effect. An unexpected reversal of the size effect for unstructured stimuli was also observed. We speculate that the presence of a similar SNARC effect, both with structured and unstructured stimuli, indicates the existence of a common access to the mental number line.

The SNARC effect is not a unitary phenomenon

Models of the spatial-numerical association of response codes (SNARC) effect-faster responses to small numbers using left effectors, and the converse for large numbers-diverge substantially in localizing the root cause of this effect along the numbers' processing chain. One class of models ascribes the cause of the SNARC effect to the inherently spatial nature of the semantic representation of numerical magnitude. A different class of models ascribes the effect's cause to the processing dynamics taking place during response selection. To disentangle these opposing views, we devised a paradigm combining magnitude comparison and stimulus-response switching in order to monitor modulations of the SNARC effect while concurrently tapping both semantic and response-related processing stages. We observed that the SNARC effect varied nonlinearly as a function of both manipulated factors, a result that can hardly be reconciled with a unitary cause of the SNARC effect.

Evidence of SQUARC and distance effects in a weight comparison task

Stimuli associated with large quantities are typically responded to faster with a right- than a left-side key, whereas stimuli associated with small quantities are typically responded to faster with a left- than a right-side key. This phenomenon is known as the spatial-quantity association of response codes (SQUARC) effect. Here, in two experiments, we explored whether a SQUARC effect can emerge for light versus heavy items. Participants judged whether the weight associated with a central target word, describing an animal (e.g. 'cow'; Experiment 1) or a material (e.g. 'iron'; Experiment 2), was lighter or heavier than the weight associated with a reference word. Responses were provided with a left- and a right-side button. Then, participants estimated the weight associated with target and reference words. In both experiments, evidence for a SQUARC effect emerged. Moreover, response times for each target word decreased with absolute difference between its rated weight and the rated weight of the reference word, in line with a distance effect. Overall, these results provide evidence of a possible spatial representation of weight.

On the genesis of spatial-numerical associations: Evolutionary and cultural factors co-construct the mental number line

Mapping numbers onto space is a common cognitive representation that has been explored in both behavioral and neuroimaging contexts. Empirical work probing the diverse nature of these spatial-numerical associations (SNAs) has led researchers to question 1) how the human brain links numbers with space, and 2) whether this link is biologically vs. culturally determined. We review the existing literature on the development of SNAs and situate that empirical work within cognitive and neuroscientific theoretical frameworks. We propose that an evolutionarily-ancient frontal-parietal circuit broadly tuned to multiple magnitude dimensions provides the phylogenetic substrate for SNAs, while enculturation and sensorimotor experience shape their specific profiles. We then use this perspective to discuss educational implications and highlight promising avenues for future research.

Switching between Multiple Codes of SNARC-Like Associations: Two Conceptual Replication Attempts with Anodal tDCS in Sham-Controlled Cross-Over Design

In societies with left-to-right reading direction, left-side vs. right-side behavioral decisions are faster for relatively small vs. large number magnitudes, and vice versa, a phenomenon termed Spatial-Numerical Associations of Response Codes (SNARC) effect. But also for non-numerical sequential items, SNARC-like effects were observed, suggesting a common neurocognitive mechanism based on the ordinal structures of both numbers and sequences. Modulation of prefrontal networks that are involved in providing spatial associations during cognitive behavior can contribute to elaborate their neuropsychological theoretical foundations. With transcranial direct current stimulation (tDCS) directed to the left prefrontal cortex, we recently showed that (i) cathodal tDCS can block the emergence of spatial-numerical associations and that (ii) anodal tDCS can reverse spatial associations of sequential order, most likely based on markedness correspondence. Two conceptual replication attempts of the latter reversal of space-order associations are presented in the current sham-controlled experiment, using either weekdays (Monday-Friday) or month names (January-December) as stimuli in the temporal order classification task. In addition, to control for possible influences of notation, number stimuli were presented as written German names (One-Five). We report on a successful modulation of spatial-numerical associations of response codes (SNARC) effects with month stimuli induced by anodal tDCS, but failed to observe the same reversal of SNARC effects for weekday stimuli. The former stimulation effect was orthogonal to the small anodal tDCS effect on written number words, which replicates the dissociation of SNARC effects for numbers vs. non-numerical sequences. Moreover, this result reinforces the hypothesis that the ordinal item and task structure was the source of dissociation (as opposed to verbal presentation). We suggest that the diverging results can be explained by the markedness correspondence account of spatial associations in a multiple coding framework. Left-hemispheric prefrontal excitation from anodal tDCS renders verbal markedness relatively more dominant, but this effect is not absolute. We discuss task contagion, study design, and individual differences in performance measures or tDCS response as possible contributors to systematic variation of the weights of multiple coding parameters for spatial-numerical associations.

A SMARC Effect for Loudness

Various reports suggest that the pitch height of musical tones may be represented along a mental space, with lower pitch heights represented on the left or lower sectors and higher pitch heights represented on the right or upper sectors of the mental space. Given that in Western languages the loudness of tones is often addressed spatially, with loud sounds referred to as “high” and quiet sounds referred to as “low,” here we investigated whether loudness might also have a spatial representation. Participants judged whether a tone was louder or quieter than a reference tone, by pressing two keys: one at the top and the other at the bottom of a response box. Participants were faster in a situation where they pressed the key at the top to report louder sounds, and the key at the bottom to report quieter sounds, than vice versa. This result supports the view that loudness, like other types of magnitudes, might be represented spatially.