Number-space interactions in the human parietal cortex: Enlightening the SNARC effect with functional near-infrared spectroscopy

What makes different number-space mappings interact?

Models of numerical cognition consider a visuo-spatial representation to be at the core of numerical processing, the 'mental number line'. Two main interference effects between number and space have been described: the SNARC effect reflects a small number/left side and large number/right side association (number-location mapping); the size-congruity effect (SCE) reflects a small number/small size and large number/large size association (number-size mapping). Critically, a thorough investigation on the representational source for these two number-space mappings is lacking, leaving open the question of whether the same representation underlies both phenomena. Here, we build on a recent study (Viarouge and de Hevia in Front Hum Neurosci 15:750964, 2021) in order to address this question in three experiments, by systematically manipulating the presence of the two conditions that might elicit an interaction between SNARC and SCE: (i) an implicit task whereby numerical and spatial information are task-irrelevant, (ii) a design in which the number-space congruency relative to both mappings vary at the same level -either both within or between blocks. Experiment 1 replicated the interaction between the two mappings when both factors were present. Experiments 2 and 3 dissociated the two factors by varying the two mappings at the same level but using an explicit comparison task (Experiment 2), or by using an implicit task but with mappings varying at different levels (Experiment 3). We found that both factors, either in combination or used in isolation, drive the interaction between the two number-space mappings. These findings are discussed in terms of the weight given to each mapping, suggesting that a single representation encompassing both number-space mappings is therefore activated whenever both mappings are given equal weight through task requirements.

Similarities of SNARC, cognitive Simon, and visuomotor Simon effects in terms of response time distributions, hand-stimulus proximity, and temporal dynamics

The spatial-numerical association of response codes (SNARC) and Simon effects are attributed to the same type of conflict according to dimensional overlap (DO) theory: the congruency of task-irrelevant spatial information and the selected response (e.g., left or right). However, previous studies have yielded inconsistent results regarding the relationship between the two effects, with some studies reporting an interaction while others did not. This discrepancy may be attributed to the use of different types of Simon effects (visuomotor and cognitive Simon effects) in these studies, as the spatial codes associated with these two types of Simon effects are distinct (exogenous and endogenous, respectively). The aim of this study was to address these inconsistencies and gain a better understanding of the similarities and differences in spatial representations generated by spatial location, semantic information, and numerical information. We attempted to classify the relationships among the SNARC and Simon effects. Specifically, the visuomotor Simon, cognitive Simon, and SNARC effects were compared from three perspectives: the response time (RT) distribution, hand-stimulus proximity, and temporal dynamics (with the drift diffusion model; DDM). Regarding RTs, the results showed that the visuomotor Simon effect decreased with increased values of RT bins, while the cognitive Simon and SNARC effects increased. Additionally, the visuomotor Simon effect was the only effect influenced by hand-stimulus proximity, with a stronger effect observed in the hand-proximal condition than in the hand-distal condition. Regarding the DDM results, only the visuomotor Simon effect exhibited a higher drift rate and longer non-decision time in the incompatible condition than in the compatible condition. Conversely, both the SNARC and cognitive Simon effects exhibited an inverse pattern regarding the drift rate and no significant difference in non-decision time between the two conditions. These findings suggest that the SNARC effect is more similar to the cognitive Simon effect than the visuomotor Simon effect, indicating that the endogenous spatial-numerical representation of the SNARC effect might share an underlying processing mechanism with the endogenous spatial-semantic representation of the cognitive Simon effect but not with the exogenous location representation of the visuomotor Simon effect. Our results further demonstrate that the origin of spatial information could impact the classification of conflicts and supplement DO theory.

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.

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.

Multiple levels of contextual influence on action-based timing behavior and cortical activation

Procedures used to elicit both behavioral and neurophysiological data to address a particular cognitive question can impact the nature of the data collected. We used functional near-infrared spectroscopy (fNIRS) to assess performance of a modified finger tapping task in which participants performed synchronized or syncopated tapping relative to a metronomic tone. Both versions of the tapping task included a pacing phase (tapping with the tone) followed by a continuation phase (tapping without the tone). Both behavioral and brain-based findings revealed two distinct timing mechanisms underlying the two forms of tapping. Here we investigate the impact of an additional-and extremely subtle-manipulation of the study's experimental design. We measured responses in 23 healthy adults as they performed the two versions of the finger-tapping tasks either blocked by tapping type or alternating from one to the other type during the course of the experiment. As in our previous study, behavioral tapping indices and cortical hemodynamics were monitored, allowing us to compare results across the two study designs. Consistent with previous findings, results reflected distinct, context-dependent parameters of the tapping. Moreover, our results demonstrated a significant impact of study design on rhythmic entrainment in the presence/absence of auditory stimuli. Tapping accuracy and hemodynamic responsivity collectively indicate that the block design context is preferable for studying action-based timing behavior.

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.

Sensorimotor ability and inhibitory control independently predict attainment in mathematics in children and adolescents

We previously linked interceptive timing performance to mathematics attainment in 5- to 11-yr-old children, which we attributed to the neural overlap between spatiotemporal and numerical operations. This explanation implies that the relationship should persist through the teenage years. Here, we replicated this finding in adolescents (n = 200, 11-15 yr). However, an alternative explanation is that sensorimotor proficiency and academic attainment are both consequences of executive function. To assess this competing hypothesis, we developed a measure of a core executive function, inhibitory control, from the kinematic data. We combined our new adolescent data with the original children's data (total n = 568), performing a novel analysis controlling for our marker of executive function. We found that the relationship between mathematics and interceptive timing persisted at all ages. These results suggest a distinct functional link between interceptive timing and mathematics that operates independently of our measure of executive function.NEW & NOTEWORTHY Previous research downplays the role of sensorimotor skills in the development of higher-order cognitive domains such as mathematics: using inadequate sensorimotor measures, differences in "executive function" account for any shared variance. Utilizing a high-resolution, kinematic measure of a sensorimotor skill previously linked to mathematics attainment, we show that inhibitory control alone cannot account for this relationship. The practical implication is that the development of children's sensorimotor skills must be considered in their intellectual development.

Attention upturned: Bias toward and away from the affected side of the body and near space in a case of complex regional pain syndrome

People with Complex Regional Pain Syndrome (CRPS) following limb injury can show neuropsychological symptoms in the absence of observable brain pathologies. These can include sensory changes, distorted body representation, and inattention to their affected limb and its surrounding space, resembling post-stroke hemispatial neglect. The precise nature and mechanisms of these neuropsychological symptoms are unclear, however insights could be gained by testing for dissociations and associations that have been observed in stroke patients. Drawing from clinical and experimental methods for investigating spatial attention bias and related symptoms in stroke patients, we conducted a detailed investigation of neuropsychological symptoms in a woman with CRPS of her left arm who initially presented to us with pronounced inattention to her affected side. The patient showed visual and tactile neglect and extinction on her affected side on confrontation tests, but no attention deficits on "bedside" tests of neglect. On sensitive computer-based measures, attention biases were found in the patient's body and near space (in Temporal Order Judgements), but not far or imagined space (on the Greyscales task and Mental Number Line Bisection). Unique to the current literature, the patient showed a reversal in her Temporal Order Judgement bias across time, from inattention (first and second session) to hyperattention (third session) to her affected side. In contrast, pain and self-reported body representation distortion were similar across the three sessions. The patient had reduced central and peripheral visual acuity, however these deficits were near symmetrical and therefore could not explain her performance on the visual attention tasks. Given that spatial attention bias has been linked to imbalance in relative activation of the two cerebral hemispheres, we administered a Global-Local processing task to test for hemispheric asymmetry. This revealed no difference in global compared to local interference refuting any hemispheric imbalance. Instead, the patient showed impaired performance (compared to controls) on incongruent trials regardless of trial type, consistent with executive impairment. We conclude that spatial attention bias in CRPS can generalize across different sensory modalities and extend beyond the affected limb to the external space around it, independent of any low-level sensory disturbances. This bias is not necessarily directed away from the affected side or stable over time. People with CRPS can also demonstrate more generalized neuropsychological changes in sensory and executive functions. Our observations refute several existing theories about the mechanisms of attention bias in CRPS, and their relationship to pain, and have potential implications for treatment.

Two processing stages of the SNARC effect

The spatial-numerical association of response codes (SNARC) effect showed that small/large numbers represented in the left/right space facilitated left/right responses, respectively. However, the processing stage (semantic representation or response selection) of the SNARC effect is still controversial. To investigate this issue, we adopted a modified magnitude comparison task in which the effects of SNARC, Stroop (semantic-representation stage), and Simon (response-selection stage) could be simultaneously induced. The processing stages of the SNARC effect were investigated by examining the interactions among these effects. According to the additive factor logic, if two effects are interactive, then they occur in the same stage; if two effects are additive, then they occur in different stages. Across two experiments, the SNARC effect interacted with the Stroop effect and with the Simon effect. These results suggested that the SNARC effect occurred in both the semantic-representation and response-selection stages and provided insight into that the SNARC effect might have two originating sources.

Knowledge Across Reference Frames: Cognitive Maps and Image Spaces

In human and non-human animals, conceptual knowledge is partially organized according to low-dimensional geometries that rely on brain structures and computations involved in spatial representations. Recently, two separate lines of research have investigated cognitive maps, that are associated with the hippocampal formation and are similar to world-centered representations of the environment, and image spaces, that are associated with the parietal cortex and are similar to self-centered spatial relationships. We review evidence supporting cognitive maps and image spaces, and we propose a hippocampal-parietal network that can account for the organization and retrieval of knowledge across multiple reference frames. We also suggest that cognitive maps and image spaces may be two manifestations of a more general propensity of the mind to create low-dimensional internal models.

Exploring the interactions among SNARC effect, finger counting direction and embodied cognition

The Spatial Numerical Association of Response Code (SNARC) is the preferential association between smaller/larger magnitudes and left/right side, respectively. Some evidence suggest a link between SNARC and a left-to-right finger counting habit. We asked 268 participants to show how they use the hands to count from 1 to 10. By means of this ecological task, 80% of the sample use first the right hand (to count from 1 to 5) and the majority of them use a palm-up posture. In Experiment 2 (N = 46) right-starters were asked to categorize 1-to-5 magnitudes as even or odd, using the left and right hand. Stimuli were presented both as Arabic numbers and by means of left and right hand photographs in palm-up and palm-down posture. Results confirmed the expected SNARC effect in the Arabic condition. With hand images we found that right hand responses were better for larger than for smaller magnitudes (SNARC, mainly for left hand palm-up stimuli), showing that the SNARC can be generalized to different codes. Finally, the interactions between magnitudes and left/right hand images in palm-up and palm-down posture suggest that embodied cognition can influence numerical processing.

Neuropsychological Changes in Complex Regional Pain Syndrome (CRPS)

Complex Regional Pain Syndrome (CRPS) is a poorly understood chronic pain condition of multifactorial origin. CRPS involves sensory, motor, and autonomic symptoms primarily affecting one extremity. Patients can also present with neuropsychological changes such as reduced attention to the CRPS-affected extremity, reminiscent of hemispatial neglect, yet in the absence of any brain lesions. However, this "neglect-like" framework is not sufficient to characterise the range of higher cognitive functions that can be altered in CRPS. This comprehensive literature review synthesises evidence of neuropsychological changes in CRPS in the context of potential central mechanisms of the disorder. The affected neuropsychological functions constitute three distinct but not independent groups: distorted body representation, deficits in lateralised spatial cognition, and impairment of non-spatially-lateralised higher cognitive functions. We suggest that many of these symptoms appear to be consistent with a broader disruption to parietal function beyond merely what could be considered "neglect-like." Moreover, the extent of neuropsychological symptoms might be related to the clinical signs of CRPS, and rehabilitation methods that target the neuropsychological changes can improve clinical outcomes in CRPS and other chronic pain conditions. Based on the limitations and gaps in the reviewed literature, we provide several suggestions to improve further research on neuropsychological changes in chronic pain.

A Newcomer's Guide to Functional Near Infrared Spectroscopy Experiments

This review presents a practical primer for functional near-infrared spectroscopy (fNIRS) with respect to technology, experimentation, and analysis software. Its purpose is to jump-start interested practitioners considering utilizing a non-invasive, versatile, nevertheless challenging window into the brain using optical methods. We briefly recapitulate relevant anatomical and optical foundations and give a short historical overview. We describe competing types of illumination (trans-illumination, reflectance, and differential reflectance) and data collection methods (continuous wave, time domain and frequency domain). Basic components (light sources, detection, and recording components) of fNIRS systems are presented. Advantages and limitations of fNIRS techniques are offered, followed by a list of very practical recommendations for its use. A variety of experimental and clinical studies with fNIRS are sampled, shedding light on many brain-related ailments. Finally, we describe and discuss a number of freely available analysis and presentation packages suited for data analysis. In conclusion, we recommend fNIRS due to its ever-growing body of clinical applications, state-of-the-art neuroimaging technique and manageable hardware requirements. It can be safely concluded that fNIRS adds a new arrow to the quiver of neuro-medical examinations due to both its great versatility and limited costs.

Response-irrelevant number, duration, and extent information triggers the SQARC effect: Evidence from an implicit paradigm

Spatial-Numerical Association of Response Codes (SNARC) and Spatial-Quantity Association of Response Codes (SQARC) effects are evident when people produce faster left-sided responses to smaller numbers, sizes, and durations and faster right-sided responses to larger numbers, sizes, and durations. SQARC effects have typically been demonstrated in paradigms where the explicit processing of quantity information is required for successful task completion. The current study tested whether the implicit presentation of task-irrelevant magnitude information could trigger a SQARC effect as has been demonstrated previously when task-irrelevant information triggers a SNARC effect. In Experiment 1, participants (n = 20) made orientation judgements for triangles varying in numerosity and physical extent. In Experiment 2, participants (n = 20) made orientation judgements for triangles varying in numerosity and for a triangle preceded by a delay of varying duration. SNARC effects were observed for the numerosity conditions of Experiments 1 and 2 replicating Mitchell et al. SQARC effects were also demonstrated for physical extent and for duration. These findings demonstrate that SQARC effects can be implicitly triggered by the presentation of the task-irrelevant magnitude.

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.

Judging risk magnitude: walking to the left and base jumping to the right

When thinking about quantifiable domains such as numbers, pitch, and size, they are implicitly mapped on to representational space with small/low/less and large/high/more of the respective domain represented on the left and right sides of representational space, respectively. Recent research has also demonstrated that more abstract domains (colours, language, political party names) are also mapped in the same way. This study investigated a new abstract domain, risk, to examine if this same pattern of effects is apparent (left = low risk/right = high risk) to get a better understanding of how risk magnitudes are processed. Experiment 1 (n = 26) presented objective, statistically calculated risk stimuli (micromorts) to participants, who indicated if the stimuli had lower or higher risks than a referent, with their left and right hands. Experiment 2 (n = 25) utilised the same task, but the risk stimuli were generated by the participants themselves. Both experiments found the expected association of risk with space-indicated by faster left-hand responses to low-risk stimuli and faster right-hand responses to high-risk stimuli. Risks appear to fit onto a standard left-right spatial association; however, the effect sizes for all analyses were small. The results of this study are not only in line with the idea of a generalised magnitude processing system, but might also inform best practices in effective communications of risks.

There's a SNARC in the Size Congruity Task

The size congruity effect involves interference between numerical magnitude and physical size of visually presented numbers: congruent numbers (either both small or both large in numerical magnitude and physical size) are responded to faster than incongruent ones (small numerical magnitude/large physical size or vice versa). Besides, numerical magnitude is associated with lateralized response codes, leading to the Spatial Numerical Association of Response Codes (SNARC) effect: small numerical magnitudes are preferably responded to on the left side and large ones on the right side. Whereas size congruity effects are ascribed to interference between stimulus dimensions in the decision stage, SNARC effects are understood as (in)compatibilities in stimulus-response combinations. Accordingly, size congruity and SNARC effects were previously found to be independent in parity and in physical size judgment tasks. We investigated their dependency in numerical magnitude judgment tasks. We obtained independent size congruity and SNARC effects in these tasks and replicated this observation for the parity judgment task. The results confirm and extend the notion that size congruity and SNARC effects operate in different representational spaces. We discuss possible implications for number representation.

Number concepts: abstract and embodied

Numerical knowledge, including number concepts and arithmetic procedures, seems to be a clear-cut case for abstract symbol manipulation. Yet, evidence from perceptual and motor behaviour reveals that natural number knowledge and simple arithmetic also remain closely associated with modal experiences. Following a review of behavioural, animal and neuroscience studies of number processing, we propose a revised understanding of psychological number concepts as grounded in physical constraints, embodied in experience and situated through task-specific intentions. The idea that number concepts occupy a range of positions on the continuum between abstract and modal conceptual knowledge also accounts for systematic heuristics and biases in mental arithmetic, thus inviting psycho-logical approaches to the study of the mathematical mind.This article is part of the theme issue 'Varieties of abstract concepts: development, use and representation in the brain'.

Spatial grounding of symbolic arithmetic: an investigation with optokinetic stimulation

Growing evidence suggests that mental calculation might involve movements of attention along a spatial representation of numerical magnitude. Addition and subtraction on nonsymbolic numbers (numerosities) seem to induce a “momentum” effect, and have been linked to distinct patterns of neural activity in cortical regions subserving attention and eye movements. We investigated whether mental arithmetic on symbolic numbers, a cornerstone of abstract mathematical reasoning, can be affected by the manipulation of overt spatial attention induced by optokinetic stimulation (OKS). Participants performed additions or subtractions of auditory two-digit numbers during horizontal (experiment 1) or vertical OKS (experiment 2), and eye movements were concurrently recorded. In both experiments, the results of addition problems were underestimated, whereas results of subtractions were overestimated (a pattern that is opposite to the classic Operational Momentum effect). While this tendency was unaffected by OKS, vertical OKS modulated the occurrence of decade errors during subtractions (i.e., fewer during downward OKS and more frequent during upward OKS). Eye movements, on top of the classic effect induced by OKS, were affected by the type of operation during the calculation phase, with subtraction consistently leading to a downward shift of gaze position and addition leading to an upward shift. These results highlight the pervasive nature of spatial processing in mental arithmetic. Furthermore, the preeminent effect of vertical OKS is in line with the hypothesis that the vertical dimension of space–number associations is grounded in universal (physical) constraints and, thereby, more robust than situated and culture-dependent associations with the horizontal dimension.

Sensorimotor lateralization scaffolds cognitive specialization

In this chapter, we review hemispheric differences for sensorimotor function and cognitive abilities. Specifically, we examine the left-hemisphere specialization for visuomotor control and its interplay with language, executive function, and musical training. Similarly, we discuss right-hemisphere lateralization for haptic processing and its relationship to spatial and numerical processing. We propose that cerebral lateralization for sensorimotor functions served as a foundation for the development of higher cognitive abilities and their hemispheric functional specialization. We further suggest that sensorimotor and cognitive functions are inextricably linked. Based on the studies discussed in this chapter our view is that sensorimotor control serves as a loom upon which the fibers of language, executive function, spatial, and numerical processing are woven together to create the fabric of cognition.

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.

Mapping of non-numerical domains on space: a systematic review and meta-analysis

The spatial numerical association of response code (SNARC) effect is characterized by low numbers mapped to the left side of space and high numbers mapped to the right side of space. In addition to numbers, SNARC-like effects have been found in non-numerical magnitude domains such as time, size, letters, luminance, and more, whereby the smaller/earlier and larger/later magnitudes are typically mapped to the left and right of space, respectively. The purpose of this systematic and meta-analytic review was to identify and summarise all empirical papers that have investigated horizontal (left-right) SNARC-like mappings using non-numerical stimuli. A systematic search was conducted using EMBASE, Medline, and PsycINFO, where 2216 publications were identified, with 57 papers meeting the inclusion criteria (representing 112 experiments). Ninety-five of these experiments were included in a meta-analysis, resulting in an overall effect size of d = .488 for a SNARC-like effect. Additional analyses revealed a significant effect size advantage for explicit instruction tasks compared with implicit instructions, yet yielded no difference for the role of expertise on SNARC-like effects. There was clear evidence for a publication bias in the field, but the impact of this bias is likely to be modest, and it is unlikely that the SNARC-like effect is a pure artefact of this bias. The similarities in the response properties for the spatial mappings of numerical and non-numerical domains support the concept of a general higher order magnitude system. Yet, further research will need to be conducted to identify all the factors modulating the strength of the spatial associations.

On pacing trials while scanning brain hemodynamics: The case of the SNARC effect

Experimental designs used to describe psychological effects on overt human behavior are seldom suited to localize their corresponding neural substrates based on the analysis of stimulus-evoked brain hemodynamic responses. This is because stimuli in behavioral studies are usually separated by intertrial intervals (ITIs) in the order of 1 second or so following a behavioral response, which is notoriously too brief a time to detect a corresponding hemodynamic response. In fact, a solution commonly adopted in neuroimaging studies is to prolong the ITI up to several seconds. In doing so, the consequences of ITI variations between behavioral and neuroimaging design variants are either benignly neglected or explicitly assumed to be negligible. Here, we provide a systematic investigation of the consequence of manipulating ITI in a design optimized to study a well-established and highly replicable psychological phenomenon-the spatial numerical association of response codes (SNARC). The present exploration encompassed standard estimates of the SNARC effect (i.e., on reaction times and accuracy), estimates of ITI effects on the emotional state of participants before and after performing the SNARC task, as well as the degree of perceived task difficulty. The results showed that, in striking contrast to the common wisdom about the nil role of ITI, the substantial number of parametric differences observed between the two ITI conditions suggests that ITI plays a critical role in shaping the meaning of hemodynamic correlate of a psychological, at least the SNARC, effect.

Physiological Aging Influence on Brain Hemodynamic Activity during Task-Switching: A fNIRS Study

Task-switching (TS) paradigm is a well-known validated tool useful for exploring the neural substrates of cognitive control, in particular the activity of the lateral and medial prefrontal cortex. This work is aimed at investigating how physiological aging influences hemodynamic response during the execution of a color-shape TS paradigm. A multi-channel near infrared spectroscopy (fNIRS) was used to measure hemodynamic activity in 27 young (30.00 ± 7.90 years) and 11 elderly participants (57.18 ± 9.29 years) healthy volunteers (55% male, age range: (19-69) years) during the execution of a TS paradigm. Two holders were placed symmetrically over the left/right hemispheres to record cortical activity [oxy-(HbO) and deoxy-hemoglobin (HbR) concentration] of the dorso-lateral prefrontal cortex (DLPFC), the dorsal premotor cortex (PMC), and the dorso-medial part of the superior frontal gyrus (sFG). TS paradigm requires participants to repeat the same task over a variable number of trials, and then to switch to a different task during the trial sequence. A two-sample t-test was carried out to detect differences in cortical responses between groups. Multiple linear regression analysis was used to evaluate the impact of age on the prefrontal neural activity. Elderly participants were significantly slower than young participants in both color- (p < 0.01, t = -3.67) and shape-single tasks (p = 0.026, t = -2.54) as well as switching (p = 0.026, t = -2.41) and repetition trials (p = 0.012, t = -2.80). Differences in cortical activation between groups were revealed for HbO mean concentration of switching task in the PMC (p = 0.048, t = 2.94). In the whole group, significant increases of behavioral performance were detected in switching trials, which positively correlated with aging. Multivariate regression analysis revealed that the HbO mean concentration of switching task in the PMC (p = 0.01, β = -0.321) and of shape single-task in the sFG (p = 0.003, β = 0.342) were the best predictors of age effects. Our findings demonstrated that TS might be a reliable instrument to gather a measure of cognitive resources in older people. Moreover, the fNIRS-related brain activity extracted from frontoparietal cortex might become a useful indicator of aging effects.

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.

Spatial representation of magnitude in gorillas and orangutans

Humans mentally represent magnitudes spatially; we respond faster to one side of space when processing small quantities and to the other side of space when processing large quantities. We determined whether spatial representation of magnitude is a fundamental feature of primate cognition by testing for such space-magnitude correspondence in gorillas and orangutans. Subjects picked the larger quantity in a pair of dot arrays in one condition, and the smaller in another. Response latencies to the left and right sides of the screen were compared across the magnitude range. Apes showed evidence of spatial representation of magnitude. While all subjects did not adopt the same orientation, apes showed consistent tendencies for spatial representations within individuals and systematically reversed these orientations in response to reversal of the task instruction. Results suggest that spatial representation of magnitude is phylogenetically ancient and that consistency in the orientation of these representations in humans is likely culturally mediated.

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

The concept of stimulus response compatibility (SRC) refers to the existence of a privileged association between a specific stimulus feature and a specific response feature. Two examples of SRC are the Spatial Numerical Association of Response Codes (SNARC) and the Markedness Association of Response Codes (MARC) effects. According to the polarity correspondence principle, these two SRC effects occur because of a match between the most salient dimensions of stimulus and response. Specifically, the SNARC effect would be caused by a match between right-sided responses and large numbers, while a match between right-sided responses and even numbers would give rise to the MARC effect. The aim of the present study was to test the validity of the polarity correspondence principle in explaining these two SRC effects. To this end, we applied transcranial direct current stimulation (tDCS) over left and right posterior parietal cortex (PPC), which is thought to be the neural basis of salience processing, during a parity judgement task. Results showed that cathodal tDCS over the PPC significantly reduced the MARC effect but did not affect the SNARC effect, suggesting a dissociation between the two effects. That is, the MARC would rely on a salience processing mechanism, whereas the SNARC would not. Despite this interpretation is in need of further experimental confirmations (i.e., testing different tasks or using different tDCS montages), our results suggest that the polarity correspondence principle can be a plausible explanation only for the MARC effect but not for the SNARC effect.

Effect of confounding variables on hemodynamic response function estimation using averaging and deconvolution analysis: An event-related NIRS study

Slow and rapid event-related designs are used in fMRI and functional near-infrared spectroscopy (fNIRS) experiments to temporally characterize the brain hemodynamic response to discrete events. Conventional averaging (CA) and the deconvolution method (DM) are the two techniques commonly used to estimate the Hemodynamic Response Function (HRF) profile in event-related designs. In this study, we conducted a series of simulations using synthetic and real NIRS data to examine the effect of the main confounding factors, including event sequence timing parameters, different types of noise, signal-to-noise ratio (SNR), temporal autocorrelation and temporal filtering on the performance of these techniques in slow and rapid event-related designs. We also compared systematic errors in the estimates of the fitted HRF amplitude, latency and duration for both techniques. We further compared the performance of deconvolution methods based on Finite Impulse Response (FIR) basis functions and gamma basis sets. Our results demonstrate that DM was much less sensitive to confounding factors than CA. Event timing was the main parameter largely affecting the accuracy of CA. In slow event-related designs, deconvolution methods provided similar results to those obtained by CA. In rapid event-related designs, our results showed that DM outperformed CA for all SNR, especially above -5 dB regardless of the event sequence timing and the dynamics of background NIRS activity. Our results also show that periodic low-frequency systemic hemodynamic fluctuations as well as phase-locked noise can markedly obscure hemodynamic evoked responses. Temporal autocorrelation also affected the performance of both techniques by inducing distortions in the time profile of the estimated hemodynamic response with inflated t-statistics, especially at low SNRs. We also found that high-pass temporal filtering could substantially affect the performance of both techniques by removing the low-frequency components of HRF profiles. Our results emphasize the importance of characterization of event timing, background noise and SNR when estimating HRF profiles using CA and DM in event-related designs.

Atypical right hemisphere response to slow temporal modulations in children with developmental dyslexia

Phase entrainment of neuronal oscillations is thought to play a central role in encoding speech. Children with developmental dyslexia show impaired phonological processing of speech, proposed theoretically to be related to atypical phase entrainment to slower temporal modulations in speech (<10Hz). While studies of children with dyslexia have found atypical phase entrainment in the delta band (~2Hz), some studies of adults with developmental dyslexia have shown impaired entrainment in the low gamma band (~35-50Hz). Meanwhile, studies of neurotypical adults suggest asymmetric temporal sensitivity in auditory cortex, with preferential processing of slower modulations by right auditory cortex, and faster modulations processed bilaterally. Here we compared neural entrainment to slow (2Hz) versus faster (40Hz) amplitude-modulated noise using fNIRS to study possible hemispheric asymmetry effects in children with developmental dyslexia. We predicted atypical right hemisphere responding to 2Hz modulations for the children with dyslexia in comparison to control children, but equivalent responding to 40Hz modulations in both hemispheres. Analyses of HbO concentration revealed a right-lateralised region focused on the supra-marginal gyrus that was more active in children with dyslexia than in control children for 2Hz stimulation. We discuss possible links to linguistic prosodic processing, and interpret the data with respect to a neural 'temporal sampling' framework for conceptualizing the phonological deficits that characterise children with developmental dyslexia across languages.

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.

How Math Anxiety Relates to Number-Space Associations

Given the considerable prevalence of math anxiety, it is important to identify the factors contributing to it in order to improve mathematical learning. Research on math anxiety typically focusses on the effects of more complex arithmetic skills. Recent evidence, however, suggests that deficits in basic numerical processing and spatial skills also constitute potential risk factors of math anxiety. Given these observations, we determined whether math anxiety also depends on the quality of spatial-numerical associations. Behavioral evidence for a tight link between numerical and spatial representations is given by the SNARC (spatial-numerical association of response codes) effect, characterized by faster left-/right-sided responses for small/large digits respectively in binary classification tasks. We compared the strength of the SNARC effect between high and low math anxious individuals using the classical parity judgment task in addition to evaluating their spatial skills, arithmetic performance, working memory and inhibitory control. Greater math anxiety was significantly associated with stronger spatio-numerical interactions. This finding adds to the recent evidence supporting a link between math anxiety and basic numerical abilities and strengthens the idea that certain characteristics of low-level number processing such as stronger number–space associations constitute a potential risk factor of math anxiety.

Space, time, and numbers in the right posterior parietal cortex: Differences between response code associations and congruency effects

The mental representations of space, time, and number magnitude are inherently linked. The right posterior parietal cortex (PPC) has been suggested to contain a general magnitude system that underlies the overlap between various perceptual dimensions. However, comparative studies including spatial, temporal, and numerical dimensions are missing. In a unified paradigm, we compared the impact of right PPC inhibition on associations with spatial response codes (i.e., Simon, SNARC, and STARC effects) and on congruency effects between space, time, and numbers. Prolonged cortical inhibition was induced by continuous theta-burst stimulation (cTBS), a protocol for transcranial magnetic stimulation (TMS), at the right intraparietal sulcus (IPS). Our results show that congruency effects, but not response code associations, are affected by right PPC inhibition, indicating different neuronal mechanisms underlying these effects. Furthermore, the results demonstrate that interactions between space and time perception are reflected in congruency effects, but not in an association between time and spatial response codes. Taken together, these results implicate that the congruency between purely perceptual dimensions is processed in PPC areas along the IPS, while the congruency between percepts and behavioral responses is independent of this region.

SNARC Effect in Different Effectors

The SNARC (spatial numerical association of response codes) effect, indicating that subjects react faster to the left for small numbers and to the right for large numbers, is used as evidence for the idea that humans use space to organize number representations. Previous studies compared the SNARC effect across sensory modalities within participants and concluded modality independence. So far, it is unknown what sensory-to-motor mappings are involved in generating the SNARC effect and whether these mappings are identical for different effectors within subjects. Hence, we tested whether the SNARC effect is effector specific. Participants performed an auditory parity judgment task and responded with three different effectors: finger (button release), eyes (saccades), and arm (pointing). The SNARC effect occurred in each effector but varied in strength across the effectors. Across subjects, we found a significant correlation of SNARC strength for finger and arm responses suggesting the use of a shared sensory-to-motor mapping. SNARC strength did not correlate, however, between finger and eyes or arm and eyes. An additional statistical analysis based on conditional probabilities provided further evidence for SNARC-effector specificity. Taken together, our results suggest that the sensory-to-motor mapping is not as tight as it would be expected if the SNARC effect was effector independent.

Implicit interactions between number and space in digit-color synesthesia

In digit-color synesthesia, a variant of grapheme-color synesthesia, digits trigger an additional color percept. Recent work on number processing in synesthesia suggests that colors can implicitly elicit numerical representations in digit-color synesthetes implying that synesthesia is bidirectional. Furthermore, morphometric investigations revealed structural differences in the parietal cortex of grapheme-color synesthetes, i.e., in the brain region where interactions between number and space occur in non-synesthetic subjects. Based upon these previous findings, we here examined whether implicitly evoked numerical representations interact with spatial representations in synesthesia in such a way that even a non-numerical, visuo-spatial task (here: line bisection) is modulated, i.e., whether synesthetes exhibit a systematic bisection bias for colored lines. Thirteen digit-color synesthetes were asked to bisect two sets of lines which were colored in their individual synesthetic colors associated with a small or a large digit, respectively. For all colored line stimuli combined, digit-color synesthetes showed--like control subjects (n = 13, matched for age, gender, IQ and handedness)--a pseudo-neglect when bisecting colored lines. Measuring the color-induced change of the bisection bias (i.e., comparing the biases when bisecting lines colored according to a small number vs those lines corresponding to a large number) revealed that only digit-color synesthetes were significantly influenced by line color. The results provide further evidence for the bidirectional nature of synesthesia and support the concept of a mental number line. In addition, they extend previous reports on bidirectionality in synesthesia by showing that even non-numerical, visuo-spatial performance can be modulated by implicit bidirectional processes.

Spatial Associations in Numerical Cognition—From Single Digits to Arithmetic

The literature on spatial associations during number processing is dominated by the SNARC (spatial–numerical association of response codes) effect. We describe spatial biases found for single digits and pairs of numbers, first in the “original” speeded parity task and then extending the scope to encompass different tasks, a range of measures, and various populations. Then we review theoretical accounts before surveying the emerging evidence for similar spatial associations during mental arithmetic. We conclude that the mental number line hypothesis and an embodied approach are useful frameworks for further studies.

The impact of mathematical proficiency on the number-space association

A specific instance of the association between numerical and spatial representations is the SNARC (Spatial Numerical Association of Response Codes) effect. The SNARC effect describes the finding that during binary classification of numbers participants are faster to respond to small/large numbers with the left/right hand respectively. Even though it has been frequently replicated, important inter-individual variability has also been reported. Mathematical proficiency is an obvious candidate source for inter-individual variability in numerical judgments, but studies investigating its influence on the SNARC effect remain scarce. The present experiment included a total of 95 University students, divided into three groups differing significantly in their mathematical proficiency levels. Using group analyses, it appeared that the three groups differed significantly in the strength of their number-space associations in a parity judgment task. This result was further confirmed on an individual level, with higher levels in arithmetic leading to relatively weaker SNARC effects. To explain this negative relationship we propose accounts based on differences in access to qualitatively different numerical representations and also consider more domain general factors, with a focus on inhibition capacities.

Prefrontal cortex activation during story encoding/retrieval: a multi-channel functional near-infrared spectroscopy study

Encoding, storage and retrieval constitute three fundamental stages in information processing and memory. They allow for the creation of new memory traces, the maintenance and the consolidation of these traces over time, and the access and recover of the stored information from short or long-term memory. Functional near-infrared spectroscopy (fNIRS) is a non-invasive neuroimaging technique that measures concentration changes of oxygenated-hemoglobin (O₂Hb) and deoxygenated-hemoglobin (HHb) in cortical microcirculation blood vessels by means of the characteristic absorption spectra of hemoglobin in the near-infrared range. In the present study, we monitored, using a 16-channel fNIRS system, the hemodynamic response during the encoding and retrieval processes (EP and RP, respectively) over the prefrontal cortex (PFC) of 13 healthy subjects (27.2 ± 2.6 years) while were performing the “Logical Memory Test” (LMT) of the Wechsler Memory Scale. A LMT-related PFC activation was expected; specifically, it was hypothesized a neural dissociation between EP and RP. The results showed a heterogeneous O₂Hb/HHb response over the mapped area during the EP and the RP, with a O₂Hb progressive and prominent increment in ventrolateral PFC (VLPFC) since the beginning of the EP. During the RP a broader activation, including the VLPFC, the dorsolateral PFC and the frontopolar cortex, was observed. This could be explained by the different contributions of the PFC regions in the EP and the RP. Considering the fNIRS applicability for the hemodynamic monitoring during the LMT performance, this study has demonstrated that fNIRS could be utilized as a valuable clinical diagnostic tool, and that it has the potential to be adopted in patients with cognitive disorders or slight working memory deficits.

The Spatial Representation of Numerical and Non-Numerical Ordered Sequences: Insights from a Random Generation Task

It is widely believed that numbers are spatially represented from left to right on the mental number line. Whether this spatial format of representation is specific to numbers or is shared by non-numerical ordered sequences remains controversial. When healthy participants are asked to randomly generate digits they show a systematic small-number bias that has been interpreted in terms of “pseudoneglect in number space”. Here we used a random generation task to compare numerical and non-numerical order. Participants performed the task at three different pacing rates and with three types of stimuli (numbers, letters, and months). In addition to a small-number bias for numbers, we observed a bias towards “early” items for letters and no bias for months. The spatial biases for numbers and letters were rate independent and similar in size, but they did not correlate across participants. Moreover, letter generation was qualified by a systematic forward direction along the sequence, suggesting that the ordinal dimension was more salient for letters than for numbers in a task that did not require its explicit processing. The dissociation between numerical and non-numerical orders is consistent with electrophysiological and neuroimaging studies and suggests that they rely on at least partially different mechanisms.

Motion artifacts in functional near-infrared spectroscopy: a comparison of motion correction techniques applied to real cognitive data

Motion artifacts are a significant source of noise in many functional near-infrared spectroscopy (fNIRS) experiments. Despite this, there is no well-established method for their removal. Instead, functional trials of fNIRS data containing a motion artifact are often rejected completely. However, in most experimental circumstances the number of trials is limited, and multiple motion artifacts are common, particularly in challenging populations. Many methods have been proposed recently to correct for motion artifacts, including principle component analysis, spline interpolation, Kalman filtering, wavelet filtering and correlation-based signal improvement. The performance of different techniques has been often compared in simulations, but only rarely has it been assessed on real functional data. Here, we compare the performance of these motion correction techniques on real functional data acquired during a cognitive task, which required the participant to speak aloud, leading to a low-frequency, low-amplitude motion artifact that is correlated with the hemodynamic response. To compare the efficacy of these methods, objective metrics related to the physiology of the hemodynamic response have been derived. Our results show that it is always better to correct for motion artifacts than reject trials, and that wavelet filtering is the most effective approach to correcting this type of artifact, reducing the area under the curve where the artifact is present in 93% of the cases. Our results therefore support previous studies that have shown wavelet filtering to be the most promising and powerful technique for the correction of motion artifacts in fNIRS data. The analyses performed here can serve as a guide for others to objectively test the impact of different motion correction algorithms and therefore select the most appropriate for the analysis of their own fNIRS experiment.