Mental number line disruption in a right-neglect patient after a left-hemisphere stroke

Differential roles of brain oscillations in numerical processing: evidence from resting-state EEG and mental number line

Recent works point to the importance of emotions in special-numerical associations. There remains a notable gap in understanding the electrophysiological underpinnings of such associations. Exploring resting-state (rs) EEG, particularly in frontal regions, could elucidate emotional aspects, while other EEG measures might offer insights into the cognitive dimensions correlating with behavioral performance. The present work investigated the relationship between rs-EEG measures (emotional and cognitive traits) and performance in the mental number line (MNL). EEG activity in theta (3-7 Hz), alpha (8-12 Hz, further subdivided into low-alpha and high-alpha), sensorimotor rhythm (SMR, 13-15 Hz), beta (16-25 Hz), and high-beta/gamma (28-40 Hz) bands was assessed. 76 university students participated in the study, undergoing EEG recordings at rest before engaging in a computerized number-to-position (CNP) task. Analysis revealed significant associations between frontal asymmetry, specific EEG frequencies, and MNL performance metrics (i.e., mean direction bias, mean absolute error, and mean reaction time). Notably, theta and beta asymmetries correlated with direction bias, while alpha peak frequency (APF) and beta activity related to absolute errors in numerical estimation. Moreover, the study identified significant correlations between relative amplitude indices (i.e., theta/beta ratio, theta/SMR ratio) and both absolute errors and reaction times (RTs). Our findings offer novel insights into the emotional and cognitive aspects of EEG patterns and their links to MNL performance.

Behavioral and neurophysiological indices of the racial bias modulation after virtual embodiment in other-race body

Racial bias-nonconscious behavioral inclinations against people of other ethnic groups-heavily contributes to inequality and discrimination. Immersive virtual reality (IVR) can reduce implicit racial bias through the feeling of owning (embodying) a virtual body of a different "race"; however, it has been demonstrated only behaviorally for the implicit attitudes. Here, we investigated the implicit (racial IAT) and the neurophysiological (the N400 component of the event-related potentials for verbal stimuli that violated negative racial stereotypes) correlates of the embodiment-induced reduction of the implicit racial bias. After embodying a Black avatar, Caucasian participants had reduced implicit racial bias (IAT) but both groups showed the typical N400. This is the first evidence to suggest that virtual embodiment affects the evaluative component of the implicit biases but not the neurophysiological index of their cognitive component (i.e., stereotyping). This can inform interventions that promote inclusivity through the implicit/indirect procedures, such as embodiment.

Learned Representation of Implied Serial Order in Posterior Parietal Cortex

Monkeys can learn the implied ranking of pairs of images drawn from an ordered set, despite never seeing all of the images simultaneously and without explicit spatial or temporal cues. We recorded the activity of posterior parietal cortex (including lateral intraparietal area LIP) neurons while monkeys learned 7-item transitive inference (TI) lists with 2 items presented on each trial. Behavior and neuronal activity were significantly influenced by the ordinal relationship of the stimulus pairs, specifically symbolic distance (the difference in rank) and joint rank (the sum of the ranks). Symbolic distance strongly predicted decision accuracy and learning rate. An effect of joint rank on performance was found nested within the symbolic distance effect. Across the population of neurons, there was significant modulation of firing correlated with the relative ranks of the two stimuli presented on each trial. Neurons exhibited selectivity for stimulus rank during learning, but not before or after. The observed behavior is poorly explained by associative or reward mechanisms, and appears more consistent with a mental workspace model in which implied serial order is mapped within a spatial framework. The neural data suggest that posterior parietal cortex supports serial learning by representing information about the ordinal relationship of the stimuli presented during a given trial.

Biased numerical cognition impairs economic decision-making in Parkinson's disease

Objective

Previous findings suggest a context‐dependent bihemispheric allocation of numerical magnitude. Accordingly, we predicted that lateralized motor symptoms in Parkinson's disease (PD), which reflect hemispheric asymmetries, would induce systematic lateralized biases in numerical cognition and have a subsequent influence on decision‐making.

Methods

In 20 PD patients and matched healthy controls we assessed numerical cognition using a number‐pair bisection and random number generation task. Decision‐making was assessed using both the dictator game and a validated questionnaire.

Results

PD patients with predominant right‐sided motor symptoms exhibited pathological biases toward smaller numerical magnitudes and formulated less favorable prosocial choices during a neuroeconomics task (i.e., dictator game). Conversely, patients with left‐sided motor symptoms exhibited pathological biases toward larger numerical magnitudes and formulated more generous prosocial choices. Our account of context‐dependent hemispheric allocation of numerical magnitude in PD was corroborated by applying our data to a pre‐existing computational model and observing significant concordance. Notably, both numerical biasing and impaired decision‐making were correlated with motor asymmetry.

Interpretation

Accordingly, motor asymmetry and functional impairment of cognitive processes in PD can be functionally intertwined. To conclude, our findings demonstrate context‐dependent hemispheric allocation and encoding of numerical magnitude in PD and how biases in numerical magnitude allocation in Parkinsonian patients can correspondingly impair economic decision‐making.

Neural signatures of third-party punishment: evidence from penetrating traumatic brain injury

The ability to survive within a cooperative society depends on impartial third-party punishment (TPP) of social norm violations. Two cognitive mechanisms have been postulated as necessary for the successful completion of TPP: evaluation of legal responsibility and selection of a suitable punishment given the magnitude of the crime. Converging neuroimaging research suggests two supporting domain-general networks; a mentalizing network for evaluation of legal responsibility and a central-executive network for determination of punishment. A whole-brain voxel-based lesion-symptom mapping approach was used in conjunction with a rank-order TPP task to identify brain regions necessary for TPP in a large sample of patients with penetrating traumatic brain injury. Patients who demonstrated atypical TPP had specific lesions in core regions of the mentalizing (dorsomedial prefrontal cortex [PFC], ventromedial PFC) and central-executive (bilateral dorsolateral PFC, right intraparietal sulcus) networks. Altruism and executive functioning (concept formation skills) were significant predictors of TPP: altruism was uniquely associated with TPP in patients with lesions in right dorsolateral PFC and executive functioning was uniquely associated with TPP in individuals with lesions in left PFC. Our findings contribute to the extant literature to support underlying neural networks associated with TPP, with specific brain-behavior causal relationships confirming recent functional neuroimaging research.

Differential influences of unilateral tDCS over the intraparietal cortex on numerical cognition

Recent neuro-imaging research identified the bilateral intraparietal sulcus (IPS) to be a key area associated with number processing. However, causal structure-function relationships are hard to evaluate from neuro-imaging techniques such as fMRI. Nevertheless, brain stimulation methods like transcranial direct current stimulation (tDCS) allow for investigating the functional relevance of the IPS for number processing. Following up on a study using bilateral bi-cephalic tDCS over the IPS, the current study aimed at evaluating the differential lateralized functional contributions of the left and right IPS to number processing using unilateral bi-cephalic tDCS over either the left or right IPS. Results indicated a right lateralization for the processing of the place-value structure of the Arabic number system. Importantly, the processing of number magnitude information was not affected by unilateral IPS corroborating the assumption that number magnitude is processed in the bilateral IPS. Taken together, these data suggest that even though number magnitude is represented bilaterally, the left and right IPS seem to contribute differentially to numerical cognition with respect to the processing of specific other aspects of numerical information.

Influence of gaze observation on random number generation

Recent findings suggest that number processing is intimately linked to space and attention orienting processes. For example, processing numbers induces shifts of spatial attention, with small numbers causing leftward shifts and large numbers causing rightward shifts, suggesting that number magnitude might be represented on a left-to-right mental number line. However, whether inducing spatial attention shifts would in turn influence number production, and whether such influence, if observed, would be restricted to the left-to-right orientation or would extend to an up-to-down orientation in space, remains a matter of debate. The present study assessed whether observing gaze movements, known to moderate spatial attention, was able to influence a random number generation task, and how different directions of the gaze moderated this influence. Participants were asked to randomly produce a number between 1 and 10 after they observed either a horizontal or a vertical eye gaze, or after they observed color changes as a control condition. The results revealed that number production was influenced by the prior presentation of specific gaze changes. Observing leftward or downward gaze led participants to produce more small than large numbers, whereas observing gaze oriented rightward and upward or observing color changes did not influence the magnitude of the numbers produced. These results show that the characteristics of the observed gaze changes primed number magnitude, but that this only held true for some movements, and these were not restricted to the left-to-right axis.

Visuospatial attention deficits in developmental dyslexia: evidence from visual and mental number line bisection tasks

Previous research has shown that individuals with DD (developmental dyslexia) demonstrated a left mini neglect on visual line (VL) bisection tasks, which has been commonly referred to as right parietal dysfunction. However, insufficient reading experience characterizes dyslexia and may call into question the validity of this interpretation, since the VL bisection task has been found to be influenced by reading habits. The current study investigated whether altered performance of individuals with DD on bisection tasks may be attributed to impaired attentional mechanisms or to insufficient reading exposure. DD and control groups performed visual and mental number line bisection tasks, which have been shown to be modulated differently by reading habits. In both tasks, the magnitude of left bisection errors was significantly larger in the DD group compared with controls. This finding suggests attentional mechanisms act differently in dyslexia and supports evidence linking dyslexia to decreased function of the left hemisphere.

Elementary school children's attentional biases in physical and numerical space

Numbers are conceptualized spatially along a horizontal mental line. This view is supported by mounting evidence from healthy adults and patients with unilateral spatial neglect. Little is known about children's representation of numbers with respect to space. This study investigated elementary school children's directional biases in physical and numerical space to better understand the relation between space and number. We also examined the nature of spatial organization in numerical space. In two separate tasks, children (n=57) were asked to bisect a physical line and verbally estimate the midpoint of number pairs. In general, results indicated leftward biases in both tasks, but the degree of deviation did not correlate between the tasks. In the number bisection task, leftward bias (underestimating the midpoint) increased as a function of numerical magnitude and interval between number pairs. In contrast, a rightward deviation was found for smaller number pairs. These findings suggest that different underlying spatial attentional mechanisms might be directed in physical and numerical space in young school children, which would be integrated in adulthood.

Neuro-anatomical correlates of a number bisection bias: A neuropsychological voxel-based morphometry study

The number bisection tasks, whereby participants estimate the midpoint of a given number interval, is frequently used to explore the idea that numbers are spatially represented within the brain across a 'mental number line'. Some neuropsychological research supports the argument that number bisection is a spatial task, recruiting parietal brain regions, whereas other data suggest that number bisection is dissociable from spatial processing and is instead dependent on working memory in the prefrontal cortices. This study explored the anatomical correlates of deficits in the number bisection task, using voxel-based morphometry in a sample of 25 neuropsychological patients with both left and right hemisphere damage. Interestingly, impairments in number bisection were strongly associated with grey matter lesions in the left hemisphere including both frontal and prefrontal cortices, extending to inferior parietal cortex. Similar prefrontal and frontal grey matter areas were found to be associated with increased leftward deviations (underestimations of the midpoint), whereas no suprathreshold clusters were observed for rightward deviations from the midpoint. Analysis of white matter integrity revealed that lesions in the tracts connecting the parietal and frontal cortices (i.e. the superior longitudinal fasciculus) were highly associated with leftward deviation impairments in number bisection. The data suggest that there is a common parieto-frontal number processing network underlying performances on number bisection, with larger numbers represented on the left side.

Approaching stimuli bias attention in numerical space

Increasing evidence suggests that common mechanisms underlie the direction of attention in physical space and numerical space, along the mental number line. The small leftward bias (pseudoneglect) found on paper-and-pencil line bisection is also observed when participants 'bisect' number pairs, estimating (without calculating) the number midway between two others. Here we investigated the effect of stimulus motion on attention in numerical space. A two-frame apparent motion paradigm manipulating stimulus size was used to produce the impression that pairs of numbers were approaching (size increase from first to second frame), receding (size decrease), or not moving (no size change). The magnitude of pseudoneglect increased for approaching numbers, even when the final stimulus size was held constant. This result is consistent with previous findings that pseudoneglect in numerical space (as in physical space) increases as stimuli are brought closer to the participant. It also suggests that the perception of stimulus motion modulates attention over the mental number line and provides further support for a connection between the neural representations of physical space and number.

Functional independence between numerical and visual space: evidence from right brain-damaged patients

What is the relationship between numerical and visual space? Here we tried to shed new light on this debated issue investigating whether and how the two forms of representation are associated or dissociated when co-activated. We carried out a series of visual-numerical bisection experiments on a large group of right brain-damaged patients (N=32) with and without left neglect. We examined (a) the degree of association between the pathological rightward error in the bisection of numerical intervals and left neglect (experiment 1); (b) if the size of the numerical interval modulates spatial errors in bisection tasks in which numerical and visual space representations are co-activated (experiment 2). The results showed that (a) numerical bisection error and left spatial neglect are doubly dissociated and that, when both are present, they are not correlated; (b) the size of the numerical interval did not affect the spatial bisection error but influenced the numerical bisection error. These data suggest that attentional processes involved in the navigation along visual space and numerical internal representations are independent neurocognitive operations. We must emphasize that our findings should be taken with caution because they are based mainly on negative results.

The heterogeneous nature of number-space interactions

It is generally accepted that the mental representation of numerical magnitude consists of a spatial “mental number line” (MNL) with smaller quantities on the left and larger quantities on the right. However, the amount of dissociations between tasks that were believed to tap onto this representational medium is accumulating, questioning the universality of this model. The aim of the present study was to unravel the functional relationship between the different tasks and effects that are typically used as evidence for the MNL. For this purpose, a group of right brain damaged patients (with and without neglect) and healthy controls were subjected to physical line bisection, number interval bisection, parity judgment, and magnitude comparison. Using principal component analysis, different orthogonal components were extracted. We discuss how this component structure captures the dissociations reported in the literature and how it can be considered as a first step toward a new unitary framework for understanding the relation between numbers and space.

Role of distinct parietal areas in arithmetic: an fMRI-guided TMS study

Although several parietal areas are known to be involved in number processing, their possible role in arithmetic operations remains debated. It has been hypothesized that the horizontal segment of the intraparietal sulcus (hIPS) and the posterior superior parietal lobule (PSPL) contribute to operations solved by calculation procedures, such as subtraction, but whether these areas are also involved in operations solved by memory retrieval, such as multiplication, is controversial. In the present study, we first identified the parietal areas involved in subtraction and multiplication by means of functional magnetic resonance imaging (fMRI) and we found an increased activation, bilaterally, in the hIPS and PSPL during both arithmetic operations. In order to test whether these areas are causally involved in subtraction and multiplication, we used transcranial magnetic stimulation (TMS) to create, in each participant, a virtual lesion of either the hIPS or PSPL, over the sites corresponding to the peaks of activation gathered in fMRI. When compared to a control site, we found an increase in response latencies in both operations after a virtual lesion of either the left or right hIPS, but not of the PSPL. Moreover, TMS over the hIPS increased the error rate in the multiplication task. The present results indicate that even operations solved by memory retrieval, such as multiplication, rely on the hIPS. In contrast, the PSPL seems to underlie processes that are nonessential to solve basic subtraction and multiplication problems.

The cognitive phenotype of spina bifida meningomyelocele

A cognitive phenotype is a product of both assets and deficits that specifies what individuals with spina bifida meningomyelocele (SBM) can and cannot do and why they can or cannot do it. In this article, we review the cognitive phenotype of SBM and describe the processing assets and deficits that cut within and across content domains, sensory modality, and material, including studies from our laboratory and other investigations. We discuss some implications of the SBM cognitive phenotype for assessment, rehabilitation, and research.

Bisecting the mental number line in near and far space

Much evidence suggests that common posterior parietal mechanisms underlie the orientation of attention in physical space and along the mental number line. For example, the small leftward bias (pseudoneglect) found in paper-and-pencil line bisection is also found when participants "bisect" number pairs, estimating (without calculating) the number midway between two others. For bisection of physical lines, pseudoneglect has been found to shift rightward as lines are moved from near space (immediately surrounding the body) to far space. We investigated whether the presentation of stimuli in near or far space also modulated spatial attention for the mental number line. Participants bisected physical lines or number pairs presented at four distances (60, 120, 180, 240cm). Clear rightward shifts in bias were observed for both tasks. Furthermore, the rate at which this shift occurred in the two tasks, as measured by least-squares regression slopes, was significantly correlated across participants, suggesting that the transition from near to far distances induced a common modulation of lateral attention in physical and numerical space. These results demonstrate a tight coupling between number and physical space, and show that even such prototypically abstract concepts as number are modulated by our on-line interactions with the world.

Multiple spatial representations of number: evidence for co-existing compressive and linear scales

Although the spatial representation of number (mental number line) is well documented, the scaling associated with this representation is less clear. Sometimes people appear to rely on compressive scaling, and sometimes on linear scaling. Here we provide evidence for both compressive and linear representations on the same numerical bisection task, in which adult participants estimate (without calculating) the midpoint between two numbers. The same leftward bias (pseudoneglect) shown on physical line bisection appears on this task, and was previously shown to increase with the magnitude of bisected numbers, consistent with compressive scaling (Longo and Lourenco in Neuropsychologia 45:1400-1407, 2007). In the present study, participants held either small (1-9) or large (101-109) number primes in memory during bisection. When participants remembered small primes, bisection responses were consistent with compressive scaling. However, when they remembered large primes, responses were more consistent with linear scaling. These results show that compressive and linear representations may be accessed flexibly on the same task, depending on the numerical context.