Causal role of the posterior parietal cortex for two-digit mental subtraction and addition: A repetitive TMS study

Stand up to better pay attention, sit down to better subtract: a new perspective on the advantage of cognitive-motor interactions

The Stroop task and subtraction rely on the different cognitive processes and cerebral regions, but both these cognitive functions interact with posture. The study of cognitive-motor interactions falls under the concept of sharing resources, implying that resources for processing are limited. Researchers try to understand this interaction by constructing dual task (DT) paradigms. None have investigated the Stroop and subtraction tasks in three inherently simple postures in two groups of young adults. This study aimed to test whether a given posture benefits a given cognitive function when cognitive and postural tasks are not overly demanding and are underpinned by common cerebral structures. This study presents the results of 60 healthy young adults performing a subtraction task in three postures (sitting, standing, and walking) and 57 healthy young adults performing the Stroop task in the same three postures. Our results showed that performance at the Stroop task, in terms of number of correct answers and interference, are better while standing or even walking compared to sitting while subtraction is better sitting compared to standing and walking. Moreover, static postural parameters did not vary when in DT compared to single task. This means that there was no additional cost on posture when achieving the cognitive activity simultaneously. The absence of impact of the DT on postural parameters in static postures and the changes in the gait pace when walking suggest that cognitive tasks can be achieved in various postures, without being too costly on posture.

Probing Our Built-in Calculator: A Systematic Narrative Review of Noninvasive Brain Stimulation Studies on Arithmetic Operation-Related Brain Areas

This systematic review presented a comprehensive survey of studies that applied transcranial magnetic stimulation and transcranial electrical stimulation to parietal and nonparietal areas to examine the neural basis of symbolic arithmetic processing. All findings were compiled with regard to the three assumptions of the triple-code model (TCM) of number processing. Thirty-seven eligible manuscripts were identified for review (33 with healthy participants and 4 with patients). Their results are broadly consistent with the first assumption of the TCM that intraparietal sulcus both hold a magnitude code and engage in operations requiring numerical manipulations such as subtraction. However, largely heterogeneous results conflicted with the second assumption of the TCM that the left angular gyrus subserves arithmetic fact retrieval, such as the retrieval of rote-learned multiplication results. Support is also limited for the third assumption of the TCM, namely, that the posterior superior parietal lobule engages in spatial operations on the mental number line. Furthermore, results from the stimulation of brain areas outside of those postulated by the TCM show that the bilateral supramarginal gyrus is involved in online calculation and retrieval, the left temporal cortex in retrieval, and the bilateral dorsolateral prefrontal cortex and cerebellum in online calculation of cognitively demanding arithmetic problems. The overall results indicate that multiple cortical areas subserve arithmetic skills.

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 functions of the angular gyrus at high temporal resolution

Here, the functions of the angular gyrus (AG) are evaluated in the light of current evidence from transcranial magnetic/electric stimulation (TMS/TES) and EEG/MEG studies. 65 TMS/TES and 52 EEG/MEG studies were examined in this review. TMS/TES literature points to a causal role in semantic processing, word and number processing, attention and visual search, self-guided movement, memory, and self-processing. EEG/MEG studies reported AG effects at latencies varying between 32 and 800 ms in a wide range of domains, with a high probability to detect an effect at 300-350 ms post-stimulus onset. A three-phase unifying model revolving around the process of sensemaking is then suggested: (1) early AG involvement in defining the current context, within the first 200 ms, with a bias toward the right hemisphere; (2) attention re-orientation and retrieval of relevant information within 200-500 ms; and (3) cross-modal integration at late latencies with a bias toward the left hemisphere. This sensemaking process can favour accuracy (e.g. for word and number processing) or plausibility (e.g. for comprehension and social cognition). Such functions of the AG depend on the status of other connected regions. The much-debated semantic role is also discussed as follows: (1) there is a strong TMS/TES evidence for a causal semantic role, (2) current EEG/MEG evidence is however weak, but (3) the existing arguments against a semantic role for the AG are not strong. Some outstanding questions for future research are proposed. This review recognizes that cracking the role(s) of the AG in cognition is possible only when its exact contributions within the default mode network are teased apart.

Causal involvement of the left angular gyrus in higher functions as revealed by transcranial magnetic stimulation: a systematic review

Transcranial magnetic stimulation (TMS) is a non-invasive technique that can transiently interfere with local cortical functioning, thus enabling inferences of causal left AG involvement in higher functions from experimentation with healthy participants. Here, we examine 35 studies that measure behavioural outcomes soon after or during targeting TMS to the left AG, by design and as documented by individual magnetic resonance images, in healthy adult participants. The reviewed evidence suggests a specific causal involvement of the left AG in a wide range of tasks involving language, memory, number processing, visuospatial attention, body awareness and motor planning functions. These core findings are particularly valuable to inform theoretical models of the left AG role(s) in higher functions, due to the anatomical specificity afforded by the selected studies and the complementarity of TMS to different methods of investigation. In particular, the variety of the operations within and between functions in which the left AG appears to be causally involved poses a formidable challenge to any attempts to identify a single computational process subserved by the left AG (as opposed to just outlining a broad type of functional contribution) that could apply across thematic areas. We conclude by highlighting directions for improvement in future experimentation with TMS, in order to strengthen the available evidence, while taking into account the anatomical heterogeneity of this brain region.

The role of the angular gyrus in arithmetic processing: a literature review

Since the pioneering work of the early 20th century neuropsychologists, the angular gyrus (AG), particularly in the left hemisphere, has been associated with numerical and mathematical processing. The association between the AG and numerical and mathematical processing has been substantiated by neuroimaging research. In the present review article, we will examine what is currently known about the role of the AG in numerical and mathematical processing with a particular focus on arithmetic. Specifically, we will examine the role of the AG in the retrieval of arithmetic facts in both typically developing children and adults. The review article will consider alternative accounts that posit that the involvement of the AG is not specific to arithmetic processing and will consider how numerical and mathematical processing and their association with the AG overlap with other neurocognitive processes. The review closes with a discussion of future directions to further characterize the relationship between the angular gyrus and arithmetic processing.

A low-dimensional structure of neurological impairment in stroke

Neurological deficits following stroke are traditionally described as syndromes related to damage of a specific area or vascular territory. Recent studies indicate that, at the population level, post-stroke neurological impairments cluster in three sets of correlated deficits across different behavioural domains. To examine the reproducibility and specificity of this structure, we prospectively studied first-time stroke patients (n = 237) using a bedside, clinically applicable, neuropsychological assessment and compared the behavioural and anatomical results with those obtained from a different prospective cohort studied with an extensive neuropsychological battery. The behavioural assessment at 1-week post-stroke included the Oxford Cognitive Screen and the National Institutes of Health Stroke Scale. A principal component analysis was used to reduce variables and describe behavioural variance across patients. Lesions were manually segmented on structural scans. The relationship between anatomy and behaviour was analysed using multivariate regression models. Three principal components explained ≈50% of the behavioural variance across subjects. PC1 loaded on language, calculation, praxis, right side neglect and memory deficits; PC2 loaded on left motor, visual and spatial neglect deficits; PC3 loaded on right motor deficits. These components matched those obtained with a more extensive battery. The underlying lesion anatomy was also similar. Neurological deficits following stroke are correlated in a low-dimensional structure of impairment, related neither to the damage of a specific area or vascular territory. Rather they reflect widespread network impairment caused by focal lesions. These factors showed consistency across different populations, neurobehavioural batteries and, most importantly, can be described using a combination of clinically applicable batteries (National Institutes of Health Stroke Scale and Oxford Cognitive Screen). They represent robust behavioural biomarkers for future stroke population studies.

Preoperative Applications of Navigated Transcranial Magnetic Stimulation

Preoperative mapping of cortical structures prior to neurosurgical intervention can provide a roadmap of the brain with which neurosurgeons can navigate critical cortical structures. In patients undergoing surgery for brain tumors, preoperative mapping allows for improved operative planning, patient risk stratification, and personalized preoperative patient counseling. Navigated transcranial magnetic stimulation (nTMS) is one modality that allows for highly accurate, image-guided, non-invasive stimulation of the brain, thus allowing for differentiation between eloquent and non-eloquent cortical regions. Motor mapping is the best validated application of nTMS, yielding reliable maps with an accuracy similar to intraoperative cortical mapping. Language mapping is also commonly performed, although nTMS language maps are not as highly concordant with direct intraoperative cortical stimulation maps as nTMS motor maps. Additionally, nTMS has been used to localize cortical regions involved in other functions such as facial recognition, calculation, higher-order motor processing, and visuospatial orientation. In this review, we evaluate the growing literature on the applications of nTMS in the preoperative setting. First, we analyze the evidence in support of the most common clinical applications. Then we identify usages that show promise but require further validation. We also discuss developing nTMS techniques that are still in the experimental stage, such as the use of nTMS to enhance postoperative recovery. Finally, we highlight practical considerations when utilizing nTMS and, importantly, its safety profile in neurosurgical patients. In so doing, we aim to provide a comprehensive review of the role of nTMS in the neurosurgical management of a patient with a brain tumor.

Causal Inferences in Repetitive Transcranial Magnetic Stimulation Research: Challenges and Perspectives

Transcranial magnetic stimulation (TMS) is used to make inferences about relationships between brain areas and their functions because, in contrast to neuroimaging tools, it modulates neuronal activity. The central aim of this article is to critically evaluate to what extent it is possible to draw causal inferences from repetitive TMS (rTMS) data. To that end, we describe the logical limitations of inferences based on rTMS experiments. The presented analysis suggests that rTMS alone does not provide the sort of premises that are sufficient to warrant strong inferences about the direct causal properties of targeted brain structures. Overcoming these limitations demands a close look at the designs of rTMS studies, especially the methodological and theoretical conditions which are necessary for the functional decomposition of the relations between brain areas and cognitive functions. The main points of this article are that TMS-based inferences are limited in that stimulation-related causal effects are not equivalent to structure-related causal effects due to TMS side effects, the electric field distribution, and the sensitivity of neuroimaging and behavioral methods in detecting structure-related effects and disentangling them from confounds. Moreover, the postulated causal effects can be based on indirect (network) effects. A few suggestions on how to manage some of these limitations are presented. We discuss the benefits of combining rTMS with neuroimaging in experimental reasoning and we address the restrictions and requirements of rTMS control conditions. The use of neuroimaging and control conditions allows stronger inferences to be gained, but the strength of the inferences that can be drawn depends on the individual experiment's designs. Moreover, in some cases, TMS might not be an appropriate method of answering causality-related questions or the hypotheses have to account for the limitations of this technique. We hope this summary and formalization of the reasoning behind rTMS research can be of use not only for scientists and clinicians who intend to interpret rTMS results causally but also for philosophers interested in causal inferences based on brain stimulation research.

Dissociating Arithmetic Operations in the Parietal Cortex Using 1 Hz Repetitive Transcranial Magnetic Stimulation: The Importance of Strategy Use

The triple-code model (TCM) of number processing suggests the involvement of distinct parietal cortex areas in arithmetic operations: the bilateral horizontal segment of the intraparietal sulcus (hIPS) for arithmetic operations that require the manipulation of numerical quantities (e.g., subtraction) and the left angular gyrus (AG) for arithmetic operations that require the retrieval of answers from long-term memory (e.g., multiplication). Although neuropsychological, neuroimaging, and brain stimulation studies suggest the dissociation of these operations into distinct parietal cortex areas, the role of strategy (online calculation vs. retrieval) is not yet fully established. In the present study, we further explored the causal involvement of the left AG for multiplication and left hIPS for subtraction using a neuronavigated repetitive transcranial magnetic stimulation (rTMS) paradigm. Stimulation sites were determined based on an fMRI experiment using the same tasks. To account for the effect of strategy, participants were asked whether they used retrieval or calculation for each individual problem. We predicted that the stimulation of the left AG would selectively disrupt the retrieval of the solution to multiplication problems. On the other hand, stimulation of the left hIPS should selectively disrupt subtraction. Our results revealed that left AG stimulation was detrimental to the retrieval and online calculation of solutions for multiplication problems, as well as, the retrieval (but not online calculation) of the solutions to subtraction problems. In contrast, left hIPS stimulation had no detrimental effect on both operations regardless of strategy.

Mental Shopping Calculations: A Transcranial Magnetic Stimulation Study

One of the most critical skills behind consumer's behavior is the ability to assess whether a price after a discount is a real bargain. Yet, the neural underpinnings and cognitive mechanisms associated with such a skill are largely unknown. While there is general agreement that the posterior parietal cortex (PPC) on the left is critical for mental calculations, and there is also recent repetitive transcranial magnetic stimulation (rTMS) evidence pointing to the supramarginal gyrus (SMG) of the right PPC as crucial for consumer-like arithmetic (e.g., multi-digit mental addition or subtraction), it is still unknown whether SMG is involved in calculations of sale prices. Here, we show that the neural mechanisms underlying discount arithmetic characteristic for shopping are different from complex addition or subtraction, with discount calculations engaging left SMG more. We obtained these outcomes by remodeling our laboratory to resemble a shop and asking participants to calculate prices after discounts (e.g., $8.80-25 or $4.80-75%), while stimulating left and right SMG with neuronavigated rTMS. Our results indicate that such complex shopping calculations as establishing the price after a discount involve SMG asymmetrically, whereas simpler calculations such as price addition do not. These findings have some consequences for neural models of mathematical cognition and shed some preliminary light on potential consumer's behavior in natural settings.

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

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

An EEG Study of a Confusing State Induced by Information Insufficiency during Mathematical Problem-Solving and Reasoning

Confusion is a complex cognitive state that is prevalent during learning and problem-solving. The aim of this study is to explore the brain activity reflected by electroencephalography (EEG) during a confusing state induced by two kinds of information insufficiencies during mathematical problem-solving, namely, an explicit situation that clearly lacked information and an implicit situation in which the missing information was hidden in the problem itself, and whether there is an EEG difference between these two situations. Two experimental tasks and three control tasks were created. Short time Fourier transformation (STFT) was used for time-frequency analysis; then the alpha task-related-power (TRP) changes and distributions, which are closely related to cognitive processing, were calculated, and repeated measures ANOVA were performed to find the significant difference between task conditions. The results showed that the alpha power decreased significantly in the regions related to calculation when the participants encountered both explicit and implicit information insufficiency tasks compared to the control tasks, suggesting that confusion can cause more brain activity in the cortical regions related to the tasks that induce confusion. In addition, the implicit information insufficiency task elicited more activity in the parietal and right temporal regions, whereas the explicit information insufficiency task elicited additional activity in the frontal lobe, which revealed that the frontal region is related to the processing of novel or unfamiliar information and the parietal-temporal regions are involved in sustained attention or reorientation during confusing states induced by information insufficiency. In conclusion, this study has preliminarily investigated the EEG characteristics of confusion states, suggests that EEG is a promising methodology to detect confusion, and provides a basis for future studies aiming to achieve automatic recognition of confusing states.

Number line estimation and complex mental calculation: Is there a shared cognitive process driving the two tasks?

It is widely accepted that different number-related tasks, including solving simple addition and subtraction, may induce attentional shifts on the so-called mental number line, which represents larger numbers on the right and smaller numbers on the left. Recently, it has been shown that different number-related tasks also employ spatial attention shifts along with general cognitive processes. Here we investigated for the first time whether number line estimation and complex mental arithmetic recruit a common mechanism in healthy adults. Participants' performance in two-digit mental additions and subtractions using visual stimuli was compared with their performance in a mental bisection task using auditory numerical intervals. Results showed significant correlations between participants' performance in number line bisection and that in two-digit mental arithmetic operations, especially in additions, providing a first proof of a shared cognitive mechanism (or multiple shared cognitive mechanisms) between auditory number bisection and complex mental calculation.

Recognition memory and featural similarity between concepts: The pupil's point of view

Differences in pupil dilation are observed for studied compared to new items in recognition memory. According to cognitive load theory, this effect reflects the greater cognitive demands of retrieving contextual information from study phase. Pupil dilation can also occur when new items conceptually related to old ones are erroneously recognized as old, but the aspects of similarity that modulate false memory and related pupil responses remain unclear. We investigated this issue by manipulating the degree of featural similarity between new (unstudied) and old (studied) concepts in an old/new recognition task. We found that new concepts with high similarity were mistakenly identified as old and had greater pupil dilation than those with low similarity, suggesting that pupil dilation reflects the strength of evidence on which recognition judgments are based and, importantly, greater locus coeruleus and prefrontal activity determined by the higher degree of retrieval monitoring involved in recognizing these items.