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

Neuroenhancement by repetitive transcranial magnetic stimulation (rTMS) on DLPFC in healthy adults

The term "neuroenhancement" describes the enhancement of cognitive function associated with deficiencies resulting from a specific condition. Nevertheless, there is currently no agreed-upon definition for the term "neuroenhancement", and its meaning can change based on the specific research being discussed. As humans, our continual pursuit of expanding our capabilities, encompassing both cognitive and motor skills, has led us to explore various tools. Among these, repetitive Transcranial Magnetic Stimulation (rTMS) stands out, yet its potential remains underestimated. Historically, rTMS was predominantly employed in studies focused on rehabilitation objectives. A small amount of research has examined its use on healthy subjects with the goal of improving cognitive abilities like risk-seeking, working memory, attention, cognitive control, learning, computing speed, and decision-making. It appears that the insights gained in this domain largely stem from indirect outcomes of rehabilitation research. This review aims to scrutinize these studies, assessing the effectiveness of rTMS in enhancing cognitive skills in healthy subjects. Given that the dorsolateral prefrontal cortex (DLPFC) has become a popular focus for rTMS in treating psychiatric disorders, corresponding anatomically to Brodmann areas 9 and 46, and considering the documented success of rTMS stimulation on the DLPFC for cognitive improvement, our focus in this review article centers on the DLPFC as the focal point and region of interest. Additionally, recognizing the significance of theta burst magnetic stimulation protocols (TBS) in mimicking the natural firing patterns of the brain to modulate excitability in specific cortical areas with precision, we have incorporated Theta Burst Stimulation (TBS) wave patterns. This inclusion, mirroring brain patterns, is intended to enhance the efficacy of the rTMS method. To ascertain if brain magnetic stimulation consistently improves cognition, a thorough meta-analysis of the existing literature has been conducted. The findings indicate that, after excluding outlier studies, rTMS may improve cognition when compared to appropriate control circumstances. However, there is also a considerable degree of variation among the researches. The navigation strategy used to reach the stimulation site and the stimulation location are important factors that contribute to the variation between studies. The results of this study can provide professional athletes, firefighters, bodyguards, and therapists-among others in high-risk professions-with insightful information that can help them perform better on the job.

The calculating brain

The human brain possesses neural networks and mechanisms enabling the representation of numbers, basic arithmetic operations, and mathematical reasoning. Without the ability to represent numerical quantity and perform calculations, our scientifically and technically advanced culture would not exist. However, the origins of numerical abilities are grounded in an intuitive understanding of quantity deeply rooted in biology. Nevertheless, more advanced symbolic arithmetic skills require a cultural background with formal mathematical education. In the past two decades, cognitive neuroscience has seen significant progress in understanding the workings of the calculating brain through various methods and model systems. This review begins by exploring the mental and neuronal representations of nonsymbolic numerical quantity and then progresses to symbolic representations acquired in childhood. During arithmetic operations (addition, subtraction, multiplication, and division), these representations are processed and transformed according to arithmetic rules and principles, leveraging different mental strategies and types of arithmetic knowledge that can be dissociated in the brain. Although it was once believed that number processing and calculation originated from the language faculty, it is now evident that mathematical and linguistic abilities are primarily processed independently in the brain. Understanding how the healthy brain processes numerical information is crucial for gaining insights into debilitating numerical disorders, including acquired conditions like acalculia and learning-related calculation disorders such as developmental dyscalculia.

Brain laterality of numbers and calculation: Complex networks and their development

This chapter reviews notions about the lateralization of numbers and calculation in the brain, including its developmental pattern. Such notions have changed dramatically in recent decades. What was once considered a function almost exclusively located in the left hemisphere has been found to be sustained by complex brain networks encompassing both hemispheres. Depending on the specific task, however, each hemisphere has its own role. Much of this progress was determined by the convergency of investigations conducted with different methods. Contrary to traditional wisdom, the right hemisphere is not involved in arithmetic just as far as generic spatial aspects are concerned. Very specific arithmetic functions like remembering the spatial templates for complex operations, or processing of zero in complex numbers, are indeed sustained in specific right-sided areas. The system used in the typical adult appears to be the result of a complex pattern of development. The numerical brain clearly evolved from less mature to more advanced brain networks because of growth and education. Children seem to be equipped with the ability to represent the number nonverbally from a very early age. The bilateral processing of number-related tasks is however a late acquisition.

Anodal High-definition Transcranial Direct Current Stimulation Over the Left (but not Right) Parietal Cortex Facilitates Mental Arithmetic

Non-invasive brain stimulation (NIBS) techniques such as transcranial direct current stimulation (tDCS) allow for investigating the functional involvement of specific brain areas in mental arithmetic. In this study, we employed for the first time high-definition (HD)-tDCS, which offers enhanced spatial precision, to explore the functional roles of the left and right intraparietal sulcus (IPS) in mental arithmetic. A total of 25 participants underwent anodal left IPS, anodal right IPS, and sham stimulation in separate sessions in counterbalanced order while solving single- and multi-step addition and subtraction problems. We found that stimulation of the left IPS, but not the right IPS or sham stimulation, improved arithmetic performance speed. These results provide further evidence for the functional involvement of the left IPS in a broad range of arithmetic tasks and highlight the potential of NIBS for cognitive enhancement.

Supplementary Information

The online version contains supplementary material available at 10.1007/s41465-024-00314-0.

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.

The two-network framework of number processing: a step towards a better understanding of the neural origins of developmental dyscalculia

Developmental dyscalculia is a specific learning disorder that persists over lifetime and can have an enormous impact on personal, health-related, and professional aspects of life. Despite its central importance, the origin both at the cognitive and neural level is not yet well understood. Several classification schemas of dyscalculia have been proposed, sometimes together with an associated deficit at the neural level. However, these explanations are (a) not providing an exhaustive framework that is at levels with the observed complexity of developmental dyscalculia at the behavioral level and (b) are largely mono-causal approaches focusing on gray matter deficits. We suggest that number processing is instead the result of context-dependent interaction of two anatomically largely separate, distributed but overlapping networks that function/cooperate in a closely integrated fashion. The proposed two-network framework (TNF) is the result of a series of studies in adults on the neural correlates underlying magnitude processing and arithmetic fact retrieval, which comprised neurofunctional imaging of various numerical tasks, the application of probabilistic fiber tracking to obtain well-defined connections, and the validation and modification of these results using disconnectome mapping in acute stroke patients. Emerged from data in adults, it represents the endpoint of the acquisition and use of mathematical competencies in adults. Yet, we argue that its main characteristics should already emerge earlier during development. Based on this TNF, we develop a classification schema of phenomenological subtypes and their underlying neural origin that we evaluate against existing propositions and the available empirical data.

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.

Impaired Arithmetic Fact Retrieval in an Adult with Developmental Dyscalculia: Evidence from Behavioral and Functional Brain Imaging Data

Developmental dyscalculia (DD) is a developmental disorder characterized by arithmetic difficulties. Recently, it has been suggested that the neural networks supporting procedure-based calculation (e.g., in subtraction) and left-hemispheric verbal arithmetic fact retrieval (e.g., in multiplication) are partially distinct. Here we compared the neurofunctional correlates of subtraction and multiplication in a 19-year-old student (RM) with DD to 18 age-matched controls. Behaviorally, RM performed significantly worse than controls in multiplication, while subtraction was unaffected. Neurofunctional differences were most pronounced regarding multiplication: RM showed significantly stronger activation than controls not only in left angular gyrus but also in a fronto-parietal network (including left intraparietal sulcus and inferior frontal gyrus) typically activated during procedure-based calculation. Region-of-interest analyses indicated group differences in multiplication only, which, however, did not survive correction for multiple comparisons. Our results are consistent with dissociable and processing-specific, but not operation-specific neurofunctional networks. Procedure-based calculation is not only associated with subtraction but also with (untrained) multiplication facts. Only after rote learning, facts can be retrieved quasi automatically from memory. We suggest that this learning process and the associated shift in activation patterns has not fully occurred in RM, as reflected in her need to resort to procedure-based strategies to solve multiplication facts.

Oscillatory electroencephalographic patterns of arithmetic problem solving in fourth graders

Numerous studies have identified neurophysiological correlates of performing arithmetic in adults. For example, oscillatory electroencephalographic (EEG) patterns associated with retrieval and procedural strategies are well established. Whereas fact retrieval has been linked to enhanced left-hemispheric theta ERS (event-related synchronization), procedural strategies are accompanied by increased bilateral alpha ERD (event-related desynchronization). It is currently not clear if these findings generalize to children. Our study is the first to investigate oscillatory EEG activity related to strategy use and arithmetic operations in children. We assessed ERD/ERS correlates of 31 children in fourth grade (aged between nine and ten years) during arithmetic problem solving. We presented multiplication and subtraction problems, which children solved with fact retrieval or a procedure. We analyzed these four problem categories (retrieved multiplications, retrieved subtractions, procedural multiplications, and procedural subtractions) in our study. In summary, we found similar strategy-related patterns to those reported in previous studies with adults. That is, retrieval problems elicited stronger left-hemispheric theta ERS and weaker alpha ERD as compared to procedural problems. Interestingly, we observed neurophysiological differences between multiplications and subtractions within retrieval problems. Although there were no response time or accuracy differences, retrieved multiplications were accompanied by larger theta ERS than retrieved subtractions. This finding could indicate that retrieval of multiplication and subtraction facts are distinct processes, and/or that multiplications are more frequently retrieved than subtractions in this age group.

rsfMRI based evidence for functional connectivity alterations in adults with developmental stuttering

Persistent developmental stuttering (PDS) is defined as a speech disorder mainly characterized by intermittent involuntary disruption in normal fluency, time patterning, and rhythm of speech. Although extensive functional neuroimaging studies have explored brain activation alterations in stuttering, the main affected brain regions/networks in PDS still remain unclear. Here, using functional magnetic resonance imaging (fMRI), we investigated resting-state whole-brain functional connectivity of 15 adults who stutter (PDS group) and 15 age-matched control individuals to reveal the connectivity abnormalities associated with stuttering. We were also interested in exploring how the severity of stuttering varies across individuals to understand the compensatory mechanism of connectivity pattern in patients showing less symptoms. Our results revealed decreased connectivity of left frontal pole and left middle frontal gyrus (MidFG) with right precentral/postcentral gyrus in stuttering individuals compared with control participants, while less symptomatic PDS individuals showed greater functional connectivity between left MidFG and left caudate. Additionally, our finding indicated reduced connectivity in the PDS group between the left superior temporal gyrus (STG) and several brain regions including the right limbic lobe, right fusiform, and right cerebellum, as well as the left middle temporal gyrus (MTG). We also observed that PDS individuals with less severe symptoms had stronger connectivity between right MTG and several left hemispheric regions including inferior frontal gyrus (IFG) and STG. The connectivity between right fronto-orbital and right MTG was also negatively correlated with stuttering severity. These findings may suggest the involvement of right MTG and left MidFG in successful compensatory mechanisms in more fluent stutterers.

Emerging neurodevelopmental perspectives on mathematical learning

Strong foundational skills in mathematical problem solving, acquired in early childhood, are critical not only for success in the science, technology, engineering, and mathematical (STEM) fields but also for quantitative reasoning in everyday life. The acquisition of mathematical skills relies on protracted interactive specialization of functional brain networks across development. Using a systems neuroscience approach, this review synthesizes emerging perspectives on neurodevelopmental pathways of mathematical learning, highlighting the functional brain architecture that supports these processes and sources of heterogeneity in mathematical skill acquisition. We identify the core neural building blocks of numerical cognition, anchored in the posterior parietal and ventral temporal-occipital cortices, and describe how memory and cognitive control systems, anchored in the medial temporal lobe and prefrontal cortex, help scaffold mathematical skill development. We highlight how interactive specialization of functional circuits influences mathematical learning across different stages of development. Functional and structural brain integrity and plasticity associated with math learning can be examined using an individual differences approach to better understand sources of heterogeneity in learning, including cognitive, affective, motivational, and sociocultural factors. Our review emphasizes the dynamic role of neurodevelopmental processes in mathematical learning and cognitive development more generally.