When problem size matters: differential effects of brain stimulation on arithmetic problem solving and neural oscillations

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.

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

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

Investigating the role of the fusiform face area and occipital face area using multifocal transcranial direct current stimulation

The functional role of the occipital face area (OFA) and the fusiform face area (FFA) in face recognition is inconclusive to date. While some research has shown that the OFA and FFA are involved in early (i.e., featural processing) and late (i.e., holistic processing) stages of face recognition respectively, other research suggests that both regions are involved in both early and late stages of face recognition. Thus, the current study aims to further examine the role of the OFA and the FFA using multifocal transcranial direct current stimulation (tDCS). In Experiment 1, we used computer-generated faces. Thirty-five participants completed whole face and facial features (i.e., eyes, nose, mouth) recognition tasks after OFA and FFA stimulation in a within-subject design. No difference was found in recognition performance after either OFA or FFA stimulation. In Experiment 2 with 60 participants, we used real faces, provided stimulation following a between-subjects design and included a sham control group. Results showed that FFA stimulation led to enhanced efficiency of facial features recognition. Additionally, no effect of OFA stimulation was found for either facial feature or whole face recognition. These results suggest the involvement of FFA in the recognition of facial features.

Understanding the Effects of Transcranial Electrical Stimulation in Numerical Cognition: A Systematic Review for Clinical Translation

Atypical development of numerical cognition (dyscalculia) may increase the onset of neuropsychiatric symptoms, especially when untreated, and it may have long-term detrimental social consequences. However, evidence-based treatments are still lacking. Despite plenty of studies investigating the effects of transcranial electrical stimulation (tES) on numerical cognition, a systematized synthesis of results is still lacking. In the present systematic review (PROSPERO ID: CRD42021271139), we found that the majority of reports (20 out of 26) showed the effectiveness of tES in improving both number (80%) and arithmetic (76%) processing. In particular, anodal tDCS (regardless of lateralization) over parietal regions, bilateral tDCS (regardless of polarity/lateralization) over frontal regions, and tRNS (regardless of brain regions) strongly enhance number processing. While bilateral tDCS and tRNS over parietal and frontal regions and left anodal tDCS over frontal regions consistently improve arithmetic skills. In addition, tACS seems to be more effective than tDCS at ameliorating arithmetic learning. Despite the variability of methods and paucity of clinical studies, tES seems to be a promising brain-based treatment to enhance numerical cognition. Recommendations for clinical translation, future directions, and limitations are outlined.

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.

Theta Band Transcranial Alternating Current Stimulation Enhances Arithmetic Learning: A Systematic Comparison of Different Direct and Alternating Current Stimulations

Over the last decades, interest in transcranial electrical stimulation (tES) has grown, as it might allow for causal investigations of the associations between cortical activity and cognition as well as to directly influence cognitive performance. The main objectives of the present work were to assess whether tES can enhance the acquisition and application of arithmetic abilities, and whether it enables a better assessment of underlying neurophysiological processes. To this end, the present, double-blind, sham-controlled study assessed the effects of six active stimulations (three tES protocols: anodal transcranial direct current stimulation (tDCS), alpha band transcranial alternating current stimulation (tACS), and theta band tACS; targeting the left dorsolateral prefrontal cortex or the left posterior parietal cortex) on the acquisition of an arithmetic procedure, arithmetic facts, and event-related synchronization/desynchronization (ERS/ERD) patterns. 137 healthy adults were randomly assigned to one of seven groups, each receiving one of the tES-protocols during learning. Results showed that frontal theta band tACS reduced the repetitions needed to learn novel facts and both, frontal and parietal theta band tACS accelerated the decrease in calculation times in fact learning problems. The beneficial effect of frontal theta band tACS may reflect enhanced executive functions, allowing for better control and inhibition processes and hence, a faster acquisition and integration of novel fact knowledge. However, there were no significant effects of the stimulations on procedural learning or ERS/ERD patterns. Overall, theta band tACS appears promising as a support for arithmetic fact training, but effects on procedural calculations and neurophysiological processes remain ambiguous.

Differences in event-related potential (ERP) responses to small tie, non-tie and 1-problems in addition and multiplication

Using ERP, we investigated the cause of the tie advantage according to which problems with repeated operands are solved faster and more accurately than non-tie problems. We found no differences in early or N400 ERP components between problems, suggesting that tie problems are not encoded faster or suffer from less interference than non-tie problems. However, a lesser negative amplitude of the N2 component was found for tie than non-tie problems. This suggests more working-memory and attentional resource requirements for non-tie problems and therefore more frequent use of retrieval for tie than non-tie problems. The possible peculiarity of problems involving a 1 was also investigated. We showed less negative N2 amplitudes for these problems than for other non-tie problems, suggesting less working-memory resources for 1-problems than other non-tie problems. This could be explained either by higher reliance on memory retrieval for 1-problems than non-1 problems or by the application of non-arithmetical rules for 1-problems.

Effects of transcranial stimulation in developmental neurocognitive disorders: A critical appraisal

Non-invasive brain stimulation (NIBS) has been highlighted as a powerful tool to promote neuroplasticity, and an attractive approach to support cognitive remediation. Here we provide a systematic review of 26 papers using NIBS to ameliorate cognitive dysfunctions in three prevalent neurodevelopmental disorders: Attention-Deficit/Hyperactivity Disorder (ADHD), Developmental Dyslexia and Developmental Dyscalculia. An overview of the state of research shows a predominance of studies using repetitive transcranial magnetic stimulation (rTMS) and transcranial direct current stimulation (tDCS) techniques, and an unequal distribution among clinical conditions. Regarding the utility of NIBS, the results are promising but also ambiguous. Twenty-three papers reported beneficial effects, but many of these effects were found only once or were only partially replicated and some studies even reported detrimental effects. Furthermore, most studies differed in at least one core aspect, the NIBS applied, the questionnaires and cognitive tests conducted, or the age group investigated, and sample sizes were mostly small. Hence, further studies are needed to rigorously examine the potential of NIBS in the remediation of cognitive functions. Finally, we discuss potential caveats and future directions. We reason that if adequately addressing these challenges NIBS can be feasible, with potential benefits in treating neurodevelopmental disorders.

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.

Effects of Anodal tDCS on Arithmetic Performance and Electrophysiological Activity

Arithmetic abilities are among the most important school-taught skills and form the basis for higher mathematical competencies. At the same time, their acquisition and application can be challenging. Hence, there is broad interest in methods to improve arithmetic abilities. One promising method is transcranial direct current stimulation (tDCS). In the present study, we compared two anodal tDCS protocols in their efficacy to improve arithmetic performance and working memory. In addition, we investigated stimulation-related electrophysiological changes. Three groups of participants solved arithmetic problems (additions and subtractions) and an n-back task before, during, and after receiving either frontal or parietal anodal tDCS (25 min; 1 mA) or sham stimulation. EEG was simultaneously recorded to assess stimulation effects on event-related (de-) synchronisation (ERS/ERD) in theta and alpha bands. Persons receiving frontal stimulation showed an acceleration of calculation speed in large subtractions from before to during and after stimulation. However, a comparable, but delayed (apparent only after stimulation) increase was also found in the sham stimulation group, while it was absent in the group receiving parietal stimulation. In additions and small subtractions as well as the working memory task, analyses showed no effects of stimulation. Results of ERS/ERD during large subtractions indicate changes in ERS/ERD patterns over time. In the left hemisphere there was a change from theta band ERD to ERS in all three groups, whereas a similar change in the right hemisphere was restricted to the sham group. Taken together, tDCS did not lead to a general improvement of arithmetic performance. However, results indicate that frontal stimulation accelerated training gains, while parietal stimulation halted them. The absence of general performance improvements, but acceleration of training effects might be a further indicator of the advantages of using tDCS as training or learning support over tDCS as a sole performance enhancer.

A Functional Domain Based Approach in Neurocognitive Rehabilitation with Transcranial Direct Current Stimulation: A Case Report

Transcranial direct current stimulation (tDCS) is a novel brain stimulation technique which has kindled hope in alleviating motor, language as well as cognitive deficits in neuronal injury. Current case report describes application of tDCS in two phases using two different protocols in a patient with hypoxic injury. In the first phase anodal stimulation of dorsolateral prefrontal cortex improved the language fluency. Subsequently, after 6 months second phase application of anodal stimulation over posterior parietal region targeted arithmetic and working memory deficits. Individualising the treatment protocols of brain stimulation, based on the lesion and the functional deficits, for neuro-rehabilitation is emphasised.

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.

Low to No Effect: Application of tRNS During Two-Digit Addition

Transcranial electric stimulation such as transcranial random noise stimulation (tRNS) and transcranial direct current stimulation (tDCS) have been used to investigate structure-function relationships in numerical cognition. Recently, tRNS was suggested to be more effective than tDCS. However, so far there is no evidence on the differential impact of tDCS and tRNS on numerical cognition using the same experimental paradigm. In the present study, we used a two-digit addition paradigm for which significant-albeit small-effects of tDCS were observed previously to evaluate the impact of parietal and frontal tRNS on specific numerical effects. While previous studies reported a modulation of numerical effects of this task through tDCS applied to parietal areas, we did not observe any effect of parietal tRNS on performance in two-digit addition. These findings suggest that tRNS seemed to influence concurrent mental arithmetic less than tDCS at least when applied over the IPS. These generally small to absent effects of tES on actual arithmetic performance in the current addition paradigm are in line with the results of a recent meta-analysis indicating that influences of tES may be more pronounced in training paradigms.

Neurocognitive Effects of Transcranial Direct Current Stimulation in Arithmetic Learning and Performance: A Simultaneous tDCS-fMRI Study

BACKGROUND

A small but increasing number of studies suggest that non-invasive brain stimulation by means of transcranial direct current stimulation (tDCS) can modulate arithmetic processes that are essential for higher-order mathematical skills and that are impaired in dyscalculic individuals. However, little is known about the neural mechanisms underlying such stimulation effects, and whether they are specific to cognitive processes involved in different arithmetic tasks.

METHODS

We addressed these questions by applying tDCS during simultaneous functional magnetic resonance imaging (fMRI) while participants were solving two types of complex subtraction problems: repeated problems, relying on arithmetic fact learning and problem-solving by fact retrieval, and novel problems, requiring calculation procedures. Twenty participants receiving left parietal anodal plus right frontal cathodal stimulation were compared with 20 participants in a sham condition.

RESULTS

We found a strong cognitive and neural dissociation between repeated and novel problems. Repeated problems were solved more accurately and elicited increased activity in the bilateral angular gyri and medial plus lateral prefrontal cortices. Solving novel problems, in contrast, was accompanied by stronger activation in the bilateral intraparietal sulci and the dorsomedial prefrontal cortex. Most importantly, tDCS decreased the activation of the right inferior frontal cortex while solving novel (compared to repeated) problems, suggesting that the cathodal stimulation rendered this region unable to respond to the task-specific cognitive demand.

CONCLUSIONS

The present study revealed that tDCS during arithmetic problem-solving can modulate the neural activity in proximity to the electrodes specifically when the current demands lead to an engagement of this area.

Brain-mechanistic responses to varying difficulty levels of approximate solutions to arithmetic problems

Approximate strategies are crucial in daily human life. The studies on the “difficulty effect” seen in approximate complex arithmetic have long been neglected. Here, we aimed to explore the brain mechanisms related to this difficulty effect in the case of complex addition, using event-related potential-based methods. Following previous path-finding studies, we used the inequality paradigm and different split sizes to induce the use of two approximate strategies for different difficulty levels. By comparing dependent variables from the medium- and large-split conditions, we anticipated being able to dissociate the effects of task difficulty based on approximate strategy in electrical components. In the fronto−central region, early P2 (150–250 ms) and an N400-like wave (250–700 ms) were significantly different between different difficulty levels. Differences in P2 correlated with the difficulty of separation of the approximate strategy from the early physical stimulus discrimination process, which is dominant before 200 ms, and differences in the putative N400 correlated with different difficulties of approximate strategy execution. Moreover, this difference may be linked to speech processing. In addition, differences were found in the fronto-central region, which may reflect the regulatory role of this part of the cortex in approximate strategy execution when solving complex arithmetic problems.

Transcranial random noise stimulation mitigates increased difficulty in an arithmetic learning task

Proficiency in arithmetic learning can be achieved by using a multitude of strategies, the most salient of which are procedural learning (applying a certain set of computations) and rote learning (direct retrieval from long-term memory). Here we investigated the effect of transcranial random noise stimulation (tRNS), a non-invasive brain stimulation method previously shown to enhance cognitive training, on both types of learning in a 5-day sham-controlled training study, under two conditions of task difficulty, defined in terms of item repetition. On the basis of previous research implicating the prefrontal and posterior parietal cortex in early and late stages of arithmetic learning, respectively, sham-controlled tRNS was applied to bilateral prefrontal cortex for the first 3 days and to the posterior parietal cortex for the last 2 days of a 5-day training phase. The training involved learning to solve arithmetic problems by applying a calculation algorithm; both trained and untrained problems were used in a brief testing phase at the end of the training phase. Task difficulty was manipulated between subjects by using either a large ("easy" condition) or a small ("difficult" condition) number of repetition of problems during training. Measures of attention and working memory were acquired before and after the training phase. As compared to sham, participants in the tRNS condition displayed faster reaction times and increased learning rate during the training phase; as well as faster reaction times for both trained and untrained (new) problems, which indicated a transfer effect after the end of training. All stimulation effects reached significance only in the "difficult" condition when number of repetition was lower. There were no transfer effects of tRNS on attention or working memory. The results support the view that tRNS can produce specific facilitative effects on numerical cognition--specifically, on arithmetic learning. They also highlight the importance of task difficulty in the neuromodulation of learning, which in the current study due to the manipulation of item repetition might have being mediated by the memory system.

Arithmetic split effect in complex subtractions: an event-related potential study

This study explores the relationship between the split effect and the use of exact versus approximate strategies in complex-subtraction calculations. One-hundred and two-digit subtraction problems were presented, with half of them being small-split problems with answers ±2 or ±5 from 50 and the other half being large-split problems with answers ±10 or ±15 from 50. Participants were asked to indicate whether the answer was less than 50. The measures were speed and accuracy of task performance, and high temporal resolution event-related potentials. Behavioral data showed that participants had a longer time requirement and a lower accuracy in solving small-split problems than in solving large-split problems. Event-related potential data show that, comparatively, the small-split problems led to more-negative, more-lateralized waves as early as 250 ms at frontal, frontocentral, and central sites. Our results, which are in agreement with previous studies, suggest that the participants used exact strategies to solve small-split problems and approximate strategies to solve large-split problems when performing complex subtractions. These results further our understanding of the brain mechanisms underlying the relationship between small/large-split effects and exact/approximate strategies in this task domain.