Spatiotemporal Dynamics of Successive Activations across the Human Brain during Simple Arithmetic Processing

Previous neuroimaging studies have offered unique insights about the spatial organization of activations and deactivations across the brain; however, these were not powered to explore the exact timing of events at the subsecond scale combined with a precise anatomical source of information at the level of individual brains. As a result, we know little about the order of engagement across different brain regions during a given cognitive task. Using experimental arithmetic tasks as a prototype for human-unique symbolic processing, we recorded directly across 10,076 brain sites in 85 human subjects (52% female) using the intracranial electroencephalography. Our data revealed a remarkably distributed change of activity in almost half of the sampled sites. In each activated brain region, we found juxtaposed neuronal populations preferentially responsive to either the target or control conditions, arranged in an anatomically orderly manner. Notably, an orderly successive activation of a set of brain regions-anatomically consistent across subjects-was observed in individual brains. The temporal order of activations across these sites was replicable across subjects and trials. Moreover, the degree of functional connectivity between the sites decreased as a function of temporal distance between regions, suggesting that the information is partially leaked or transformed along the processing chain. Our study complements prior imaging studies by providing hitherto unknown information about the timing of events in the brain during arithmetic processing. Such findings can be a basis for developing mechanistic computational models of human-specific cognitive symbolic systems.

Profiles of mathematical deficits in children with dyslexia

Despite a high rate of concurrent mathematical difficulties among children with dyslexia, we still have limited information regarding the prevalence and severity of mathematical deficits in this population. To address this gap, we developed a comprehensive battery of cognitive tests, known as the UCSF Mathematical Cognition Battery (MCB), with the aim of identifying deficits in four distinct mathematical domains: number processing, arithmetical procedures, arithmetic facts retrieval, and geometrical abilities. The mathematical abilities of a cohort of 75 children referred to the UCSF Dyslexia Center with a diagnosis of dyslexia, along with 18 typically developing controls aged 7 to 16, were initially evaluated using a behavioral neurology approach. A team of professional clinicians classified the 75 children with dyslexia into five groups, based on parents' and teachers' reported symptoms and clinical history. These groups included children with no mathematical deficits and children with mathematical deficits in number processing, arithmetical procedures, arithmetic facts retrieval, or geometrical abilities. Subsequently, the children underwent evaluation using the MCB to determine concordance with the clinicians' impressions. Additionally, neuropsychological and cognitive standardized tests were administered. Our study reveals that within a cohort of children with dyslexia, 66% exhibit mathematical deficits, and among those with mathematical deficits, there is heterogeneity in the nature of these deficits. If these findings are confirmed in larger samples, they can potentially pave the way for new diagnostic approaches, consistent subtype classification, and, ultimately personalized interventions.

Distinct Contributions of the Cerebellum and Basal Ganglia to Arithmetic Procedures

Humans exhibit complex mathematical skills attributed to the exceptional enlargement of neocortical regions throughout evolution. In the current work, we initiated a novel exploration of the ancient subcortical neural network essential for mathematical cognition. Using a neuropsychological approach, we report that degeneration of two subcortical structures, the cerebellum and basal ganglia, impairs performance in symbolic arithmetic. We identify distinct computational impairments in male and female participants with cerebellar degeneration (CD) or Parkinson's disease (PD). The CD group exhibited a disproportionate cost when the arithmetic sum increased, suggesting that the cerebellum is critical for iterative procedures required for calculations. The PD group showed a disproportionate cost for equations with increasing addends, suggesting that the basal ganglia are critical for chaining multiple operations. In Experiment 2, the two patient groups exhibited intact practice gains for repeated equations at odds with an alternative hypothesis that these impairments were related to memory retrieval. Notably, we discuss how the counting and chaining operations relate to cerebellar and basal ganglia function in other task domains (e.g., motor processes). Overall, we provide a novel perspective on how the cerebellum and basal ganglia contribute to symbolic arithmetic. Our studies demonstrate the constraints on the computational role of two subcortical regions in higher cognition.

Spatiotemporal dynamics of successive activations across the human brain during simple arithmetic processing

Previous neuroimaging studies have offered unique insights about the spatial organization of activations and deactivations across the brain, however these were not powered to explore the exact timing of events at the subsecond scale combined with precise anatomical source information at the level of individual brains. As a result, we know little about the order of engagement across different brain regions during a given cognitive task. Using experimental arithmetic tasks as a prototype for human-unique symbolic processing, we recorded directly across 10,076 brain sites in 85 human subjects (52% female) using intracranial electroencephalography (iEEG). Our data revealed a remarkably distributed change of activity in almost half of the sampled sites. Notably, an orderly successive activation of a set of brain regions - anatomically consistent across subjects-was observed in individual brains. Furthermore, the temporal order of activations across these sites was replicable across subjects and trials. Moreover, the degree of functional connectivity between the sites decreased as a function of temporal distance between regions, suggesting that information is partially leaked or transformed along the processing chain. Furthermore, in each activated region, distinct neuronal populations with opposite activity patterns during target and control conditions were juxtaposed in an anatomically orderly manner. Our study complements the prior imaging studies by providing hitherto unknown information about the timing of events in the brain during arithmetic processing. Such findings can be a basis for developing mechanistic computational models of human-specific cognitive symbolic systems.

Significance statement

Our study elucidates the spatiotemporal dynamics and anatomical specificity of brain activations across >10,000 sites during arithmetic tasks, as captured by intracranial EEG. We discovered an orderly, successive activation of brain regions, consistent across individuals, and a decrease in functional connectivity as a function of temporal distance between regions. Our findings provide unprecedented insights into the sequence of cognitive processing and regional interactions, offering a novel perspective for enhancing computational models of cognitive symbolic systems.

Direct intracranial recordings in the human angular gyrus during arithmetic processing

The role of angular gyrus (AG) in arithmetic processing remains a subject of debate. In the present study, we recorded from the AG, supramarginal gyrus (SMG), intraparietal sulcus (IPS), and superior parietal lobule (SPL) across 467 sites in 30 subjects performing addition or multiplication with digits or number words. We measured the power of high-frequency-broadband (HFB) signal, a surrogate marker for regional cortical engagement, and used single-subject anatomical boundaries to define the location of each recording site. Our recordings revealed the lowest proportion of sites with activation or deactivation within the AG compared to other subregions of the inferior parietal cortex during arithmetic processing. The few activated AG sites were mostly located at the border zones between AG and IPS, or AG and SMG. Additionally, we found that AG sites were more deactivated in trials with fast compared to slow response times. The increase or decrease of HFB within specific AG sites was the same when arithmetic trials were presented with number words versus digits and during multiplication as well as addition trials. Based on our findings, we conclude that the prior neuroimaging findings of so-called activations in the AG during arithmetic processing could have been due to group-based analyses that might have blurred the individual anatomical boundaries of AG or the subtractive nature of the neuroimaging methods in which lesser deactivations compared to the control condition have been interpreted as "activations". Our findings offer a new perspective with electrophysiological data about the engagement of AG during arithmetic processing.

Preschool language and visuospatial skills respectively predict multiplication and addition/subtraction skills in middle school children

A converging body of evidence from neuroimaging, behavioral and neuropsychology studies suggests that different arithmetic operations rely on distinct neuro-cognitive processes: while addition and subtraction may rely more on visuospatial reasoning, multiplication would depend more on verbal abilities. In this paper, we tested this hypothesis in a longitudinal study measuring language and visuospatial skills in 358 preschoolers, and testing their mental calculation skills at the beginning of middle school. Language skills at 5.5 years significantly predicted multiplication, but not addition nor subtraction scores at 11.5 years. Conversely, early visuospatial skills predicted addition and subtraction, but not multiplication scores. These results provide strong support for the existence of a double dissociation in mental arithmetic operations, and demonstrate the existence of long-lasting links between language/visuospatial skills and specific calculation abilities. Using structural equation modelling, we analyzed longitudinal data from 358 children. Language skills in preschool significantly predicted multiplication, but not addition nor subtraction scores in middle school. The reverse was true for preschool visuo-spatial skills. Importantly, this pattern remained unchanged when we controlled addition and multiplication operations for overall difficulty and for the magnitude of the operands. These results provide strong support for the existence of a double dissociation in mental arithmetic operations. This article is protected by copyright. All rights reserved.

Electrocorticographic evidence of a common neurocognitive sequence for mentalizing about the self and others

Neuroimaging studies of mentalizing (i.e., theory of mind) consistently implicate the default mode network (DMN). Nevertheless, the social cognitive functions of individual DMN regions remain unclear, perhaps due to limited spatiotemporal resolution in neuroimaging. Here we use electrocorticography (ECoG) to directly record neuronal population activity while 16 human participants judge the psychological traits of themselves and others. Self- and other-mentalizing recruit near-identical cortical sites in a common spatiotemporal sequence. Activations begin in the visual cortex, followed by temporoparietal DMN regions, then finally in medial prefrontal regions. Moreover, regions with later activations exhibit stronger functional specificity for mentalizing, stronger associations with behavioral responses, and stronger self/other differentiation. Specifically, other-mentalizing evokes slower and longer activations than self-mentalizing across successive DMN regions, implying lengthier processing at higher levels of representation. Our results suggest a common neurocognitive pathway for self- and other-mentalizing that follows a complex spatiotemporal gradient of functional specialization across DMN and beyond.

Overlapping Neuronal Population Responses in the Human Parietal Cortex during Visuospatial Attention and Arithmetic Processing

Engagement of posterior parietal cortex (PPC) in visuospatial attention and arithmetic processing has been extensively documented using neuroimaging methods. Numerous studies have suggested a close connection between visuospatial attention and arithmetic processing. However, the extant evidence in humans stems from neuroimaging methods that have relied on group analyses without much knowledge about the profile of neurophysiological engagement within localized neuronal populations at the individual brain level. Hence, it has remained unclear if the overlap of two functions in the PPC is the product of averaging, or they truly stem from a common profile of activity within the same neuronal populations in the human PPC. In the current study, we leveraged the anatomical precision and high signal-to-noise ratio of intracranial electrocorticography and probed the engagement of discrete PPC neuronal populations in seven neurosurgical patients (n = 179 total PPC sites covered; 26 sites on average per individual participant). We aimed to study the extent of parietal activations within each individual brain during visuospatial attention versus arithmetic tasks and the profile of electrophysiological responses within a given recording site during these tasks. Our findings indicated that about 40% of PPC sites did not respond to either visuospatial attention or arithmetic stimuli-or episodic memory conditions that were used as an adjunct control condition. Of those that were activated during either visuospatial attention or arithmetic conditions, a large majority showed overlapping responses during both visuospatial attention and arithmetic conditions. Most interestingly, responses during arithmetic processing were greatest in sites along the intraparietal sulcus region showing preference to contralateral, instead of ipsilateral, visual probes in the visuospatial attention task. Our results provide novel data about the relationship between numerical and spatial orientation at the neuronal population level and shed light on the complex functional organization of the PPC that could not be attained with noninvasive methods.

Gender bias in academia: A lifetime problem that needs solutions

Despite increased awareness of the lack of gender equity in academia and a growing number of initiatives to address issues of diversity, change is slow, and inequalities remain. A major source of inequity is gender bias, which has a substantial negative impact on the careers, work-life balance, and mental health of underrepresented groups in science. Here, we argue that gender bias is not a single problem but manifests as a collection of distinct issues that impact researchers' lives. We disentangle these facets and propose concrete solutions that can be adopted by individuals, academic institutions, and society.

Neuronal Population Responses in the Human Ventral Temporal and Lateral Parietal Cortex during Arithmetic Processing with Digits and Number Words

Past research has identified anatomically specific sites within the posterior inferior temporal gyrus (PITG) and the intraparietal sulcus (IPS) areas that are engaged during arithmetic processing. Although a small region of the PITG (known as the number form area) is selectively engaged in the processing of numerals, its surrounding area is activated during both digit and number word processing. In eight participants with intracranial electrodes, we compared the timing and selectivity of electrophysiological responses in the number form area-surround and IPS regions during arithmetic processing with digits and number words. Our recordings revealed stronger electrophysiological responses in the high-frequency broadband range in both regions to digits than number words, with the difference that number words elicited delayed activity in the IPS but not PITG. Our findings of distinct profiles of responses in the PITG and the IPS to digits compared with number words provide novel information that is relevant to existing theoretical models of mathematical cognition.

Brain Mechanisms of Arithmetic: A Crucial Role for Ventral Temporal Cortex

Elementary arithmetic requires a complex interplay between several brain regions. The classical view, arising from fMRI, is that the intraparietal sulcus (IPS) and the superior parietal lobe (SPL) are the main hubs for arithmetic calculations. However, recent studies using intracranial electroencephalography have discovered a specific site, within the posterior inferior temporal cortex (pITG), that activates during visual perception of numerals, with widespread adjacent responses when numerals are used in calculation. Here, we reexamined the contribution of the IPS, SPL, and pITG to arithmetic by recording intracranial electroencephalography signals while participants solved addition problems. Behavioral results showed a classical problem size effect: RTs increased with the size of the operands. We then examined how high-frequency broadband (HFB) activity is modulated by problem size. As expected from previous fMRI findings, we showed that the total HFB activity in IPS and SPL sites increased with problem size. More surprisingly, pITG sites showed an initial burst of HFB activity that decreased as the operands got larger, yet with a constant integral over the whole trial, thus making these signals invisible to slow fMRI. Although parietal sites appear to have a more sustained function in arithmetic computations, the pITG may have a role of early identification of the problem difficulty, beyond merely digit recognition. Our results ask for a reevaluation of the current models of numerical cognition and reveal that the ventral temporal cortex contains regions specifically engaged in mathematical processing.

Decoding the processing stages of mental arithmetic with magnetoencephalography

Elementary arithmetic is highly prevalent in our daily lives. However, despite decades of research, we are only beginning to understand how the brain solves simple calculations. Here, we applied machine learning techniques to magnetoencephalography (MEG) signals in an effort to decompose the successive processing stages and mental transformations underlying elementary arithmetic. Adults subjects verified single-digit addition and subtraction problems such as 3 + 2 = 9 in which each successive symbol was presented sequentially. MEG signals revealed a cascade of partially overlapping brain states. While the first operand could be transiently decoded above chance level, primarily based on its visual properties, the decoding of the second operand was more accurate and lasted longer. Representational similarity analyses suggested that this decoding rested on both visual and magnitude codes. We were also able to decode the operation type (additions vs. subtraction) during practically the entire trial after the presentation of the operation sign. At the decision stage, MEG indicated a fast and highly overlapping temporal dynamics for (1) identifying the proposed result, (2) judging whether it was correct or incorrect, and (3) pressing the response button. Surprisingly, however, the internally computed result could not be decoded. Our results provide a first comprehensive picture of the unfolding processing stages underlying arithmetic calculations at a single-trial level, and suggest that externally and internally generated neural codes may have different neural substrates.

The Developmental Trajectory of the Operational Momentum Effect

Mental calculation is thought to be tightly related to visuospatial abilities. One of the strongest evidence for this link is the widely replicated operational momentum (OM) effect: the tendency to overestimate the result of additions and to underestimate the result of subtractions. Although the OM effect has been found in both infants and adults, no study has directly investigated its developmental trajectory until now. However, to fully understand the cognitive mechanisms lying at the core of the OM effect it is important to investigate its developmental dynamics. In the present study, we investigated the development of the OM effect in a group of 162 children from 8 to 12 years old. Participants had to select among five response alternatives the correct result of approximate addition and subtraction problems. Response alternatives were simultaneously presented on the screen at different locations. While no effect was observed for the youngest age group, children aged 9 and older showed a clear OM effect. Interestingly, the OM effect monotonically increased with age. The increase of the OM effect was accompanied by an increase in overall accuracy. That is, while younger children made more and non-systematic errors, older children made less but systematic errors. This monotonous increase of the OM effect with age is not predicted by the compression account (i.e., linear calculation performed on a compressed code). The attentional shift account, however, provides a possible explanation of these results based on the functional relationship between visuospatial attention and mental calculation and on the influence of formal schooling. We propose that the acquisition of arithmetical skills could reinforce the systematic reliance on the spatial mental number line and attentional mechanisms that control the displacement along this metric. Our results provide a step in the understanding of the mechanisms underlying approximate calculation and an important empirical constraint for current accounts on the origin of the OM effect.

A Translational Framework of Educational Neuroscience in Learning Disorders

Neuroimaging has undergone enormous progress during the last two and a half decades. The combination of neuroscientific methods and educational practice has become a focus of interdisciplinary research in order to answer more applied questions. In this realm, conditions that hamper learning success and have deleterious effects in the population - such as learning disorders (LD) - could especially profit from neuroimaging findings. At the moment, however, there is an ongoing debate about how far neuroscientific research can go to inform the practical work in educational settings. Here, we put forward a theoretical translational framework as a method of conducting neuroimaging and bridging it to education, with a main focus on dyscalculia and dyslexia. Our work seeks to represent a theoretical but mainly empirical guide on the benefits of neuroimaging, which can help people working with different aspects of LD, who need to act collaboratively to reach the full potential of neuroimaging. We provide possible ideas regarding how neuroimaging can inform LD at different levels within our multidirectional framework, i.e., mechanisms, diagnosis/prognosis, training/intervention, and community/education. In addition, we discuss methodological, conceptual, and structural limitations that need to be addressed by future research.

Finger Tracking Reveals the Covert Stages of Mental Arithmetic

We introduce a novel method capable of dissecting the succession of processing stages underlying mental arithmetic, thus revealing how two numbers are transformed into a third. We asked adults to point to the result of single-digit additions and subtractions on a number line, while their finger trajectory was constantly monitored. We found that the two operands are processed serially: the finger first points toward the larger operand, then slowly veers toward the correct result. This slow deviation unfolds proportionally to the size of the smaller operand, in both additions and subtractions. We also observed a transient operator effect: a plus sign attracted the finger to the right and a minus sign to the left and a transient activation of the absolute value of the subtrahend. These findings support a model whereby addition and subtraction are computed by a stepwise displacement on the mental number line, starting with the larger number and incrementally adding or subtracting the smaller number.

In how many ways is the approximate number system associated with exact calculation?

The approximate number system (ANS) has been consistently found to be associated with math achievement. However, little is known about the interactions between the different instantiations of the ANS and in how many ways they are related to exact calculation. In a cross-sectional design, we investigated the relationship between three measures of ANS acuity (non-symbolic comparison, non-symbolic estimation and non-symbolic addition), their cross-sectional trajectories and specific contributions to exact calculation. Children with mathematical difficulties (MD) and typically achieving (TA) controls attending the first six years of formal schooling participated in the study. The MD group exhibited impairments in multiple instantiations of the ANS compared to their TA peers. The ANS acuity measured by all three tasks positively correlated with age in TA children, while no correlation was found between non-symbolic comparison and age in the MD group. The measures of ANS acuity significantly correlated with each other, reflecting at least in part a common numerosity code. Crucially, we found that non-symbolic estimation partially and non-symbolic addition fully mediated the effects of non-symbolic comparison in exact calculation.

Are 22q11.2 distal deletions associated with math difficulties?

Approximately 6% of school-aged children have math difficulties (MD). A neurogenetic etiology has been suggested due to the presence of MD in some genetic syndromes such as 22q11.2DS. However, the contribution of 22q11.2DS to the MD phenotype has not yet been investigated. This is the first population-based study measuring the frequency of 22q11.2DS among school children with MD. Children (1,564) were identified in the schools through a screening test for language and math. Of these children, 152 (82 with MD and 70 controls) were selected for intelligence, general neuropsychological, and math cognitive assessments and for 22q11.2 microdeletion screening using MLPA. One child in the MD group had a 22q11.2 deletion spanning the LCR22-4 to LCR22-5 interval. This child was an 11-year-old girl with subtle anomalies, normal intelligence, MD attributable to number sense deficit, and difficulties in social interactions. Only 19 patients have been reported with this deletion. Upon reviewing these reports, we were able to characterize a new syndrome, 22q11.2 DS (LCR22-4 to LCR22-5), characterized by prematurity; pre- and postnatal growth restriction; apparent hypotelorism, short/upslanting palpebral fissures; hypoplastic nasal alae; pointed chin and nose; posteriorly rotated ears; congenital heart defects; skeletal abnormalities; developmental delay, particularly compromising the speech; learning disability (including MD, in one child); intellectual disability; and behavioral problems. These results suggest that 22q11.2 DS (LCR22-4 to LCR22-5) may be one of the genetic causes of MD.

Contributions from specific and general factors to unique deficits: two cases of mathematics learning difficulties

Mathematics learning difficulties are a highly comorbid and heterogeneous set of disorders linked to several dissociable mechanisms and endophenotypes. Two of these endophenotypes consist of primary deficits in number sense and verbal numerical representations. However, currently acknowledged endophenotypes are underspecified regarding the role of automatic vs. controlled information processing, and their description should be complemented. Two children with specific deficits in number sense and verbal numerical representations and normal or above-normal intelligence and preserved visuospatial cognition illustrate this point. Child H.V. exhibited deficits in number sense and fact retrieval. Child G.A. presented severe deficits in orally presented problems and transcoding tasks. A partial confirmation of the two endophenotypes that relate to the number sense and verbal processing was obtained, but a much more clear differentiation between the deficits presented by H.V. and G.A. can be reached by looking at differential impairments in modes of processing. H.V. is notably competent in the use of controlled processing but has problems with more automatic processes, such as nonsymbolic magnitude processing, speeded counting and fact retrieval. In contrast, G.A. can retrieve facts and process nonsymbolic magnitudes but exhibits severe impairment in recruiting executive functions and the concentration that is necessary to accomplish transcoding tasks and word problem solving. These results indicate that typical endophenotypes might be insufficient to describe accurately the deficits that are observed in children with mathematics learning abilities. However, by incorporating domain-specificity and modes of processing into the assessment of the endophenotypes, individual deficit profiles can be much more accurately described. This process calls for further specification of the endophenotypes in mathematics learning difficulties.