The functional architectures of addition and subtraction: Network discovery using fMRI and DCM

Add, subtract and multiply: Meta-analyses of brain correlates of arithmetic operations in children and adults

Mathematical operations are cognitive actions we take to calculate relations among numbers. Arithmetic operations, addition, subtraction, multiplication, and division are elemental in education. Addition is the first one taught in school and is most popular in functional magnetic resonance imaging (fMRI) studies. Division, typically taught last is least studied with fMRI. fMRI meta-analyses show that arithmetic operations activate brain areas in parietal, cingulate and insular cortices for children and adults. Critically, no meta-analysis examines concordance across brain correlates of separate arithmetic operations in children and adults. We review and examine using quantitative meta-analyses data from fMRI articles that report brain coordinates separately for addition, subtraction, multiplication, and division in children and adults. Results show that arithmetic operations elicit common areas of concordance in fronto-parietal and cingulo-opercular networks in adults and children. Between operations differences are observed primarily for adults. Interestingly, higher within-group concordance, expressed in activation likelihood estimates, is found in brain areas associated with the cingulo-opercular network rather than the fronto-parietal network in children, areas also common between adults and children. Findings are discussed in relation to constructivist cognitive theory and practical directions for future research.

Temporal-spatial deciphering mental subtraction in the human brain

Mental subtraction, involving numerical processing and operation, requires a complex interplay among several brain regions. Diverse studies have utilized scalp electroencephalograph, electrocorticogram, or functional magnetic resonance imaging to resolve the structure pattern and functional activity during subtraction operation. However, a high resolution of the spatial-temporal understanding of the neural mechanisms involved in mental subtraction is unavailable. Thus, this study obtained intracranial stereoelectroencephalography recordings from 20 patients with pharmacologically resistant epilepsy. Specifically, two sample-delayed mismatch paradigms of numeric comparison and subtracting results comparison were used to help reveal the time frame of mental subtraction. The brain sub-regions were chronologically screened using the stereoelectroencephalography recording for mental subtraction. The results indicated that the anterior cortex, containing the frontal, insular, and parahippocampous, worked for preparing for mental subtraction; moreover, the posterior cortex, such as parietal, occipital, limbic, and temporal regions, cooperated during subtraction. Especially, the gamma band activities in core regions within the parietal-cingulate-temporal cortices mediated the critical mental subtraction. Overall, this research is the first to describe the spatiotemporal activities underlying mental subtraction in the human brain. It provides a comprehensive insight into the cognitive control activity underlying mental arithmetic.

Supplementary Information

The online version contains supplementary material available at 10.1007/s11571-023-09937-z.

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.

Top-down modulation of DLPFC in visual search: a study based on fMRI and TMS

Effective visual search is essential for daily life, and attention orientation as well as inhibition of return play a significant role in visual search. Researches have established the involvement of dorsolateral prefrontal cortex in cognitive control during selective attention. However, neural evidence regarding dorsolateral prefrontal cortex modulates inhibition of return in visual search is still insufficient. In this study, we employed event-related functional magnetic resonance imaging and dynamic causal modeling to develop modulation models for two types of visual search tasks. In the region of interest analyses, we found that the right dorsolateral prefrontal cortex and temporoparietal junction were selectively activated in the main effect of search type. Dynamic causal modeling results indicated that temporoparietal junction received sensory inputs and only dorsolateral prefrontal cortex →temporoparietal junction connection was modulated in serial search. Such neural modulation presents a significant positive correlation with behavioral reaction time. Furthermore, theta burst stimulation via transcranial magnetic stimulation was utilized to modulate the dorsolateral prefrontal cortex region, resulting in the disappearance of the inhibition of return effect during serial search after receiving continuous theta burst stimulation. Our findings provide a new line of causal evidence that the top-down modulation by dorsolateral prefrontal cortex influences the inhibition of return effect during serial search possibly through the retention of inhibitory tagging via working memory storage.

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.

Inhibitory temporo-parietal effective connectivity is associated with explicit memory performance in older adults

Successful explicit memory encoding is associated with inferior temporal activations and medial parietal deactivations, which are attenuated in aging. Here we used dynamic causal modeling (DCM) of functional magnetic resonance imaging data to elucidate effective connectivity patterns between hippocampus, parahippocampal place area (PPA), and precuneus during encoding of novel visual scenes. In 117 young adults, DCM revealed pronounced activating input from the PPA to the hippocampus and inhibitory connectivity from the PPA to the precuneus during novelty processing, with both being enhanced during successful encoding. This pattern could be replicated in two cohorts (N = 141 and 148) of young and older adults. In both cohorts, older adults selectively exhibited attenuated inhibitory PPA-precuneus connectivity, which correlated negatively with memory performance. Our results provide insight into the network dynamics underlying explicit memory encoding and suggest that age-related differences in memory-related network activity are, at least partly, attributable to altered temporo-parietal neocortical connectivity.

Systematic Fusion of Multi-Source Cognitive Networks With Graph Learning - A Study on Fronto-Parietal Network

Cognitive tasks induce fluctuations in the functional connectivity between brain regions which constitute cognitive networks in the human brain. Although several cognitive networks have been identified, consensus still cannot be achieved on the precise borders and distribution of involved brain regions for each network, due to the multifarious use of diverse brain atlases in different studies. To address the problem, the current study proposed a novel approach to generate a fused cognitive network with the optimal performance in discriminating cognitive states by using graph learning, following the synthesization of one cognitive network defined by different brain atlases, and the construction of a hierarchical framework comprised of one main version and other supplementary versions of the specific cognitive network. As a result, the proposed method demonstrated better results compared with other machine learning methods for recognizing cognitive states, which was revealed by analyzing an fMRI dataset related to the mental arithmetic task. Our findings suggest that the fused cognitive network provides the potential to develop new mind decoding approaches.

Arithmetic learning in children: An fMRI training study

Arithmetic learning is characterized by a change from procedural strategies to fact retrieval. fMRI training studies in adults have revealed that this change coincides with decreased activation in the prefrontal cortex (PFC) and that within the parietal lobe, a shift occurs from the intraparietal sulcus (IPS) to the angular gyrus (AG) during this change. It remains to be determined whether similar changes can be observed in children, particularly because children often recruit the hippocampus (HC) during fact retrieval, an observation that has not consistently been found in adults. In order to experimentally manipulate arithmetic strategy change, 26 typically developing 9- to-10-year-olds completed a six day at-home training of complex multiplication items (e.g. 16 × 4). Before and after training, children were presented with three multiplication conditions during fMRI: (1) complex to-be-trained/trained items, (2) complex untrained items and (3) single-digit items. Behavioral data indicated that training was successful. Similar to adults, children showed greater activity in the IPS and PFC for the untrained condition post-training, indicating that the fronto-parietal network during procedural arithmetic problem solving is already in place in children of this age. We did not observe the expected training-related changes in the HC. In contrast to what has been observed in adults, greater activity in the AG was not observed for the trained items. These results show that the brain processes that accompany the learning of arithmetic facts are different in children as compared to adults.

Functional neuroanatomy of arithmetic in monolingual and bilingual adults and children

Prior studies on the brain bases of arithmetic have not focused on (or even described) their participants' language backgrounds. Yet, unlike monolinguals, early bilinguals have the capacity to solve arithmetic problems in both of their two languages. This raises the question whether this ability, or any other experience that comes with being bilingual, affects brain activity for arithmetic in bilinguals relative to monolinguals. Here, we used functional magnetic resonance imaging to compare brain activity in 44 English monolinguals and 44 Spanish-English early bilinguals, during the solving of arithmetic problems in English. We used a factorial design to test for a main effect of bilingual Language Experience. Based on the known modulating roles of arithmetic operation and age, we used two arithmetic tasks (addition and subtraction) and studied two age groups (adults and children). When collapsing across operations and age, we found broad bilateral activation for arithmetic in both the monolingual group and the bilingual group. However, an analysis of variance revealed that there was no effect of Language Experience, nor an interaction of Language Experience with Operation or Age Group. Bayesian analyses within regions of interest chosen for their role in arithmetic further supported the finding of no effect of Language Experience on brain activity underlying arithmetic. We conclude that early bilingualism does not influence the functional neuroanatomy of simple arithmetic.

Selection of the Better Dual-Timed Up and Go Cognitive Task to Be Used in Patients With Stroke Characterized by Subtraction Operation Difficulties

Background: The Timed Up and Go Test (TUG) with serial subtraction is commonly used to assess cognitive-dual task performance during walking for fall prediction. Some stroke patients cannot perform number subtraction and it is unclear which cognitive task can be used to substitute for the subtraction task in the TUG test. The aim of this study was to determine the type of cognitive task that produced the highest decrease on both motor and cognitive performances during TUG-dual in stroke patients.

Methods: A total of 23 persons with stroke but capable of completing subtraction (ST) and 19 persons with subtraction operation difficulties (SOD) participated. Both groups have a similar age range (ST: 59.3 ± 10.4 years and SOD: 62.0 ± 6.8 years) and stroke onset duration (ST: 44.13 ± 62.29 months and SOD: 42.34 ± 39.69 months). The participants performed TUG without a cognitive task (TUG-single) followed by a cognitive task when seated (cognitive-single). In addition, TUG with a cognitive task (TUG-dual) was performed, with the activity randomly selected from four cognitive tasks, including alternate reciting, auditory working memory, clock task, and phonologic fluency. The main outcome variables—TUG duration measured by OPAL accelerometer and cognitive-dual task effect (DTE)—were analyzed using repeated-measures analyses of variance (ANOVA).

Results: The number of correct responses when seated were significantly lower in the SOD as compared to the ST (p < 0.05) during all cognitive tasks, except the phonologic fluency. During TUG-cognitive, TUG duration in the ST was significantly longer for all cognitive tasks compared with TUG-single (p < 0.0001), whereas TUG duration in the SOD was significantly increased only during the phonologic fluency task (p < 0.01). In the ST, there was a significant difference in cognitive DTE between the subtraction and the phonologic fluency tasks (p < 0.01). The highest cognitive cost was found in the subtraction task, whereas the highest cognitive benefit was shown in the phonologic fluency task. No significant cognitive DTE was found among the cognitive tasks in the SOD.

Conclusion: For stroke persons with SOD, phonologic fluency is suitable to be used in the TUG-cognitive assessment. In contrast, subtraction (by 3s) is recommended for the assessment of TUG-cognitive in stroke persons who can perform subtraction.

What's in a Hub?-Representing Identity in Language and Mathematics

Hubs emerge in structural and resting state network analysis as areas highly connected to other parts of the brain and have been shown to respond to several task domains in functional imaging studies. A cognitive explanation for this multi-functionality is still wanting. We propose, that hubs subserve domain-general meta-cognitive functions, relevant to a variety of domain-specific networks and test this hypothesis for the example of processing explicit identity information. To isolate this meta-cognitive function from the processing of domain-specific context, we investigate the overlapping activations to linguistic identity processes (e.g. Mr. Dietrich is the dentist) on the one hand and numerical identity processes (e.g. do "3 × 8" and "36-12" give the same number) on the other hand. The main question was, whether these overlapping activations would fall within areas, consistently identified as hubs by network-based analyses. Indeed, the two contrasts showed significant conjunctions in the left inferior parietal lobe (IPL), precuneus (PC), and posterior cingulate. Accordingly, identity processing may well be one domain-general meta-cognitive function that hub-areas provide to domain-specific networks. For the parietal lobe we back up our hypothesis further with existing reports of activation peaks for other tasks that depend on identity processing, e.g., episodic recollection, theory of mind, and visual perspective taking.

Sex differences in brain activation patterns with mental stress in patients with coronary artery disease

Background

Stress is an important contributor to myocardial ischemia and the progression of coronary artery disease (CAD), and women are more susceptible than men to these effects. Little is known, however, about the neural basis of these sex differences.

Methods

We investigated sex differences in neural correlates of mental stress in a sample of 53 female and 112 male participants (N = 165) with CAD, with and without mental stress-induced myocardial ischemia (MSI), during exposure to mental arithmetic tasks and public speaking stress tasks using high-resolution positron emission tomography (HR-PET) and radiolabeled water imaging of the brain.

Results

Women compared to men had significantly greater activation with stress in the right frontal (BA 9, 44), right parietal lobe (Area 3, 6, 40), right posterior cingulate gyrus (BA 31), bilateral cerebellum, and left temporal/fusiform gyrus (BA 37) and greater deactivation in bilateral anterior cingulate gyrus (BA 24, 32), bilateral medial frontal gyrus (BA 6, 8, 9, 10), right parahippocampal gyrus, and right middle temporal gyrus (BA 21). Women with MSI (but not those without MSI) showed significantly greater activation than men in the right posterior cingulate gyrus (BA 31) and greater deactivation in several frontal and temporal lobe areas.

Conclusion

Men and women with CAD show differences in responses to stress in brain limbic areas that regulate emotion, and these functional responses differ by MSI status. Our results suggest that the cingulate gyrus may be involved in sex differences in MSI.

Electronic supplementary material

The online version of this article (10.1186/s13293-019-0248-4) contains supplementary material, which is available to authorized users.

Reduced Dynamic Interactions Within Intrinsic Functional Brain Networks in Early Blind Patients

Neuroimaging studies in early blind (EB) patients have shown altered connections or brain networks. However, it remains unclear how the causal relationships are disrupted within intrinsic brain networks. In our study, we used spectral dynamic causal modeling (DCM) to estimate the causal interactions using resting-state data in a group of 20 EB patients and 20 healthy controls (HC). Coupling parameters in specific regions were estimated, including the medial prefrontal cortex (mPFC), posterior cingulate cortex (PCC), and inferior parietal lobule (IPC) in the default mode network (DMN); dorsal anterior cingulate cortex (dACC) and bilateral anterior insulae (AI) in the salience network (SN), and bilateral frontal eye fields (FEF) and superior parietal lobes (SPL) within the dorsal attention network (DAN). Statistical analyses found that all endogenous connections and the connections from the mPFC to bilateral IPCs in EB patients were significantly reduced within the DMN, and the effective connectivity from the PCC and lIPC to the mPFC, and from the mPFC to the PCC were enhanced. For the SN, all significant connections in EB patients were significantly decreased, except the intrinsic right AI connections. Within the DAN, more significant effective connections were observed to be reduced between the EB and HC groups, while only the connections from the right SPL to the left SPL and the intrinsic connection in the left SPL were significantly enhanced. Furthermore, discovery of more decreased effective connections in the EB subjects suggested that the disrupted causal interactions between specific regions are responsive to the compensatory brain plasticity in early deprivation.

The neural correlates of arithmetic difficulty depend on mathematical ability: evidence from combined fNIRS and ERP

Mathematical abilities are essential for an individual, as they predict career prospects among many other abilities. However, little is known about whether neural correlates of arithmetic problem difficulty differ between individuals with high and low math ability. For instance, the difficulty of two-digit addition and subtraction increases whenever a carry or borrow operation is required. Therefore, we systematically investigated the spatial and temporal neural correlates of the carry and borrow effects for high and low performers in a written production paradigm using combined functional near-infrared spectroscopy (fNIRS) and event-related potential (ERP) measurements. Effects of arithmetic difficulty interacted with an individual's math ability. High performers showed increased frontal activation especially in the left inferior frontal gyrus associated with the carry and borrow effects, whereas low performers did not. Furthermore, high and low performers even differed in their early processing of the borrow effect, as reflected by differences in slow waves at 1000-1500 ms at frontal sites. We conclude that the processing of arithmetic difficulty relies on an individual's mathematical ability, and suggest that individual differences should be taken into account when investigating mental arithmetic in an ecologically valid assessment.

Affective and cooperative social interactions modulate effective connectivity within and between the mirror and mentalizing systems

Decoding the meaning of others' actions, a crucial step for social cognition, involves different neural mechanisms. While the "mirror" and "mentalizing" systems have been associated with, respectively, the processing of biological actions versus more abstract information, their respective contribution to intention understanding is debated. Processing social interactions seems to recruit both neural systems, with a different weight depending on cues emphasizing either shared action goals or shared mental states. We have previously shown that observing cooperative and affective social interactions elicits stronger activity in key nodes of, respectively, the mirror (left posterior superior temporal sulcus (pSTS), superior parietal cortex (SPL), and ventral/dorsal premotor cortex (vPMC/dPMC)) and mentalizing (ventromedial prefrontal cortex (vmPFC)) systems. To unveil their causal organization, we investigated the effective connectivity underlying the observation of human social interactions expressing increasing cooperativity (involving left pSTS, SPL, and vPMC) versus affectivity (vmPFC) via dynamic causal modeling in 36 healthy human subjects. We found strong evidence for a model including the pSTS and vPMC as input nodes for the observed interactions. The extrinsic connectivity of this model undergoes oppositely valenced modulations, with cooperativity promoting positive modulations of connectivity between pSTS and both SPL (forward) and vPMC (mainly backward), and affectivity promoting reciprocal positive modulations of connectivity between pSTS and vmPFC (mainly backward). Alongside fMRI data, such divergent effective connectivity suggests that different dimensions underlying the processing of social interactions recruit distinct, although strongly interconnected, neural pathways associated with, respectively, the bottom-up visuomotor processing of motor intentions, and the top-down attribution of affective/mental states.