Regional differences in cerebral blood flow during recitation of the multiplication table and actual calculation: a positron emission tomography study

The neural correlates of retrieval and procedural strategies in mental arithmetic: A functional neuroimaging meta-analysis

Mental arithmetic is a complex skill of great importance for later academic and life success. Many neuroimaging studies and several meta-analyses have aimed to identify the neural correlates of mental arithmetic. Previous meta-analyses of arithmetic grouped all problem types into a single meta-analytic map, despite evidence suggesting that different types of arithmetic problems are solved using different strategies. We used activation likelihood estimation (ALE) to conduct quantitative meta-analyses of mental arithmetic neuroimaging (n = 31) studies, and subsequently grouped contrasts from the 31 studies into problems that are typically solved using retrieval strategies (retrieval problems) (n = 18) and problems that are typically solved using procedural strategies (procedural problems) (n = 19). Foci were compiled to generate probabilistic maps of activation for mental arithmetic (i.e., all problem types), retrieval problems, and procedural problems. Conjunction and contrast analyses were conducted to examine overlapping and distinct activation for retrieval and procedural problems. The conjunction analysis revealed overlapping activation for retrieval and procedural problems in the bilateral inferior parietal lobules, regions typically associated with magnitude processing. Contrast analyses revealed specific activation in the left angular gyrus for retrieval problems and specific activation in the inferior frontal gyrus and cingulate gyrus for procedural problems. These findings indicate that the neural bases of arithmetic systematically differs according to problem type, providing new insights into the dynamic and task-dependent neural underpinnings of the calculating brain.

Music, Math, and Working Memory: Magnetoencephalography Mapping of Brain Activation in Musicians

Musical transposing is highly demanding of working memory, as it involves mentally converting notes from one musical key (i.e., pitch scale) to another key for singing or instrumental performance. Because musical transposing involves mental adjustment of notes up or down by a specific amount, it may share cognitive elements with arithmetical operations of addition and subtraction. We compared brain activity during high and low working memory load conditions of musical transposing versus math calculations in classically trained musicians. Magnetoencephalography (MEG) was sensitive to differences of task and working memory load. Frontal-occipital connections were highly active during transposing, but not during math calculations. Right motor and premotor regions were highly active in the more difficult condition of the transposing task. Multiple frontal lobe regions were highly active across tasks, including the left medial frontal area during both transposing and calculation tasks but the right medial frontal area only during calculations. In the more difficult calculation condition, right temporal regions were highly active. In coherence analyses and neural synchrony analyses, several similarities were seen across calculation tasks; however, latency analyses were sensitive to differences in task complexity across the calculation tasks due to the high temporal resolution of MEG. MEG can be used to examine musical cognition and the neural consequences of music training. Further systematic study of brain activity during high versus low memory load conditions of music and other cognitive tasks is needed to illuminate the neural bases of enhanced working memory ability in musicians as compared to non-musicians.

Linear and nonlinear profiles of weak behavioral and neural differentiation between numerical operations in children with math learning difficulties

Mathematical knowledge is constructed hierarchically during development from a basic understanding of addition and subtraction, two foundational and inter-related, but semantically distinct, numerical operations. Early in development, children show remarkable variability in their numerical problem-solving skills and difficulties in solving even simple addition and subtraction problems are a hallmark of math learning difficulties. Here, we use novel quantitative analyses to investigate whether less distinct representations are associated with poor problem-solving abilities in children during the early stages of math-skill acquisition. Crucially, we leverage dimensional and categorical analyses to identify linear and nonlinear neurobehavioral profiles of individual differences in math skills. Behaviorally, performance on the two different numerical operations was less differentiated in children with low math abilities, and lower problem-solving efficiency stemmed from weak evidence-accumulation during problem-solving. Children with low numerical abilities also showed less differentiated neural representations between addition and subtraction operations in multiple cortical areas, including the fusiform gyrus, intraparietal sulcus, anterior temporal cortex and insula. Furthermore, analysis of multi-regional neural representation patterns revealed significantly higher network similarity and aberrant integration of representations within a fusiform gyrus-intraparietal sulcus pathway important for manipulation of numerical quantity. These findings identify the lack of distinct neural representations as a novel neurobiological feature of individual differences in children's numerical problem-solving abilities, and an early developmental biomarker of low math skills. More generally, our approach combining dimensional and categorical analyses overcomes pitfalls associated with the use of arbitrary cutoffs for probing neurobehavioral profiles of individual differences in math abilities.

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.

Mapping of Arithmetic Processing by Navigated Repetitive Transcranial Magnetic Stimulation in Patients with Parietal Brain Tumors and Correlation with Postoperative Outcome

BACKGROUND

Preserving functionality is important during neurosurgical resection of brain tumors. Specialized centers also map further brain functions apart from motor and language functions, such as arithmetic processing (AP). The mapping of AP by navigated repetitive transcranial magnetic stimulation (nrTMS) in healthy volunteers has been reported.

OBJECTIVE

The present study aimed to correlate the results of mapping AP with functional patient outcomes.

METHODS

We included 26 patients with parietal brain tumors. Because of preoperative impairment of AP, mapping was not possible in 8 patients (31%). We stimulated 52 cortical sites by nrTMS while patients performed a calculation task. Preoperatively and postoperatively, patients underwent a standardized number-processing and calculation test (NPCT). Tumor resection was blinded to nrTMS results, and the change in NPCT performance was correlated to resected AP-positive spots as identified by nrTMS.

RESULTS

The resection of AP-positive sites correlated with a worsening of the postoperative NPCT result in 12 cases. In 3 cases, no AP-positive sites were resected and the postoperative NPCT result was similar to or better than preoperatively. Also, in 3 cases, the postoperative NPCT result was better than preoperatively, although AP-positive sites were resected.

CONCLUSIONS

Despite presenting only a few cases, nrTMS might be a useful tool for preoperative mapping of AP. However, the reliability of the present results has to be evaluated in a larger series and by intraoperative mapping data.

Short-term cognitive training recapitulates hippocampal functional changes associated with one year of longitudinal skill development

Objective

A goal of developmental cognitive neuroscience is to uncover brain mechanisms underlying successful learning. While longitudinal studies capture brain changes following 'schooling as usual', short-term training studies can more directly link learning to brain changes. We investigated whether eight weeks of cognitive training recapitulates longitudinal changes in hippocampal engagement and connectivity.

Methods

Nineteen children underwent a training program focused on improving arithmetic skills, along with fifteen children in a no-contact control group. Before and after training, or no-contact, both groups performed an arithmetic task during neuroimaging and a strategy assessment.

Results

Training increased activity in the anterior hippocampus, and gains in memory-based strategies were associated with decreased lateral fronto-parietal activity and increased hippocampus-parietal connectivity. No changes were observed in the no-contact control group.

Conclusions

Our results demonstrate that short-term training can recapitulate long-term neurodevelopmental changes accompanying learning and identifies plasticity of hippocampal responses as a common locus of cognitive skill development in children.

Functional dissociations between four basic arithmetic operations in the human posterior parietal cortex: a cytoarchitectonic mapping study

Although lesion studies over the past several decades have focused on functional dissociations in posterior parietal cortex (PPC) during arithmetic, no consistent view has emerged of its differential involvement in addition, subtraction, multiplication, and division. To circumvent problems with poor anatomical localization, we examined functional overlap and dissociations in cytoarchitectonically defined subdivisions of the intraparietal sulcus (IPS), superior parietal lobule (SPL) and angular gyrus (AG), across these four operations. Compared to a number identification control task, all operations except addition, showed a consistent profile of left posterior IPS activation and deactivation in the right posterior AG. Multiplication and subtraction differed significantly in right, but not left, IPS and AG activity, challenging the view that the left AG differentially subserves retrieval during multiplication. Although addition and multiplication both rely on retrieval, multiplication evoked significantly greater activation in right posterior IPS, as well as the prefrontal cortex, lingual and fusiform gyri, demonstrating that addition and multiplication engage different brain processes. Comparison of PPC responses to the two pairs of inverse operations: division versus multiplication and subtraction versus addition revealed greater activation of left lateral SPL during division, suggesting that processing inverse relations is operation specific. Our findings demonstrate that individual IPS, SPL and AG subdivisions are differentially modulated by the four arithmetic operations and they point to significant functional heterogeneity and individual differences in activation and deactivation within the PPC. Critically, these effects are related to retrieval, calculation and inversion, the three key cognitive processes that are differentially engaged by arithmetic operations. Our findings point to distribute representation of these processes in the human PPC and also help explain why lesion and previous imaging studies have yielded inconsistent findings.

Role of distinct parietal areas in arithmetic: an fMRI-guided TMS study

Although several parietal areas are known to be involved in number processing, their possible role in arithmetic operations remains debated. It has been hypothesized that the horizontal segment of the intraparietal sulcus (hIPS) and the posterior superior parietal lobule (PSPL) contribute to operations solved by calculation procedures, such as subtraction, but whether these areas are also involved in operations solved by memory retrieval, such as multiplication, is controversial. In the present study, we first identified the parietal areas involved in subtraction and multiplication by means of functional magnetic resonance imaging (fMRI) and we found an increased activation, bilaterally, in the hIPS and PSPL during both arithmetic operations. In order to test whether these areas are causally involved in subtraction and multiplication, we used transcranial magnetic stimulation (TMS) to create, in each participant, a virtual lesion of either the hIPS or PSPL, over the sites corresponding to the peaks of activation gathered in fMRI. When compared to a control site, we found an increase in response latencies in both operations after a virtual lesion of either the left or right hIPS, but not of the PSPL. Moreover, TMS over the hIPS increased the error rate in the multiplication task. The present results indicate that even operations solved by memory retrieval, such as multiplication, rely on the hIPS. In contrast, the PSPL seems to underlie processes that are nonessential to solve basic subtraction and multiplication problems.

Stiffness control of balance during quiet standing and dual task in older adults: the MOBILIZE Boston Study

Distractions affect postural control, but this mechanism is not well understood. Diversion of resources during cognitive stress may lead to decreased motor drive and postural muscle tone. This may appear as decreased postural stiffness and increased postural sway amplitude. We hypothesized that dual tasking leads to decreased stiffness and increased sway amplitude. Postural sway (center of pressure; COP) data were used from 724 participants aged 77.9 ± 5.3 yr, a representative sample of community-dwelling older adults, the MOBILIZE Boston Study cohort. Subjects stood barefoot with eyes open for 30 s per trial on a force plate. Five trials were performed each with and without a serial subtractions-by-3 task. Sway data were fit to a damped oscillator inverted pendulum model. Amplitudes (COP and center of mass), mechanical stiffness, and damping of the sway behavior were determined. Sway amplitudes and damping increased with the dual task (P < 0.001); stiffness decreased only mediolaterally (P < 0.001). Those with difficulty doing the dual task exhibited larger sway and less damping mediolaterally (P ≤ 0.001) and an increased stiffness with dual task anteroposteriorly (interaction P = 0.004). Dual task could still independently explain increases in sway (P < 0.001) after accounting for stiffness changes. Thus the hypothesis was supported only in mediolateral sway. The simple model helped to explain the dual task related increase of sway only mediolaterally. It also elucidated the differential influence of cognitive function on the mechanics of anteroposterior and mediolateral sway behaviors. Dual task may divert the resources necessary for mediolateral postural control, thus leading to falls.

Flexible transfer of knowledge in mental arithmetic--an fMRI study

Recent imaging studies could show that fact acquisition in arithmetic is associated with decreasing activation in several frontal and parietal areas, and relatively increasing activation within the angular gyrus, indicating a switch from direct calculation to retrieval of a learned fact from memory. So far, however, little is known about the transfer of learned facts between arithmetic operations. The aim of the present fMRI study was to investigate whether and how newly acquired arithmetic knowledge might transfer from trained multiplication problems to related division problems. On the day before scanning, ten complex multiplication problems were trained. Within the scanner, trained multiplication problems were compared with untrained multiplication problems, and division problems related to multiplication (transfer condition) were compared with unrelated division problems (no-transfer condition). Replicating earlier results, untrained multiplication problems activated several frontal and parietal brain areas more strongly than trained multiplication problems, while trained multiplication problems showed relatively stronger activation in the left angular gyrus than untrained multiplication problems. Concerning division, an ROI analysis indicated that activation in the left angular gyrus was relatively stronger for the transfer condition than for the no-transfer condition. We also observed distinct inter-individual differences with regard to transfer that modulated activation within the left angular gyrus. Activation within the left angular gyrus was generally higher for participants who showed a transfer effect for division problems. In conclusion, the present study yielded some evidence that successful transfer of knowledge between arithmetic operations is accompanied by modifications of brain activation patterns. The left angular gyrus seems not only to be involved in the retrieval of stored arithmetic facts, but also in the transfer between arithmetic operations.

What can functional brain imaging studies tell us about typical and atypical cognitive development in children?

Functional brain imaging has been largely reserved for adults. However, in recent years there have been increasing attempts to use functional brain imaging to inform our understanding of child development. These have taken three main forms: (1) Children with known or suspected neurological disorders may undergo brain imaging for medical diagnostic purposes and/or for the purpose of research into the nature of the disorders. (2) There have been a few studies where children, usually over the age of 8, have undergone functional brain imaging. (3) Results from brain imaging studies of adults have influenced theories about children's development. This chapter discusses the impact of brain imaging studies on our understanding of working memory; reading; and arithmetic. The different forms of brain imaging converge in demonstrating that different brain regions show differential activation for different domains and for different components within the domains: e.g. different reading strategies and different components of arithmetic. They show important similarities between children and adults, though it must be remembered that very few studies have involved young children. They also indicate that experience influences brain function, as well as the other way around.

Event-related potentials of single-digit addition, subtraction, and multiplication

This study compared the event-related potentials elicited by single-digit addition, subtraction, and multiplication problems. With a delayed verification paradigm, 18 Chinese undergraduates were first asked to solve the arithmetic problems that were presented visually for 200 ms and, after 1.5 s, to judge whether a presented solution was correct or not. Results showed that, compared to addition and subtraction, multiplication elicited a greater N300 at the left frontal electrodes peaking around 320 ms (in the interval between 275 and 334 ms after the onset of the arithmetic problem). To control for the confounding effects of task difficulty and solution size, comparisons were further made between "large" addition problems (with sums between 11 and 17) and "small" multiplication problems (with products between 6 and 24). Similar results were obtained (i.e., a significant difference between addition and multiplication in the N300 component between 296 and 444 ms). Source analyses demonstrated that a single dipole in the left anterior brain areas could have contributed to the topographies of the difference waveforms ("multiplication-addition", "multiplication-subtraction", and "'small' multiplication-'large' addition"). These results are interpreted in terms of the greater reliance on phonological processing for the retrieval of multiplication facts than for the retrieval of addition and subtraction facts.

Correlation between blood flow velocity in the middle cerebral artery and EEG during cognitive effort

Cognitive effort modifies blood flow velocity (BFV) in the middle cerebral artery (MCA) which can be recorded by transcranial Doppler sonography (TCD). EEG parameters can be used as indicators of cortical activation. To find temporal and spatial relation between circulatory and bioelectric phenomena, we used combined EEG and TCD measurements during cognitive experiments. Bilateral BFV in the MCAs and 16-channel scalp EEG were recorded during mental arithmetic (MA) and verbal fluency (VF) tests in 12 healthy volunteers. Temporal profile of BFV, heart rate (HR), EEG central frequency (CF), relative alpha power (ralphap), and laterality index (Li) for BFV and CF were statistically analysed. During mental effort, BFV changes showed a reproducible pattern, which was different in MA and VF tests. The Li(BFV) correlated with handedness in 9/12 subjects (75%) in the VF, and in 6/12 subjects (50%) in the MA test. Significant correlation was found between Li(BFV) and Li(CF) during VF (r(2) = 0.69). Li was more indicative for the hemispheric dominance in the VF than in the MA test. During VF test, correlation between HR and BFV was significant in 7/12 subjects. CF and ralphap provide real time assessment of the functional state of the brain tissue during cognition. The correlation between CF and BFV during mental activity suggests a short latency neurogenic and a long latency, supposedly chemical regulation of regional blood flow. Parallel analysis of EEG and flow parameters increases the confidence of determining hemispheric dominance and provides an alternative to study physiological consequences of cognitive processes.

Comparing extent of activation: a robust permutation approach

The number of contiguous voxels activated in a brain image can differ between groups or conditions even though the amplitude of activation does not markedly differ. Existing techniques test for differences in amplitude given that extent (number of contiguous voxels) exceeds some threshold. We present a technique that tests for differences in extent of activation given that amplitude of activation exceeds some threshold. The technique was motivated by apparent differences in extent of regional cerebral blood flow (rCBF) between hypertensive and normotensive participants performing cognitive tasks. These data are used to illustrate our test for extent of activation. We threshold the estimated parameter map for each subject, count the number of voxels exceeding the threshold over a defined region enclosing activated cortical area, and test the hypothesis of difference in the number of activated voxels between the two groups. Due to the large number of zeros resulting from the thresholding and the occurrence of extreme observations, we use a Robust permutation test [Lambert, D., 1985. Robust two-sample permutation tests. Ann. Stat., 13, 606-625], which is based on the sum of censored log-likelihood ratios. This statistic has desirable properties relative to the usual permutation test in contaminated distributions, i.e., idealized histogram with outliers, and provides an appropriate and robust test of extent of activation between conditions or groups.

Intraoperative mapping of the cortical areas involved in multiplication and subtraction: an electrostimulation study in a patient with a left parietal glioma

OBJECTIVES

Advances in neuroimaging studies have recently improved the understanding of the functional anatomy of the calculation processes, having in particular underlined the central role of the angular gyrus (AG). In this study, the authors applied this knowledge to the surgical resection of a glioma invading the left AG, by localising and sparing the cortical areas involved in two different components of calculation (multiplication and subtraction), using direct electrical stimulations.

METHODS

A calculation mapping was performed in a patient without deficit except a slightly impaired performance for serial arithmetic subtraction, during the resection under local anaesthesia of a left parieto-occipital glioma invading the dominant AG. After somatosensory and language mappings, cortical areas involved in single digit multiplications and subtractions of seven were mapped using the method of electrostimulation, before glioma removal.

RESULTS

Distinct sites specifically involved in multiplication or subtraction were detected within the left AG, with a precise spatial distribution and overlapping. All the eloquent (somatosensory, language, and calculation) areas were surgically spared. Postoperatively, the patient had a transient complete deficit for arithmetic subtraction, without either multiplication or language disturbance. The tumour removal was complete.

CONCLUSIONS

These findings suggest: firstly, the usefulness of an intraoperative calculation mapping during the removal of a lesion involving the left dominant AG, to avoid permanent postoperative deficit of arithmetic processes while optimising the quality of tumour resection; secondly, the possible existence of a well ordered and dynamic anatomo-functional organisation for different components of calculation within the left AG.