Arithmetic skills are associated with left fronto-temporal gray matter volume in 536 children and adolescents

Large individual differences in arithmetic skills exist, impacting educational and societal participation. Understanding the neurocognitive mechanisms underlying these differences is crucial for improving instruction and assessment. Functional imaging studies have implicated several brain regions in arithmetic processing, including the parietal cortex (intraparietal sulcus, left angular gyrus), left middle temporal gyrus (MTG), and left inferior frontal gyrus (IFG). The intraparietal sulcus is associated with numerical quantity representation, while the left angular gyrus is linked to retrieving solutions from memory. The left MTG might support retrieval from memory due to its role in phonological processing, and the left IFG is implicated when calculations become more demanding. The hippocampus's role in encoding and retrieving arithmetic problem-answer associations, especially in early learning, has also been suggested. While these studies identify brain regions involved in arithmetic processing, they don't necessarily explain individual differences in arithmetic skills. Prior functional neuroimaging studies comparing individuals with high versus low math skills have yielded inconsistent results. Likewise, structural neuroimaging studies investigating the structural correlates of arithmetic skills have shown mixed results and suffered from small sample sizes. The current study aims to address these limitations by combining data from six different datasets to create a large sample size (n=536) to investigate the relationship between gray matter volume and arithmetic skills more robustly.

Previous research using functional and structural neuroimaging techniques has explored the neural correlates of arithmetic skills. Functional studies consistently implicate regions of the parietal cortex, particularly the intraparietal sulcus (IPS) and the left angular gyrus (AG), suggesting their roles in quantity representation and memory retrieval, respectively. However, studies have also shown that the left middle temporal gyrus (MTG) and left inferior frontal gyrus (IFG) are crucial for arithmetic processing. The MTG's contribution is linked to its role in phonological processing and memory retrieval for memorized facts. The IFG's involvement seems related to increased demand and verbal working memory usage. Structural neuroimaging studies revealed inconsistent results, some reporting reduced GMV in the parietal lobe and frontal gyri for individuals with lower math abilities while others showing positive correlations between GMV and math skills in various regions. However, these studies are characterized by small sample sizes, often underpowered for reliably detecting brain-behavior associations, thus leading to variability in findings. This study aims to overcome these limitations using a larger sample size.

Data were combined from six datasets, including structural brain imaging and arithmetic skill assessments from children and adolescents (aged 7.5-15 years). Datasets were collected from two sites: Lyon, France, and Chicago, Illinois, USA. Different scanners were used across sites, and different tests were used to assess arithmetic skills (Woodcock-Johnson III Tests of Achievement [WJ-III] and the Comprehensive Mathematical Abilities Test [CMAT]). Demographic information across six datasets was analyzed, and behavioral data including sex, scanning site, ADHD status, age, verbal IQ, non-verbal IQ, vocabulary, reading, and arithmetic were analyzed using descriptive statistics and correlations. Voxel-based morphometry (VBM) was utilized to analyze the relationship between gray matter volume (GMV) and arithmetic skills in seven regions of interest (ROIs): bilateral intraparietal sulcus (IPS), left angular gyrus (AG), left middle temporal gyrus (MTG), left inferior frontal gyrus (IFG), and bilateral hippocampus. Linear mixed-effect models were used to analyze the relationship between GMV in each ROI and arithmetic skill, controlling for total intracranial volume (TIV), age, sex, and ADHD status. Scanning site and arithmetic test were included as random effects. Bayesian mixed-effect models were used to estimate the Bayes factor (BF) to assess the strength of evidence for the null hypothesis (no relationship between GMV and arithmetic skill) versus the alternative hypothesis (a relationship exists). To ensure that the relationship between arithmetic skill and GMV wasn't merely due to other cognitive skills, further frequentist mixed-model analyses were performed with additional covariates of language and cognitive skills (vocabulary, reading, verbal IQ, non-verbal IQ). Exploratory whole-brain analyses and analyses on cortical thickness were also performed, but these did not reveal additional significant relationships.

The study included 536 children and adolescents (ages 7.5-15 years). Behavioral analysis revealed medium-to-large correlations between verbal and nonverbal IQ, vocabulary, reading, and arithmetic skills. Scanner site correlated with age and ADHD status, due to age differences and ADHD diagnosis inclusion across datasets. VBM analysis revealed a significant positive relationship between arithmetic skill and GMV only in the left IFG and left MTG after controlling for TIV, age, sex, and ADHD status. Bayesian analysis showed substantial evidence for the relationships between GMV and arithmetic skills in these regions (BF10= 4.95 for left IFG and BF10 = 37.61 for left MTG). In contrast, Bayesian analysis revealed strong evidence against a relationship between GMV and arithmetic skills in the other ROIs (left AG, hippocampus, left and right IPS). Frequentist analyses including language and cognitive measures as covariates confirmed the significant relationship between arithmetic skill and GMV in both the left IFG and left MTG, even after controlling for reading, vocabulary, and verbal and nonverbal IQ.

This study, the largest structural brain-wide association study (BWAS) of arithmetic skills to date, identified a positive relationship between arithmetic skill and GMV in the left IFG and left MTG. This contrasts with previous studies that often implicated the parietal cortex. The left IFG's involvement is supported by previous functional neuroimaging studies showing increased activity with problem complexity. One proposed explanation involves the left IFG's role in suppressing verbal interference during calculations. The MTG's role aligns with previous studies demonstrating its association with arithmetic skills and its contribution to phonological processing. The absence of a relationship between arithmetic skill and GMV in regions like the parietal cortex, indicated by the Bayesian analysis, challenges prior findings and highlights the importance of large sample sizes in BWAS. The results suggest that left fronto-temporal regions play a key role in individual differences in arithmetic skills, possibly through phonological coding and verbal interference suppression.

This study demonstrates a strong association between arithmetic skills and gray matter volume in the left inferior frontal gyrus (IFG) and left middle temporal gyrus (MTG) using the largest sample size to date. This challenges previous findings that highlighted parietal regions. Future research should investigate the specific cognitive processes supported by these regions during arithmetic processing and explore potential interactions between various brain regions during mathematical operations. Investigating these relationships across different age groups and with varying arithmetic problem types would also be beneficial.

Several limitations need to be acknowledged. First, the use of a composite arithmetic score from tests combining various arithmetic operations prevents investigation of specific operation effects. Second, the use of VBM, capturing a mixture of gray matter measures, might limit the specificity of the findings compared to other methods like deformation-based morphometry or surface-based analyses. Third, the large sample size, while impressive, does not allow for reliable sub-group analyses based on age. Future research could address these limitations.