Typical Development, Brain Microstructure, & Mathematical Skills 22

To date, most of the studies examining mathematical skills and brain microstructure have focused on children. In one of the first studies to examine the microstructural correlates of mathematical processing, van Eimeren, Niogi, McCandliss, Holloway, & Ansari (2008) used an anatomical regions of interest approach to relate FA to two standardized measures of mathematical abilities from the Wechsler Individual Achievement Test (numerical operations and mathematical reasoning) in children

between ages 7-9 (n = 13). Numerical operations is a test of written calculation and involves simple arithmetic problems including addition, subtraction, multiplication and division. Mathematical reasoning includes more complex problems including single and multi-step arithmetic, identifying geometric shapes, interpreting graphs, identifying mathematical patterns, and solving problems related to statistics and probability. After correcting for age and reaction time in the regression analysis, van Eimeren et al. (2008) found a correlation between the numerical operations subtest and FA in the left superior corona radiata and the left inferior longitudinal fasciculus. The authors speculated that the inferior longitudinal fasciculus may be related to the efficiency with which the

participants were able to process Arabic numerals since inferior temporal regions have been related to the visual representations of calculation problems and processing numerical symbols (Dehaene, 1992). Since the left superior corona radiata has been related to reading skills (Ben-Shachar et al., 2007), van Eimeren and colleaugues suggest that these left temporoparietal regions may become co-opted for exact, verbal

mathematical skills. White matter integrity in the left superior corona radiata has also been correlated with beta values in the left angular gyrus during an arithmetic task with small and large problem sizes (van Eimeren et al., 2010). This association was

particularly strong for simple arithmetic problems that had a high probability of being solved by retrieval strategies. In summary, these results highlighted the importance of the left inferior longitudinal fasciculus and the left superior corona radiata in mathematical skills.

ROI approaches have also been employed using deterministic tractography in the superior longitudinal fasciculus, a tract with fronto-parietal projections (Tsang et al.,

2009). The authors assessed mental arithmetic using three measures: simple math facts, exact two-digit addition, and approximate two digit addition. Simple math facts was a verification task that included simple multiplication and addition problems, whereas exact and approximate addition included larger addition problems where the participant had to select the correct answer from two options. For approximate addition neither response was numerically correct, and the participant had to select the correct answer rounded to the nearest decade. FA in the left anterior superior longitudinal fasciculus was correlated with approximate addition (but not exact addition or simple math facts) in children ages 10-15 years old (n = 34) (Tsang et al., 2009). Importantly, this correlation remained after removing variance due to age, intelligence, rapid digit naming, written calculation, and reading. However, this study was unable to replicate the association between exact arithmetic and left parietal white matter that van Eimeren et al. (2008) reported.

Magnitude comparison has shown to be a sensitive measure of math achievement (Holloway & Ansari, 2009) and is thought to be a foundational skill for later

mathematical skills. Therefore, it may be particularly informative to determine the neural correlates of such basic number processing. In the first study to relate basic number processing (magnitude comparison) to white matter microstructure, Cantlon et al. (2011) examined three regions of the corpus callosum including the genu, isthmus, and the splenium using deterministic tractography. In a group of 18 children (6 years old) and 14 adults (23 years old), they examined how corpus callosum white matter integrity was related to accuracy on a magnitude comparison task with digits (Arabic numerals) and dots. FA in the left isthmus of the corpus callosum was related to performance on

symbolic and non-symbolic versions of the task in both adults and children. This finding is significant in that the isthmus of the corpus callosum connects the two hemispheres of the parietal cortex. The authors speculated that weak white matter integrity of the left isthmus may be related to more right hemisphere activation in children compared to adults during numerical tasks. They additionally hypothesized that this interhemispheric connection could play an important role in the maturation of numerical representations.

1.5.2 Atypical Development, Brain Microstructure, & Mathematical

Skills

Several DTI studies have explored the brain-behaviour correlations in populations with specific deficits in mathematics (i.e. developmental dyscalculia, fetal alcohol

spectrum disorder, velocardiofacial syndrome, etc). Ultimately, it is very hard to interpret research examining brain-behaviour correlations in atypically developing participants, and it is even more difficult to make generalizations about neurocognitive processes in typical development. Any associations between brain microstructure and mathematical skills in atypically developing populations could be specific to the disorder or a

byproduct of the neuropathology as opposed to a general cognitive process observable in all individuals. Nevertheless, a review of these studies is useful in order to examine whether there are any consistent findings across multiple disorders.

Only one study has examined the neuroanatomical correlates of developmental dyscalculia, a developmental learning disability that is characterized by specific deficits in mathematics in the absence of any other cognitive disabilities (Shalev, 2004).

Specifically, Rykhlevskaia, Uddin, Kondos, and Menon (2009) revealed FA reductions in right temporoparietal white matter in children with dyscalculia. FA in this region was

additionally correlated with numerical operations but not mathematical reasoning or word reading (for a description of these tests see van Eimeren et al. (2008) above). Using this cluster as a seeding region for probabilistic tractography, Rykhlevskaia et al. (2009) found a significantly lower probability of connectivity to the right inferior temporal gyrus. These findings converge with those of van Eimeren et al. (2008) who found correlations with numerical operations, but not mathematical reasoning, in the inferior longitudinal fasciculus. Indeed, Rykhlevskaia et al. (2009) suggested that the inferior longitudinal fasciculus may run through the temporoparietal cluster. One noteworthy difference between the two studies is that van Eimeren et al. (2008) found a correlation in the left hemisphere whereas Rykhlevskaia et al. (2009) found one in the right. One might speculate that these hemispheric differences may be a result of atypical numerical

processing in dyscalculic children, however, further research would need to explore this possibility, especially since this group of children only had modest mathematical

difficulties. Predominantly right hemisphere correlations have also been found in youths with multiple sclerosis (Till et al., 2011). Specifically, Till et al. (2011) found that the corpus callosum, right parietal and right frontal white matter were associated with performance on the calculation subtest of the Woodcock Johnson, however, these

correlations were not present in the matched control group. Only the corpus callosum was a significant predictor of calculation skills after age, IQ and working memory were taken into account. Since FA was averaged across all white matter in each lobe (separately for each hemisphere) and a ROI analysis was used for the corpus callosum, it is somewhat unsurprising that only correlations in the corpus callosum remained significant after accounting for these factors. Each of the four lobes contains a large number of white

matter pathways and mathematical processing likely only uses a portion of these pathways. Therefore, correlating mathematical skills with FA that has been averaged across multiple white matter tracts is unlikely to produce significant results since the mean FA will not be sensitive to individual differences in microstructure. Again, these results conflict with the literature on typically developing children, which primarily find left hemisphere correlations.

In the study of white matter integrity in another atypical population, Barnea- Goraly, Eliez, Menon, Bammer, and Reiss (2005) presented findings in velocardiofacial syndrome (VCFS) that are more convergent with studies on typically developing

populations. VCFS is a genetic syndrome that has a wide variety of symptoms that

includes an uneven cognitive profile with greater impairments in non-verbal skills such as visuospatial skills and mathematics. A whole brain regression was used to determine whether arithmetic skills, measured by subtests in the Wechsler Intelligence Scale for Children-III and or the Wechsler Adult Intelligence Scale-III, were related to FA after including IQ and age as nuisance factors (Barnea-Goraly et al., 2005). Results of this analysis revealed a region of left parietal white matter underlying the intraparietal sulcus, the supramarginal and angular gyri that was associated with individual differences in children’s math skills. The authors reasoned that their findings parallel previous neuroimaging studies (Eliez et al., 2001), and that their results suggest parietal circuits play an important and critical role in numerical and mathematical processing. However, these results cannot be generalized to mathematical processing in typical populations. Indeed, Barnea-Goraly et al. (2005) did not find the same correlation in control subjects. Therefore, it is unclear whether the relationship between these white matter

microstructures and mathematical skills are related to general cognitive processing or whether they are a product of the neuropathology of the disorder.

The white matter correlates of mathematical proficiency have also been examined in children with Fetal Alcohol Spectrum Disorder (FASD) (Lebel, Rasmussen, Wyper, Andrew, & Beaulieu, 2010). Children with FASD have a mixed profile of cognitive abilities, but have particular deficits on measures of mathematics (Lebel et al., 2010). The Quantitative Concepts subtest of the Woodcock-Johnson III was used as an assessment of mathematical skills. This test assesses math concepts, symbols and vocabulary. Voxel- based analyses revealed several correlations including several positively correlated clusters: two in left parietal white matter, the left cerebellum, and one negative cluster in the bilateral brainstem. Tractography from these regions confirmed that the left superior longitudinal fasciculus, left corticospinal tract, corpus callosum, cerebellar pundicle and bilateral projection fibers were the contributing tracts in these correlations.