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COGNITIVE NEUROSCIENCE AND NEUROPSYCHOLOGY

White matter microstructures underlying mathematical abilities in children Lucia van Eimerena, Sumit N. Niogib, Bruce D. McCandlissb, Ian D. Hollowaya and Daniel Ansaria a

Numerical Cognition Laboratory, Department of Psychology, University of Western Ontario, Ontario, Canada and bSackler Institute for Developmental Psychobiology, Weill Cornell Medical College, New York Correspondence to Daniel Ansari, PhD, Department of Psychology and Graduate Program in Neuroscience, University of Western Ontario, Ontario, Canada, N6G 2K3 Tel: + 1519 6612111 x80548; fax: + 1519 6613961; e-mail: [email protected] Received 1 May 2008; accepted 5 May 2008

The role of gray matter function and structure in mathematical cognition has been well researched. Comparatively little is known about white matter microstructures associated with mathematical abilities. Di¡usion tensor imaging data from 13 children (7^9 years) and two measures of their mathematical competence were collected. Relationships between children’s mathematical competence and fractional anisotropy were found in two left hemisphere white matter regions. Although the superior corona radiata was found to

be associated with both numerical operations and mathematical reasoning, the inferior longitudinal fasciculus was correlated with numerical operations speci¢cally. These ¢ndings suggest a role for microstructure in left white matter tracts for the development of mathematical skills. Moreover, the ¢ndings point to the involvement of di¡erent white matter tracts for numerical operations c 2008 and mathematical reasoning. NeuroReport 19:1117^1121  Wolters Kluwer Health | Lippincott Williams & Wilkins.

Keywords: di¡usion tensor imaging, fractional anisotropy, inferior longitudinal fasciculus, mathematical ability, numerical cognition, superior corona radiata, white matter

Introduction The use of magnetic resonance diffusion tensor imaging (DTI) to quantify white matter microstructures has become an important tool for relating individual difference in brain structure to cognitive functions [1,2]. In particular, the measurement of fractional anisotropy (FA) has been successful in identifying the microstructural correlates of cognitive functions such as reading ability [3], working memory [4], and visuospatial attention [5]. In white matter, water diffuses more readily along versus across axons. The FA is a normalized measure of this diffusion, representing the degree of constrained water diffusion along the axons and is an indicator of white matter integrity. The more constrained and the less isotropic the diffusion is, the higher the FA value (range: 0–1) will be [6]. In earlier investigations, the assessment of FA has revealed relationships between microstructural connectivity in the brain and individual differences in reading achievement [3]. Klingberg and colleagues [7] demonstrated that individual differences in reading ability are correlated with variability in FA values of left temporo-parietal white matter structures in both dyslexic and normal adult readers. Therefore, these white matter structures may contribute to reading competencies by strengthening the functional connectivity between language-related gray matter areas. Subsequent studies focused on younger individuals at the early stages of reading development [8–11]. Consistent with the adult data [7], these studies revealed associations between individual differences in children’s reading ability and FA values in left temporo-parietal regions, such as the left superior corona radiata (SCR) [8–11], the left superior

longitudinal fasciculus [8–9,11], the posterior limb of the internal capsule [8], and the corpus callosum [8,10]. Although DTI has been successful in clarifying the importance of left-lateralized white matter structures for reading and its development, there has been little empirical consideration of the relationship between white matter microstructures and individual differences in mathematical cognition. Barnea-Goraly and colleagues [12] correlated FA values with scores of arithmetic ability in children (aged 7–19 years) with velocardiofacial syndrome. The authors revealed that individual differences in the performance of the velocardiofacial syndrome patients on a mental arithmetic test correlated with FA values in left parietal white matter structures that are adjacent to gray matter regions of the left intraparietal sulcus, a region that has been associated with calculation in functional neuroimaging studies [13]. Although the study by Barnea-Goraly et al. [12] provided insights into the white matter structures associated with individual differences in mathematical competence, the findings cannot be readily generalized to typically developing children, as the data were derived from patients with a genetic developmental disorder which leads to atypical brain development [14]. To investigate the relationship between white matter and mathematical competence, we collected DTI data as well as performance data using two standardized tests of mathematical cognition from 13 typically developing children (7–9-year olds). Using the recently developed and validated Reproducible Objective Quantification Scheme (ROQS) [11,15] for the analysis of DTI data, we extracted FA values from a group of well-defined white matter microstructures,

c Wolters Kluwer Health | Lippincott Williams & Wilkins 0959- 4965  Vol 19 No 11 16 July 2008 1117 Copyright © Lippincott Williams & Wilkins. Unauthorized reproduction of this article is prohibited.

NEUROREPORT which were then correlated with the measures of mathematical ability. Against the background of neuropsychological and functional neuroimaging data [12–13] revealing a relationship between left temporo-parietal cortex and exact mathematical competencies, we predicted a relationship between left-lateralized white matter microstructures and individual differences in children’s mathematical abilities.

Methods Participants Thirteen children (four females) were selected from a large MRI study of the functional and structural neuroanatomy underlying the development of mathematical competencies. The following inclusion criteria were used to select participants (from a pool of 32 participants): (i) according to school records and information provided by the parents, participants were healthy, right-handed, had normal or corrected-to-normal vision and were fluent in English; (ii) participants’ data had no significant motion or image artifacts during the DTI sequence; (iii) participants had normal to slightly above normal overall performance in mathematical achievement as measured by children’s Mathematics Composition Standard Score (mean: 102.08, range: 83–120) of the Wechsler Individual Achievement Test, second edition [16]. The children were 7–9.3 years old (mean age: 8.4 years), representing an age range in which crucial arithmetical concepts are acquired for the first time [17]. Children were recruited from elementary schools in and around Hanover, New Hampshire, USA. Parents of the children gave informed consent and children gave informed assent. These procedures were approved by the Committee for the Protection of Human Subjects at Dartmouth College. Standardized tests of mathematical abilities Children’s mathematical abilities were assessed using two subtests of the Wechsler Individual Achievement Test, second edition: (a) Numerical Operation and (b) Mathematical Reasoning [16]. Numerical Operation is a paper-andpencil test assessing children’s ability to solve written calculation problems and simple equations involving all basic operations: addition, subtraction, multiplication, and division. Mathematical Reasoning includes identification of geometric shapes, solving single and multistep problems, interpreting graphs, identifying mathematical patterns, and solving problems related to statistics and probability. Measure of basic reaction time As part of the above-mentioned functional MRI study, participants had to perform a basic reaction time (RT) task. For this task, participants were required to decide which of two randomly arranged geometric patterns looked more like a line. The RT of correct responses in this task will be used here to give a measure of individual differences in basic speed-of-processing. This measure was then used to assess the degree to which children’s mathematical scores account for significant variance in FA values after controlling for individual differences in speed-of-processing. Magnetic resonance imaging acquisition and analysis Magnetic resonance DTI was acquired in a 3T Phillips Intera Allegra whole body MRI scanner (Phillips Medial Systems,

VAN EIMEREN ETAL.

the Netherlands) using an 8-Channel Phillips Sense headcoil. Thirty-two gradient directions were measured at b¼1000 s/mm2, one volume with b¼0 s/mm2, 70 axial slices (2 mm thickness, gap¼2 mm) with 128  128 resolution, and a field of view of 240 mm resulting in a voxel size of 1.875 mm. All preprocessing steps were conducted using DTI Studio software (S. Mori, Johns Hopkins University) to manually control for motion or image artifacts during the DTI sequence. Subsequently FA maps were obtained, as well as average nondiffusion weighted images (b¼0 s/mm2), average diffusion coefficient images (b¼1000 s/mm2) and lastly primary eigenvectors of the diffusion tensor. An individualized regions of interest (ROI) approach using non-transformed data was used to avoid potential disadvantages of the voxel-based approaches, such as the need for large sample size and artifacts caused by spatial normalization and smoothing techniques, which often make it impossible to distinguish between differences in microstructure and those attributable to variability in gross anatomical shape and size [11,15,18–20]. Regions were selected on the basis of earlier findings implicating them in reading or other cognitive processes [3–5,7–12]. ROIs (Table 1) were selected in each individual brain using ROQS [15], an analysis package developed by the second two authors ROQS segments white matter structures on the basis of a user-defined seed voxel. In addition to avoiding the aforementioned problems of the voxel-based approach, ROQS is a fast technique that has been shown to have higher interrater and intrarater reliability [11,15] than hand-drawn ROIs. Two independent raters used the ROQS technique to define ROIs and extract the FA values. A Pearson’s correlation between the FA values extracted by the two raters for all subjects and regions of interests was found to be high r¼0.87, Po0.001. Furthermore, to stringently assess the interrater reliability, intraclass correlation coefficients were calculated using the FA values extracted from each ROI. This was found to be high (mean r¼0.73, SD¼0.19). ROI averages were created for considerably large tracts by selecting adjacent ROIs in different axial slices. For example, for the left SCR, FA values were extracted and averaged across two ROQS ROIs: one at the level of the corpus callosum, and the other at a level just superior to the cingulum bundles.

Results Partial correlations (controlling for the effects of chronological age, using coefficients from Spearman’s RHO, twotailed) were run between the raw scores of the standardized measures of mathematical abilities (Numerical Operation and Mathematic Reasoning) and the extracted mean FA values of each ROI. The correlations were adjusted for multiple correlations using the Bonferroni correction. As a total of 30 correlations were run, the minimum P value necessary for a correlation to survive the Bonferroni correction is: 0.00167. As can be seen in Table 1, we found that Numerical Operation raw scores correlated significantly with FA values in the left inferior longitudinal fasciculus (left ILF) (Fig. 1). In addition, we observed that raw scores for Numerical Operation as well as Mathematical Reasoning correlated with FA values in the left SCR (Fig. 2).

1118 Vol 19 No 11 16 July 2008 Copyright © Lippincott Williams & Wilkins. Unauthorized reproduction of this article is prohibited.

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WHITE MATTER MICROSTRUCTURES UNDERLYING MATH

Table1 Partial Spearman’s correlations (controlling for chronological age) between the mean fractional anisotropy values of ROQS ROIs and scores on the Numerical Operation and Mathematic Reasoning tests NO

MR

White matter structures

Abbreviation

rx,y,z

P value

rx,y,z

P value

Corpus callosum Genu of corpus callosum Splenium of corpus callosum Left anterior limb of the internal capsule Left posterior limb of the internal capsule Left cingulum bundle Right cingulum bundle Left superior corona radiata Right superior corona radiata Left anterior corona radiata Right anterior corona radiata Left inferior longitudinal fasciculus Right inferior longitudinal fasciculus Left superior longitudinal fasciculus Right superior longitudinal fasciculus

CC G S Left ALIC Left PLIC Left CB Right CB Left SCR Right SCR Left ACR Right ACR Left ILF Right ILF Left SLF Right SLF

0.005 0.295 0.212 0.076 0.277 0.421 0.506 0.753 0.333 0.096 0.522 0.856 0.35 0.298 0.44

0.98 0.35 0.51 0.82 0.38 0.17 0.09 0.0047 0.29 0.77 0.08 0.0004 0.27 0.35 0.15

0.174 0.134 0.239 0.23 0.38 0.349 0.176 0.66 0.351 0.329 0.353 0.4 0.395 0.45 0.379

0.59 0.68 0.45 0.47 0.22 0.27 0.58 0.0195 0.27 0.3 0.26 0.2 0.2 0.14 0.23

NO, numerical operation; MR, mathematic reasoning; ROIs, regions of interest; ROQS, Reproducible Objective Quanti¢cation Scheme.

ined these relationships because the involvement of left temporo-parietal white matter was hypothesized a priori. Furthermore, this region has been earlier implicated in reading and may therefore reveal important commonalities in the white matter microstructures underlying both reading and mathematical abilities. To investigate the extent to which the observed correlations are specific to variability in mathematical abilities, a series of regression analyses were run. In these analyses, chronological age and the above-described measure of basic reaction times (mean: 653.88 ms; SD: 98.37) were entered as predictors of FA values before assessing the variance in FA explained by the measures of mathematical competence. As can be seen from the results in Table 2, we found that variance in FA values of left SCR was significantly accounted for by individual differences in raw scores of the Numerical Operation task. Moreover, a nonsignificant trend was found when regressing Mathematical Reasoning onto FA values in the left SCR. In addition, we found that Numerical Operation strongly predicts FA values in the left ILF even after accounting for variance explained by for chronological age and individual differences in basic RT (Table 3).

(b)

Raw score on numerical operation

(a)

25 20 15 10

Discussion

5 0 0.5 0.55 0.6 0.65 0.7 0.75 0.8 Mean FA value of the left inferior longitudinal fasciculus (ILF)

Fig.1 Relationship of Numerical Operation scores and white matter microstructure FA in the left inferior longitudinal fasciculus (ILF). (a) Example of a Reproducible Objective Quanti¢cation Scheme region of Interest of the left ILF. (b) Scatter plot showing relationship between raw scores on the Numerical Operations tests and the FA (fractional anisotropy) value of the left ILF.

Although the correlations between the two mathematical measures and the left SCR did not reach the Bonferronicorrected significant threshold (0.00167), we further exam-

Although there has been a recent surge in functional neuroimaging studies investigating the neural mechanisms underlying mathematical cognition at the cortical level [12], there has thus far been very little research investigating the relationship between white matter organization and individual differences in mathematical cognition. In this study, we collected DTI data along with measures of mathematical abilities in typically developing children to address this open question. We found that individual differences in the performance in the Numerical Operation, but not the Mathematics Reasoning test correlate most strongly with FA values in the left ILF. This microstructure has been related to language, although its specific role in linguistic processing remains controversial [21]. More commonly the ILF, as part of the ventral stream, has been associated with visual

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VAN EIMEREN ETAL.

(a)

(b) Raw score on numerical operation

25 20 15 10 5 0 0.3

0.4 0.5 0.6 0.7 Mean FA value of individual area selected by ROQS

0.8

0.4 0.5 0.6 0.7 Mean FA value of individual area selected by ROQS

0.8

Raw score on math reasoning

45 40 35 30 25 20 0.3

Fig. 2 Relationship of mathematical performance and white matter microstructure fractional anisotropy (FA) in the left superior corona radiate (SCR). (a) Example of a Reproducible Objective Quanti¢cation Scheme (ROQS) region of interest of the left SCR. (b) Scatter plots showing relationship between raw scores on the two mathematical tests and the FA values of the left SCR.

Table 2 Regression models with mean FA values in the left superior corona radiata as dependent variable Model 1

R2

b

Step

Predictor

1 2 3

Age (years) 0.260 RT 0.213 NO 0.841*

DR2

Model 2 Step

0.068 0.106 0.435

0.068 0.039 0.329*

1 2 3

b

R2

DR2

0.068 0.106 0.381

0.068 0.039 0.275#

Predictor Age (years) 0.260 RT 0.213 MR 0.641#

In model 1 chronological age and basic reaction time are entered in the ¢rst two steps and Numerical Operation is entered as the ¢nal step. Model 2 is equivalent in the ¢rst two steps with Mathematical Reasoning scores entered in the third step. FA, fractional anisotropy; MR, mathematical reasoning; NO, numerical operation; RT, reaction time. b is the standardized regression coe⁄cient. *Po0.05; #P¼0.077.

Table 3 Regression model with mean FA values in the left inferior longitudinal fasciculus as dependent variable b

Model Step

Predictor

1 2 3

Age (years) RT NO

0.188 0.025 0.964*

R2

0.035 0.036 0.468

DR2

0.035 0.001 0.432*

Chronological age and basic reaction time were entered in the ¢rst two steps and scores on the Numerical Operations in the third step. FA, fractional anisotropy; NO, numerical operation; RT, reaction time. b is the standardized regression coe⁄cient. *Po0.05.

discrimination, memory, as well as object and face recognition [22]. In addition, a prominent neuropsychological model of number processing predicts that inferior temporal regions are associated with the processing of

numerical symbols and the visual representations of calculation problems [23]. Therefore, the ILF may be related to the efficiency with which children are able to process the numerical symbols (e.g. Arabic numerals) presented in the Numerical Operations test. Convergent with these data are recent findings [25] that FA in the longitudinal fasciculi correlate with children’s calculation abilities. In addition, correlation and regression analyses suggest a relationship between FA values in the left SCR and children’s scores on both mathematical achievement tests. This finding cannot be solely explained by age-related differences, maturational factors or speed-of-processing, as mathematical scores accounted for unique variance in FA even after controlling for chronological age and a measure of basic reaction time. This was particularly so for Numerical Operations, while Mathematical Reasoning only account for marginally significant variance in our regression analyses.

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WHITE MATTER MICROSTRUCTURES UNDERLYING MATH

The left SCR has repeatedly been related to individual differences in reading achievement [3]. This may suggest important commonalities in left-lateralized white matter structures underlying reading abilities and mathematical competence, such as access to phonological representations [25]. In addition to playing a significant role in reading abilities, left temporo-parietal regions have long been associated with calculation abilities. Thus, the present findings converge with existing data to suggest that left temporo-parietal regions are involved in exact, verbal mathematical competencies [13,23]. In addition to the fact that mathematical scores accounted for unique variance in left SCR FA values after controlling for the variance explained by individual differences in chronological age and processing speed, a general association between the left SCR and cognitive abilities across domains seems unlikely because this microstructure has been earlier found to be uncorrelated with measures of visuo-spatial attention [5], cognitive control [2], working memory [4] as well as digit recall and nonverbal IQ [11]. Conclusion We have identified a group of left-lateralized white matter microstructures whose relative degree of integrity (as measured by FA) is significantly related to individual differences in children’s mathematical abilities. The left SCR, which has been earlier associated with individual differences in reading, is also related to children’s mathematical reasoning and calculation abilities. In addition, the left ILF was found to be strongly related to children’s performance on a paper-and-pencil test of calculation. Thus, the present findings suggest an association between individual differences in left hemisphere white matter structures and mathematical competencies of typically developing children. Future studies should investigate how these white matter microstructures develop over time and whether these structures develop atypically in children with mathematical difficulties, such as developmental dyscalculia.

Acknowledgements This work was supported by grants from the National Science Foundation (SBE-0354400 and REC 0337715) and the Natural Sciences and Engineering Council of Canada. The authors thank Bea Goffin for her help with the data analysis.

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NEUROREPORT 4. Nagy Z, Westerberg H, Klingberg T. Maturation of white matter is associated with the development of cognitive functions during childhood. J Cogn Neurosci 2004; 16:1227–1233. 5. Tuch DS, Salat DH, Wisco JJ, Zaleta AK, Hevelone ND, Rosas HD. Choice reaction time performance correlates with diffusion anisotropy in white matter pathways supporting visuospatial attention. Proc Natl Acad Sci 2005; 102:12212–12217. 6. Basser PJ, Pierpaoli C. Microstructural and physiological features of tissues elucidated by quantitative-diffusion-tensor MRI. J Magn Reson B 1996; 111:209–219. 7. Klingberg T, Hedehus M, Temple E, Salz T, Gabrieli JDE, Moseley ME, et al. Microstructure of temporo-parietal white matter as a basis for reading ability: evidence from diffusion tensor magnetic resonance imaging. Neuron 2000; 25:493–500. 8. Beaulieu C, Plewes C, Paulson LA, Roy D, Snook L, Concha L, et al. Imaging brain connectivity in children with diverse reading ability. Neuroimage 2005; 25:1266–1271. 9. Deutsch GK, Dougherty RF, Bammer R, Siok WT, Gabrieli JD, Wandell B. Children’s reading performance is correlated with white matter structure measured by diffusion tensor imaging. Cortex 2005; 41:354–363. 10. Dougherty RF, Ben-Shachar M, Deutsch GK, Hernandez A, Fox GR, Wandell BA. Temporal-callosal pathway diffusivity predicts phonological skills in children. Proc Natl Acad Sci 2007; 104:8556–8561. 11. Niogi SM, McCandliss BD. Left lateralized white matter microstructure accounts for individual differences in reading ability and disability. Neuropsychologia 2006; 44:2178–2188. 12. Barnea-Goraly N, Eliez S, Menon V, Bammer R, Reiss AL. Arithmetic ability and parietal alterations: a diffusion tensor imaging study in velocardiofacial syndrome. Cogn Brain Res 2005; 25:735–740. 13. Dehaene S, Piazza M, Pinel P, Cohen L. Three parietal circuits for number processing. Cogn Neuropsychol 2003; 20:487–506. 14. Eliez S, Schmitt JE, White CD, Reiss AL. Children and adolescents with velocardiofacial syndrome: a volumetric MRI study. Am J Psychiatry 2000; 157:409–415. 15. Niogi SM, Mukherjee P, McCandliss BD. Diffusion tensor imaging segmentation of white matter structures using a Reproducible Objective Quantification Scheme (ROQS). Neuroimage 2007; 35:166–174. 16. The Psychological Corporation. Manual for the Wechsler Individual Achievement Test (WIAT). San Antonio: TX; 1992. 17. Butterworth B. The development of arithmetical abilities. J Child Psychol Psychiatry 2005; 46:3–18. 18. Ciccarelli O, Toosy AT, Parker GJM, Wheeler-Kingshott CAM, Barker GJ, Miller DH, et al. Diffusion tractography based group mapping of major white-matter pathways in the human brain. Neuroimage 2003; 19:1545–1555. 19. Jones DK, Symms MR, Cercignani M, Howard RJ. The effect of filter size on VBM analyses of DT-MRI data. Neuroimage 2005; 26:546–554. 20. Tisserand DJ, Pruessner JC, Arigita EJS, van Boxtel MPJ, Evans AC, Jolles J, et al. Regional frontal cortical volumes decrease differentially in aging: an MRI study to compare volumetric approaches and voxel-based morphometry. Neuroimage 2002; 17:657–669. 21. Mandonnet E, Nouet A, Gatignol P, Capelle L, Duffau H. Does the left inferior longitudinal fasciculus play a role in language? A brain stimulation study. Brain 2007; 130:623–629. 22. Schmahmann JD, Pandya DN. Fiber pathways of the brain. New York: Oxford UP; 2006. 23. Dehaene S. Varieties of numerical abilities. Cognition 1992; 44:1–42. 24. Simmons FR, Singleton C. Do weak phonological representation impact on arithmetic development? A review of research into arithmetic and dyslexia. Dyslexia 2008; 14:77–94. 25. Davis N, Cannistraci C, Lorang C, Fuchs L, Rogers B, Schrader W, et al. Correlated brain tissue structure and function in mathematical processing. In: Ewing-Cobbs L, editor. Cognitive and Neuroimaging Correlates of Fact Retrieval, Calculation and Estimation in Children with Learning Disabilities. Symposium conducted at the International Neuropsychological Association, Waikoloa, Hawaii. 2008.

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