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. 2013 Sep 3;35(6):2619–2631. doi: 10.1002/hbm.22355

White matter microstructure correlates of mathematical giftedness and intelligence quotient

Francisco J Navas‐Sánchez 1,2,✉, Yasser Alemán‐Gómez 1,2, Javier Sánchez‐Gonzalez 3, Juan A Guzmán‐De‐Villoria 4, Carolina Franco 5, Olalla Robles 5,6, Celso Arango 2,5, Manuel Desco 1,2,7
PMCID: PMC6868969  PMID: 24038774

Abstract

Recent functional neuroimaging studies have shown differences in brain activation between mathematically gifted adolescents and controls. The aim of this study was to investigate the relationship between mathematical giftedness, intelligent quotient (IQ), and the microstructure of white matter tracts in a sample composed of math‐gifted adolescents and aged‐matched controls. Math‐gifted subjects were selected through a national program based on detecting enhanced visuospatial abilities and creative thinking. We used diffusion tensor imaging to assess white matter microstructure in neuroanatomical connectivity. The processing included voxel‐wise and region of interest‐based analyses of the fractional anisotropy (FA), a parameter which is purportedly related to white matter microstructure. In a whole‐sample analysis, IQ showed a significant positive correlation with FA, mainly in the corpus callosum, supporting the idea that efficient information transfer between hemispheres is crucial for higher intellectual capabilities. In addition, math‐gifted adolescents showed increased FA (adjusted for IQ) in white matter tracts connecting frontal lobes with basal ganglia and parietal regions. The enhanced anatomical connectivity observed in the forceps minor and splenium may underlie the greater fluid reasoning, visuospatial working memory, and creative capabilities of these children. Hum Brain Mapp 35:2619–2631, 2014. © 2013 Wiley Periodicals, Inc.

Keywords: mathematical giftedness, adolescents, DTI, fractional anisotropy, intelligence, IQ, corpus callosum, fronto‐parietal, white matter

INTRODUCTION

The neural basis of intelligence and the processes that underlie giftedness are areas of increasing interest. Gifted children are precocious in their intellectual development and show intelligence quotient (IQ) values that are higher than 2 standard deviations above the population mean. However, enhanced abilities in a domain‐specific area are not necessarily dependent on IQ, but rather a reflection of other neurobiological characteristics [Kalbfleisch, 2004], such as cortical dynamics of maturation, genetic factors, or brain volume. Defining giftedness only by higher IQ could lead to confusion in the identification of gifted subjects. Math‐gifted subjects perform better in novel problem solving by using innovative selection criteria and are able to perceive complex relations and form concepts faster than nongifted subjects [Jung et al., 2010; O'Boyle et al., 2005]. In addition, they store and manipulate outcomes more efficiently and creatively. The creative aspects of intelligence are accompanied by enhanced cognitive processes such as fluid reasoning and working memory [Geake and Hansen, 2005]. Math‐gifted subjects show higher capabilities in fluid reasoning, working memory, and mental imagery [Desco et al., 2011; Lee et al., 2006; O'Boyle et al., 2005].

Previous neuroimaging studies of math‐giftedness suggested that the organization of a math‐gifted brain could be different from that of a nongifted brain. These studies reported functional characteristics of math‐gifted adolescents performing visuospatial and fluid reasoning tasks [Desco et al., 2011; Lee et al., 2006; O'Boyle et al., 2005]. The combination of a special form of bilateralism in a fronto‐parietal network and enhanced functioning of the right hemisphere seems to be the neurobiological substrate of math‐giftedness [Benbow, 1986; Benbow and Lubinski, 1993; Geschwind and Galaburda, 1984; O'Boyle et al., 1995, 1991]. These characteristics involve heightened connectivity between the left and right hemispheres [Singh and O'Boyle, 2004], as well as enhanced intrahemispheric connectivity between the frontal and parietal cortices [Desco et al., 2011]. To our knowledge, no studies on white matter microstructure have confirmed heightened connectivity in math‐gifted subjects.

In this study, we investigate the white matter microstructure underlying math giftedness. We used diffusion tensor imaging (DTI) to provide a framework for analysis and quantification of the diffusion properties of white matter. Specifically, fractional anisotropy (FA) makes it possible to assess myelin and axonal microstructure in white matter [Basser, 1997; Basser and Pierpaoli, 1996; Pierpaoli and Basser, 1996]. Increased FA may depend on increased fiber density, increased myelination of fiber tracts, higher directionally coherent organization of fibers within voxels [Beaulieu, 2002], or increased axonal diameter [Mori and Zhang, 2006]. Some studies have shown a relationship between FA and intelligence [Schmithorst and Holland, 2007; Schmithorst et al., 2005; Yu et al., 2008], arithmetic and mathematical calculation scores [Tsang et al., 2009; van Eimeren et al., 2010], working memory scores [Nagy et al., 2004], and visuospatial processing [Klingberg, 2006; Mabbott et al., 2006; Wolbers et al., 2006] in white matter fronto‐parietal areas. These correlations were thought to reflect a positive relationship between white matter organization and higher intelligence, thus supporting the Parieto‐Frontal Integration Theory [Jung and Haier, 2007].

The objective of our study was to investigate the relationship between math‐giftedness/IQ and white matter FA in a sample composed of math‐gifted adolescents and age‐matched controls. We hypothesized that math‐gifted subjects, independently of their IQ, would have bilateral increased FA in the intrahemispheric tracts, particularly in the fronto‐parietal regions, and in the interhemispheric commissure tracts, especially in the corpus callosum.

METHODS

Subjects

The sample recruited for the study included a total of 36 adolescents aged between 11.8 and 15 years who were divided into two groups: math‐gifted subjects and age‐matched controls. The inclusion criteria for both groups were as follows: age 11–15 years, right‐handedness, Spanish as mother tongue, and at least 5 years' schooling in the Spanish education system. Handedness was determined in all subjects using item# 5A of the Neurological Evaluation Scale [Buchanan and Heinrichs, 1989].

The exclusion criteria for both groups were as follows: medical, neurological, or psychiatric illness; history of head injury with loss of consciousness; presence of metallic implants, body tattoos, or orthodontic appliances; mental retardation; pervasive developmental disorders; and pregnancy or breast‐feeding.

Math‐gifted subjects

The math‐gifted group comprised 13 adolescents (5 girls) aged 12–14 years (mean 13.8 years, SD = 0.6) with a mean of 7.8 years of formal education (SD = 0.7). The students were enrolled in the Stimulus of Mathematical Talent Program (ESTALMAT (http://www.uam.es/proyectosinv/estalmat//), “Programa de Estímulo del Talento Matemático”) of the Spanish Royal Academy of Mathematical, Physical, and Natural Sciences in Madrid. To enter the ESTALMAT program, children who are particularly good at math and willing to participate are proposed by teachers and parents. These subjects undergo a screening process consisting of a personal interview and math‐related tests. If they pass this preliminary assessment, they undergo a second examination based on a variety of tests that include logical thinking, geometrical representations, and abstract and deductive reasoning. The ESTALMAT tests are intended to select only a few subjects (typically 20 out of 300 in the Madrid region per year). The objective of the tests is to detect the six complex mathematical abilities proposed by K. Kiesswetter [Heller et al., 2000], as follows: (1) organizing materials; (2) recognizing patterns or rules; (3) changing the representation of the problem and recognizing patterns and rules in this new area; (4) comprehending and working with highly complex structures; (5) reversing and inverting processes; and (6) finding related problems. These six abilities could be categorized as cognitive, motivational, and creative.

Test answers were examined by mathematicians considering not only whether the answers were correct, but also the argumentation followed to achieve the solution. Each exam has six different tests in which visuospatial thinking, intuition, creativity, abstraction, manipulation, and capabilities of thought management are assessed. The tests chosen are as original as possible; subjects that have training would not have a clear advantage over the others. In comparison with other standardized measures such as SAT‐Math (Scholastic Assessment Test, Mathematics Section), ESTALMAT emphasizes problem solving by creative thinking, rather than using concepts and previous expertise gained at school.

Controls

The control group included 23 adolescents (4 females) aged 12–15 years (mean 13.4 years, SD = 0.8). Controls were recruited to match math‐gifted subjects for age and academic level, but not explicitly for IQ. The study was presented first in the schools attended by math‐gifted subjects, and the selection process of control subjects involved an initial interview to confirm suitability (i.e., age, sex, parental consent, availability, and basic exclusion criteria).

Cognitive Assessment

Intellectual functioning was estimated using the Vocabulary, Information, and Block Design subtests from the Spanish version of the Wechsler Intelligence Scale for Children—Revised. IQ was estimated from these three subtests following [Ringe et al., 2002; Silverstein, 1985] and is reported to show good correspondence with full‐scale IQ (FSIQ) [Satler, 2001]. The cognitive assessment was performed by a child neuropsychologist and a child psychiatrist, who also analyzed the subjects' school records.

The study was approved by the Hospital Ethics and Clinical Research Boards. Written informed consent was obtained from both subjects and parents before the study was performed.

Magnetic Resonance Imaging Acquisition Protocols

Data were acquired with a Philips Intera 1.5 T MRI scanner (Philips Medical Systems, Best, The Netherlands). The protocol included a high‐resolution structural image (T 1‐weighted gradient‐echo; tepetition time (TR) = 25 ms; echo time (TE) = 9.2 ms; matrix size = 256 × 256 × 175; flip angle = 30°; slice thickness = 1 mm; voxel size 1 × 1 × 1 mm3 3D) and a DTI study.

DTI data were acquired using a single‐shot spin echo‐planar imaging sequence with the following scanning parameters: imaging plane, axial; phase encoding direction, A–P; TE = 68 ms, TR = 11,886 ms; flip angle = 90°; echo‐planar imaging (EPI) factor = 77; number of slices = 60; interslice gap = 0 mm; voxel size = 2.0 × 2.0 × 2.0 mm3; and acquisition matrix 128 × 128. A single nondiffusion‐weighted image and 16 diffusion weighted images were acquired. The diffusion weighted images were obtained for a b‐value = 0 and 800 s/mm2 over 16 noncollinear directions following an icosahedral scheme.

Data Preprocessing and Analysis

Diffusion‐weighted studies were processed using the software package FSL 4.1 (FMRIB Software Library, FMRIB, Oxford, UK) [Smith et al., 2004]. Eddy‐current and head motion artifacts were corrected using the eddy correct routine implemented in FSL. In this step, all diffusion volumes were registered to the T 2‐b 0 image using an affine transformation. The corresponding diffusion gradient vectors were properly reoriented using the resulting transformations.

Brain masks were obtained from the b 0 image using Brain Extraction Tool [Smith, 2002], and FMRIB's diffusion toolbox [Behrens et al., 2003] was used to fit the tensors and to compute the FA maps.

On the FA maps, we performed both voxel‐wise and region of interest (ROI) analyses to study IQ effects on white matter microstructure. After controlling for IQ, we studied the differences between the math‐gifted group and the controls.

Voxel‐Based Analysis

Voxel‐wise statistical analysis of the FA data was performed using FSL tools according to the following workflow. All subjects' FA maps were nonlinearly registered to a target image identified automatically as the most “representative” subject in the study. The most representative FA image was chosen by performing all possible pairwise registrations (linear and nonlinear) between subjects. From this, the subject's image with the minimum mean deformation necessary to nonlinearly align it to the other subjects was used as the reference. Normalization into the Montreal Neurological Institute (MNI) standard space was performed using the FMRIB Nonlinear Image Registration Tool. All normalized FA images were averaged to obtain a study‐specific “Mean FA” template. FA maps were smoothed using a 6‐mm Full‐Width at Half Maximum (FWHM) Gaussian filter. We used an explicit mask that includes the major white matter pathways but excludes peripheral tracts showing significant intersubject variability and/or partial volume effects with gray matter or cerebrospinal fluid tissues. Only voxels with FA > 0.3 were selected for further analysis.

Finally, a general linear model was applied using nonparametric permutation inference [Nichols and Holmes, 2002]. A statistical analysis using ANCOVA model was carried out on the FA maps to detect possible significant effects of the factor “Math‐giftedness” (statistical threshold of P < 0.05, corrected for multiple comparisons) and the continuous covariate “IQ.” P‐values were corrected using the FDR tool available in the FSL package (http://fsl.fmrib.ox.ac.uk/fsl/fslwiki/FDR).

Before performing these analyses, we also checked possible gender and age effects on the FA, together with potential interactions with the factor “Math‐giftedness” and the covariate “IQ.”

Atlas‐Based Segmentation of White Matter Tracts

We extracted the mean FA values of the tracts using an ROI analysis in order to generate an individualized atlas for each subject in native space. To parcel the individual FA maps into different tracts, we used the ICBM‐DTI‐81 white matter labels atlas, which is one of the standard atlases of FSL [Mori et al., 2008; Wakana et al., 2004]. The JHU‐FA template was rigidly registered to the mean FA to move the white matter labels into the study‐specific template space. These labels were then warped into individual spaces by applying the inverted spatial transformation matrices generated by the normalization of the individual FA maps to obtain individual white matter tract parcels. Individualized ROIs were also used to anatomically label the results obtained in the voxel‐wise analysis step (Fig. 1).

Figure 1.

Figure 1

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Atlas‐based parcellation method. On the left side, anatomically defined fibers in the ICBM‐DTI‐81 white matter labels atlas in MNI space. FA maps of each subject were registered to the template in MNI space. The transformation matrices obtained were inverted and applied to the atlas. On the right side, the resulting atlas transformation in the native space of each subject.

White matter structures included in the atlas‐based segmentation analysis (for each hemisphere) were: Genu, Body, and Splenium of corpus callosum and the whole Corpus callosum; Anterior limb of internal capsule; Posterior limb of internal capsule; Retrolenticular part of internal capsule; External capsule; Anterior corona radiata; Superior corona radiata; Posterior corona radiata; Posterior thalamic radiation; Sagittal striatum (including inferior longitudinal fasciculus and inferior fronto‐occipital fasciculus); Cingulum (cingulate gyrus); Superior longitudinal fasciculus; Superior fronto‐occipital fasciculus and Uncinate fasciculus.

Mean FA measurements obtained for each ROI were analyzed with SPSS v13 using the Univariate General Linear Model with “Math‐giftedness” as a fixed factor, and “IQ” as a between‐subject continuous covariate if an effect on FA was recorded. All the results obtained in the ROI analysis underwent a Bonferroni correction for multiple comparisons (P < 0.05).

RESULTS

The results of the cognitive assessment showed significant differences in IQ. The math‐gifted group had a mean estimated FSIQ of 130.7 (SD = 10.7; range, 112–149). Controls were recruited randomly from the same schools as the math‐gifted adolescents and had a mean estimated FSIQ of 105.5 (SD = 15.7), with a wider IQ range than the math‐gifted subjects (88–140). There are significant between‐group differences in both VIQ and PIQ scores (P < 0.001). In both groups, there are no significant differences between Verbal (VIQ) and Performance IQ (PIQ) scores, thus suggesting a balanced intellectual profile (see Table 1). Years of education and parental socioeconomic status were similar in both groups.

Table 1.

Mean and standard deviation (SD) of demographic data for each group

Controls (n = 23) Math‐gifted (n = 13) Pa
Mean SD Mean SD
Age (years) 13.42 0.86 13.75 0.57
Age (months) 160.91 10.31 165.01 7
Gender (male\female) 19\4 8\5
Handedness (right\left\mixed) 23\0\0 13\0\0
Estimated full‐scale IQ 105.48 15.71 130.77 10.68 <0.001
Verbal IQ 106.83 16.67 125.08 12.07 <0.001
Performance IQ 99.83 23.1 128.85 12.14 <0.001
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a Student's t test of differences between groups.

Relationship Between FA and IQ

In the voxel‐wise analysis of the whole sample, IQ correlated positively with FA, mainly in the corpus callosum. The atlas‐based analysis showed that the effect of IQ correlated with mean FA for the whole corpus callosum (Pearson's r = 0.48; P < 0.003) and its parts: genu (r = 0.38; P < 0.021), body (r = 0.476; P < 0.003), and splenium (r = 0.46; P < 0.005). These results are plotted in Figure 2.

Figure 2.

Figure 2

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Correlation between FA and IQ in the voxel‐wise analysis. A: Correlation between FA and IQ in the corpus callosum and cingulum in the voxel‐wise analysis (P = 0.05 uncorrected). Significant clusters were overlaid on the mean FA image from all subjects. B: Correlation scatter‐plot from the atlas‐based parcellation with FA obtained from each part of the corpus callosum in native space. Math‐gifted subjects are represented in the graphs in red color circles; controls in blue.

We also found significant clusters in association tracts (Table 2); however, only the fornix (r = 0.36; P < 0.031) and anterior limb of the left internal capsule (r = 0.38; P < 0.022) had an IQ effect on mean FA for the whole tract.

Table 2.

Anatomical regions showed significant correlation between FA and IQ in the voxel‐wise analysis

Voxel‐wise Analysis: Correlation FA‐IQ
Anatomical region Hemisphere x y z Z‐value Cluster size
Genu of corpus callosum Left −2 5 25 3.35 6,603
Body of corpus callosum Left −3 5 24 3.1 6,603
Splenium of corpus callosum Left 0 −36 8 2.13 34
Cingulum Right 11 −35 30 3.35 1,885
Cingulum (hippocampus) Right 25 −48 1 3.54 603
Left −26 −36 10 2.7 55
Forceps major Right 7 −44 9 2.08 31
Fornix Right 1 2 8 2.34 74
Anterior limb of internal capsule Left −9 2 5 2.47 336
External capsule (uncinate) Left −33 40 −2 3.03 350
Anterior thalamic radiation Left −2 −11 −6 3.35 663
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The table only reports Z‐values >1.90 (P < 0.05, uncorrected).

Differences in FA Between Math‐Gifted Subjects and Controls

In the voxelwise analysis, after adjustment for the effect of IQ, the math‐gifted group showed significantly higher FA bilaterally in association tracts, in the anterior and superior corona radiata (including corticospinal tract), and in the genu and the splenium of the corpus callosum, particularly in the forceps minor and major (Table 3; Fig. 3). Most of the association tracts with higher bilateral FA connect frontal lobes with basal ganglia (anterior and posterior limbs of the internal capsules, right external capsule, and thalamic radiations) and temporo‐parietal regions (uncinate, superior, and inferior longitudinal fasciculi) adjacent to the inferior parietal lobule. Controls did not show any region with significantly higher FA than math‐gifted group. Figure 4 shows the between‐group differences in the atlas‐based parcellation analysis in native space, plotted with statistical “F‐values.” No significant group × IQ interaction was observed in the tracts analyzed.

Table 3.

Anatomical regions with significant increased FA in math‐gifted subjects compared with controls obtained in the voxel‐wise analysis

Voxel‐wise analysis: FA math‐gifted > controls
Anatomical region Local maxima
Hemisphere x y z Z‐value Cluster size
Corticospinal tract Right 17 −21 70 2.84 9,387
Left −23 −21 50 3.29 2,252
Anterior corona radiata (cingulum, fminor) Right 22 30 27 3.66 9,387
Left −17 40 10 2.66 875
Anterior corona radiata (IFOF/Unc) Left −23 36 −1 2.94 291
Superior corona radiata Right 19 −5 40 3.31 9,387
Left −25 7 22 3.3 2,252
Posterior corona radiata Right 26 −31 22 2.49 25
Left −27 −32 23 2.69 44
External capsule Right 29 −8 16 2.61 38
Anterior limb internal capsule Right 22 16 7 2.96 191
Left −23 11 14 2.64 2,252
Posterior limb internal capsule Right 15 −15 14 3.18 9,387
Left −22 −15 17 3.37 2,252
Retrolenticular part of internal capsule Right 33 −36 14 2.49 30
Anterior thalamic radiation Right 18 −14 12 3.18 9,387
Left −16 −5 8 2.68 2,252
Posterior thalamic radiation Left −35 −46 13 2.97 343
Superior longitudinal fasciculus Right 45 −21 44 2.89 179
Left −38 −36 31 3.62 310
Inferior longitudinal fasciculus Right 35 −70 −3 3.05 85
Left −49 −17 −17 2.58 293
Inferior fronto‐occipital fasciculus Right 21 −87 17 3.01 45
Forceps minor Right 18 48 −2 3.26 9,387
Left −16 43 21 3.04 875
Forceps major Right 19 −85 17 2.4 40
Genu of corpus callosum Left −14 37 9 2.4 875
Splenium of corpus callosum Left −23 −85 1 2.55 30
Uncinate fasciculus Left −25 39 −1 2.79 291
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The table only reports Z‐values >2.60 (P < 0.05, corrected for multiple comparisons).

Figure 3.

Figure 3

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Between‐group contrast in voxel‐wise analysis. The cluster shows significantly increased FA in the math‐gifted group compared with the controls (P < 0.05 corrected for multiple comparisons), after adjustment for IQ. Significant clusters are superimposed on the mean FA image in MNI space. The color bar shows the Z‐score for this contrast. Increased FA was observed bilaterally in the prefrontal lobes, cortico‐striatal tracts, and fronto‐parietal fasciculus in math‐gifted adolescents.

Figure 4.

Figure 4

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Between‐group differences in the atlas‐based parcellation analysis in native space. The graphs represent anatomical regions in which the math‐gifted group (in red) showed significantly more FA than controls (in blue), after adjustment for the potential effects of IQ.

To ensure that IQ effects are not confounded with those of the construct of “mathematical giftedness,” we also prepared an IQ‐matched subsample with high‐IQ controls (IQ = 108–137, n = 9) and math‐gifted subjects (IQ = 112–149, n = 13). No significant between‐group difference in IQ scores was found. In this subsample, the “Gifted” group still showed significantly higher FA in the same tracts as in the analysis reported above, and in the left uncinate and right posterior corona radiata.

To verify potential gender‐ and age‐related effects on FA, we used an ANCOVA model including “Age” as a continuous variable and “Gender” as a factor. The introduction of “Age” as a continuous covariate led to a nonsignificant effect in the ANCOVA model, and the main effect of “Group” did not change. In the same way, the introduction of the factor “Gender” in the ANCOVA model (together with the interactions Gender × IQ and Gender × Group) in both voxelwise and ROI analyses did not reveal a significant effect of Gender or the Group × Gender interaction in any tract. As an additional verification, we repeated the whole analysis for the male subsample only, and the results remained unchanged. Furthermore, after checking potential interactions such as “Group × Gender” and “IQ × Gender,” we did not observe any significant effect.

Consequently, because age‐ and gender‐related effects were not significant and did not affect the overall results, we decided to exclude them for the sake of model parsimony, which is an important consideration when sample size is reduced.

DISCUSSION

We investigated the association between math‐giftedness/IQ and the microstructure of white matter tracts in a sample composed of math‐gifted adolescents and age‐matched controls. To our knowledge, this study is the first to assess adolescents with math‐giftedness using DTI.

We observed that IQ score correlates positively with FA of the corpus callosum. Math‐gifted subjects showed increased FA independently of their IQ in fronto‐parietal and fronto‐striatal association tracts and in some regions of the corpus callosum.

As for the neurobiological substrate of math‐giftedness, the organization of a math‐gifted brain can involve functional bilateralism and enhanced fronto‐parietal connectivity [Singh and O'Boyle, 2004]. The fronto‐parietal network and enhanced interhemispheric connectivity have been associated with high‐level intelligence [Gray and Thompson, 2004; Gray et al., 2003; Jung and Haier, 2007], mathematical skills [Tsang et al., 2009; van Eimeren et al., 2010], and creativity [Finke, 1996; Takeuchi et al., 2010]. A previous fMRI study from our group with the same math‐gifted sample supported this model and provided new fMRI evidence from executive functioning and two complexity levels of fluid reasoning tasks [Desco et al., 2011].

Interhemispheric White Matter Microstructure and High‐Level Intelligence

We found in the whole sample a positive correlation between IQ and FA in much of the corpus callosum and in some frontal and parietal association tracts. Consistent with our hypothesis, heightened anatomical connectivity in the corpus callosum seems to correlate with higher intelligence. The corpus callosum is the most important structure for communication of information between homologous regions of the cerebral hemispheres [Hofer and Frahm, 2006]. The corpus callosum microstructure is associated with hemisphere dominance in healthy people [Haberling et al., 2011], working memory processing [Fryer et al., 2008], and intelligence [Hutchinson et al., 2009; Yu et al., 2008]. Besides the effect of IQ on the corpus callosum described above, we also observed an additional independent effect of math‐giftedness localized in the genu and splenium. The prefrontal cortices are interconnected along the forceps minor and genu, the most anterior part of the corpus callosum. Increased white matter organization in the prefrontal part of the corpus callosum might be related to improved high‐level cognitive processes such as fluid reasoning, executive functioning, and working memory [Carpenter et al., 2000; Christoff et al., 2001; Colom et al., 2003; Curtis and D'Esposito, 2003; D'Esposito et al., 1995; Gray et al., 2003; Klingberg et al., 1997; Kroger et al., 2002; Newman et al., 2003; Prabhakaran et al., 1997; Smith and Jonides, 1999]. Increased FA in the corpus callosum in atypical hemispheric dominance (bilateralism) and high IQ might enhance the capacity for information processing between hemispheres.

The greater abilities in visuospatial processing shown by math‐gifted subjects might be related to increased FA in the forceps major and splenium, which connect both the right and the left parieto‐occipital cortices [Fryer et al., 2008; Harris et al., 2000.; Just et al., 2001; Klingberg, 2006; Knauff et al., 2002; Owen et al., 1996; Todd and Marois, 2004; Van den Heuvel et al., 2003]. The development of inter‐parietal white matter junction is also important for mathematical skills [Cantlon et al., 2011; Matejko et al., in press; Tsang et al., 2009]. Enhanced white matter organization in the frontal and parietal lobes might underlie high‐level cognition with improved visuospatial working memory, mathematical, and executive capabilities.

The between‐group differences observed in the FA of the corpus callosum could represent a facilitated communication between hemispheres and might lead to enhanced functional bilateralism [O'Boyle et al., 1995, 1991; Singh and O'Boyle, 2004]. The activation of both hemispheres, as observed in previous fMRI studies [Desco et al., 2011], and the interactions between them are essential for integration of information and complex logical reasoning [Dehaene et al., 1999]. Enhanced integration of information between hemispheres in children with high intellectual capabilities might be due to corpus callosum microstructure [Prescott et al., 2010].

Intrahemispheric White Matter Microstructure in Math‐Giftedness

Math‐gifted subjects showed increased FA bilaterally in tracts connecting the frontal lobes with the temporo‐parietal cortices, after adjustment for the IQ effect. Data from previous functional neuroimaging studies [Christoff et al., 2001; Kroger et al., 2002; Newman et al., 2003; Prabhakaran et al., 1997] and DTI studies [Klingberg, 2006; Schmithorst et al., 2005] converge toward a bilateral fronto‐parietal network as a neural substrate of enhanced information processing and intelligence [Jung and Haier, 2007]. Increased white matter organization in frontal lobe tracts supports enhanced high‐level cognition functions, which contribute to improved cognitive performance in working memory, fluency, and executive functioning [Burzynska et al., 2011; Nagy et al., 2004]. The increased white matter organization of the frontal lobe in math‐gifted adolescents could be one of the neurobiological traits underlying math giftedness.

The major tract that connects frontal lobes and temporo‐parietal regions is the superior longitudinal fasciculus, which is crucial for integration of information within hemispheres. The math‐gifted group showed higher white matter integrity in regions of the superior longitudinal fasciculus adjacent to the inferior parietal lobule. In our previous fMRI study with this study sample, we reported that major between‐group differences appeared with more complex tasks, mainly in the frontal cortex and right inferior parietal lobule [Desco et al., 2011]. The inferior parietal lobule (BA40) has been associated with multimodal information processing, mental imagery [Wolbers et al., 2006], and creativity [Finke, 1996; Takeuchi et al., 2010]. Recent neuroimaging literature (using either fMRI or DTI) showed the crucial role that parietal lobules play in mathematical processing, such as arithmetical or calculation tasks [Cantlon et al., 2011; Dehaene et al., 2003; Hoppe et al., 2012; Matejko et al., in press; Tsang et al., 2009; van Eimeren et al., 2008, 2010].

Some studies of the neurobiological traits of math‐giftedness show the anterior cingulate gyrus to be a key structure [O'Boyle, et al., 2005; Prescott et al., 2010]. Our results did not show a group effect in this region. Functional connectivity studies could reveal statistically correlated regions with few direct structural connections between them. Functional correlations can be mediated by indirect structural connections (i.e., via a third region). Therefore, the potential role played by the anterior cingulate gyrus as a hub in functional connectivity does not necessarily lead to increased FA.

Mathematical thinking requires contributions from both academic and creative capabilities, and gifted subjects showed neurobiological characteristics that encompassed these requirements. The greater activation of the fronto‐parietal network observed in our previous study [Desco et al., 2011] was consistently accompanied by increased white matter organization in anatomical connections between the frontal and the parietal lobes.

Math‐Giftedness and IQ

Math‐giftedness can be assumed to partially correlate with a high IQ, although it does not seem to be the same construct [Kalbfleisch, 2004]. Our results suggest that increased anatomical intrahemispheric connectivity in the fronto‐parietal network may underlie math‐giftedness, independently of IQ, which in turn seems more related to interhemispheric connectivity. These findings were replicated in the comparison of the math‐gifted subjects with a subsample of nine high IQ‐matched controls. Both the frontoparietal and frontostriatal white matter tracts are associated with “giftedness,” and FA of the genu of the corpus callosum was moderately correlated with IQ in this subsample. This replication of the results, albeit with a lower number of cases, shows the robustness of the detected effects. The findings support the existence of a different substrate for “IQ” and “Giftedness.”

A functional connectivity study using Structural Equation Modeling performed by Prescott et al. [2010] reported results that were consistent with ours: heightened intrahemispheric frontoparietal connectivity together with enhanced interhemispheric frontal connectivity. Furthermore, our results suggest the existence of neurobiological correlates underlying the enhanced connectivity in gifted subjects and segregate the effect of “IQ” and “Giftedness” per se.

Our findings support that “IQ” and “Giftedness” are different concepts. We suggest that gifted adolescents, regardless of the advantages of their high IQ, have a different brain structure that is more associated with an innovative way of processing information during complex cognitive tasks or novel problem solving. Increased FA in frontoparietal and frontostriatal networks was not observed in controls with a similar IQ to that of the gifted group.

Math‐gifted subjects were selected for the ESTALMAT program, which in comparison with SAT‐Math emphasizes problem solving by creative thinking rather than using concepts and previous expertise and knowledge gained at school. Although the neural substrate that underlies the relationship between math‐giftedness and creativity is still unclear, “creative thinking” is implicit in the concept of Giftedness. Indeed, the neurobiological and related cognitive characteristics of gifted people have been combined in a neuropsychological model of high creative intelligence [Geake and Dodson, 2005; Geake and Hansen, 2005]. This model of creative intelligence features fluid analogizing, analogies with several plausible but no necessary correct solutions [Hofstadter, 1995, 2001], as the vehicle by which dynamic information processing occurs in the brain. Creative thinking has also been related to enhanced interhemispheric and intrahemispheric white matter organization along the corpus callosum and fronto‐parietal areas [Takeuchi et al., 2010]. Connections between the prefrontal lobes and basal ganglia are thought to enable key processes of creativity, such as problem solving [Kalbfleisch, 2004; Takeuchi et al., 2010]. Some authors reported a link between intelligence and creativity [Carroll, 1993; Jung et al., 2010; Sternberg, 2000, 2001]. Jung et al. observed a correlation between FSIQ and the composite creativity index in divergent thinking [Jung et al., 2010]. The enhanced white matter organization in fronto‐parietal regions observed in the math‐gifted group would facilitate processing of information that is crucial for higher intellectual capabilities and for creativity.

Our study has several limitations. With regard to cognitive characterization of the two groups, the selection of math‐gifted subjects was based solely on their performance in the ESTALMAT admission tests, which examine additional cognitive abilities, especially creativity (see “Methods”). Consequently, the definition of math‐giftedness used in this study is based on the criteria established by ESTALMAT. As is the case for the definition of IQ, our definition of “giftedness” in this work is purely operational. Both depend on the outcome of the (very different) tests used to assess them. Most of the studies cited in this article reported conclusions about math‐gifted adolescents selected using other tests, such as SAT‐Math, which assess pure mathematical skills.

Because the controls never took the ESTALMAT tests, we cannot rule out the possibility that some of them are math‐gifted. However, we can realistically assume that their proportion in our sample is negligible, given the low number of math‐gifted subjects in the population.

In the statistical analyses, we acknowledge that linear covariance in the ANCOVA model may be subject to limitations, because the groups have different IQ ranges. Nevertheless, a verification run using IQ‐matched subanalyses showed the same results.

A further limitation of the study is that the groups were not matched by gender. Developmental differences have been observed in the brains of boys and girls [Tang et al., 2010]. As an additional verification, we repeated the whole analysis for the male subsample only, and the results remained unchanged. In fact, after checking potential interactions such as “Group × Gender” and “IQ × Gender,” we did not observe any significant effect. We used an estimated IQ, which is only an approximation of the FSIQ. However, this estimated score has been validated for the normal population (see “Cognitive Assessment” in “Methods”). The relationship between math‐giftedness and creativity warrants further assessment in neuroimaging studies.

CONCLUSIONS

Our results suggest that IQ and math‐giftedness correlate differently with white matter microstructure. In the whole sample, IQ correlated with FA positively in a large part of the corpus callosum. Moreover, math‐gifted subjects showed higher FA than controls (independently of IQ) in fronto‐parietal and fronto‐striatal association tracts, as well as in the forceps of the corpus callosum.

Our results support the hypothesis that white matter organization in math‐gifted adolescents is different both in fronto‐parietal tracts and in the corpus callosum. This finding could explain the functional bilateralism in fronto‐parietal networks observed in math‐gifted subjects in previous fMRI studies. Math‐gifted subjects are qualitatively and quantitatively different, not only in terms of brain activation but also in terms of white matter organization in brain regions that underlie high‐level cognitive processes and creativity.

ACKNOWLEDGMENTS

All the authors wish to express our appreciation of the invaluable contribution of the late Dr. Santiago Reig to this work.

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