NeuroImage 52 (2010) 358–363

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Structure-function relationships underlying calculation: A combined diffusion tensor imaging and fMRI study L. van Eimeren a, R.H. Grabner b, K. Koschutnig c, G. Reishofer d, F. Ebner c, D. Ansari a,⁎ a

Numerical Cognition Laboratory, Department of Psychology, University of Western Ontario, Ontario, Canada Swiss Federal Institute of Technology (ETH), Zurich, Switzerland Division of Neuroradiology, Medical University of Graz, Graz, Austria d Division of MR Physics, Medical University of Graz, Graz, Austria b c

a r t i c l e

i n f o

Article history: Received 12 December 2009 Revised 26 March 2010 Accepted 1 April 2010 Available online 9 April 2010 Keywords: DTI fMRI Structure–function relationship Calculation Angular gyrus Superior corona radiata

a b s t r a c t Both neuropsychological and functional neuroimaging studies have identified brain regions that are critical for the neurocognitive processes related to the calculation of arithmetic problems. In particular, the left angular gyrus (lAG) has been repeatedly implicated in arithmetic problem solving and found to be most activated during the retrieval of arithmetic facts. While significant progress has been made in determining the functional role of specific grey matter areas underlying calculation, very little is known about the relationship between these activated regions and their underlying white matter structures. In this study, we collected both diffusion tensor imaging (DTI) and functional magnetic resonance imaging (fMRI) data while participants performed a mental arithmetic task. Fractional anisotropy (FA) values were extracted from predefined, hypothesis-driven, white matter regions and correlated with fMRI activation values, which were extracted from anatomically defined grey matter regions. Results indicated structure–function relationships on multiple levels. Specifically, a link between the integrity of the left superior corona radiata (SCR) and neural activity in the lAG during calculation was observed, which was found to be particularly strong for problems that have a high probability of being solved via the retrieval of arithmetic facts (problems with a relatively small problem size). The findings reported provide a link between functional activation and structural integrity of grey and white matter regions in the left temporoparietal cortex, thereby contributing to our understanding of the role of both the function and structure of this brain region in calculation. © 2010 Elsevier Inc. All rights reserved.

Introduction Neuropsychological and neuroimaging studies have established a strong association between neural activation in the left angular gyrus (lAG) and arithmetic problem solving (for a review, see Ansari, 2008; Zamarian et al., 2009). Considering that the lAG has been frequently associated with language processing (for a review, see Price, 2000), it has been argued that this association reflects the lAG's role in the retrieval of verbally stored arithmetic facts (for a meta-analysis, see Dehaene et al., 2003). Evidence supporting this notion comes from results showing (a) greater activation in the lAG for exact compared to approximate calculation (Dehaene et al., 1999), (b) investigations revealing increases in the activation of the lAG after training on arithmetic facts (e.g., Delazer et al., 2003; Ischebeck et al., 2006), (c) greater lAG activation during the processing of small (compared to large) arithmetic problems typically solved through fact retrieval (Grabner et al., 2007, 2009a; Jost et al., ⁎ Corresponding author. Department of Psychology and Graduate Program in Neuroscience, University of Western Ontario, Ontario, Canada N6G 2K3. Fax: +1 519 661 3961. E-mail address: [email protected] (D. Ansari). 1053-8119/$ – see front matter © 2010 Elsevier Inc. All rights reserved. doi:10.1016/j.neuroimage.2010.04.001

2009), and (d) an association between lAG activation and self-reported use of retrieval strategies during arithmetic problem solving (Grabner et al., 2009b). In addition, it has been shown that activation of the lAG and the left supramarginal gyrus during mental arithmetic increases over developmental time (Rivera et al., 2005), suggesting that this region's involvement in mental arithmetic is the outcome of a developmental trajectory that presumably involves an increasing use of retrieval strategies with chronological age. While significant progress has been made in understanding the functional role of grey matter regions such as the lAG in calculation, little is known about the relationship between these activated cortical regions and the underlying white matter structures. These structures may be involved in mediating grey matter function during cognitive processes, such as calculation, and thus the study of white matter structures and their association with the activation of grey matter structure may add to our understanding of well-documented neural networks subserving the processing of mental arithmetic problems. One approach to address this outstanding question is to examine the extent to which variability in activation of task-related cortical areas (such as the lAG during calculation) is related to white matter structures in close anatomical proximity.

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The use of diffusion tensor imaging (DTI) has become an increasingly effective tool for investigating white matter microstructure and its relation to cognitive functions (e.g., Beaulieu et al., 2005; Klingberg et al., 2000; Nagy et al., 2004; Niogi and McCandliss, 2006; van Eimeren et al., 2008) as well as functional connectivity (e.g., Koch et al., 2002; van den Heuvel et al., 2009). This non-invasive neuroimaging method is based on measuring water diffusion along the myelinated axons and the directionality of this diffusion (i.e., anisoptropy) within a given voxel. In particular, the normalized measurement of fractional anisotropy (FA) gives indices of white matter integrity by representing the degree of constrained water diffusion along the axons and the myelin. The greater the directionality and the less isotropic the diffusion is, the higher the FA value (range 0–1) will be. A large body of DTI data has revealed the importance of left-lateralized white matter structures for reading development (Ben-Shachar et al., 2007). In particular, both developmental and pathological reading studies have revealed a reliable association between reading achievements and two white matter tracks, the left superior corona radiata (lSCR; Deutsch et al., 2005; Klingberg et al., 2000; Niogi and McCandliss, 2006; Odegard et al., 2009) and the left superior longitudinal fasciculus (lSLF; Beaulieu et al., 2005; Deutsch et al., 2005; Niogi and McCandliss, 2006). This correlation between white matter integrity and individual differences in reading ability suggest a contributing role of these fiber tracts to reading competencies by possibly strengthening the connectivity between language-related grey matter areas. In addition, some recent studies (Barnea-Goraly et al., 2005; Lebel et al., 2010; van Eimeren et al., 2008) suggest that the integrity of leftlateralized white matter structures is also related to mathematical cognition. Barnea-Goraly and colleagues (2005) observed that individual differences in the arithmetic performance of children with velocardiofacial syndrome (VCFS, a genetic syndrome causing significant impairments in non-verbal skills, such as visuo-spatial cognition and mathematical abilities) are correlated with FA values in left parietal regions. These white matter clusters were found adjacent to grey matter regions of the left intraparietal sulcus (IPS), which has been consistently associated with number processing in functional neuroimaging studies (for a review and meta-analysis, see Dehaene et al., 2003). In a more recent study, Lebel and colleagues (2010) investigated the white matter correlates of mathematical abilities in children with fetal alcohol spectrum disorder (FASD) and revealed that the mathematical abilities of these children was found to be correlated with four white matter clusters two were within the left parietal regions. However, it is important to note that findings from both studies cannot be readily generalized to the normal developing brain as only individuals with developmental disorders with local and/or diffuse brain abnormalities were investigated. In a study of typically developing children, van Eimeren and colleagues (2008) revealed that the FA of several left-lateralized white matter microstructures was significantly related to individual differences in mathematical abilities. Their approach was to relate individual differences in FA of well-defined white matter structures to individual differences in two standardized measures of mathematical achievement (Numerical Operation and Mathematical Reasoning – subtests of the Wechsler Individual Achievement Test). Their main finding suggested that the lSCR was related to both achievement scores, indicating a more general role of the SCR in the neural network underlying arithmetic processing. Because of a previously established strong association between the lSCR and reading ability (Ben-Shachar et al., 2007), van Eimeren et al. (2008) discussed their findings as possible evidence for a common white matter network underlying both reading abilities and mathematical achievements. It could therefore be proposed that the lSCR is related to verbally mediated processes in mental arithmetic, such retrieval of arithmetic facts from long-term memory, which is thought to be subserved by the lAG (Grabner et al., 2009a,b). More recently, a study by Tsang et al. (2009) investigated the relationship between the anterior portion of the superior longitudinal

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fasciculus (aSLF) and both approximate and exact arithmetic. The authors found that FA values in the left aSLF correlated with approximate but not exact addition or simple math facts. Against this background, it was concluded that connections between the inferior parietal and inferior frontal cortex via the aSLF seem to mediate neuronal processes that are important for approximate, but not exact, mathematical processing performance. The existing data, therefore, might suggest that while the aSLF is related to approximate number processing, the left SCR is related to numerical processing that requires the computation of exact answers. One way of further constraining the precise roles played by the lSCR and the lSLF in arithmetic processing is to assess the degree with which between-subjects variability in the integrity of this structure (individual differences in FA) is correlated with individual differences in the degree with which participants activate the lAG during a calculation task. In other words, it can be hypothesized that if individual differences in the integrity of the lSCR or lSLF are related to the processing of exact mental arithmetic, there should be a relationship between individual differences in the FA of these white matter microstructures and variability in the activation of the lAG measured while participants solve arithmetic problems. Furthermore, against the background of findings suggesting that the lAG is particularly strongly activated during arithmetic fact retrieval (Grabner et al., 2009a,b) and the lSCR's strong association with reading competencies, we anticipated this structure–function correlation to be strongest when its FA values are correlated with fMRI parameter estimates for problems of a relatively small problem size. This hypothesis is based on the finding that arithmetic problems with a relatively small problem size are frequently solved with the use of retrieval strategies (Campbell and Xue, 2001; LeFevre et al., 1996). Therefore, by looking at relationships between FA and fMRI parameters for small and large problem sizes separately, one can assess the extent to which any relationships depend on the type of problem and the probability of retrieval. Furthermore, the association between the SLF and approximate addition but not exact addition reported by Tsang et al. suggests that this white matter microstructure is unlikely to be associated with processes related to exact calculation and the retrieval of arithmetic facts. Accordingly, we hypothesize that there should be no association between the FA values of the SLF and the fMRI parameters of the lAG. Because the SLF has been associated with approximate but not exact arithmetic, it serves as stringent control white matter microstructure for the examination of any specific relationship between activation of the lAG during exact mental arithmetic and variability in participants' FA of the lSCR. To investigate these hypotheses, both DTI and fMRI data were collected from a group of healthy adults. The fMRI data were acquired while participants solved arithmetic problems of all four basic operations (i.e., addition, subtraction, multiplication and division). Parameter estimates (beta values) of the functional data acquired during calculation were extracted from three left-lateralized regions. These regions have been repeatedly implicated in neuroimaging studies of calculation (e.g., Dehaene et al., 1999, 2003; Delazer et al., 2003; Kong et al., 2005; Menon et al., 2000a,b; Simon et al., 2002; Stanescu-Cosson et al., 2000): (1) angular gyrus (AG), associated with retrieval processes; (2) superior parietal lobe (SPL), associated with numerical processing and attention; (3) inferior frontal opercularis (InfFrOp), associated with executive processes involved in calculation. To provide information of the specificity of any left-lateralized structure–function relationship, fMRI beta values of these anatomical regions were also extracted from the right hemisphere. While all of the above regions have been implicated in processes related to calculation, our primary interest was in the relationship between the lAG and the underlying white matter microstructures, given the central role of this region in previous studies (Dehaene et al., 2003; Delazer et al., 2003; Ischebeck et al., 2006; Grabner et al., 2007; Grabner et al., 2009a,b).

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Given previous findings (van Eimeren et al., 2008) relating the white matter integrity of the lSCR with both reading and calculation, functional anisotropy (FA) values were extracted from the left and the right SCR. In addition, FA values were also extracted from the left and the right SLF. As discussed above, the SLF has recently been associated with approximate but not exact arithmetic (Tsang et al., 2009) and thus provides another means to constrain the specificity of any relationships between the lSCR and activation of the lAG during exact calculation. In order to investigate our hypotheses, FA values from the SCR and the SLF were correlated with fMRI parameter estimates extracted for all arithmetic problems, as well as separate fMRI beta values for problems with relatively small and large problems sizes. Materials and methods Participants Nineteen male adults (mean: 26.4 years, SD: 2.97 years) were selected from a larger sample of the aforementioned study by Grabner et al. (2009a,b), who investigated the neural underpinnings of retrieval and procedural strategies during calculation. All participants were healthy, right-handed and had normal or corrected-to-normal vision. The study was approved by the local ethics committee (Medical University of Graz, Austria). Materials and procedure One hundred sixty arithmetic problems were presented in a pseudo-randomized order as part of an event-related fMRI design (8 runs with 20 problems each). The problems were based on the procedures described in Campbell and Xue (2001). All four arithmetic operation types were included, composed of 20 small and 20 large problems each. Only problems with integers between 2 and 9 were used. Small problems in addition and multiplication were defined as problems with the product smaller than 25 (e.g., “8 + 2”), and large problems with products larger than 25 (e.g., “6 × 8”). In subtraction and division, small and large problems were defined on the basis of the inverse relationship to addition and multiplication, respectively. More information on the arithmetic problems can be found in Grabner et al. (2009a,b). Each problem was presented for 2 s, followed by the presentation of the correct result and a distractor (duration 2 s). Participants had to indicate the position of the solution by button press of the corresponding index finger. The side of the correct answer was counterbalanced throughout the experiment. After the presentation of the response options, an inter-trial interval of 1–5 s (jittered in 1 s steps across the problems) was presented. Each run started with the presentation of the number of the run (3 s) and a fixation period of 25 s; a similar fixation period was presented at the end of each run. fMRI acquisition and analysis The functional imaging was performed in a 3.0 T Tim Trio system (Siemens Medical Systems Erlangen, Germany) using an eight-channel head coil. In the experiment, a single shot gradient echo (EPI) sequence (TR = 2000 ms, TE = 30 ms, 90° flip angle, matrix size = 64 × 64, slice thickness = 3 mm, spatial resolution = 3 mm× 3 mm) was used. In total, 787 functional volumes (first 2 were discarded) with 30 transverse slices (3 mm thickness, 0.75 mm gap) were acquired in descending order. fMRI data was analyzed using SPM5 (Wellcome Department of Imaging Neuroscience, London, UK). The functional data of each participant were motion-corrected, spatially normalized into the standard MNI space (Montreal Neurological Institute) and smoothed using a Gaussian kernel of 9 mm FWHM.

fMRI beta values were extracted from each anatomically defined bilateral region of interest (using Anatomical Automatic Labeling atlas; Tzourio-Mazoyer et al., 2002) for all four arithmetic operations and two levels of problem size. As outlined in the introduction, the following regions of interest (ROIs) were selected: (1) angular gyrus (AG), (2) superior parietal lobe (SPL), and (3) inferior frontal opercularis (InfFrOp). DTI acquisition and analysis Diffusion tensor magnetic resonance imaging was acquired in the same session as the functional imaging. Twelve gradient directions with three repeats were measured at an average b = 1000 s/mm2, 3 images with b = 0 s/mm2, 46 axial slices (3 mm thickness, no gap) with 75× 75 resolution, and a field of view of 225 mm resulting in a pixel size of 3 mm. All preprocessing steps were conducted using DTIStudio software (S. Mori, John Hopkins University) controlling for motion or image artifacts during the DTI sequence only. Fractional anisotropy (FA) maps were then extracted along with average non-diffusion weighted images (b = 0 s/mm2), average diffusion coefficient images (ADC, b = 1000 s/mm2) and lastly, primary eigenvectors of the diffusion tensor. As specific white matter regions have been previously associated with mathematical cognition (Barnea-Goraly et al., 2005; van Eimeren et al., 2008), a region of interest (ROI) approach was used. This approach avoids the potential disadvantages of the voxel-based approaches, such as the need for larger sample sizes and artifacts caused by spatial normalization or smoothing techniques (Jones et al., 2005; Niogi et al., 2007), which often make it impossible to distinguish between differences in microstructure and those attributable to variability in gross anatomical shape and size. Regions were selected on the basis of a previous finding outlining the SCR as a key white matter region associated with general arithmetical abilities (van Eimeren et al., 2008) and the SLF having been previously associated with approximate but not exact arithmetic (Tsang et al., 2009). Each of these white matter tracks was selected bilaterally in each individual brain using the Reproducible Objective Quantification Scheme (ROQS; Niogi et al., 2007), which runs with Interactive Data Language v6.0 (IDL, Research Systems Inc., Boulder, CO). ROQS is a process that segments white matter structures on the basis of a userdefined seed pixel within one axial slice. Hence, to produce an FA value which represents the tract at large and not of a single slice, we selected ROIs in 4 separate but adjacent axial slices and averaged their extracted FA values. In other words, the FA value of each bilateral tract (SCR left and right; SLF left and right) is the mean of four FA values that were extracted from ROIs, which lay on top of each other. Results Spearman's correlations were run separately for each bilateral white matter area, resulting in two analytical steps (Table 1). The extracted mean FA values for each ROI were correlated with the fMRI beta values for all arithmetic operations (AAO), small problem sizes (SPS) and large problem sizes (LPS). Significant positive correlations were found between the FA values of the lSCR and beta values of the lAG for activations that are associated with all arithmetic operations (AAO) (r = 0.526, p b 0.05) as well as activations associated with solving problems of a small problem size (SPS) (r = 0.614, p b 0.01) (see Fig. 1). In addition, we found that the FA values of the right SCR were correlated with beta values associated with activation for small problem sizes (SPS) in the lAG (r = 0.530, p b 0.05). No other significant correlations between any FA values of white matter and any beta values of grey matter were found to be significant (see Table 1 for all correlational data).

0.06 0.13 −0.23 0.11

†

*p b .05. p b 0.1. p = .06.

SLF

$

LPS SPS

0.05 −0.24 −0.25 0.002 −0.04 −0.04 −0.30 0.37 −0.37 −0.15 −0.17 −0.08 −0.21 −0.08 −0.22 0.13 −0.36 −0.12 −0.25 0.02 −0.04 0.13 −0.03 −0.03 0.07 −0.09 0.07 −0.08 −0.02 0.09 0.01 −0.05 −0.18 0.11 −0.03 −0.13 0.03 0.15 −0.03 −0.1 −0.17 0.16 −0.08 −0.12 0.22 0.21 −0.25 −0.15 0.44† 0.29 0.15 0.09

0.21 0.16 −0.29 −0.27 0.61$ 0.53* 0.14 −0.08 0.53⁎ 0.34 0.22 −0.09 left right left right SCR

Fractional Anisotropy values

361

Discussion

0.31 0.22 −0.18 −0.38

right InfFrOp

AAO LPS SPS

left InfFrOp

AAO LPS SPS AAO

right SPL

LPS SPS AAO

left SPL

LPS AAO

SPS right AG

AAO

LPS SPS left AG

fMRI beta weights

Table 1 Spearman's correlation coefficiants of the Fractional Anisotropy (FA) values of two bilateral white matter tracts and the Beta weights for all arithmetic operations (AAO), small problem sizes (SPS) and large problem sizes (LPS) extracted from three bilateral grey matter regions of interest.

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Over the last decades functional neuroimaging studies of calculation have significantly added to our understanding of the neural mechanisms underlying calculation (for reviews, see Ansari, 2008; Dehaene et al., 2003; Zamarian et al., 2009). In addition to the growing number of neuropsychological and functional neuroimaging studies of the neurocognitive processes underlying calculation, there has been some recent work investigating the structural underpinnings of mathematical cognition through an examination of the integrity and organization of white matter (Barnea-Goraly et al., 2005; Tsang et al., 2009; van Eimeren et al. 2008; Lebel et al., 2010). However, work on the functional role of grey matter structures in calculation, on the one hand, and investigations of the relationship between white matter and individual differences in mathematical competence, on the other hand, have been conducted in relative isolation, even though the relationship between brain function and structure is one of the fundamental concerns of current neuroscience and cognitive neuroscience research (Toosy et al., 2004). The present study set out to relate functional neuroimaging data to measures of white matter integrity in order to establish a direct link between these largely separate approaches. Specifically, the goal of this study was to explore the possibilities of combining functional magnetic resonance (fMRI) data with diffusion tensor imaging (DTI) data to better understand the neural mechanisms that underlie mathematical cognition. With a region of interest approach (all anatomically defined) that was based on previous findings in both fMRI (Dehaene et al., 2003) and DTI data (van Eimeren et al., 2008), we demonstrated that activation differences in the lAG during calculation are related to individual differences in the FA of the lSCR. In other words, higher white matter integrity of the lSCR is associated with stronger activation of the lAG measured while participants solve arithmetic problems. In addition, the FA values of the left and right SCR were positively related to beta values in the lAG for arithmetic processing of small, but not large problems. It should be noted here that ROIs for both the extraction of the DTI and fMRI data were based on anatomy alone and are thus completely independent methods for ROI definition. The SCR has been previously associated with individual differences in mathematical competence in children. Specifically, van Eimeren et al. (2008) explored whether there was a relationship between the integrity of well-known white matter microstructures and individual differences in children's mathematical competence. The present study extends these findings by revealing that the lSCR is correlated with the relative degree of activation in the lAG during arithmetic problem solving. In other words, individuals with greater integrity of the lSCR white matter are also individuals who exhibit relatively greater activation of the AG during calculation. But the present findings do not merely reveal a very general association between individual differences in lSCR integrity and activation of the lAG but also suggest that this relationship might be mediated by arithmetic problem size and, thus, by the type of strategy used (retrieval vs. procedural). More specifically, while the lSCR correlates with activation differences of the lAG during arithmetic problem solving of small problem size, the correlation is non-significant for problems with a large problem size). However, it is important to note that the correlation of the lSCR and activation in the lAG for activation estimates extracted for problems of a relatively large problem size can be considered to be marginally (p = .06) significant. Therefore, any discussion of the difference in correlation between lSCR integrity and activation during small and large problems needs to be undertaken with caution. In view of this, it should be highlighted that the strongest finding in the present study is that there is a relationship between activation of the lAG (for all problem types) and individual differences in the FA of the lSCR.

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Fig. 1. Structure–function relationship between the left superior corona radiata (SCR) and the left angular gyrus (AG) (anatomical information in Panel A) for activations related to all arithmetic operations and specifically to arithmetic problems of a smaller problem size. Both scatterplots can be viewed separately in Panel B. The graph represents the monotonic function, which was plotted given that Spearman's correlations do not assume a linear relationship between variables.

While small problems are indeed mainly solved by fact retrieval, as outlined by Campbell and Xue (2001), large multiplications also have a very high probability of retrieval use. In other words, the category of large problems in the current paper contains a subset of large multiplication problems that have a high probability of retrieval. Thus, the marginal significant correlation between lSCR and lAG for the large problems could be explained by the application of a retrieval strategy during the calculation of a subset of the problems within the large problem size category. An extensive review of the literature suggest that the lAG has been most strongly associated with the processing of small problem sizes and fact retrieval processes during mental arithmetic (Dehaene et al., 1999, 2003; Delazer et al., 2003; Grabner et al., 2007, 2009a; Ischebeck et al., 2006; Jost et al., 2009; Rivera et al., 2005; Zamarian et al., 2009). Therefore, the present data may point to a relationship between the lSCR and lAG that is somewhat specific for processing of mental arithmetic with a relatively small problem size and therefore a higher probability of being retrieved from memory. However, whether or not the relationship between variability of the integrity of the lSCR and activation of the lAG is specific for retrieval of arithmetic fact must await further investigations that more directly measure the retrieval of arithmetic fact. Although problems with a small problem size have been associated with retrieval, the distinction between small and large problems remains an indirect measure of fact retrieval. It might be contended that it is not all together surprising that individuals who have greater white matter integrity also show greater levels of activation in grey matter structures. However, if such a

general relationship existed, the FA values in the SLF should also have been found to correlate with the amount of activation in the lAG during calculation. Yet, none of the correlations between the SLF and grey matter regions were found to be significant. Thus, the relationship between structure and function is specific to the SCR and the lAG and may point to different roles of SCR and SLF in exact and approximate number processing, respectively. Furthermore, white matter microstructure of the lSCR is specifically related to activation of the lAG as FA values in the lSCR were not found to be significantly correlated with fMRI parameter estimates for calculation from any of the other parietal or frontal ROIs. As noted in the introduction of this paper, the lSCR has been associated with reading abilities (Deutsch et al., 2005; Klingberg et al., 2000; Niogi and McCandliss, 2006; Odegard et al., 2009). The current findings, together with those of van Eimeren et al. (2008) showing an association between the lSCR and calculation, may suggest that the lSCR is a common structural correlate for reading and arithmetic. Indeed, it has frequently been suggested that the retrieval of arithmetic facts may rely on phonology (Simmons and Singleton, 2008). Evidence consistent with this hypothesis was presented in a recent behavioral study in which an association between phonological processing and the solving of arithmetic problems of a small problem size was found in a group of children in 4th and 5th grade (DeSmedt et al., 2010). The present findings, however, cannot directly speak to the relationships between reading and mental arithmetic and the potential relationship of both with the structural integrity of the SCR. In future studies, functional activation of the lAG should be

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measured during both calculation and reading tasks to investigate the relationship between these two cognitive processes and their structural correlates more directly. It may also be useful to look at operations-specific effects (calculating structure–function relationships separately for each of the four arithmetic operations). While in the present study fMRI was measured during the calculation of problems from all four operations, there were only 20 problems per operation. Therefore, the investigation of operation-specific structure–function correlations should be undertaken in the context of a study where larger numbers of items were presented for each arithmetic operation and problem size. In conclusion, the present data represent a first step toward an integration of functional and structural white matter data in the domain of calculation. Specifically, the present data reveal that there is a direct link between activation levels in the lAG associated with calculation processes and individual differences in white matter integrity of the SCR, which has been previously linked to arithmetical abilities. These findings highlight that both structure and function of the left temporoparietal cortex play a role in mental arithmetic and particularly so when problems have a high probability of being solved via the retrieval of arithmetic facts. Beyond the domain of mental arithmetic, the present analyses of the relationships between individual differences in FA and activation parameters derived from anatomatically defined ROIs may help to further constrain the roles of both white matter microstructures as well as cortical regions of focal activation across domains. Acknowledgments This research was partly supported by grants from the Provincial Government of Styria, Austria, the Canadian Institutes of Health Research (CIHR), the Ontario Ministry for Research and Innovation and the National Sciences and Engineering Council of Canada (NSERC). We would like to thank Gavin Buckingham and Bea Goffin for their comments on a previous draft and Rachel Bosma for her help with the analysis of the DTI data. References Ansari, D., 2008. Effects of development and enculturation on number representation in the brain. Nature Reviews Neuroscience 9 (4), 278–291. Barnea-Goraly, N., Eliez, S., Menon, V., Bammer, R., Reiss, A.L., 2005. Arithmetic ability and parietal alterations: a diffusion tensory imaging study in Velocardiofacial syndrome. Cogn. Brain Res. 25 (3), 735–740. Beaulieu, C., Plewes, C., Paulson, L.A., Roy, D., Snook, L., Concha, L., et al., 2005. Imaging brain connectivity in children with diverse reading ability. NeuroImage 25 (4), 1266–1271. Ben-Shachar, M., Dougherty, R.F., Wandell, B.A., 2007. White matter pathways in reading. Curr. Opin. Neurobiol. 17 (2), 258–270. Campbell, J.I.D., Xue, Q.L., 2001. Cognitive arithmetic across cultures. J. Exp. Psychol. Gen. 130, 299–315. Dehaene, S., Spelke, E., Pinel, P., Stanescu, R., Tsivkin, S., 1999. Sources of mathematical thinking: behavioral and brain-imaging evidence. Science 284 (5416), 970–974. Dehaene, S., Piazza, M., Pinel, P., Cohen, L., 2003. Three parietal circuits for number processing. Cogn. Neuropsychol. 20 (3–6), 487–506. Delazer, M., Domahs, F., Bartha, L., Brenneis, C., Lochy, A., Trieb, T., Benke, T., 2003. Learning complex arithmetic – an fMRI study. Cogn. Brain Res. 18 (1), 76–88. DeSmedt, B., Taylor, J., Archibald, L., Ansari, D., 2010. How is phonological processing related to individual differences in children's arithmetic skills? Developmental Science 13, 508–520. Deutsch, G.K., Dougherty, R.F., Bammer, R., Siok, W.T., Gabrieli, J.D., Wandell, B., 2005. Children's reading performance is correlated with white matter structure measured by diffusion tensor imaging. Cortex 41 (3), 354–363. Grabner, R.H., Ansari, D., Reishofer, G., Stern, E., Ebner, F., Neuper, C., 2007. Individual differences in mathematical competence predict parietal brain activation during mental calculation. NeuroImage 38, 346–356. Grabner, R.H., Ischebeck, A., Reishofer, G., Koschutnig, K., Delazer, M., Ebner, F., Neuper, C., 2009a. Fact learning in complex arithmetic and figural-spatial tasks: the role of the angular gyrus and its relation to mathematical competence. Hum. Brain Mapp. 30, 2936–2952.

363

Grabner, R.H., Ansari, D., Koschutnig, K., Reishofer, G., Ebner, F., Neuper, C., 2009b. To retrieve or to calculate? Left angular gyrus mediates the retrieval of arithmetic facts during problem solving. Neuropsychologia 47, 604–608. Ischebeck, A., Zamarian, L., Seidentopf, C., Koppelstätter, F., Benke, T., Felber, S., Delazer, M., 2006. How specifically do we learn? Imaging the learning of multiplication and subtraction. NeuroImage 30 (4), 1365–1375. Jones, D.K., Symms, M.R., Cercignani, M., Howard, R.J., 2005. The effect of filter size on VBM analyses of DT-MRI data. NeuroImage 26 (2), 546–554. Jost, K., Khader, P., Burke, M., Bien, S., Rösler, F., 2009. Dissociating the solution processes of small, large and zero multiplications by means of fMRI. NeuroImage 46 (1), 308–318. Koch, M.A., Norris, D.G., Hund-Georgiadis, 2002. An investigation of functional and anatomical connectivity using magnetic resonance imaging. NeuroImage 16 (1), 241–250. Kong, H., Wang, C.M., Kwong, K., Vangel, M., Chua, E., Gollub, R., 2005. The neural substrate of arithmetic operations and procedure complexity. Cogn. Brain Res. 22 (3), 397–405. Klingberg, T., Hedehus, M., Temple, E., Salz, T., Gabrieli, J.D.E., Moseley, M.E., et al., 2000. Microstructure of temporo-parietal white matter as a basis for reading ability: evidence from diffusion tensor magnetic resonance imaging. Neuron 25 (2), 493–500. Lebel, C., Rasmussen, C., Wyper, K., Andrew, G., Beaulieu, C., 2010. Brain microstructure is related to math ability in children with fetal alcohol spectrum disorder. Alcohol. Clin. Exp. Res. 34 (2), 1–10. LeFevre, J., Sadesky, G.S., Bisanz, J., 1996. Selection of procedures in mental addition: reassessing the problem size effect in adults. J. Exp. Psychol. Learn. Mem. Cogn. 22 (1), 216–230. Menon, V., Rivera, S.M., White, C.D., Eliez, S., Glover, G.H., Reiss, A.L., 2000a. Functional optimization of arithmetic processing in perfect performers. Cogn. Brain Res. 9 (3), 343–345. Menon, V., Rivera, S.M., White, C.D., Glover, G.H., Reiss, A.L., 2000b. Dissociating prefrontal and parietal activation during arithmetic processing. NeuroImage 12 (4), 357–365. Nagy, Z., Westerberg, H., Klingberg, T., 2004. Maturation of white matter is associated with the development of cognitive functions during childhood. J. Cogn. Neurosci. 16 (7), 1227–1233. Niogi, S.N., McCandliss, B.D., 2006. Left lateralized white matter microstructure accounts for individual differences in reading ability and disability. Neuropsychologia 44 (11), 2178–2188. Niogi, S.N., Mukherjee, P., McCandliss, B.D., 2007. Diffusion tensor imaging segmentation of white matter structures using a Reproducible Objective Quantification Scheme (ROQS). NeuroImage 35, 166–174. Odegard, T.N., Farris, E.A., Ring, J., McColl, R., Black, J., 2009. Brain connectivity in nonreading impaired children and children diagnosed with developmental dyslexia. Neuropsychologia 47 (8–9), 1972–1977. Price, C.J., 2000. The anatomy of language: contributions from functional neuroimaging. Journal of Anatomy 197, 335–359. Rivera, S.M., Reiss, A.L., Eckert, M.A., Menon, V., 2005. Developmental changes in mental arithmetic: evidence for increased functional specialization in the left inferior parietal cortex. Cereb. Cortex 15 (11), 1779–1790. Simon, O., Mangin, L., Cohen, L., Le Bihan, D., Dehaene, S., 2002. Topographical layout of hand, eye, calculation, and language-related areas in the human parietal lobe. Neuron 33 (3), 475–487. Simmons, F.R., Singleton, C., 2008. Do weak phonological representations impact on arithmetic development? A review of research into arithmetic and dyslexia. Dyslexia 14 (2), 77–94. Stanescu-Cosson, R., Pinel, P., Van De Moortele, P.F., Le Bihan, D., Cohen, L., Dehaene, S., 2000. Understanding dissociations in dyscalculia - a brain imaging study of the impact of number size on the cerebral networks for exact and approximate calculation. Brain 123, 2240–2255. Toosy, A.T., Ciccarelli, O., Parker, G.J.M., Wheeler-Kingshott, C.A.M., Miller, D.H., Thompson, A.J., 2004. Characterizing function–structure relationships in the human visual system with functional MRI and diffusion tensor imaging. NeuroImage 21 (4), 1452–1463. Tsang, J.M., Dougherty, R.F., Deutsch, G.K., Wandell, B.A., Ben-Shachar, M., 2009. Frontoparietal white matter diffusion properties predict mental arithmetic skills in children. Proceedings of the National Academy of Sciences USA 106 (52), 22546–22551. Tzourio-Mazoyer, N., Landeau, B., Papathanassiou, D., Crivello, F., Etard, O., Delcroix, N., et al., 2002. Automated anatomical labeling of activations in SPM using a macroscopic anatomical parcellation of the MNI MRI single-subject brain. NeuroImage 15 (1), 273–289. van Eimeren, L., Niogi, S.N., McCandliss, B.D., Holloway, I.D., Ansari, D., 2008. White matter microstructures underlying mathematical abilities in children. NeuroReport 19 (11), 1117–1121. van den Heuvel, M., Mandl, R.C.W., Kahn, R.S., Hulshoff Pol, H.E., 2009. Functionally linked resting-state networks reflect the underlying structural connectivity architecture of the human brain. Hum. Brain Mapp. 30 (10), 3127–3141. Zamarian, L., Ischebeck, A., Delazer, M., 2009. Neuroscience of learning arithmetic evidence from brain imaging studies. Neuroscience and Biobehavioral Reviews 33 (6), 909–925.