Brain Structure and Function

, Volume 224, Issue 1, pp 337–350 | Cite as

Relating individual differences in white matter pathways to children’s arithmetic fluency: a spherical deconvolution study

  • Brecht PolspoelEmail author
  • Maaike Vandermosten
  • Bert De Smedt
Original Article


Connectivity between brain regions is integral to efficient complex cognitive processing, making the study of white matter pathways in clarifying the neural mechanisms of individual differences in arithmetic abilities critical. This white matter connectivity underlying arithmetic has only been investigated through classic diffusion tensor imaging, which, due to methodological limitations, might lead to an oversimplification of the underlying anatomy. More complex non-tensor models, such as spherical deconvolution, however, allow a much more fine-grained delineation of the underlying brain anatomy. Against this background, the current study is the first to use spherical deconvolution to investigate white matter tracts and their relation to individual differences in arithmetic fluency in typically developing children. Participants were 48 typically developing 9–10-year-olds, who were all in grade 4, and who underwent structural diffusion-weighted magnetic resonance imaging scanning. Theoretically relevant white matter tracts were manually delineated with a region of interest approach, after which the hindrance modulated orientational anisotropy (HMOA) index, which provides information on the structural integrity of the tract at hand, was derived for each tract. These HMOA indices were correlated with measures of arithmetic fluency, using frequentist and Bayesian approaches. Our results point towards an association between the HMOA of the right inferior longitudinal fasciculus and individual differences in arithmetic fluency. This might reflect the efficiency with which children process Arabic numerals. Other previously found associations between white matter and individual differences in arithmetic fluency were not observed.


Arithmetic Children Diffusion tensor imaging Spherical deconvolution Inferior longitudinal fasciculus 



This study was supported by a project of the Fund for Scientific Research Flanders (G.0946.12), by a federal research action (IUAP P7/11), and by a project of the Fund for Scientific Research Flanders and the Austrian Science Fund (G.0027.16). We would also like to thank all participants, their parents, and the Department of Radiology of the University Hospital in Leuven for their support.


This study was funded by a project of the Fund for Scientific Research Flanders (G.0946.12), by a Belgian federal research action (IUAP P7/11), and by a project of the Fund for Scientific Research Flanders and the Austrian Science Fund (G.0027.16).

Compliance with ethical standards

Informed consent

Written informed consent was obtained from all individual participants included in the study, as well as from a parent or legal guardian of each participating child.

Ethical approval

All procedures involving human participants were in accordance with the ethical standards of the institutional and/or national research committee and with the 1964 Helsinki declaration and its later amendments or comparable ethical standards. The study was approved by the Medical Ethical Committee of the University of Leuven (S59167).

Conflict of interest

The authors declare that they have no conflict of interest.

Supplementary material

429_2018_1770_MOESM1_ESM.docx (582 kb)
Supplementary material 1 (docx 582 KB)


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Parenting and Special Education Research UnitKU LeuvenLeuvenBelgium
  2. 2.Experimental ORL, Department of NeurosciencesKU LeuvenLeuvenBelgium

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