Left fronto-parietal white
matter correlates with
individual differences in
children’s ability to solve
additions and multiplications:
a tractography study
Leen Van Beek, Pol Ghesquière, Lieven Lagae & Bert De Smedt
Parenting and Special Education research unit
Development and Regeneration research unit
Friday 4th April 2014
Content
1.
2.
3.
4.
Introduction
Method
Results
Conclusion
Introduction
Temporo-parietal
regions: arithmetic
Prefrontal & frontal regions:
executive functions
FRONTO-PARIETAL NETWORK IN ARITHMETIC
(Arsalidou & Taylor, 2011)
Diffusion tensor imaging (DTI)
‘free’ diffusion
Grey matter & CSF
D is equal in all directions
ISOTROPIC
‘hindered’ diffusion
White matter
D is not equal in all directions
ANISOTROPIC
DTI tractography
Whole brain
Arcuate Fasciculus
DTI outcome: FA as quantitative measure
Fractional anisotropy (FA) = degree of anisotropy (= ‘shape’)
λ1
λ2
λ3
Previous DTI studies in mathematics
•
•
•
•
•
•
•
•
Barnea-Goraly et al, 2005
Lebel et al., 2010
Rykhlevskaia et al., 2009
Till et al., 2011
van Eimeren et al., 2010
Matejko et al., 2013
van Eimeren et al., 2008
Tsang et al., 2009
Previous DTI studies in mathematics
•
•
•
•
•
•
•
•
Barnea-Goraly et al, 2005
Lebel et al., 2010
Rykhlevskaia et al., 2009
Till et al., 2011
van Eimeren et al., 2010
Matejko et al., 2013
van Eimeren et al., 2008
Tsang et al., 2009
Atypical populations
Previous DTI studies in mathematics
•
•
•
•
•
•
•
•
Barnea-Goraly et al, 2005
Lebel et al., 2010
Rykhlevskaia et al., 2009
Till et al., 2011
van Eimeren et al., 2010
Matejko et al., 2013
van Eimeren et al., 2008
Tsang et al., 2009
Adults & adolescents
Previous DTI studies in mathematics
•
•
•
•
•
•
•
•
Barnea-Goraly et al, 2005
Lebel et al., 2010
Rykhlevskaia et al., 2009
Till et al., 2011
van Eimeren et al., 2010
Matejko et al., 2013
van Eimeren et al., 2008
Tsang et al., 2009
Typically developing children
Aim
• Examine the association between individual differences in
arithmetical competence and the quality of the white matter
pathways that connect frontal and temporo-parietal regions
that are active during arithmetic
• Verify whether this association is modulated by the type of
operation
Method: participants
•
•
•
•
18 typically developing children
M = 12.0 years; SD = 0.4; age range 11.5 – 12.9 years; 8 boys
Native Dutch speakers
Predominantly right-handed and normal intelligence
Method: behavioral measures
• Arithmetical competence:
•
•
•
Tempo Test Arithmetic (De Vos, 1992)
Addition, subtraction, multiplication & division
Intellectual ability:
WISC-III-NL - Vocabulary and Block Design (De Kort et al., 2005)
Working memory:
Digit Recall forward/backward & Block Recall forward/backward
Reading ability
Word reading test (Brus & Voeten, 1979)
Pseudo-word reading test (Van den Bos et al., 1994)
Method: DTI data acquisition
• Preprocessing in ExploreDTI (Leemans et al., 2009)
• Tractography in TrackVis (Wang and Wedeen, 2007)


Delineation of the 3 segments of the Arcuate
Fasciculus (AF)
Tracts were individually delineated in native space
according to validated protocols
(Catani et al., 2005; Catani and de Schotten, 2008; Wakana et al., 2007)
Method: DTI data acquisition
• Delineation in both left and right hemisphere
• For each tract the FA value was extracted
• Delineation by 2 raters (FA intra-class correlation coefficient >.94)
Results
Pearson partial correlations (controlled for quality index of DTI acquisition) between mean FA
and arithmetical competence (n=18)
Arithmetical competence
Left AF
Right AF
Addition
Subtraction
Multiplication
Division
direct
.409
-.011
.470
.202
anterior
.704**
.219
.722**
.353
posterior
.294
-.076
.269
-.144
direct
.166
-.155
.191
.185
anterior
.395
.215
.384
.143
posterior
.259
-.185
.303
.097
** Bonferroni corrected p < .01; AF = arcuate fasciculus
Results
• Specificity of the observed correlations?

Specific for addition/multiplication?
YES

Specific for left hemisphere?
YES

Specific for anterior part?
YES
Results
• Specificity of the observed correlations?

Controlling for age, IQ and working memory
→ Associations remain significant (p < .01)

Controlling for word reading
→ Associations remain significant (p < .01)

Controlling for pseudo-word reading
→ Associations decrease (ns)
Conclusion
Association between fronto-parietal white matter and
individual differences in children’s arithmetical competence
1. Consistent with previous DTI studies in mathematics
2. Extends beyond
−
Atypically developing children
(Barnea-Goraly et al., 2005; Lebel et al., 2010; Rykhlevskaia et al., 2009; Till et al., 2011)
−
Children of a broad age range
(Tsang et al., 2009; van Eimeren et al., 2010)
−
(Young) adults
(Matejko et al., 2013)
3. Not explained by age, intelligence and working memory
Conclusion
4. Modulated by arithmetic operation:
associations with addition/multiplication and not with
subtraction/division
5. Might reflect the use of different strategies:
fact retrieval for addition/multiplication versus more quantity-based
procedural strategies for subtraction and division
6. Might be explained by phonological decoding
Further reading
leen.vanbeek@ppw.kuleuven.be