A brain connectivity characterization of children with different levels of mathematical achievement based on graph metrics

Autoři: Sulema Torres-Ramos aff001;  Ricardo A. Salido-Ruiz aff001;  Aurora Espinoza-Valdez aff001;  Fabiola R. Gómez-Velázquez aff002;  Andrés A. González-Garrido aff002;  Israel Román-Godínez aff001
Působiště autorů: Departamento de Ciencias Computacionales, Universidad de Guadalajara, Guadalajara, México aff001;  Instituto de Neurociencias, Universidad de Guadalajara, Guadalajara, México aff002
Vyšlo v časopise: PLoS ONE 15(1)
Kategorie: Research Article
doi: 10.1371/journal.pone.0227613


Recent studies aiming to facilitate mathematical skill development in primary school children have explored the electrophysiological characteristics associated with different levels of arithmetic achievement. The present work introduces an alternative EEG signal characterization using graph metrics and, based on such features, a classification analysis using a decision tree model. This proposal aims to identify group differences in brain connectivity networks with respect to mathematical skills in elementary school children. The methods of analysis utilized were signal-processing (EEG artifact removal, Laplacian filtering, and magnitude square coherence measurement) and the characterization (Graph metrics) and classification (Decision Tree) of EEG signals recorded during performance of a numerical comparison task. Our results suggest that the analysis of quantitative EEG frequency-band parameters can be used successfully to discriminate several levels of arithmetic achievement. Specifically, the most significant results showed an accuracy of 80.00% (α band), 78.33% (δ band), and 76.67% (θ band) in differentiating high-skilled participants from low-skilled ones, averaged-skilled subjects from all others, and averaged-skilled participants from low-skilled ones, respectively. The use of a decision tree tool during the classification stage allows the identification of several brain areas that seem to be more specialized in numerical processing.

Klíčová slova:

Arithmetic – Clustering coefficients – Cognitive science – Decision trees – Electroencephalography – Neural networks – Scalp – Signal processing


1. Eva OD, Lazar AM. Comparison of classifiers and statistical analysis for EEG signals used in brain computer interface motor task paradigm. International Journal of Advanced Research in Artificial Intelligence (IJARAI). 2015;1(4):8–12.

2. Shalev RS, Gross-Tsur V. Developmental dyscalculia. Pediatric Neurology. 2001;24(5):337—342. doi: 10.1016/s0887-8994(00)00258-7 11516606

3. Moazami-Goudarzi M, Sarnthein J, Michels L, Moukhtieva R, Jeanmonod D. Enhanced frontal low and high frequency power and synchronization in the resting EEG of parkinsonian patients. Neuroimage. 2008;41(3):985–997. doi: 10.1016/j.neuroimage.2008.03.032 18457962

4. Lowe MJ, Sakaie KE, Beall EB, Calhoun VD, Bridwell DA, Rubinov M, et al. Modern methods for interrogating the human connectome. Journal of the International Neuropsychological Society. 2016;22(2):105–119. doi: 10.1017/S1355617716000060 26888611

5. Graziano AB, Peterson M, Shaw GL. Enhanced learning of proportional math through music training and spatial-temporal training. Neurological Research. 1999;21(2):139–152. doi: 10.1080/01616412.1999.11740910 10100200

6. Jiang Zy. Study on EEG power and coherence in patients with mild cognitive impairment during working memory task. Journal of Zhejiang University Science B. 2005;6(12):1213–1219.

7. Klados MA, Pandria N, Micheloyannis S, Margulies D, Bamidis PD. Math anxiety: Brain cortical network changes in anticipation of doing mathematics. International Journal of Psychophysiology. 2017;122:24–31. doi: 10.1016/j.ijpsycho.2017.05.003 28479367

8. Hidasi Z, Czigler B, Salacz P, Csibri É, Molnár M. Changes of EEG spectra and coherence following performance in a cognitive task in Alzheimer’s disease. International Journal of Psychophysiology. 2007;65(3):252–260. doi: 10.1016/j.ijpsycho.2007.05.002 17586077

9. Vecchiato G, Susac A, Margeti S, Fallani FDV, Maglione AG, Supek S, et al. High-resolution EEG analysis of power spectral density maps and coherence networks in a proportional reasoning task. Brain Topography. 2013;26(2):303–314. doi: 10.1007/s10548-012-0259-5 23053602

10. Moore RA, Mills M, Marshman P, Corr PJ. Behavioural Inhibition System (BIS) sensitivity differentiates EEG theta responses during goal conflict in a continuous monitoring task. International Journal of Psychophysiology. 2012;85(2):135–144. doi: 10.1016/j.ijpsycho.2012.06.006 22732350

11. González-Garrido AA, Gómez-Velázquez FR, Salido-Ruiz RA, Espinoza-Valdez A, Vélez-Pérez H, Romo-Vazquez R, et al. The analysis of EEG coherence reflects middle childhood differences in mathematical achievement. Brain and Cognition. 2018;124:57–63. doi: 10.1016/j.bandc.2018.04.006 29747149

12. Grillner S, Kozlov A, Kotaleski JH. Integrative neuroscience: linking levels of analyses. Current Opinion in Neurobiology. 2005;15(5):614–621. doi: 10.1016/j.conb.2005.08.017 16146688

13. Bosch P, Herrera M, López J, Maldonado S. Mining EEG with SVM for Understanding Cognitive Underpinnings of Math Problem Solving Strategies. Behavioural neurology. 2018;2018. doi: 10.1155/2018/4638903 29670667

14. Dimitriadis SI, Sun Y, Thakor NV, Bezerianos A. Causal Interactions between Frontal–Parieto-Occipital Predict Performance on a Mental Arithmetic Task. Frontiers in Human Neuroscience. 2016;10:454. doi: 10.3389/fnhum.2016.00454 27683547

15. Wang Q, Sourina O. Real-time mental arithmetic task recognition from EEG signals. IEEE Transactions on Neural Systems and Rehabilitation Engineering. 2013;21(2):225–232. doi: 10.1109/TNSRE.2012.2236576 23314778

16. Spüler M, Walter C, Rosenstiel W, Gerjets P, Moeller K, Klein E. EEG-based prediction of cognitive workload induced by arithmetic: a step towards online adaptation in numerical learning. ZDM. 2016;48(3):267–278. doi: 10.1007/s11858-015-0754-8

17. Wang S, Li Y, Wen P, Zhu G. Analyzing EEG signals using graph entropy based principle component analysis and J48 decision tree. In: Proceedings of the 6th International Conference on Signal Processing Systems (ICSPS 2014). International Journal of Signal Processing Systems; 2014. p. 1–6.

18. Arvaneh M, Guan C, Ang KK, Quek HC. EEG channel selection using decision tree in brain-computer interface. In: Proceedings of the Second APSIPA Annual Summit and Conference; 2010. p. 225–230.

19. Medaglia JD, Lynall ME, Bassett DS. Cognitive network neuroscience. Journal of Cognitive Neuroscience. 2015;27(8):1471–1491. doi: 10.1162/jocn_a_00810 25803596

20. Vecchio F, Miraglia F, Quaranta D, Granata G, Romanello R, Marra C, et al. Cortical connectivity and memory performance in cognitive decline: a study via graph theory from EEG data. Neuroscience. 2016;316:143–150. doi: 10.1016/j.neuroscience.2015.12.036 26724581

21. Vecchio F, Miraglia F, Piludu F, Granata G, Romanello R, Caulo M, et al. “Small World” architecture in brain connectivity and hippocampal volume in Alzheimer’s disease: a study via graph theory from EEG data. Brain imaging and Behavior. 2017;11(2):473–485. doi: 10.1007/s11682-016-9528-3 26960946

22. Talia D, Trunfio P, Marozzo F. Chapter 1—Introduction to Data Mining. In: Talia D, Trunfio P, Marozzo F, editors. Data Analysis in the Cloud. Computer Science Reviews and Trends. Boston: Elsevier; 2016. p. 1–25. Available from: http://www.sciencedirect.com/science/article/pii/B9780128028810000019.

23. Wilkinson GS, Robertson GJ. Wide range achievement test 4 (WRAT4). Lutz, FL: Psychological Assessment Resources. 2006.

24. Reilly C, Atkinson P, Das KB, Chin RF, Aylett SE, Burch V, et al. Academic achievement in school-aged children with active epilepsy: A population-based study. Epilepsia. 2014;55(12):1910–1917. doi: 10.1111/epi.12826 25330985

25. Gómez-Velázquez FR, Berumen G, González-Garrido AA. Comparisons of numerical magnitudes in children with different levels of mathematical achievement. An ERP study. Brain research. 2015;1627:189–200. doi: 10.1016/j.brainres.2015.09.009 26385418

26. Zhang H, Yolton K, Webster GM, Sjödin A, Calafat AM, Dietrich KN, et al. Prenatal PBDE and PCB exposures and reading, cognition, and externalizing behavior in children. Environmental health perspectives. 2016;125(4):746–752. doi: 10.1289/EHP478 27385187

27. Lai KW, Hum YC, Salim MIM, Ong SB, Utama NP, Myint YM, et al. Advances in medical diagnostic technology. Springer; 2014.

28. Jadhav P, Shanamugan D, Chourasia A, Ghole A, Acharyya A, Naik G. Automated detection and correction of eye blink and muscular artefacts in EEG signal for analysis of Autism Spectrum Disorder. In: Engineering in Medicine and Biology Society (EMBC), 2014 36th Annual International Conference of the IEEE. IEEE; 2014. p. 1881–1884.

29. Klados MA, Papadelis C, Braun C, Bamidis PD. REG-ICA: a hybrid methodology combining blind source separation and regression techniques for the rejection of ocular artifacts. Biomedical Signal Processing and Control. 2011;6(3):291–300. doi: 10.1016/j.bspc.2011.02.001

30. Vigário RN. Extraction of ocular artefacts from EEG using independent component analysis. Electroencephalography and Clinical Neurophysiology. 1997;103(3):395–404. doi: 10.1016/s0013-4694(97)00042-8 9305288

31. Jung TP, Makeig S, Humphries C, Lee TW, Mckeown MJ, Iragui V, et al. Removing electroencephalographic artifacts by blind source separation. Psychophysiology. 2000;37(2):163–178. doi: 10.1111/1469-8986.3720163 10731767

32. James CJ, Hesse CW. Independent component analysis for biomedical signals. Physiological Measurement. 2004;26(1):R15. doi: 10.1088/0967-3334/26/1/R02

33. Jutten C. Independent components analysis versus principal components analysis. Signal Processing IV, Theories and Applications (EUSIPCO’88) Grenoble, France. 1988; p. 643–646.

34. Jutten C. Blind separation of sources: algorithm for separation of convolutive mixtures. In: Proc. Int. Workshop on Higher Order Statistics, Chanirousse; 1991. p. 273–276.

35. Flexer A, Bauer H, Pripfl J, Dorffner G. Using ICA for removal of ocular artifacts in EEG recorded from blind subjects. Neural Networks. 2005;18(7):998–1005. doi: 10.1016/j.neunet.2005.03.012 15990276

36. Pedregosa F, Varoquaux G, Gramfort A, Michel V, Thirion B, Grisel O, et al. Scikit-learn: Machine Learning in Python. Journal of Machine Learning Research. 2011;12:2825–2830.

37. Srinivasan R, Winter WR, Ding J, Nunez PL. EEG and MEG coherence: measures of functional connectivity at distinct spatial scales of neocortical dynamics. Journal of Neuroscience Methods. 2007;166(1):41–52. doi: 10.1016/j.jneumeth.2007.06.026 17698205

38. Deng S, Winter W, Thorpe S, Srinivasan R. EEG Surface Laplacian using realistic head geometry. International Journal of Bioelectromagnetism. 2011;13(4):173–177.

39. Hjorth B. An on-line transformation of EEG scalp potentials into orthogonal source derivations. Electroencephalography and clinical neurophysiology. 1975;39(5):526–530. doi: 10.1016/0013-4694(75)90056-5 52448

40. Nunez P, Silberstein R, Cadusch P, Wijesinghe R, Westdorp A, Srinivasan R. A theoretical and experimental study of high resolution EEG based on surface Laplacians and cortical imaging. Electroencephalography and Clinical Neurophysiology. 1994;90(1):40–57. doi: 10.1016/0013-4694(94)90112-0 7509273

41. Deng S, Winter W, Thorpe S, Srinivasan R. Improved surface laplacian estimates of cortical potential using realistic models of head geometry. IEEE Transactions on Biomedical Engineering. 2012;59(11):2979–2985. doi: 10.1109/TBME.2012.2183638 22249595

42. Chorlian DB, Rangaswamy M, Porjesz B. EEG coherence: topography and frequency structure. Experimental Brain Research. 2009;198(1):59. doi: 10.1007/s00221-009-1936-9 19626316

43. Nunez PL, Silberstein RB, Shi Z, Carpenter MR, Srinivasan R, Tucker DM, et al. EEG coherency II: experimental comparisons of multiple measures. Clinical Neurophysiology. 1999;110(3):469–486. doi: 10.1016/s1388-2457(98)00043-1 10363771

44. Schwartz S, Kessler R, Gaughan T, Buckley AW. Electroencephalogram coherence patterns in autism: an updated review. Pediatric Neurology. 2017;67:7–22. doi: 10.1016/j.pediatrneurol.2016.10.018 28065825

45. Kühn-Popp N, Kristen S, Paulus M, Meinhardt J, Sodian B. Left hemisphere EEG coherence in infancy predicts infant declarative pointing and preschool epistemic language. Social Neuroscience. 2016;11(1):49–59. doi: 10.1080/17470919.2015.1024887 25833090

46. Horschig JM, Smolders R, Bonnefond M, Schoffelen JM, van den Munckhof P, Schuurman PR, et al. Directed Communication between Nucleus Accumbens and Neocortex in Humans Is Differentially Supported by Synchronization in the Theta and Alpha Band. PLOS ONE. 2015;10(9):1–20. doi: 10.1371/journal.pone.0138685

47. Vildavski VY. About your comment in researchgate to: “In theory magnitude squared coherence, being a correlation index ranges 0-1, but what is the range of EEG magnitude squared coherence in humans?”; 2019. e-mail, Personal communication.

48. Thatcher R, Krause P, Hrybyk M. Cortico-cortical associations and EEG coherence: a two-compartmental model. Electroencephalography and clinical neurophysiology. 1986;64(2):123–143. doi: 10.1016/0013-4694(86)90107-0 2424729

49. Barry RJ, Clarke AR, McCarthy R, Selikowitz M. Adjusting EEG coherence for inter-electrode distance effects: an exploration in normal children. International Journal of Psychophysiology. 2005;55(3):313–321. doi: 10.1016/j.ijpsycho.2004.09.001 15708644

50. Knyazeva M, Kiper D, Vildavski V, Despland P, Maeder-Ingvar M, Innocenti G. Visual Stimulus “Dependent Changes in Interhemispheric EEG Coherence in Humans”. Journal of neurophysiology. 2000;82:3095–107. doi: 10.1152/jn.1999.82.6.3095

51. Rubinov M, Sporns O. Complex network measures of brain connectivity: Uses and interpretations. NeuroImage. 2010;52(3):1059—1069. https://doi.org/10.1016/j.neuroimage.2009.10.003. 19819337

52. Sporns O. Structure and function of complex brain networks. Dialogues in clinical neuroscience. 2013;15(3):247. 24174898

53. Rousseeuw PJ. Silhouettes: a graphical aid to the interpretation and validation of cluster analysis. Journal of Computational and Applied Mathematics. 1987;20:53–65. doi: 10.1016/0377-0427(87)90125-7

54. Knox EM, Ng RT. Algorithms for mining distance based outliers in large datasets. In: Proceedings of the International Conference on Very Large Data Bases. Citeseer; 1998. p. 392–403.

55. Knorr EM, Ng RT. Finding intentional knowledge of distance-based outliers. In: VLDB. vol. 99; 1999. p. 211–222.

56. Hawkins DM. Identification of outliers. vol. 11. Springer; 1980.

57. Lotte F, Bougrain L, Cichocki A, Clerc M, Congedo M, Rakotomamonjy A, et al. A review of classification algorithms for EEG-based brain–computer interfaces: a 10 year update. Journal of neural engineering. 2018;15(3):031005. doi: 10.1088/1741-2552/aab2f2 29488902

58. Hastie T, Tibshirani R. Classification by pairwise coupling. In: Advances in neural information processing systems; 1998. p. 507–513.

59. Allwein EL, Schapire RE, Singer Y. Reducing multiclass to binary: A unifying approach for margin classifiers. Journal of machine learning research. 2000;1(Dec):113–141.

60. Han J, Pei J, Kamber M. Data mining: concepts and techniques. Elsevier; 2011.

61. Witten IH, Frank E, Hall MA, Pal CJ. Data Mining: Practical machine learning tools and techniques. Morgan Kaufmann; 2016.

62. Quinlan JR. C4. 5: Programs for machine learning. Elsevier; 2014.

63. Hall M, Frank E, Holmes G, Pfahringer B, Reutemann P, Witten IH. The WEKA data mining software: an update. ACM SIGKDD explorations newsletter. 2009;11(1):10–18. doi: 10.1145/1656274.1656278

64. Wei J, Zhao L, Yan G, Duan R, Li D. The temporal and spatial features of event-related EEG spectral changes in 4 mental conditions. Electroencephalography and Clinical Neurophysiology. 1998;106(5):416–423. doi: 10.1016/s0013-4694(97)00161-2 9680154

65. Kitaura Y, Nishida K, Yoshimura M, Mii H, Katsura K, Ueda Sea. Functional localization and effective connectivity of cortical theta and alpha oscillatory activity during an attention task. Clinical Neurophysiology Practice. 2017;2:193–200. doi: 10.1016/j.cnp.2017.09.002 30214995

66. Williams CC, Kappen M, Hassall CD, Wright B, Krigolson OE. Thinking theta and alpha: Mechanisms of intuitive and analytical reasoning. NeuroImage. 2019;. doi: 10.1016/j.neuroimage.2019.01.048

67. Ansari D. Effects of development and enculturation on number representation in the brain. Nature Reviews Neuroscience. 2008;9(4):278. doi: 10.1038/nrn2334 18334999

68. Holloway ID, Price GR, Ansari D. Common and segregated neural pathways for the processing of symbolic and nonsymbolic numerical magnitude: An fMRI study. Neuroimage. 2010;49(1):1006–1017. doi: 10.1016/j.neuroimage.2009.07.071 19666127

69. Price GR, Ansari D. Symbol processing in the left angular gyrus: evidence from passive perception of digits. Neuroimage. 2011;57(3):1205–1211. doi: 10.1016/j.neuroimage.2011.05.035 21620978

70. Delazer M, Ischebeck A, Domahs F, Zamarian L, Koppelstaetter F, Siedentopf C, et al. Learning by strategies and learning by drill—evidence from an fMRI study. Neuroimage. 2005;25(3):838–849. doi: 10.1016/j.neuroimage.2004.12.009 15808984

71. Grabner RH, Ansari D, Reishofer G, Stern E, Ebner F, Neuper C. Individual differences in mathematical competence predict parietal brain activation during mental calculation. Neuroimage. 2007;38(2):346–356. doi: 10.1016/j.neuroimage.2007.07.041 17851092

72. Abboud S, Maidenbaum S, Dehaene S, Amedi A. A number-form area in the blind. Nature communications. 2015;6:6026. doi: 10.1038/ncomms7026 25613599

73. Schwartz F, Epinat-Duclos J, Léone J, Poisson A, Prado J. Impaired neural processing of transitive relations in children with math learning difficulty. NeuroImage: Clinical. 2018;20:1255–1265. doi: 10.1016/j.nicl.2018.10.020

74. Szűcs D, Goswami U. Developmental dyscalculia: fresh perspectives; 2013.

75. Hesse PN, Schmitt C, Klingenhoefer S, Bremmer F. Preattentive processing of numerical visual information. Frontiers in Human Neuroscience. 2017;11(70). doi: 10.3389/fnhum.2017.00070 28261078

76. Soltanlou M, Artemenko C, Dresler T, Fallgatter AJ, Nuerk HC, Ehlis AC. Oscillatory EEG Changes During Arithmetic Learning in Children. Developmental neuropsychology. 2019; p. 1–14.

77. Soltanlou M, Artemenko C, Dresler T, Haeussinger FB, Fallgatter AJ, Ehlis AC, et al. Increased arithmetic complexity is associated with domain-general but not domain-specific magnitude processing in children: a simultaneous fNIRS-EEG study. Cognitive, Affective, & Behavioral Neuroscience. 2017;17(4):724–736. doi: 10.3758/s13415-017-0508-x

78. Ansari D, Garcia N, Lucas E, Hamon K, Dhital B. Neural correlates of symbolic number processing in children and adults. Neuroreport. 2005;16(16):1769–1773. doi: 10.1097/01.wnr.0000183905.23396.f1 16237324

79. Cantlon JF, Brannon EM, Carter EJ, Pelphrey KA. Functional imaging of numerical processing in adults and 4-y-old children. PLoS biology. 2006;4(5):e125. doi: 10.1371/journal.pbio.0040125 16594732

80. Kaufmann L, Koppelstaetter F, Siedentopf C, Haala I, Haberlandt E, Zimmerhackl LB, et al. Neural correlates of the number–size interference task in children. Neuroreport. 2006;17(6):587. doi: 10.1097/00001756-200604240-00007 16603917

81. Arsalidou M, Taylor MJ. Is 2+ 2 = 4? Meta-analyses of brain areas needed for numbers and calculations. Neuroimage. 2011;54(3):2382–2393. doi: 10.1016/j.neuroimage.2010.10.009 20946958

82. Price GR, Yeo DJ, Wilkey ED, Cutting LE. Prospective relations between resting-state connectivity of parietal subdivisions and arithmetic competence. Developmental cognitive neuroscience. 2018;30:280–290. doi: 10.1016/j.dcn.2017.02.006 28268177

83. Mizuhara H, Wang LQ, Kobayashi K, Yamaguchi Y. Long-range EEG phase synchronization during an arithmetic task indexes a coherent cortical network simultaneously measured by fMRI. Neuroimage. 2005;27(3):553–563. doi: 10.1016/j.neuroimage.2005.04.030 15921932

84. Widagdo M, Pierson J, Helme R. Age-related changes in qEEG during cognitive tasks. International journal of neuroscience. 1998;95(1-2):63–75. doi: 10.3109/00207459809000650 9845017

85. Masuda N, Sakaki M, Ezaki T, Watanabe T. Clustering coefficients for correlation networks. Frontiers in neuroinformatics. 2018;12:7. doi: 10.3389/fninf.2018.00007 29599714

86. Vanbinst K, Ceulemans E, Peters L, Ghesquière P, De Smedt B. Developmental trajectories of children’s symbolic numerical magnitude processing skills and associated cognitive competencies. Journal of experimental child psychology. 2018;166:232–250. doi: 10.1016/j.jecp.2017.08.008 28946044

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