Skip to main content
Log in

Considering structural connectivity in the triple code model of numerical cognition: differential connectivity for magnitude processing and arithmetic facts

  • Original Article
  • Published:
Brain Structure and Function Aims and scope Submit manuscript

Abstract

The current study provides a generalizable account of the anatomo-functional associations as well as the connectivity of representational codes underlying numerical processing as suggested by the triple code model (TCM) of numerical cognition. By evaluating the neural networks subserving numerical cognition in two specific and substantially different numerical tasks with regard to both grey matter localizations as well as white matter tracts we (1) considered the possibility of additional memory-related cortex areas crucial for arithmetic fact retrieval (e.g., the hippocampus); (2) specified the functional involvement of prefrontal areas in number magnitude processing, and, finally; (3) identified the connections between these anatomo-functional instantiations of the representations involved in number magnitude processing and arithmetic fact retrieval employing probabilistic fiber tracking. The resulting amendments to the TCM are summarized in a schematic update, and ideas concerning the possible functional interplay between number magnitude processing and arithmetic fact retrieval are discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

Notes

  1. We re-ran the analysis of tracts omitting the left-handed participant. However, since this did neither alter the results substantially nor even visibly, we decided to keep all participants.

References

  • Addis DR, Moscovitch M, Crawley AP, McAndrews MP (2004) Recollective qualities modulate hippocampal activation during autobiographical memory retrieval. Hippocampu 14(6):752–762

    Article  Google Scholar 

  • Anderson JR (2005) Human symbol manipulation within an integrated cognitive architecture. Cogn Sci 29(3):313–341

    Article  PubMed  Google Scholar 

  • Anderson JR, Qin Y, Sohn MH, Stenger VA, Carter CS (2003) An information-processing model of the BOLD response in symbol manipulation tasks. Psychon Bull Rev 10(2):241–261

    Article  PubMed  Google Scholar 

  • Arsalidou M, Taylor MJ (2011) Is 2 + 2 = 4? Meta-analyses of brain areas needed for numbers and calculations. NeuroImage 54:2382–2393

    Article  PubMed  Google Scholar 

  • Ashcraft MH, Kirk EP (2001) The relationships among working memory, math anxiety, and performance. J Exp Psychol Gen 130:224–237

    Article  CAS  PubMed  Google Scholar 

  • Atique B, Erb M, Gharabaghi A, Grodd W, Anders S (2011) Task-specific activity and connectivity within the mentalizing network during emotion and intention mentalizing. Neuroimage 55(4):1899–1911

    Article  PubMed  Google Scholar 

  • Baddeley AD (1966) The influence of acoustic and semantic similarity on long-term memory for word sequences. Q J Exp Psychol 18(4):302–309

    Article  CAS  PubMed  Google Scholar 

  • Baetens K, Ma N, Steen J, Van Overwalle F (2014) Involvement of the mentalizing network in social and non-social high construal. Soc Cogn Affect Neurosci 9:817–824

    Article  PubMed  PubMed Central  Google Scholar 

  • Basser PJ, Mattiello J, Le Bihan D (1994) Estimation of the effective self-diffusion tensor from the NMR spin echo. J Magn Res B 103:247–254

    Article  CAS  Google Scholar 

  • Bürgel U, Amunts K, Hoemke L, Mohlberg H, Gilsbach JM, Zilles K (2006) White matter fiber tracts of the human brain: three-dimensional mapping at microscopic resolution, topography and intersubject variability. Neuroimage 29(4):1092–1105

    Article  PubMed  Google Scholar 

  • Cansino S, Maquet P, Dolan RJ, Rugg MD (2002) Brain activity underlying encoding and retrieval of source memory. Cereb Cortex 10:1048–1056

    Article  Google Scholar 

  • Caspers S, Geyer S, Schleicher A, Mohlberg H, Amunts K, Zilles K (2006) The human inferior parietal cortex: cytoarchitectonic parcellation and interindividual variability. Neuroimage 33(2):430–448

    Article  PubMed  Google Scholar 

  • Caspers S, Eickhoff SB, Rick T, von Kapri A, Kuhlen T, Huang R, Shah NJ, Zilles K (2011) Probabilistic fibre tract analysis of cytoarchitectonically defined human inferior parietal lobule areas reveals similarities to macaques. Neuroimage 58(2):362–380

    Article  PubMed  Google Scholar 

  • Catani M, Thiebaut de Schotten M (2012) Atlas of Human Brain Connections. Oxford University Press

  • Cho S, Metcalfe AWS, Young CB, Ryali S, Geary DC, Menon V (2012) Hippocampal-prefrontal engagement and dynamic causal interactions in the maturation of children’s fact retrieval. J Cogn Neurosci 24:1849–1866

    Article  PubMed  PubMed Central  Google Scholar 

  • Dehaene S, Cohen L (1995) Towards an anatomical and functional model of number processing. Math Cogn 1:83–120

    Google Scholar 

  • Dehaene S, Cohen L (1997) Cerebral pathways for calculation: double dissociation between rote verbal and quantitative knowledge of arithmetic. Cortex 33:219–250

    Article  CAS  PubMed  Google Scholar 

  • Dehaene S, Piazza M, Pinel P, Cohen L (2003) Three parietal circuits for number processing. Cogn Neuropsychol 20:487–506

    Article  PubMed  Google Scholar 

  • Delazer M, Domahs F, Bartha L, Brenneis C, Lochy A, Trieb T, Benke T (2003) Learning complex arithmetic—a fMRI study. Cogn Brain Res 18:76–88

    Article  CAS  Google Scholar 

  • Eickhoff S, Stephan KE, Mohlberg H, Grefkes C, Fink GR, Amunts K, Zilles K (2005) A new SPM toolbox for combining probabilistic cytoarchitectonic maps and functional imaging data. NeuroImage 25(4):1325–1335

    Article  PubMed  Google Scholar 

  • Eger E, Sterzer P, Russ MO, Giraud AL, Kleinschmidt A (2003) A supramodal number representation in human intraparietal cortex. Neuron 37:719–725

    Article  CAS  PubMed  Google Scholar 

  • Epstein RA (2008) Parahippocampal and retrosplenial contributions to human spatial navigation. Trends Cogn Sci 12:388–396

    Article  PubMed  PubMed Central  Google Scholar 

  • Grabner RH, Ansari D, Koschutnig K, Reishofer G, Ebner F, Neuper C (2009) To retrieve or to calculate? Left angular gyrus mediates the retrieval of arithmetic facts during problem solving. Neuropsychologia 47:604–608

    Article  PubMed  Google Scholar 

  • Imbo I, Vandierendonck A, De Rammelaere S (2007a) The role of working memory in the carry operation of mental arithmetic: number and value of the carry. Q J Exp Psychol 60:708–731

    Article  Google Scholar 

  • Imbo I, Vandierendonck A, Vergauwe E (2007b) The role of working memory in carrying and borrowing. Psychol Res 71:467–483

    Article  PubMed  Google Scholar 

  • Ischebeck A, Zamarian L, Egger K, Schocke M, Delazer M (2007) Imaging early practice effects in arithmetic. NeuroImage 36:993–1003

    Article  PubMed  Google Scholar 

  • Klein E, Nuerk HC, Wood G, Knops A, Willmes K (2009) The exact vs. approximate distinction in numerical cognition may not be exact, but only approximate How different processes work together in multi-digit addition. Brain Cogn 2:369–381

    Article  Google Scholar 

  • Klein E, Moeller K, Nuerk HC, Willmes K (2010) On the cognitive foundations of basic auditory number processing. Behav Brain Funct 6:42

    Article  PubMed  PubMed Central  Google Scholar 

  • Klein E, Moeller K, Glauche V, Weiller C, Willmes K (2013) Processing pathways in mental arithmetic—evidence from probabilistic fiber tracking. PLoS ONE 8(1):e55455

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Kong J, Wang C, Kwong K, Vangel M, Chuac E, Gollub R (2005) The neural substrate of arithmetic operations and procedure complexity. Cogn Brain Res 22:397–405

    Article  Google Scholar 

  • Kreher BW, Schnell S, Mader I, Ilyasov KA, Hennig J, Kiselev V, Saur D (2008) Connecting and merging fibres: pathway extraction by combining probability maps. NeuroImage 43:81–89

    Article  CAS  PubMed  Google Scholar 

  • Krueger F, Landgraf S, van der Meer E, Deshpande G, Hu X (2011) Effective connectivity of the multiplication network: a functional MRI and multivariate Granger Causality Mapping study. Hum Brain Mapp 32(9):1419–1431. doi:10.1002/hbm.21119

    Article  PubMed  Google Scholar 

  • LeFevre JA, Sadesky GS, Bisanz J (1996) Selection of procedures in mental addition: reassessing the problem size effect in adults. J Exp Psychol Learn Mem Cogn 22:216–230

    Article  Google Scholar 

  • Maguire EA (2001) The retrosplenial contribution to human navigation: a review of lesion and neuroimaging findings. Scand J Psychol 42:225–238

    Article  CAS  PubMed  Google Scholar 

  • Miller EK (2000) The prefrontal cortex and cognitive control. Nat Rev Neurosci 1:58–65

    Google Scholar 

  • Montaldi D, Mayes AR (2010) The role of recollection and familiarity in the functional differentiation of the medial temporal lobes. Hippocampus 20(11):1291–1314

    Article  PubMed  Google Scholar 

  • Newton JM, Ward NS, Parker GJM, Deichmann R, Alexander DC, Friston K, Frackowiak RSJ (2006) Non-invasive mapping of corticofugal fibres from multiple motor areas—relevance to stroke recovery. Brain 129:1844–1858

    Article  PubMed  PubMed Central  Google Scholar 

  • Oishi K, Faria AV, Zijl PCM, Mori S (2011) MRI atlas of the human white matter, 2nd edn. Academic Press, New York

    Google Scholar 

  • Parker GJM, Haroon HA, Wheeler-Kingshott CAM (2003) A framework for a streamline-based probabilistic index of connectivity (PICo) using a structural interpretation of MRI diffusion measurements. J Magn Res Imaging 18:242–254

    Article  Google Scholar 

  • Pesenti M, Thioux M, Seron X, De Volder A (2000) Neuroanatomical substrates of Arabic number processing, numerical comparison and simple addition: a PET study. J Cogn Neurosci 12(3):461–479

    Article  CAS  PubMed  Google Scholar 

  • Piefke M, Weiss PH, Zilles K, Markowitsch HJ, Fink GR (2003) Differential remoteness and emotional tone modulate the neural correlated of autobiographical memory. Brain 126:650–668

    Article  PubMed  Google Scholar 

  • Qin S, Cho S, Chen T, Rosenberg-Lee M, Geary DC, Menon V (2014) Su Hippocampal-neocortical functional reorganization underlies children’s cognitive development. Nat Neurosci 17:1263–1269

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Raichle ME, MacLeod AM, Snyder AZ, Powers WJ, Gusnard DA, Shulman GL (2001) A default mode of brain function. Proc Natl Acad Sci USA 98(2):676–682

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Rosenberg-Lee M, Chang TT, Young CB, Wu S, Menon V (2011) Functional dissociations between four basic arithmetic operations in the human posterior parietal cortex: a cytoarchitectonic mapping study. Neuropsychologia 49(9):2592–2608

    Article  PubMed  PubMed Central  Google Scholar 

  • Rugg MD, Yonelinas AP (2003) Human recognition memory: a cognitive neuroscience perspective. Trends Cogn Sci 7(7):313–319

    Article  PubMed  Google Scholar 

  • Rusconi E, Galfano G, Rebonato E, Umiltà C (2006) Bidirectional links in the network of multiplication facts. Psychol Res 70(1):32–42

    Article  PubMed  Google Scholar 

  • Saur D, Kreher BW, Schnell S, Kuemmerer D, Kellermeyer P, Vry MS, Umarova RM, Musso M, Glauche V, Abel S, Huber W, Rijntjes M, Hennig J, Weiller C (2008) Ventral and dorsal pathways for language. Proc Natl Acad Sci USA 105:18035–18040

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Saur D, Schelter B, Schnell S, Kratochvil D, Küpper H, Kellmeyer P, Kümmerer D, Klöppel S, Glauche V, Lange R, Mader W, Feess D, Timmer J, Weiller C (2010) Combining functional and anatomical connectivity reveals brain networks for auditory language comprehension. NeuroImage 49:3187–3197

    Article  PubMed  Google Scholar 

  • Scheperjans F, Eickhoff SB, Hömke L, Mohlberg H, Hermann K, Amunts K, Zilles K (2008) Probabilistic maps, morphometry, and variability of cytoarchitectonic areas in the human superior parietal cortex. Cereb Cortex 18(9):2141–2157

    Article  PubMed  PubMed Central  Google Scholar 

  • Schmahmann JD, Pandya DN (2006) Fiber pathways of the brain. Oxford Univ Press, New York

    Book  Google Scholar 

  • Seghier ML (2013) The angular gyrus: multiple functions and multiple subdivisions. Neuroscientist 19(1):43–61

    Article  PubMed  PubMed Central  Google Scholar 

  • Spunt RP, Satpute AB, Lieberman MD (2011) Identifying the what, why, and how of an observed action: an fMRI study of mentalizing and mechanizing during action observation. J Cogn Neurosci 23(1):63–74

    Article  PubMed  Google Scholar 

  • Supekar K, Swigart AG, Tenison C, Jolles DD, Rosenberg-Lee M, Fuchs L, Menon V (2013) Neural predictors of individual differences in response to math tutoring in primary-grade school children. Proc Natl Acad Sci USA 110:8230–8235

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Svoboda E, McKinnon MC, Levine B (2006) The functional neuroanatomy of autobiographical memory: a meta-analysis. Neuropsychologia 44:2189–2208

    Article  PubMed  PubMed Central  Google Scholar 

  • Uddin LQ, Supekar K, Amin H, Rykhlevskaia E, Nguyen DA, Greicius MD, Menon V (2010) Dissociable connectivity within human angular gyrus and intraparietal sulcus: evidence from functional and structural connectivity. Cereb Cortex 20(11):2636–2646

    Article  PubMed  PubMed Central  Google Scholar 

  • Vann SD, Aggleton JP, Maguire EA (2009) What does the retrosplenial cortex do? Nat Rev Neurosci 10:792–802

    Article  CAS  PubMed  Google Scholar 

  • Wedeen VJ, Rosene DL, Wang R, Dai G, Mortazavi F, Hagmann P, Kaas JH, Tseng WY (2012) The geometric structure of the brain fiber pathways. Science 335(6076):1628–1634

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Weiller C, Bormann T, Saur D, Musso M, Rijntjes M (2011) How the ventral pathway got lost—and what its recovery might mean. Brain Lang 118:29–39

    Article  PubMed  Google Scholar 

  • Willmes K, Moeller K, Klein E (2014) Where numbers meet words—a common ventral network for semantic classification. Scand J Psychol 55:202–211

    Article  PubMed  Google Scholar 

  • Wood G, Nuerk HC, Moeller K, Geppert B, Schnitker R, Weber J, Willmes K (2008) All for one but not one for all: how multiple number representations are recruited in one numerical task. Brain Res 1187:154–166

    Article  CAS  PubMed  Google Scholar 

  • Wu SS, Chang TT, Majid A, Caspers S, Eickhoff SB, Menon V (2009) Functional heterogeneity of inferior parietal cortex during mathematical cognition assessed with cytoarchitectonic probability maps. Cereb Cortex 12:2930–2945

    Article  Google Scholar 

  • Zaitsev M, Hennig J, Ilyasov KA (2006) Geometric distortions applied to diffusion tensor imaging. Annual Meeting of the international society for magnetic resonance in medicine, Seattle

  • Zaunmueller L, Domahs F, Dressel K, Lonnemann J, Klein E, Ischebeck A, Willmes K (2009) Rehabilitation of arithmetic fact retrieval via extensive practice: a combined fMRI and behavioural case-study. Neuropsychol Rehabil 19:422–443

    Article  Google Scholar 

Download references

Acknowledgments

This research was supported by the German Research Foundation (DFG) to Klaus Willmes (Wl 1804/6-1), Hans-Otto Karnath (KA 1258/11-1), Korbinian Moeller (MO 2525/2-1), and André Knops (KN 959/2-1) as well as by the Leibniz-Competition Fund (SAW) providing funding to Elise Klein (SAW-2014-IWM-4). We are indebted to the “Brain Imaging Facility of the Interdisciplinary Centre for Clinical Research within the Faculty of Medicine at the RWTH Aachen University” for their precious help in acquiring the MRI/fMRI data.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Elise Klein.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary material 1 (DOCX 3066 kb)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Klein, E., Suchan, J., Moeller, K. et al. Considering structural connectivity in the triple code model of numerical cognition: differential connectivity for magnitude processing and arithmetic facts. Brain Struct Funct 221, 979–995 (2016). https://doi.org/10.1007/s00429-014-0951-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00429-014-0951-1

Keywords

Navigation