A Dynamical Clustering Model of Brain Connectivity Inspired by the N-Body Problem

  • Gautam Prasad
  • Josh Burkart
  • Shatanu H. Joshi
  • Talia M. Nir
  • Arthur W. Toga
  • Paul M. Thompson
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8159)


We present a method for studying brain connectivity by simulating a dynamical evolution of the nodes of the network. The nodes are treated as particles, and evolved under a simulated force analogous to gravitational acceleration in the well-known N-body problem. The particle nodes correspond to regions of the cortex. The locations of particles are defined as the centers of the respective regions on the cortex and their masses are proportional to each region’s volume. The force of attraction is modeled on the gravitational force, and explicitly made proportional to the elements of a connectivity matrix derived from diffusion imaging data. We present experimental results of the simulation on a population of 110 subjects from the Alzheimer’s Disease Neuroimaging Initiative (ADNI), consisting of healthy elderly controls, early mild cognitively impaired (eMCI), late MCI (LMCI), and Alzheimer’s disease (AD) patients. Results show significant differences in the dynamic properties of connectivity networks in healthy controls, compared to eMCI as well as AD patients.


gravity n-body simulation diffusion connectivity MRI 


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  1. 1.
    Sporns, O., Tononi, G., Kötter, R.: The human connectome: a structural description of the human brain. PLoS Computational Biology 1(4), 1–42 (2005)CrossRefGoogle Scholar
  2. 2.
    Hagmann, P., Cammoun, L., Gigandet, X., Meuli, R., Honey, C., Wedeen, V., Sporns, O.: Mapping the structural core of human cerebral cortex. PLoS Biology 6(7), e159 (2008)Google Scholar
  3. 3.
    Friston, K.: Functional and effective connectivity in neuroimaging: a synthesis. Human Brain Mapping 2(1-2), 56–78 (2004)CrossRefGoogle Scholar
  4. 4.
    He, Y., Chen, Z., Evans, A.: Small-world anatomical networks in the human brain revealed by cortical thickness from MRI. Cerebral Cortex 17(10), 2407–2419 (2007)CrossRefGoogle Scholar
  5. 5.
    Biswal, B., Zerrin Yetkin, F., Haughton, V., Hyde, J.: Functional connectivity in the motor cortex of resting human brain using echo-planar MRI. Magnetic Resonance in Medicine 34(4), 537–541 (1995)CrossRefGoogle Scholar
  6. 6.
    Zhou, C., Zemanová, L., Zamora, G., Hilgetag, C., Kurths, J.: Hierarchical organization unveiled by functional connectivity in complex brain networks. Physical Review Letters 97(23), 238103 (2006)CrossRefGoogle Scholar
  7. 7.
    Pollard, H.: Mathematical introduction to celestial mechanics, vol. 1. Prentice-Hall (1966)Google Scholar
  8. 8.
    Dormand, J., Prince, P.: A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 6(1), 19–26 (1980)MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Trojanowski, J., Vandeerstichele, H., Korecka, M., Clark, C., Aisen, P., Petersen, R., Blennow, K., Soares, H., Simon, A., Lewczuk, P.: Update on the biomarker core of the Alzheimer’s Disease Neuroimaging Initiative subjects. Alzheimer’s & Dementia: The Journal of the Alzheimer’s Association 6(3), 230 (2010)CrossRefGoogle Scholar
  10. 10.
    Sled, J., Zijdenbos, A., Evans, A.C.: A nonparametric method for automatic correction of intensity nonuniformity in MRI data. IEEE Transactions on Medical Imaging 17(1), 87–97 (1998)CrossRefGoogle Scholar
  11. 11.
    Holmes, C., Hoge, R., Collins, L., Woods, R., Toga, A., Evans, A.: Enhancement of MR images using registration for signal averaging. Journal of Computer Assisted Tomography 22(2), 324–333 (1998)CrossRefGoogle Scholar
  12. 12.
    Jenkinson, M., Bannister, P., Brady, M., Smith, S.: Improved optimization for the robust and accurate linear registration and motion correction of brain images. NeuroImage 17(2), 825–841 (2002)CrossRefGoogle Scholar
  13. 13.
    Fischl, B., Van Der Kouwe, A., Destrieux, C., Halgren, E., Ségonne, F., Salat, D., Busa, E., Seidman, L., Goldstein, J., Kennedy, D.: Automatically parcellating the human cerebral cortex. Cerebral Cortex 14(1), 11–22 (2004)CrossRefGoogle Scholar
  14. 14.
    Behrens, T., Berg, H., Jbabdi, S., Rushworth, M., Woolrich, M.: Probabilistic diffusion tractography with multiple fibre orientations: What can we gain? NeuroImage 34(1), 144–155 (2007)CrossRefGoogle Scholar
  15. 15.
    Rubinov, M., Sporns, O.: Complex network measures of brain connectivity: uses and interpretations. NeuroImage 52(3), 1059–1069 (2010)CrossRefGoogle Scholar
  16. 16.
    Toga, A., Thompson, P.: Connectomics sheds new light on Alzheimer’s disease. Biological Psychiatry 73(5), 390–392 (2013)CrossRefGoogle Scholar
  17. 17.
    Van Essen, D.: A tension-based theory of morphogenesis and compact wiring in the central nervous system. Nature, 313–318 (1997)Google Scholar
  18. 18.
    Eastwood, J., Hockney, R., Lawrence, D.: P3M3DP-The three-dimensional periodic particle-particle/particle-mesh program. Computer Physics Communications 19, 215–261 (1980)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  • Gautam Prasad
    • 1
  • Josh Burkart
    • 2
  • Shatanu H. Joshi
    • 1
  • Talia M. Nir
    • 1
  • Arthur W. Toga
    • 1
  • Paul M. Thompson
    • 1
  1. 1.Imaging Genetics Center, Laboratory of Neuro ImagingUCLA School of MedicineLos AngelesUSA
  2. 2.Department of PhysicsUC BerkeleyBerkeleyUSA

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