Brain Resting State is Critical by gdf57j


									                                                                                                                Brain Resting State is Critical                                                                                                                                                        SFN 2008
                                                                                                                                                                                                                                                                                                     Washington, DC
                                                                                                                                                             Dante R. Chialvo                                                                                                                         798.5/UU90

                                                                                 Physiology, Feinberg School of Medicine, Northwestern University, Chicago, IL 60611. USA.

                                                                                                                         Networks link’s statistics for different threshold ρ values                                               Network’s statistical properties
                 All you want to know                                                                                                                                                                            T         ρ      <k>         N              C             L     D    Cran    Lran      Dran

  Brain “rest” is defined - more or less unsuccessfully - as the state                                       Brain
                                                                                                                                                                                          (ρ +)                                                   Positive correlated networks

  in which there is no explicit brain input or output. Could it be                                                                                                                        “Friends Net”
                                                                                                                                                                                                                 2.0      0.1     133       40000          0.065         2.72    4    0.005   2.61       4
                                                                                                                                                                                                                 2.3      0.3     127       40000          0.516         6.83    31   0.048   2.71       5
  comparable to any known dynamical state?                                                                                                                                                                       3.0      0.09    128       40000          0.064         2.73    4    0.003   2.65       4
                                                                                                                                                                                                                Brain     0.62    128       26985           0.45          4.4    13   0.061   2.62       5
  We have proposed that the brain stays near the critical point of a                                                                      Supercritical                                                                                        Negative correlated networks
  second order phase transition, where neuronal groups generate a                                            Ising                        Subcritical                                     (ρ -)                  2.0      -0.06   26        29370           0.01         3.24    5    0.01    3.38       8

  diversity of flexible collective behaviors, due to the known                                               model
                                                                                                                                                                                          “Enemy Net”
                                                                                                                                                                                                                 2.3      -0.38   26         4784            0           4.17    13    0.1    2.95       7

  abundance of metastable states at the transition. It is from this                                                                                                                                              3.0      -0.10   23        40000            0           3.72    6     0.0    3.7        6
                                                                                                                                                                                                                Brain     -0.71   27         1684            0           3.54    11   0.14    2.69       5
  viewpoint, that the dynamics of brain resting might correspond to
  a critical state.

  This conjecture is tested here comparing fMRI brain resting state
  data from healthy subjects with a paradigmatic critical system,
  the Ising model.
                                                                                                             Critical Ising networks ~ brain networks                       Identical behavior of degree, clustering                                                    Check list
                                                                                                                     Subcritical     Critical             Supercritical     correlation and path length in critical
  The analysis shows striking similarities between the two systems,                                                                                                         Ising networks and brain networks
  lending support to the conjecture that the functioning brain                                                                                                                                                                           Ising                             Voxel-based
  operates near a critical point.                                                                                                                                                                                                       Critical                    Functional Brain Networks
                                                                                                                                                                             Clustering and Path          Assortativity
       Manuscript and related papers:                                                                                                                                                                                                    1. Brain networks are small world, with dense
                                                                                                                                                                                                                                                             local correlations.
                                                                                                                                                                                                                                                         2. The distribution of the number of links
             Voxel-based correlation networks                                    Nodes spatial location
                                                                                                                                                                                                                                                           measured with the appropriate resolution is
                                                                                                                                                                   BRAIN                                                                                   scale-free.
                                                                                                             ρ + Nets                                                                                                                                    3. Brain networks are assortative, a tendency
                                                                                                                                                                                                                                                           for nodes with similar number of links to be
                                                                                                                                                                                                                                                           directly connected.
                                                                                     Undirected Degree (k)
                                                                                                                                                                                                                                                         4. Positively correlated cortical domains
                                                                                                                      Subcritical    Critical             Supercritical
                                                                                                                                                                                                                                                           coexist with approximately equal size anti-
                                                                                                                                                                                                                                                           correlated non-local domains.
                                                        Steps to extract the networks (a, b) and
                                                        computing (c - i) graph properties ([a-i]
                                                        From van den Heuvel et al., Neuroimage,

                                                                                                                                                                                                                                                                    Still, so what?
                                                        2008; [k] from Eguiluz et al., Phys. Rev.
                                                        Letters, 2005)                                                                                                     Roughed balanced correlation landscape is
Networks are collections of nodes joined by links. Sites are connected                                                                                                     typical in critical Ising and brain networks
by a link if their mutual correlation is larger than a certain value ρ .
                                                                                                                                                                                                                                          • A toy model with only local excitatory interactions
                                                                                                                                                                                                                                            exhibits, at the phase transition, all the relevant
                                                                                                                                                                   BRAIN                                                                    correlation properties described for the brain resting
                                                                Critical Point                                ρ - Nets                                                                                                                      state large-scale spatio-temporal patterns.
                                                                                                                                                                                                                                          • Anti-correlated patterns appearing in absence of
                                                                    TC                                                                                                                                                                      “inhibitory connections” are related to emergent
                                                                                                                                                                                                                                            collective properties.
                                               T<TC                 T~TC                         T>TC
                                                                                                                                                                                                  ~1                                      • Being collective properties, most of these correlation
                                                                                                                            Average of five subjects                                                                                        effects should be seen only at relatively low
       Only local positive interactions                                                                                                                                                                                                   • An “order parameter”, characterizing cortical balance
                                          Subcritical               Critical              SuperCritical                                                                      Balance is disrupted in Chronic Pain                           might be derived from these concepts, able to
          E=−J Σ <i,j> Si Sj – B Σk Sk       Snapshots of spins states in the Ising model.
                                                                                                                                                                             Patients (Baliki et al. , J. Neurosc. 2008).
                                          Long range correlations emerges at the critical point                                                                                                                                             parametrize brain fMRI in health and disease.
The Ising model is a toy model of a magnet, it simulates the local
interactions between spins. Depending on the temperature, there is                                                                                                                                                                Work in collaboration with J. Foss (NWU), D. Fraiman and P. Balenzuela
collective order or disorder; a continuous 2nd order phase transition.                                                                                                           Funded by NIH NINDS NS58661                      (Physics, FCEN, UBA and Mathematics and Sciences Univ. San Andres,
                                                                                                                                                                                                                                  Buenos Aires, Argentina).

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