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Connecting the (Brain) Dots: Understanding Brain Functional Networks

A sta­tis­ti­cal model of the net­work of con­nec­tions between brain regions (Kurzweil):

- “Researchers at the Uni­ver­sity of Cam­bridge have devel­oped a sim­ple math­e­mat­i­cal model of the brain which pro­vides a remark­ably com­plete sta­tis­ti­cal account of the com­plex web of con­nec­tions between var­i­ous brain regions.”

- “The brain shares a pat­tern of con­nec­tions that is sim­i­lar to other com­plex net­works such as social net­works and the Web. How­ever, until now, it was not known what rules were involved in the for­ma­tion of the human brain network.”

StudySim­ple mod­els of human brain func­tional net­works (PNAS)

  • Abstract: Human brain func­tional net­works are embed­ded in anatom­i­cal space and have topo­log­i­cal properties—small-worldness, mod­u­lar­ity, fat-tailed degree distributions—that are com­pa­ra­ble to many other com­plex net­works. Although a sophis­ti­cated set of mea­sures is avail­able to describe the topol­ogy of brain net­works, the selec­tion pres­sures that drive their for­ma­tion remain largely unknown. Here we con­sider gen­er­a­tive mod­els for the prob­a­bil­ity of a func­tional con­nec­tion (an edge) between two cor­ti­cal regions (nodes) sep­a­rated by some Euclid­ean dis­tance in anatom­i­cal space. In par­tic­u­lar, we pro­pose a model in which the embed­ded topol­ogy of brain net­works emerges from two com­pet­ing fac­tors: a dis­tance penalty based on the cost of main­tain­ing long-range con­nec­tions; and a topo­log­i­cal term that favors links between regions shar­ing sim­i­lar input. We show that, together, these two bio­log­i­cally plau­si­ble fac­tors are suf­fi­cient to cap­ture an impres­sive range of topo­log­i­cal prop­er­ties of func­tional brain net­works. Model para­me­ters esti­mated in one set of func­tional MRI (fMRI) data on nor­mal vol­un­teers pro­vided a good fit to net­works esti­mated in a sec­ond inde­pen­dent sam­ple of fMRI data. Fur­ther­more, slightly detuned model para­me­ters also gen­er­ated a rea­son­able sim­u­la­tion of the abnor­mal prop­er­ties of brain func­tional net­works in peo­ple with schiz­o­phre­nia. We there­fore antic­i­pate that many aspects of brain net­work orga­ni­za­tion, in health and dis­ease, may be par­si­mo­niously explained by an eco­nom­i­cal clus­ter­ing rule for the prob­a­bil­ity of func­tional con­nec­tiv­ity between dif­fer­ent brain areas.

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