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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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