In the 1990s, it emerged that the brain generates random noise, and hence cannot be described by deterministic chaos. When neuroscientists incorporated this randomness into their models, they found that it created systems on the border between order and disorder — self-organised criticality.
More recently, experiments have confirmed that these models accurately describe what real brain tissue does. They build on the observation that when a single neuron fires, it can trigger its neighbours to fire too, causing a cascade or avalanche of activity that can propagate across small networks of brain cells. This results in alternating periods of quiescence and activity – remarkably like the build-up and collapse of a sand pile.
That and what follows are from an article, Disorderly genius: How chaos drives the brain, by David Robson in New Scientist (June 29, 2009):
… In technical terms, systems on the edge of chaos are said to be in a state of “self-organised criticality”. These systems are right on the boundary between stable, orderly behaviour – such as a swinging pendulum – and the unpredictable world of chaos, as exemplified by turbulence.
The quintessential example of self-organised criticality is a growing sand pile. As grains build up, the pile grows in a predictable way until, suddenly and without warning, it hits a critical point and collapses. These “sand avalanches” occur spontaneously and are almost impossible to predict, so the system is said to be both critical and self-organising. Earthquakes, avalanches and wildfires are also thought to behave like this, with periods of stability followed by catastrophic periods of instability that rearrange the system into a new, temporarily stable state.
… It might seem precarious to have a brain that plunges randomly into periods of instability, but the disorder is actually essential to the brain’s ability to transmit information and solve problems. “Lying at the critical point allows the brain to rapidly adapt to new circumstances,” says Andreas Meyer-Lindenberg from the Central Institute of Mental Health in Mannheim, Germany.
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As it processes information, the brain often synchronises large groups of neurons to fire at the same frequency, a process called “phase-locking”. Like broadcasting different radio stations at different frequencies, this allows different “task forces” of neurons to communicate among themselves without interference from others.
The brain also constantly reorganises its task forces, so the stable periods of phase-locking are interspersed with unstable periods in which the neurons fire out of sync in a blizzard of activity. This, again, is reminiscent of a sand pile. Could it be another example of self-organised criticality in the brain?
In 2006, Meyer-Lindenberg and his team made the first stab at answering that question. They used brain scans to map the connections between regions of the human brain and discovered that they form a “small-world network” – exactly the right architecture to support self-organised criticality.
… For the brain, it’s the perfect compromise. One of the characteristics of small-world networks is that you can communicate to any other part of the network through just a few nodes – the “six degrees of separation” reputed to link any two people in the world. In the brain, the number is 13.
Meyer-Lindenberg created a computer simulation of a small-world network with 13 degrees of separation. Each node was represented by an electrical oscillator that approximated a neuron’s activity. The results confirmed that the brain has just the right architecture for its activity to sit on the tipping point between order and disorder, although the team didn’t measure neural activity itself (Proceedings of the National Academy of Sciences, vol 103, p 19518).
That clinching evidence arrived earlier this year, when Ed Bullmore of the University of Cambridge and his team used brain scanners to record neural activity in 19 human volunteers. They looked at the entire range of brainwave frequencies, from 0.05 hertz all the way up to 125 hertz, across 200 different regions of the brain.
The team found that the duration both of phase-locking and unstable resynchronisation periods followed a power-law distribution. Crucially, this was true at all frequencies, which means the phenomenon is scale invariant – the other key criterion for self-organised criticality.
What’s more, when the team tried to reproduce the activity they saw in the volunteers’ brains in computer models, they found that they could only do so if the models were in a state of self-organised criticality (PLoS Computational Biology, vol 5, p e1000314). “The models only showed similar patterns of synchronisation to the brain when they were in the critical state,” says Bullmore.
Read the full piece. It’s interesting and there are links to the supporting research. [ link ]
-Julie
