Making room for a little chaos in your brain
The idea that the brain might be in a critical state has been around for a while now. Ever since neuroscientists began wondering about where the noisy neural activity recorded in vivo came from, criticality has stood up as one of the main candidates to consider. But what is criticality?
The term can be traced back to Statistical Mechanics, where it is used to describe the special conditions and phenomena that one can observe in a physical system that is about to transit from one phase to another. Just think about a glass of water around zero degrees Celsius. Below this temperature, the water will freeze and become solid, while if the temperature is increased a bit, it will remain in its liquid state (although cold enough to serve as a good refresher). If the temperature is maintained exactly at zero degrees Celsius, the system would be in a particular and fragile state, neither a complete solid nor liquid, and some of its thermodynamical properties would change drastically around that point. This state, which is referred to as a critical point, may have even more spectacular implications for other systems –the critical opalescence of some materials been one of the most visually spectacular examples: the liquid fluctuates between being opaque or transparent, since its optical properties are particularly volatile near the critical point, as you can see in Binary Mixture Critical Opalescence, around minute 1:10.
The idea of the brain, or part of it, being in a state close to a critical point has attracted a lot of attention, since the activity of neurons, just like the optical properties in the critical opalescence, usually displays strong and erratic fluctuations. Even more, the volatility and chaotic nature of such a state implies that our neural circuits would be extremely receptive to incoming stimuli from the outside world, a property which seems highly desirable for a organ responsible for the animal’s survival in a potentially dangerous and changing environment. From a theoretical perspective, many attempts have been done to provide a solid and plausible framework for the critical brain hypothesis 1. A crucial detail, however, has been missing in most of these attempts: the critical point is just a point in the huge ocean of possible states the system may be in. Why the working point of the brain would be near the critical point, and more importantly, how could the brain self-tune its own state to such a fragile state remains an elusive question. Any change in the neural or synaptic properties, due to learning for instance, would potentially drive the system away from criticality, and even rectification (homeostatic) mechanisms would have a hard time trying to maintain a proper proximity with the critical point.
An interesting explanation has been proposed recently 2 by researchers from the University of Granada (Spain). In their work, they take a close look at the structure of the mesoscopic neural networks of the human brain, which have been obtained with recent neuroimaging techniques 3. The connectivity pattern found is consistent with what is called “hierarchical-modular” networks, which combines a certain level of nested modularity with the coexistence of multiple spatial scales (see figure 2). The authors have shown that this type of networks induce a remarkable effect on the properties of the neural system: they extend conditions for criticality from a single point to a certain volume, called a Griffith phase. This expansion constitutes a major advance in understanding the presence of criticality in the brain, since it is much easier to maintain the properties of neural circuits within a critical volume than within proximity to a single critical point. So instead of just a point (or molecule) in the huge ocean of possibilities, we just need to stay swimming at our favorite beach.
This work opens exciting new questions: how is the criticality, and the associated noisy and chaotic behavior, used by neural circuits embedded in such hierarchical-modular structures? Do the findings hold when we look at our brains with a finer level of detail? How are these nested structures maintained? For now, we just have to bear in mind that our brain have a proper way to make room for a little chaos in their agenda.
I once heard on a science program that a self-similar fractal is the best type of shape (whatever they meant by “best”?) for an antenna, and they showed an antenna from a cell phone. It appeared to be a square whittled wire-thin by a Cantor-like series of square cutouts. Like that pattern that fractal artists call a Menger Sponge.
Does this have anything to do with a Griffith Phase?