Modeling Brain Rhythms
Since the EEG was invented in the 1920s, rhythmic electrical activity has been observed in the brains of humans and animals. However, it is still not fully understood how brain rhythms come about. What (if anything) brain rhythms might be good for has been the subject of some fascinating speculation, but hardly anything is rigorously known about this question. Brain rhythms are the result of synchronous, rhythmic firing of large ensembles of neurons. Beginning with Norbert Wiener's work on alpha rhythms in the 1960s, mathematicians have therefore tried to understand what might make large ensembles of neurons fire in synchrony. For a single population of neurons with purely excitatory or purely inhibitory interactions, much is now understood about this question. However, real brains contain both excitatory and inhibitory neurons, and rhythms in networks of this sort are still not very well understood. I will present some of my own contributions (joint with Nancy Kopell, Boston University) in this area. It is widely believed that ensembles of excitatory neurons can amplify their effect on other parts of the brain by synchronizing. I will present a way of making this mathematically precise. I will also show that asynchrony, not synchrony, maximizes the effect of ensembles of inhibitory neurons.