I was asked this question on Quora recently:
The brain has neurons which approximately perform function evaluations on their inputs. How would this cause brainwaves of different frequencies? Why are they related to the level of arousal in the brain (sleep/meditation etc)?
Is there some sort of “controller” that synchronizes the firing?
This is an excellent set of questions!
1. Why does the brain have waves?
There is no consensus on their functional role, but some researchers think oscillations facilitate flexible coordination and communication among neurons.
2. The brain has neurons which can approximately be understood as performing function evaluations on their inputs, though the actual mechanisms are more complex. But how would this cause brainwaves of different frequencies to exist?
There are several possible mechanisms that can cause the input-output transformation of neurons to lead to oscillations when the neurons are connected in networks. Furthermore, neurons themselves often have intrinsic oscillatory properties (other than basic spiking), such as rebound excitation following inhibition.
3. Is there some sort of “controller” that synchronizes the firing?
There is no single controller causing synchronization or oscillation — there are actually several local and meso-scale mechanisms, often involving inhibitory interneurons*. (Note that synchronization and oscillation are distinct phenomena. You can have synchronized non-oscillatory processes, and oscillations that are not synch-ed.)
What are brain waves?
Even though we use the generic term ‘brain waves’, there are actually a variety of distinct mechanisms at work that lead to rhythmic behavior in different frequency bands. And in many cases we still don’t know what the mechanism is that causes a particular brain rhythm, or can’t decide among multiple plausible mechanisms.
Even though I’m a computational neuroscientist, I find it hard to conceptually integrate all the different perspectives on neural activity. But I’ve been thinking about this a lot lately, so here goes!
The most fine-grained perspective involves measuring the voltage of an individual neuron. This voltage can change in various ways. The most well known is the spike, or action potential. Spikes travel efficiently down the axon, and typically cause vesicle release in the synapse, which allows neurotransmitters to affect the post-synaptic neuron. But spiking is not the only kind of voltage fluctuation in a neuron. There are also ‘sub-threshold’ fluctuations, which are often oscillatory. These oscillations may represent oscillatory and/or synchronized inputs to the neuron that are insufficient to cause spiking. Single-electrode and multi-electrode recordings of cell activities can pick up both the sub-threshold fluctuations and the supra-threshold spiking.
Brain waves were first discovered through electroencephalography (EEG), which has been around for a century or so. Unlike electrode-based recording, EEG is non-invasive (meaning we don’t have to poke any sharp objects into anyone). But the main drawback of EEG is that it is a coarse-grained measure of neural activity. It measures the cumulative electrical activity of very large numbers of neurons.
It’s also important to realize that EEG essentially measures the synchronized inputs to a brain area, rather than the firing outputs. This has to do with the biophysics of the technique, which you can read about in more detail in my answer to the question “Are EEG voltages related to the average action potential firing rate of the cortical neurons near the electrode or are the voltages the average of low frequency voltage oscillations of the neurons?” EEG effectively measures the degree of synchronization of neurons that send inputs to the brain region directly underneath the EEG electrode.
Other techniques that can pick up oscillatory activity include magnetoencephalography (MEG) and Electrocorticography (ECoG).
Brain rhythms tend to be grouped into frequency bands. The most well-studied bands have been assigned Greek letters that reflect the order of their discovery. Here’s a list of the bands, along with their frequency ranges in hertz (Hz). I’ve linked to their Wikipedia pages, when available.
- Slow 3: 0.025-0.067
- Slow 2: 0.200-0.500
- Slow 1: 0.500-1.429
- Delta: 1 – 4
- Theta: 4 – 8
- Mu and SMR: 7.5 – 12.5
- Alpha: 9 – 13
- Beta: 14 – 30
- Gamma: 30 – 80
- Fast: 80 – 200
- Ultrafast: 200 – 600.000
What are the mechanisms that cause brain waves?
Through a combination of experimental techniques and theoretical approaches, neuroscientists have come up with several mechanisms that can explain oscillations in various frequency bands. In many cases it is not clear which mechanism is in fact at work.
I can’t really go though all the theoretical mechanisms that have been proposed, but I can talk about one that is very intuitive to understand: the PING model of Gamma activity. This model, developed by Nancy Kopell, has been widely corroborated by experimental work. (There may be different types of Gamma, however, and not all of them are covered by this model.)
PING stands for pyramidal-interneuronal network gamma, and involves interaction between excitatory cells and inhibitory cells, resulting in the creation of a nonlinear oscillator. The following diagram  illustrates the mechanism quite nicely:
The E(xcitatory) cells excite the I(nhibitory) cells, which in turn inhibit the same excitatory cells. This results in an oscillation whose frequency is determined by the rate of integration of the I-cells. Fast I-cells can produce fast rhythms.
There are plenty of other mechanisms for oscillations, but the PING model will give you a flavor of how they can be constructed. Arousal levels can by incorporated into models by incorporating factors such as neurotransmitter level fluctuations, and the effects of such fluctuation on the sub-threshold and/or firing properties of neurons. Changes in behavioral state can also change the inputs to various brain areas from the body and from the outside world, which in turn will affect the network activity mode. This is a vast topic for theory and computational modeling.
What is the purpose of brain waves?
This is actually still a very contentious issue. The field of neuroscience can be broadly divided into researchers who care about oscillations, and researchers who don’t. People who don’t care about oscillations are more interested in the firing activities and the input-output transformations of neurons and networks. Some of these researcher even go so far as to claim that oscillations are ‘epiphenomena’ — mere side-effects of the ‘main’ neural processes, such as integration, contrast enhancement, switching, resetting, and so on. I was broadly in the ‘skeptics’ category for many years, but I’ve started to realized that oscillations can’t be ignored. The power in various frequency bands often correlates strongly with behavioral measures, so oscillations are at the very least telling us something important about how the brain works.
One theory of brain waves that is becoming popular is the idea of coordination, or “communication through coherence”. The idea is that neurons which are in the same sub-threshold oscillatory state are more likely to be able to communicate spikes with each other. This is shown diagrammatically below . The black neuron is out of phase with the blue neuron, so it communicates with the blue neuron less effectively that the red neuron.
As I mentioned earlier, synchrony and rhythmicity are completely distinct. Presumably you can get coherence without any rhythms, just by synchronizing groups of neurons. But maybe rhythmic behavior is more easy to control.
I’ve only scratched the surface of this topic. There is definitely a lot more to the story of brain waves, and in the coming decades hopefully researchers will work towards an integrated theory.
 Cortical enlightenment: are attentional gamma oscillations driven by ING or PING? | pdf
 A mechanism for cognitive dynamics: neuronal communication through neuronal coherence. | pdf
* What do inhibitory neurons do in the brain? by Yohan John on Neurologism
Are EEG voltages related to the average action potential firing rate of the cortical neurons near the electrode or are the voltages the average of low frequency voltage oscillations of the neurons?
What changes occur in the brain when we close our eyes?
Is working memory associated with synchronization between oscillations in the prefrontal cortex and oscillations elsewhere in the brain? (e.g. parietal cortex)?
Medical Imaging: How strong is the correlation between a fMRI and an EEG?
Does the membrane time constant of neurons put a constraint on the frequencies seen in neuronal brain waves?