Where oscillations come from
Pacemaker cells, excitation-inhibition loops, thalamocortical circuits, and why aligned pyramidal neurons make a field the scalp can see. The mechanisms behind alpha, spindles, slow waves, and gamma.
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Your Brian2 network of four thousand neurons, none of which oscillated alone, fell into a rhythm when you tuned the inhibition. That is the general answer to where oscillations come from: from the interaction of excitation and inhibition with a delay, which makes a population fire, silence itself, recover, and fire again. The specific rhythms of EEG each have a specific circuit. Let’s take them in order of frequency, and then ask why any of it reaches the scalp.
Two ways to make a rhythm
A pacemaker. Some neurons oscillate alone, because they carry channels whose interplay produces a limit cycle: a slow inward current that depolarizes, a slow outward current that repolarizes, repeat. Thalamic relay neurons have a low-threshold calcium current and a hyperpolarization-activated current that together make them burst rhythmically when they are hyperpolarized and quiet. Sinoatrial cells in the heart are the same idea.
A loop with a delay. A population of excitatory cells drives a population of inhibitory cells, which shut the excitatory cells down, which removes the drive to the inhibitory cells, which lets the excitatory cells recover. The period is set by the synaptic and membrane time constants. This is the mechanism of gamma (fast, local, inhibitory interneurons with fast synapses) and, with slower elements and long-range loops, of alpha and spindles.
Slow waves, under 1 Hz
In deep sleep the whole cortex alternates between an up state, where neurons fire, and a down state, where they are silent, roughly once a second. The mechanism is cortical: during the up state, activity-dependent potassium currents and synaptic depression build up until the network collapses into silence; during silence they recover until a few neurons’ spontaneous firing reignites the network. Slow waves are the largest signal in EEG because the whole cortex does this nearly in synchrony. Your sleep band was detecting them.
Spindles, 11 to 16 Hz
The thalamus’s reticular nucleus, a shell of inhibitory neurons, inhibits the relay neurons, which respond with a rebound burst (the calcium current), which excites the reticular cells, and round again at spindle frequency. The bursts are relayed to cortex, which produces the waxing-and-waning spindle. It gates sensory input during sleep and is tied to memory consolidation.
Alpha, 8 to 12 Hz
The classic account is thalamocortical: relay neurons in the visual thalamus, when not driven by input, fall into a rhythm near 10 Hz through pacemaker properties and their loop with the reticular nucleus, and visual cortex follows. The newer account adds a cortical generator: layer 5 pyramidal neurons in visual cortex can pace at alpha on their own. Both are probably true. The functional story (idling, or active inhibition) is in the Phase 1 explainer.
Beta and gamma, 15 to 80 Hz
Gamma is the loop with a delay at its fastest: pyramidal cells drive fast-spiking inhibitory interneurons, which inhibit them back within a few milliseconds. The period is set by the inhibitory synapse’s time constant, around 10 to 25 ms, giving 40 to 100 Hz. Gamma is local (a few millimetres), tied to active processing, and weak on the scalp. Beta over motor cortex is a longer-range rhythm associated with holding a state, and its brief bursts, rather than its average power, appear to be the meaningful unit.
Millions of neurons in visual cortex each produce a tiny current when they fire. Under what condition does the sum reach the scalp as a measurable voltage?
When they fire together and their currents point the same way. Currents that are out of phase cancel; currents that point in random directions cancel. Pyramidal neurons have long dendrites all oriented perpendicular to the cortical surface, so their synaptic currents are aligned like tiny parallel batteries. When they are also synchronized, as in a rhythm, the sum is a dipole layer big enough to reach the scalp. Interneurons, whose dendrites point every way, contribute almost nothing to EEG however active they are.
Why the scalp sees any of it
EEG is not spikes. Spikes are too brief and too asynchronous; they cancel. EEG is mostly the slower synaptic currents in the dendrites of pyramidal neurons, which last tens of milliseconds and can synchronize. A patch of cortex a few square centimetres, with its pyramidal cells receiving synchronized input, forms a current dipole layer whose field passes through the skull (blurred, as the forward model showed) to the scalp. Alpha is visible because visual cortex is large, superficial, and synchronized. Gamma is barely visible because it is local and fast. Deep structures like the hippocampus are essentially invisible however rhythmic, because they are far away and their geometry is not a neat open layer.
The local field potentialLocal field potential (LFP)The slow, summed electrical activity of many neurons near an electrode, below a few hundred hertz, as opposed to individual spikes. Glossary entry recorded by an intracortical electrode is the same synaptic current summed over a millimetre instead of centimetres, which is why LFP has more gamma and sharper features than EEG, and why intracortical BCIs sometimes decode from LFP when the spikes are gone.
Deep dive Cross-frequency coupling 2 min
Slow rhythms often modulate fast ones: gamma bursts ride on the peaks of theta in the hippocampus; spindles ride on the up-states of slow waves. This nesting is thought to organize when different computations happen and when synapses can change, and it is the mechanism by which closed-loop slow-wave stimulation could affect memory: enlarge the slow wave, and you change when the spindles and the hippocampal replay they carry occur.
Deep dive Pathological rhythms 3 min
Seizures are runaway synchrony: too much excitation, too little inhibition, and the whole network locks into a rhythm that spreads. Parkinson’s disease produces excessive beta synchrony in the basal ganglia, and deep brain stimulation may work in part by disrupting it, which is why adaptive DBS that triggers on beta bursts is in trials. Absence epilepsy is spindle circuitry gone wrong. Understanding the normal generator is how each of these was worked out.
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