phenomenon

brain oscillation phase amplitude coupling

Coupling between the phase and amplitude of neural oscillations, indicating brain state.
30 related articles · 6 formulas

Description

Brain oscillation phase-amplitude coupling (PAC) refers to the phenomenon where the amplitude (strength) of a faster neural oscillation is modulated by the phase (timing) of a slower oscillation. For example, the amplitude of gamma waves (30–100 Hz) may be higher during the peak of a theta wave (4–8 Hz) and lower during its trough. This cross-frequency coupling is thought to be a fundamental mechanism for coordinating neural activity across different spatial and temporal scales, allowing distinct brain regions to communicate and bind information into coherent perceptions, memories, or actions.

History

PAC was first described in the hippocampus of rodents in the 1990s, with key contributions from György Buzsáki and colleagues. It was later found in the human brain, particularly during memory tasks and in the default mode network.

How it works

Neurons in different brain regions oscillate at different frequencies. PAC provides a way for slower, global oscillations to gate or 'carry' faster, local computations. The phase of the slow oscillation sets a time window during which fast oscillations can occur, effectively creating a temporal code: information is processed in bursts that are locked to specific phases of the slow rhythm. This is measured using electroencephalography (EEG) or local field potentials, where the amplitude of the fast oscillation is plotted against the phase of the slow one; a consistent relationship indicates coupling. The mechanism is believed to involve synaptic interactions and neuromodulatory systems that alter neuronal excitability in a phase-dependent manner.

In practice

PAC is used as a biomarker for neurological and psychiatric conditions: altered coupling has been observed in Alzheimer's disease, schizophrenia, and epilepsy, and it is being explored as a target for non-invasive brain stimulation therapies.

Fun fact

In the corpus article 'Мозг на волне: как фаза и амплитуда выдают болезнь', PAC is described as a potential early diagnostic marker for Parkinson's disease, detectable before motor symptoms appear.

Concept graph →

Formulas

$$P = \sin^2(\theta)$$
Probability oscillates with a phase angle.
What is in the formula
Pvariableprobability of oscillation — probability
θvariablemixing angle or phase — phase angle radian
p_{garrowγ}=\sin^2(\frac{2\kappab_0q\sqrt{mn}l}{c}) · 2605.14050v1
$$\omega_{\mathrm{b},z}^2 = -\sigma_{z0} \frac{\partial \omega_z^2}{\partial \sigma_{z0}}$$
Connects axial breathing mode frequency to trap frequency derivative.
What is in the formula
\omega_{\mathrm{b},zvariableaxial breathing mode frequency — angular frequency radian per second
\sigma_{z0}variableaxial width at equilibrium — length metre
\omega_zvariableaxial trap frequency — angular frequency radian per second
\frac{\partial}{\paroperatorpartial derivative with respect to equilibrium axial width — partial derivative
ω_{{b},z}^2=-σ_{z0}\frac{\partialω_z^2}{\partialσ_{z0}} · 2606.29370
$$z(t) = x(t) + i\mathcal{H}[x(t)] = a(t)e^{i\phi(t)}$$
Represents a signal with instantaneous amplitude and phase.
What is in the formula
zvariableAnalytic signal — analytic signal
xvariableReal signal — signal
avariableInstantaneous amplitude — instantaneous amplitude
φvariableInstantaneous phase — instantaneous phase radian
tvariableTime variable — time second
HoperatorHilbert transform, shifts phase by -90° — hilbert transform operator
ioperatorImaginary unit, √(-1) — imaginary unit
z_j(t)=c_j(t)+i\mathcal{h}[c_j(t)]=a_j(t)e^{iφ_j(t)} · 2607.02228v1
$$\omega = \sqrt{k/m}, \quad A = \sqrt{2E/k}$$
Frequency and amplitude of a harmonic oscillator depend on mass and stiffness.
What is in the formula
ωvariableangular frequency — angular frequency radian per second
kvariablespring constant — spring constant newton per metre
mvariablemass — mass kilogram
Avariableamplitude — amplitude metre
Evariabletotal energy — energy joule
√operatorsquare root operation — square root
ω=\sqrt{k/m},\quada=\sqrt{2e/k} · 2606.23490
$$\theta_{a,0} = \frac{g_{a\gamma}}{2} \frac{\sqrt{2\rho}}{\mu}$$
Amplitude of axion-induced polarization oscillations.
What is in the formula
\theta_{a,0}variableAmplitude of polarization oscillation — angle radian
g_{a\gamma}variableAxion-photon coupling constant — coupling constant reciprocal gev
\rhovariableLocal axion dark matter density — mass density kilogram per cubic metre
\muvariableAxion mass — mass kilogram
θ_{a,0}=\frac{g_{aγ}}{2}\frac{\sqrt{2ρ}}{μ} · 2607.04550v1
$$\xi = \frac{v}{2\pi\nu_0}$$
Relates dynamic correlation length to sound velocity and peak frequency.
What is in the formula
ξvariabledynamic correlation length — correlation length metre
vvariablesound velocity — velocity metre per second
ν₀variablepeak frequency — frequency hertz
πconstantRatio of a circle's circumference to its diameter — pi = 3.14159
\xi=\frac{v_t}{2πν_0} · 2607.14764

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