Method at a glance
- Modality: multimodal
- Measures: The consistency of the phase difference between two oscillatory signals over time, independent of their amplitudes. Ranges 0 (no consistent lag) to 1 (perfect lagged synchrony). In interoception research it quantifies how stably a brain signal holds a fixed lag to a bodily rhythm — most often the gastric rhythm against voxelwise BOLD.
- Procedure: Band-pass both signals to a common frequency band, Hilbert-transform each and take the angle to obtain instantaneous phase, then compute the modulus of the time-averaged complex phase difference. Because raw PLV is inflated by signal properties unrelated to coupling, it is compared to a null built by circularly shifting one signal in time (e.g. ±60 s, hundreds of shifts); the reported statistic is usually PLV-delta — empirical PLV minus the median null PLV. Group inference then tests empirical against null maps with permutation-based cluster-mass correction.
- Also called: PLV, phase synchrony, PLV-delta, phase synchronization index
Strengths
- Amplitude-independent. Detects timing relationships that correlation-based connectivity measures miss, and is not driven by the magnitude of either signal.
- Detects lagged coupling. The gastric–brain relationship is a fixed phase lag, not a zero-lag correlation; PLV is built for exactly this and standard functional connectivity is not.
- Comes with a principled null. The time-shift surrogate preserves each signal’s spectral content while destroying their temporal relationship, which is the right null for ‘is this coupling, or just two signals in the same band?’
- Well established in EEG/MEG since Lachaux et al. (1999); the interoception application inherits a mature literature.
Limitations
- Inflated by anything the two signals share, including artefact. In Gastric network work, head motion and CSF signal are themselves phase-locked to the gastric rhythm, so PLV picks them up as coupling. Removing them shrinks the estimated network 17-fold (Levakov et al. (2023)). The null model does not protect against this, because the confound is genuinely synchronized.
- Not reliable as an individual-difference measure — at least here. Run-to-run PLV-delta in the same participants correlates at r ≈ −.14 to .08, while both constituent signals retest well. A person’s coupling value is, on current evidence, not a stable property of the person.
- Requires a narrow band and a defined frequency. Works for the gastric rhythm (stable ~0.05 Hz peak) and poorly for signals without one. It is not portable to cardiac–BOLD coupling, where the cardiac frequency sits far above the BOLD band.
- Preprocessing determines the answer. Global signal regression changes both the size of the surviving map and its similarity to prior work, with no principled resolution (Gastric network).
- Silent about direction. PLV is symmetric; it cannot say whether the stomach drives the brain or the reverse. Causal claims in this literature come from vagotomy and stimulation, never from PLV.
Connections
- Key studies: Levakov et al. (2023)
- Related methods: Electrogastrography (EGG), Event-related potentials
Two signals can be related by when rather than by how much. PLV measures that: if signal A’s peak reliably arrives 6 seconds after signal B’s, PLV is high even when their amplitudes have nothing to do with each other.
It came into interoception research from EEG (Lachaux et al. 1999) via Rebollo et al. (2018), who needed a statistic for a relationship no correlation measure would find — cortical BOLD holding a stable lag to the stomach’s 20-second cycle. Every Gastric network finding in this wiki is a PLV finding.
The null model is the load-bearing part
Raw PLV between two band-passed signals is meaningless, because two arbitrary signals filtered into the same narrow band will hold some apparent phase relationship. So the empirical PLV is compared to a distribution built by circularly shifting the gastric signal in time by at least ±60 s, several hundred times, and taking the median. The reported quantity is the difference:
PLV-delta = empirical PLV − median null PLV
This is the right null for the question “is there coupling beyond what the signals’ own spectra guarantee?” It is not a null for “is this coupling physiological?” — and that gap is where the field’s problem lives. A head-motion regressor that is genuinely phase-locked to gastric activity produces a real, above-null PLV. The statistic is working correctly and answering a question adjacent to the one asked.
The reliability problem is not PLV’s fault, but it is PLV’s problem
Levakov et al. (2023) make the cleanest available demonstration: two signals that each retest well, combined by a statistic that does not retest at all.
| quantity | test–retest |
|---|---|
| EGG peak frequency | r = .74 (months apart, different setups) |
| resting functional connectivity | strongly within-subject identifiable |
| PLV-delta (gastric ↔ brain) | r ≈ −.14 to .08 |
Why a derived quantity should be so much noisier than its inputs is not established. Candidates: PLV-delta averages a small number of runs of ~15 min, giving few gastric cycles (~45 per run) to estimate phase consistency from; and the subtraction of a null median compounds the noise in both terms. Nobody has done the power analysis that would say how long a recording must be for PLV-delta to stabilize — which is the most useful methodological study this literature is currently missing.
Until that exists, PLV supports group-level claims about whether a coupling exists, and should not be used to rank people. See Can brain–body coupling be measured in a person?.