Phase-locking value (PLV)
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 is-brain-body-coupling-a-reliable-individual-difference.