Generating and transducing infra-slow BOLD across whole brain models

BOLD functional connectivity is partly a property of how the brain is measured, not just how it works — and this paper shows exactly why.

The core insight is simple but consequential: the BOLD signal only captures very slow fluctuations (below 0.1 Hz), yet the brain's fast neural rhythms operate at much higher frequencies. To get fast activity into that slow band, something in the measurement chain must perform a mathematical operation called squaring — multiplying a signal by itself. This is not optional. A linear readout simply cannot translate fast rhythms into slow ones. The question is where that squaring happens: inside the neurons, or inside the blood vessels responding to neural activity.

The paper compares four standard whole-brain modeling frameworks. Two of them (Jansen-Rit/LaNMM and the mean-field MPR model) place the squaring inside the neural dynamics — specifically in the curved shape of the neuron's firing-rate function, which generates "intermodulation distortion," meaning slow difference-frequency signals emerge from the mixing of fast rhythms. The third model (Stuart-Landau with power readout) places the squaring at the vascular stage, treating BOLD as detecting signal power (|z|²). The fourth (Stuart-Landau with linear readout) does no squaring at all and serves as a baseline.

The punchline is a negative result with real teeth: neural squaring and vascular squaring produce indistinguishable functional connectivity (FC) — the matrix of correlations between brain regions that neuroscientists routinely fit models to. Both produce the same resting-state-network-like, non-Gaussian eigenstructure. A linear readout produces something qualitatively different (more Gaussian, more phase-locking-like). This means you cannot look at a resting-state FC fit and infer whether the underlying dynamics are near a critical point or what mechanism is generating the slow fluctuations. The FC eigenstructure is partly a readout artifact.

One important caveat: the source document is explicitly a draft scaffold with only two core simulations completed and several open modeling choices flagged. The theoretical argument appears fully developed, but this is not a finished paper, and some claims may shift before publication.