The cortical column as a tuned receiver: a network mechanism for temporal-interference stimulation

Temporal-interference (TI) stimulation promises what other non-invasive methods cannot: focal, steerable stimulation deep in the brain, produced where two high-frequency currents overlap and their amplitudes beat at a low difference frequency. Yet a puzzle sits at its core. An amplitude-modulated field carries no power at that beat frequency, so no passive, linear part of a neuron can follow it; recovering the beat requires a nonlinearity, usually sought in single-cell ion channels. Here we show that the recovery, and its tuning, are properties of the neural population rather than the single cell. In a neural mass---the $ $$10^4$-neuron unit that generates the EEG---the firing-rate nonlinearity acts as a square-law detector that demodulates the beat, while the recurrent synaptic network, poised near a Hopf bifurcation, resonantly amplifies the recovered rhythm at its own natural frequency. Detection is inherited from the single neuron; the sharp, frequency-selective amplification is emergent---set by how near the network sits to criticality, and tunable by its own connectivity. Demonstrated in a heuristic cortical column and in an exact next-generation mean field, the mechanism reproduces TI's known behavior: it is independent of the carrier once the membrane polarization is matched, largest when the beat matches a region's intrinsic rhythm, and---because the resonance amplifies oscillatory timing far more than mean rate---locks spike timing without changing firing rate, as observed in vivo. Because the gain depends on brain state, TI efficacy should be as much a property of the brain as of the device: the cortical column behaves as a tuned AM radio receiver.

: temporal interference; transcranial stimulation; neural mass model; amplitude demodulation; Hopf bifurcation; cross-frequency coupling; Jansen--Rit; LaNMM.