Cross-scale echoes of ultrafast oscillations in the human brain

Ultrafast oscillations (UFOs) are brief bursts of high-frequency (2-8 kHz) activity recorded using depth electrodes in epileptic brain tissue. While reliably detected at small scales using microelectrodes, UFOs have thus far likely not been observed at larger scales using macroelectrodes. Here we show that faint echoes of these bursting patterns can be detected in macroelectrode signals using a model of cross-scale propagation. To model this cross-scale effect, we extend the classical damped wave equation to include an explicit scale coordinate governed by the dilation operator. We then use Green's functions to obtain an expression for the spectral echo expected at the macroelectrode scale. This echo takes the form of a carrier envelope modulated by the temporal structure of the original microscale bursting event. We test the predicted signature echo pattern in human intracranial recordings from eleven epilepsy patients implanted with both micro- and macroelectrodes. Statistically significant echoes are confirmed in two out of eleven patients, appearing in 2% of all tested micro-macro pairs.