Figure 1.

Selective entrainment of brain rhythms using dithered stimulation. When stimulation is perfectly periodic as depicted in (D1) (f _s denotes the stimulation frequency), neural oscillators may be entrained at the stimulation frequency but also at sub- and super-harmonics of the stimulation frequency. Corresponding entrainment regions (Arnold tongues) are represented in (C1) for uncoupled neural oscillators modelled using the sine circle map (described in section 2.1). Stimulation is provided at 130 Hz (red dashed line), with stimulation amplitude shown on the vertical axis, and the natural frequency of oscillators on the horizontal axis. Entrainment is observed when the rotation number (colour scale in (C)) is an integer ratio (only regions of frequency-locking determined as described in section 4.2 are shown). Entrainment at various rotation numbers is illustrated in (B1)–(B4). As an example, DBS in PD patients can entrain cortical gamma oscillations at half the stimulation frequency, which corresponds to 1:2 entrainment ((A), adapted from [25] with no permission required). With dithering, stimulation is not perfectly periodic (D2), and past a certain dithering level (level of noise in the stimulation period), only the 1:1 Arnold tongue subsists (green tongue in (C2)).