Perturbations both trigger and delay seizures due to generic properties of slow-fast relaxation oscillators
Fig 3
Isochrons and PRCs for the phenomenor model (7).
Panel (A) shows the limit cycle Γpheno, 16 equispaced isochrons, the v and a nullclines (dashed black and green curves, respectively) and the fixed point, P, at their intersection. The distribution of isochrons clarifies the time dependency of perturbations: as panel (B) shows, a pulse of amplitude A applied at a time t1 (t2) causes a negative (positive) phase shift, delaying (promoting) the transition to seizure. This time dependency can be directly inferred from panel (A): a pulse of amplitude A applied at a point on the cycle z1 = γ(θ1) = γ(t1/T) (z2 = γ(θ2) = γ(t2/T)) displaces the trajectory to a point (
). Since
(
) the perturbation causes a phase shift
(
) delaying (advancing) the phase of the oscillator. The panel (C) shows the PRCs for the phenomenor for positive voltage pulses of different amplitudes summarising the timing (phasic) effect of a given perturbation.