Effects of direct GPe-related pathways on regulating absence seizures.

<p>A, B: Two dimensional state analysis (A) and frequency analysis (B) in different parameter spaces. Here we consider three direct GPe-related pathways: the excitatory STN-GPe pathway (A₁, B₁), the inhibitory GPe recurrent pathway (A₂, B₂) and the inhibitory striatal D2-GPe pathway (A₃, B₃), corresponding to parameter spaces (−<i>v</i>_<i>cp</i>₂, <i>v</i>_<i>p</i>₂<i>ζ</i>), (−<i>v</i>_<i>cp</i>₂, −<i>v</i>_{<i>p</i>₂<i>p</i>₂}) and (−<i>v</i>_<i>cp</i>₂, −<i>v</i>_{<i>p</i>₂<i>d</i>₂}), respectively. In (A₁)–(A₃), two dynamical state regions are observed: the SWD oscillation region (II) and the low firing region (IV). The suppression of SWDs appears to the right of the white dashed line in (A₁) and (A₂), where the arrows denote the suppression directions of SWDs. The red lines in (A₁)-(A₃) represent the default coupling strengths of these direct GPe-related pathways. The asterisk (“*”) regions surrounded by black dashed lines in (B₁)-(B₃) denote the typical 2–4 Hz SWD oscillation regions. C: The triggering mean firing rate (TMFR) as a function of −<i>v</i>_<i>cp</i>₂ for the excitatory STN-GPe pathway (C₁) and inhibitory GPe recurrent pathway (C₂). D: The relative ratios (RRs) as a function of −<i>v</i>_<i>cp</i>₂ for the excitatory STN-GPe pathway (D₁) and inhibitory GPe recurrent pathway (D₂). E: Typical time series of <i>ϕ</i>_<i>e</i> by changing −<i>v</i>_<i>cp</i>₂ under two conditions of the inhibitory striatal D2-GPe pathway (“default” and “block”). The pink region in (E) denotes the suppression of SWDs by increasing −<i>v</i>_<i>cp</i>₂. Obviously, blockade of the inhibitory striatal D2-GPe pathway does not impact the model dynamics significantly.