Computing the delay margin of the subthalamo-pallidal feedback loop

William Pasillas-Lépine (1)

1 L2S - Laboratoire des signaux et systèmes

In the last ten years, several models of basal ganglia dynamics have been proposed in order to explain the abnormal neural oscillations that appear in Parkinson's disease. Recently, Nevado Holgado et al. [1] have shown that a two-dimensional nonlinear model of the subthalamopallidal feedback loop, which interconnects the subthalamic nucleus (STN) and the external part of the globus pallidus (GPe), exhibits oscillations in the beta band when the parameters of the model are those of the pathological state. They proposed, moreover, a simplified model for which the condition for oscillations can be computed analytically. In our work, we consider a slightly more general model of the subthalamopallidal feedback loop, that includes a self-excitation loop of the STN onto itself and allows more general activation functions. It coincides with the model of Wilson and Cowan [2], with the difference that interconnection delays are included and that the refractory period is neglected.

Mots clés: Networks of excitatory and inhibitory populations; Neural oscillations; Stability; Delays; Parkinson's disease; Subthalamic nucleus; Globus pallidus; Basal ganglia

Domaines: Automatique / Robotique; Neurosciences

William Pasillas-Lépine. Computing the delay margin of the subthalamo-pallidal feedback loop. Computational Neuroscience & Neurotechnology Bernstein Conference & Neurex Annual Meeting 2011, Oct 2011, Freiburg, Germany. ⟨hal-00832529⟩