Closed-loop firing rate regulation of two interacting excitatory and inhibitory neural populations of the basal ganglia

Ihab Haidar (1) , William Pasillas-Lépine (1) , Antoine Chaillet (1) , Elena Panteley (1) , Stéphane Palfi (2) , Suhan Senova (2)

1 L2S - Laboratoire des signaux et systèmes
2 Service de neuro-chirurgie

This paper develops a new closed-loop firing rate regulation strategy for a population of neurons in the subthalamic nucleus, derived using a model-based analysis of the basal ganglia. The system is described using a firing rate model, in order to analyse the generation of beta-band oscillations. On this system, a proportional regulation of the firing rate reduces the gain of the subthalamo-pallidal loop in the parkinsonian case, thus impeding pathological oscillation generation. A filter with a well-chosen frequency is added to this proportional scheme, in order to avoid a potential instability of the feedback loop due to actuation and measurement delays. Our main result is a set of conditions on the parameters of the stimulation strategy that guarantee both its stability and a prescribed delay margin. A discussion on the applicability of the proposed method and a complete set of mathematical proofs is included.

Domains: Engineering Sciences [physics]; Automatic

Ihab Haidar, William Pasillas-Lépine, Antoine Chaillet, Elena Panteley, Stéphane Palfi, et al.. Closed-loop firing rate regulation of two interacting excitatory and inhibitory neural populations of the basal ganglia. Biological Cybernetics (Modeling), 2016, 110 (1), pp.55-71. ⟨10.1007/s00422-015-0678-y⟩. ⟨hal-01270695⟩