title: Closed-loop firing rate regulation of two interacting excitatory and inhibitory neural populations of the basal ganglia.
abstract: 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.
authors.affiliation: Laboratoire des signaux et systèmes, CNRS - CentraleSupélec - Univ. Paris Sud, Gif-sur-Yvette, France.
authors.forename: Ihab
authors.initials: I
authors.lastname: Haidar
authors.affiliation: Laboratoire des signaux et systèmes, CNRS - CentraleSupélec - Univ. Paris Sud, Gif-sur-Yvette, France. pasillas@lss.supelec.fr.
authors.forename: William
authors.initials: W
authors.lastname: Pasillas-Lépine
authors.affiliation: Laboratoire des signaux et systèmes, CNRS - CentraleSupélec - Univ. Paris Sud, Gif-sur-Yvette, France.
authors.forename: Antoine
authors.initials: A
authors.lastname: Chaillet
authors.affiliation: Laboratoire des signaux et systèmes, CNRS - CentraleSupélec - Univ. Paris Sud, Gif-sur-Yvette, France.|ITMO University, Saint Petersburg, Russia.
authors.forename: Elena
authors.initials: E
authors.lastname: Panteley
authors.affiliation: AP-HP, Hôpital H. Mondor, Service de Neurochirurgie, Créteil, France.|IMRB, Inserm, U955, Equipe 14, Créteil, France.|Faculté de médecine, Université Paris Est, Créteil, France.
authors.forename: Stéphane
authors.initials: S
authors.lastname: Palfi
authors.affiliation: AP-HP, Hôpital H. Mondor, Service de Neurochirurgie, Créteil, France.|IMRB, Inserm, U955, Equipe 14, Créteil, France.|Faculté de médecine, Université Paris Est, Créteil, France.
authors.forename: Suhan
authors.initials: S
authors.lastname: Senova
mesh_terms: D001479:Basal Ganglia / Q000502:physiology*; D025461:Feedback, Physiological / Q000502:physiology*; D006801:Humans; D008954:Models, Biological; D009433:Neural Inhibition / Q000502:physiology*; D009474:Neurons / Q000502:physiology*; D010300:Parkinson Disease / Q000503:physiopathology
keywords: Basal ganglia; Closed-loop stimulation; Deep brain stimulation; Firing rate models; Neural oscillations; Parkinson’s disease; Time-delay systems