Speaker: 
Alessio Franci
Date: 
Fri, 04/06/2012 -
10:00 to 12:30
Lieu: 
Supélec, salle des séminaires du L2S
Résumé/Abstract: 
In the first part of this thesis, motivated by the development of deep brain stimulation for Parkinson's disease, we consider the problem of reducing the synchrony of a neuronal population via a closed-loop electrical stimulation. This, under the constraints that only the mean membrane voltage of the ensemble is measured and that only one stimulation signal is available (mean-field feedback). The neuronal population is modeled as a network of interconnected Landau-Stuart oscillators controlled by a linear single-input single-output feedback device. Based on the associated phase dynamics, we analyze existence and robustness of phase-locked solutions, modeling the pathological state, and derive necessary conditions for an effective desynchronization via mean-field feedback. Sufficient conditions are then derived for two control objectives: neuronal inhibition and desynchronization. Our analysis suggests that, depending on the strength of feedback gain, a proportional mean-field feedback can either block the collective oscillation (neuronal inhibition) or desynchronize the ensemble. In the second part, we explore two possible ways to analyze related problems on more biologically sound models. In the first, the neuronal population is modeled as the interconnection of nonlinear input-output operators and neuronal synchronization is analyzed within a recently developed input-output approach. In the second, excitability and synchronizability properties of neurons are analyzed via the underlying bifurcations. Based on the theory of normal forms, a novel reduced model is derived to capture the behavior of a large class of neurons remaining unexplained in other existing reduced models.

Alessio Franci

a le plaisir de vous inviter à sa soutenance de

Thèse de Doctorat

portant sur le sujet

Pathological synchronization in neuronal populations: a control theoretic perspective

Cette soutenance aura lieu à Supélec, campus de Gif-sur-Yvette, le

Vendredi 6 avril 2012 à 10h00

Salle des séminaires du L2S

Vous êtes cordialement conviés au pot qui suivra dans la salle du conseil du L2S

Membres du jury:

Dirk AEYELS
, professeur (Univ. Gent) - Rapporteur
Antoine CHAILLET
, maître de conférences (Univ. Paris SUD 11) - Encadrant
Jamal DAAFOUZ
, professeur (Institut National Polytechnique de Lorraine) - Rapporteur
Constance HAMMOND
, directeur de recherche INSERM (INMED) - Examinateur
Françoise LAMNABHI-LAGARRIGUE
, directeur de recherche CNRS (Laboratoire des signaux et système) - Directeur de thèse
William PASILLAS-LEPINE
, chargé de recherche CNRS (Laboratoire des signaux et système) - Encadrant
Rodolphe SEPULCHRE
, professeur (Univ. Liège) - Examinateur

Abstract. In the first part of this thesis, motivated by the development of deep brain stimulation for Parkinson's disease, we consider the problem of reducing the synchrony of a neuronal population via a closed-loop electrical stimulation. This, under the constraints that only the mean membrane voltage of the ensemble is measured and that only one stimulation signal is available (mean-field feedback). The neuronal population is modeled as a network of interconnected Landau-Stuart oscillators controlled by a linear single-input single-output feedback device. Based on the associated phase dynamics, we analyze existence and robustness of phase-locked solutions, modeling the pathological state, and derive necessary conditions for an effective desynchronization via mean-field feedback. Sufficient conditions are then derived for two control objectives: neuronal inhibition and desynchronization. Our analysis suggests that, depending on the strength of feedback gain, a proportional mean-field feedback can either block the collective oscillation (neuronal inhibition) or desynchronize the ensemble.

In the second part, we explore two possible ways to analyze related problems on more biologically sound models. In the first, the neuronal population is modeled as the interconnection of nonlinear input-output operators and neuronal synchronization is analyzed within a recently developed input-output approach. In the second, excitability and synchronizability properties of neurons are analyzed via the underlying bifurcations. Based on the theory of normal forms, a novel reduced model is derived to capture the behavior of a large class of neurons remaining unexplained in other existing reduced models.