Delay-induced oscillations in Wilson and Cowan's model: an analysis of the subthalamo-pallidal feedback loop in healthy and parkinsonian subjects
Identifieur interne : 000F80 ( Main/Exploration ); précédent : 000F79; suivant : 000F81Delay-induced oscillations in Wilson and Cowan's model: an analysis of the subthalamo-pallidal feedback loop in healthy and parkinsonian subjects
Auteurs : William Pasillas-Lépine [France]Source :
- Biological cybernetics [ 0340-1200 ] ; 2013.
Descripteurs français
- Pascal (Inist)
- Rétroaction, Trichite, Fût, Pathologie du système nerveux, Inhibition, Odeur, Capteur tactile, Vibrisse, Retard, Modélisation, Stabilité asymptotique, Effet local, Equilibre multiple, Oscillation, Modèle entrée sortie, Condition nécessaire suffisante, Méthode domaine fréquence, Critère Nyquist, Maladie de Parkinson, ..
English descriptors
- KwdEn :
- Asymptotic stability, Barrel, Biological Clocks (physiology), Delay, Feedback regulation, Feedback, Physiological (physiology), Frequency domain method, Globus Pallidus (pathology), Humans, Inhibition, Input output model, Local effect, Modeling, Models, Neurological, Multiple equilibrium, Necessary and sufficient condition, Nervous system diseases, Neurons (physiology), Nonlinear Dynamics, Nyquist criterion, Odor, Oscillation, Parkinson Disease (pathology), Parkinson disease, Subthalamic Nucleus (pathology), Tactile sensor, Vibrissa, Whisker.
- MESH :
- pathology : Globus Pallidus, Parkinson Disease, Subthalamic Nucleus.
- physiology : Biological Clocks, Feedback, Physiological, Neurons.
- Humans, Models, Neurological, Nonlinear Dynamics.
- mix :
Abstract
The model proposed by Wilson and Cowan (1972) describes the dynamics of two interacting subpopulations of excitatory and inhibitory neurons. It has been used to model neural structures like the olfactory bulb, whisker barrels, and the subthalamo-pallidal system. It is well-known that this system can exhibit an oscillatory behavior that is amplified by the presence of delays. In the absence of delays, the conditions for stability are well-known. The aim of our paper is to clarify these conditions when delays are included in the model. The first ingredient of our methods is a new necessary and sufficient condition for the existence of multiple equilibria. This condition is related to those for local asymptotic stability. In addition, a sufficient condition for global stability is also proposed. The second and main ingredient is a stability analysis of the system in the frequency-domain, based on the Nyquist criterion, that takes the four independent delays into account. The methods proposed in this paper can be applied to analyse the stability of the subthalamo-pallidal feedback loop, a deep brain structure involved in Parkinson's disease. Our stability conditions are easy to compute and characterize sharply the system's parameters for which spontaneous oscillations appear.
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feedback loop in healthy and parkinsonian subjects</title><author><name sortKey="Pasillas Lepine, William" sort="Pasillas Lepine, William" uniqKey="Pasillas Lepine W" first="William" last="Pasillas-Lépine">William Pasillas-Lépine</name><affiliation wicri:level="4"><inist:fA14 i1="01"><s1>Laboratoire des signaux et systèmes (L2S), CNRS/SUPELEC/Université Paris-Sud</s1><s2>91192 Gif-sur-Yvette</s2><s3>FRA</s3><sZ>1 aut.</sZ></inist:fA14><country>France</country><placeName><region type="region" nuts="2">Île-de-France</region><settlement type="city">Gif-sur-Yvette</settlement></placeName><orgName type="university">Université Paris-Sud</orgName></affiliation></author></analytic><series><title level="j" type="main">Biological cybernetics</title><title level="j" type="abbreviated">Biol. cybern.</title><idno type="ISSN">0340-1200</idno><imprint><date when="2013">2013</date></imprint></series></biblStruct></sourceDesc><seriesStmt><title level="j" type="main">Biological cybernetics</title><title level="j" type="abbreviated">Biol. cybern.</title><idno type="ISSN">0340-1200</idno></seriesStmt></fileDesc><profileDesc><textClass><keywords scheme="KwdEn" xml:lang="en"><term>Asymptotic stability</term><term>Barrel</term><term>Biological Clocks (physiology)</term><term>Delay</term><term>Feedback regulation</term><term>Feedback, Physiological (physiology)</term><term>Frequency domain method</term><term>Globus Pallidus (pathology)</term><term>Humans</term><term>Inhibition</term><term>Input output model</term><term>Local effect</term><term>Modeling</term><term>Models, Neurological</term><term>Multiple equilibrium</term><term>Necessary and sufficient condition</term><term>Nervous system diseases</term><term>Neurons (physiology)</term><term>Nonlinear Dynamics</term><term>Nyquist criterion</term><term>Odor</term><term>Oscillation</term><term>Parkinson Disease (pathology)</term><term>Parkinson disease</term><term>Subthalamic Nucleus (pathology)</term><term>Tactile sensor</term><term>Vibrissa</term><term>Whisker</term></keywords><keywords scheme="MESH" qualifier="pathology" xml:lang="en"><term>Globus Pallidus</term><term>Parkinson Disease</term><term>Subthalamic Nucleus</term></keywords><keywords scheme="MESH" qualifier="physiology" xml:lang="en"><term>Biological Clocks</term><term>Feedback, Physiological</term><term>Neurons</term></keywords><keywords scheme="MESH" xml:lang="en"><term>Humans</term><term>Models, Neurological</term><term>Nonlinear Dynamics</term></keywords><keywords scheme="Pascal" xml:lang="fr"><term>Rétroaction</term><term>Trichite</term><term>Fût</term><term>Pathologie du système nerveux</term><term>Inhibition</term><term>Odeur</term><term>Capteur tactile</term><term>Vibrisse</term><term>Retard</term><term>Modélisation</term><term>Stabilité asymptotique</term><term>Effet local</term><term>Equilibre multiple</term><term>Oscillation</term><term>Modèle entrée sortie</term><term>Condition nécessaire suffisante</term><term>Méthode domaine fréquence</term><term>Critère Nyquist</term><term>Maladie de Parkinson</term><term>.</term></keywords><keywords scheme="mix" xml:lang="en"><term>Basal ganglia</term><term>Delays</term><term>Firing-rate models</term><term>Neural oscillations</term><term>Parkinson's disease</term><term>Wilson and Cowan's model</term></keywords></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">The model proposed by Wilson and Cowan (1972) describes the dynamics of two interacting subpopulations of excitatory and inhibitory neurons. It has been used to model neural structures like the olfactory bulb, whisker barrels, and the subthalamo-pallidal system. It is well-known that this system can exhibit an oscillatory behavior that is amplified by the presence of delays. In the absence of delays, the conditions for stability are well-known. The aim of our paper is to clarify these conditions when delays are included in the model. The first ingredient of our methods is a new necessary and sufficient condition for the existence of multiple equilibria. This condition is related to those for local asymptotic stability. In addition, a sufficient condition for global stability is also proposed. The second and main ingredient is a stability analysis of the system in the frequency-domain, based on the Nyquist criterion, that takes the four independent delays into account. The methods proposed in this paper can be applied to analyse the stability of the subthalamo-pallidal feedback loop, a deep brain structure involved in Parkinson's disease. Our stability conditions are easy to compute and characterize sharply the system's parameters for which spontaneous oscillations appear.</div></front></TEI><affiliations><list><country><li>France</li></country><region><li>Île-de-France</li></region><settlement><li>Gif-sur-Yvette</li></settlement><orgName><li>Université Paris-Sud</li></orgName></list><tree><country name="France"><region name="Île-de-France"><name sortKey="Pasillas Lepine, William" sort="Pasillas Lepine, William" uniqKey="Pasillas Lepine W" first="William" last="Pasillas-Lépine">William Pasillas-Lépine</name></region></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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