Multiscale analysis of hybrid processes and reduction of stochastic neuron models

Gilles Wainrib

Description

Niveau: Supérieur
Multiscale analysis of hybrid processes and reduction of stochastic neuron models. Gilles Wainrib joint work with: Khashayar Pakdaman and Michele Thieullen Institut J.Monod- CNRS,Univ.Paris 6,Paris 7 - Labo. Proba et Modeles Aleatoires Univ.Paris 6,Paris 7,CNRS CREA Ecole polytechnique January, 2010

• stochastic neuron


• multiscale analysis


• neuron models


• modeles aleatoires


• deterministic neuron


• time-scale separation

Sujets

• École polytechnique
• Multiple-scale analysis

Informations

• Publié par: chaeh
• Nombre de lectures: 9
• Langue: English
• Poids de l'ouvrage: 1 Mo

Extrait

Multiscale analysis of hybrid processes and reduction of
stochastic neuron models.

Gilles Wainrib
joint work with:
Khashayar Pakdaman and Mich`le Thieullen

Institut J.Monod- CNRS,Univ.Paris 6,Paris 7 - Labo. Proba et Mod`les Al´atoires Univ.Paris 6,Paris 7,CNRS
CREA Ecole polytechnique

January, 2010

Part I : Introduction

Deterministic neuron model

Hodgkin Huxley (HH) model (Hodgkin Huxley - J.Physiol. 1952):

dV
Cm
dt
dm
dt
dh
dt
dn
dt

=

=

=

=

3 4
I−gL(V−VL)−gNam h(V−VNa)−gKn(V−VK)

−1
τm(V) (m∞(V)−m)

−1
τh(V) (h∞(V)−h)

−1
τn(V) (n∞(V)−n)

→Conductance-based neuron model

Time-scale separation and reduction

Sodium activation dynamic is faster than the other variables :τm→0

Three-dimensional reduced system:

dV
Cm
dt
dh
dt
dn
dt

=

=

=

m=m∞(V)

3 4
I−gL(V−VL)−gNam∞(V)h(V−VNa)−gKn(V−VK)

τh(V) (h∞(V)−h)

τn(V) (n∞(V)−n)

Time-scale separation and reduction

Sodium activation dynamic is faster than the other variables :τm→0

Three-dimensional reduced system:

dV
Cm
dt
dh
dt
dn
dt

=

=

=

m=m∞(V)

3 4
I−gL(V−VL)−gNam∞(V)h(V−VNa)−gKn(V−VK)

τh(V) (h∞(V)−h)

τn(V) (n∞(V)−n)

Reduction of neuron models : key step in theoretical (singular perturbations) and
numerical analysis
Rinzel 1985, Kepler et al. 1992, Meunier 1992, Suckley et al.2003, Rubin et al. 2007,
...