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Nonlinear optimal control of a mean-field model of neural population dynamics

We apply the framework of nonlinear optimal control to a biophysically realistic neural mass model, which consists of two mutually coupled populations of deterministic excitatory and inhibitory neurons. External control signals are realized by time-dependent inputs to both populations. Optimality is...

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Autores principales: Salfenmoser, Lena, Obermayer, Klaus
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Frontiers Media S.A. 2022
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9382303/
https://www.ncbi.nlm.nih.gov/pubmed/35990368
http://dx.doi.org/10.3389/fncom.2022.931121
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author Salfenmoser, Lena
Obermayer, Klaus
author_facet Salfenmoser, Lena
Obermayer, Klaus
author_sort Salfenmoser, Lena
collection PubMed
description We apply the framework of nonlinear optimal control to a biophysically realistic neural mass model, which consists of two mutually coupled populations of deterministic excitatory and inhibitory neurons. External control signals are realized by time-dependent inputs to both populations. Optimality is defined by two alternative cost functions that trade the deviation of the controlled variable from its target value against the “strength” of the control, which is quantified by the integrated 1- and 2-norms of the control signal. We focus on a bistable region in state space where one low- (“down state”) and one high-activity (“up state”) stable fixed points coexist. With methods of nonlinear optimal control, we search for the most cost-efficient control function to switch between both activity states. For a broad range of parameters, we find that cost-efficient control strategies consist of a pulse of finite duration to push the state variables only minimally into the basin of attraction of the target state. This strategy only breaks down once we impose time constraints that force the system to switch on a time scale comparable to the duration of the control pulse. Penalizing control strength via the integrated 1-norm (2-norm) yields control inputs targeting one or both populations. However, whether control inputs to the excitatory or the inhibitory population dominate, depends on the location in state space relative to the bifurcation lines. Our study highlights the applicability of nonlinear optimal control to understand neuronal processing under constraints better.
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spelling pubmed-93823032022-08-18 Nonlinear optimal control of a mean-field model of neural population dynamics Salfenmoser, Lena Obermayer, Klaus Front Comput Neurosci Neuroscience We apply the framework of nonlinear optimal control to a biophysically realistic neural mass model, which consists of two mutually coupled populations of deterministic excitatory and inhibitory neurons. External control signals are realized by time-dependent inputs to both populations. Optimality is defined by two alternative cost functions that trade the deviation of the controlled variable from its target value against the “strength” of the control, which is quantified by the integrated 1- and 2-norms of the control signal. We focus on a bistable region in state space where one low- (“down state”) and one high-activity (“up state”) stable fixed points coexist. With methods of nonlinear optimal control, we search for the most cost-efficient control function to switch between both activity states. For a broad range of parameters, we find that cost-efficient control strategies consist of a pulse of finite duration to push the state variables only minimally into the basin of attraction of the target state. This strategy only breaks down once we impose time constraints that force the system to switch on a time scale comparable to the duration of the control pulse. Penalizing control strength via the integrated 1-norm (2-norm) yields control inputs targeting one or both populations. However, whether control inputs to the excitatory or the inhibitory population dominate, depends on the location in state space relative to the bifurcation lines. Our study highlights the applicability of nonlinear optimal control to understand neuronal processing under constraints better. Frontiers Media S.A. 2022-08-03 /pmc/articles/PMC9382303/ /pubmed/35990368 http://dx.doi.org/10.3389/fncom.2022.931121 Text en Copyright © 2022 Salfenmoser and Obermayer. https://creativecommons.org/licenses/by/4.0/This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
spellingShingle Neuroscience
Salfenmoser, Lena
Obermayer, Klaus
Nonlinear optimal control of a mean-field model of neural population dynamics
title Nonlinear optimal control of a mean-field model of neural population dynamics
title_full Nonlinear optimal control of a mean-field model of neural population dynamics
title_fullStr Nonlinear optimal control of a mean-field model of neural population dynamics
title_full_unstemmed Nonlinear optimal control of a mean-field model of neural population dynamics
title_short Nonlinear optimal control of a mean-field model of neural population dynamics
title_sort nonlinear optimal control of a mean-field model of neural population dynamics
topic Neuroscience
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9382303/
https://www.ncbi.nlm.nih.gov/pubmed/35990368
http://dx.doi.org/10.3389/fncom.2022.931121
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