Incremental stability of delayed neural fields: a unifying framework for endogenous and exogenous sources of pathological oscillations
Identifieur interne : 000322 ( Pmc/Corpus ); précédent : 000321; suivant : 000323Incremental stability of delayed neural fields: a unifying framework for endogenous and exogenous sources of pathological oscillations
Auteurs : Georgios Is. Detorakis ; Antoine ChailletSource :
- BMC Neuroscience [ 1471-2202 ] ; 2015.
Url:
DOI: 10.1186/1471-2202-16-S1-P24
PubMed: NONE
PubMed Central: 4697613
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<record><TEI><teiHeader><fileDesc><titleStmt><title xml:lang="en">Incremental stability of delayed neural fields: a unifying framework for endogenous and exogenous sources of pathological oscillations</title><author><name sortKey="Is Detorakis, Georgios" sort="Is Detorakis, Georgios" uniqKey="Is Detorakis G" first="Georgios" last="Is. Detorakis">Georgios Is. Detorakis</name><affiliation><nlm:aff id="I1">University Paris Sud, Orsay, Paris, 91400, France</nlm:aff></affiliation><affiliation><nlm:aff id="I2">LSS, Supélec, Gif sur Yvette, Paris, 91190, France</nlm:aff></affiliation></author><author><name sortKey="Chaillet, Antoine" sort="Chaillet, Antoine" uniqKey="Chaillet A" first="Antoine" last="Chaillet">Antoine Chaillet</name><affiliation><nlm:aff id="I1">University Paris Sud, Orsay, Paris, 91400, France</nlm:aff></affiliation><affiliation><nlm:aff id="I2">LSS, Supélec, Gif sur Yvette, Paris, 91190, France</nlm:aff></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">PMC</idno><idno type="pmc">4697613</idno><idno type="url">http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4697613</idno><idno type="RBID">PMC:4697613</idno><idno type="doi">10.1186/1471-2202-16-S1-P24</idno><idno type="pmid">NONE</idno><date when="2015">2015</date><idno type="wicri:Area/Pmc/Corpus">000322</idno><idno type="wicri:explorRef" wicri:stream="Pmc" wicri:step="Corpus" wicri:corpus="PMC">000322</idno></publicationStmt><sourceDesc><biblStruct><analytic><title xml:lang="en" level="a" type="main">Incremental stability of delayed neural fields: a unifying framework for endogenous and exogenous sources of pathological oscillations</title><author><name sortKey="Is Detorakis, Georgios" sort="Is Detorakis, Georgios" uniqKey="Is Detorakis G" first="Georgios" last="Is. Detorakis">Georgios Is. Detorakis</name><affiliation><nlm:aff id="I1">University Paris Sud, Orsay, Paris, 91400, France</nlm:aff></affiliation><affiliation><nlm:aff id="I2">LSS, Supélec, Gif sur Yvette, Paris, 91190, France</nlm:aff></affiliation></author><author><name sortKey="Chaillet, Antoine" sort="Chaillet, Antoine" uniqKey="Chaillet A" first="Antoine" last="Chaillet">Antoine Chaillet</name><affiliation><nlm:aff id="I1">University Paris Sud, Orsay, Paris, 91400, France</nlm:aff></affiliation><affiliation><nlm:aff id="I2">LSS, Supélec, Gif sur Yvette, Paris, 91190, France</nlm:aff></affiliation></author></analytic><series><title level="j">BMC Neuroscience</title><idno type="eISSN">1471-2202</idno><imprint><date when="2015">2015</date></imprint></series></biblStruct></sourceDesc></fileDesc><profileDesc><textClass></textClass></profileDesc></teiHeader><back><div1 type="bibliography"><listBibl><biblStruct><analytic><author><name sortKey="Bressloff, Pc" uniqKey="Bressloff P">PC Bressloff</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Veltz, R" uniqKey="Veltz R">R Veltz</name></author><author><name sortKey="Faugeras, O" uniqKey="Faugeras O">O Faugeras</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Nevado Holgado, Aj" uniqKey="Nevado Holgado A">AJ Nevado Holgado</name></author><author><name sortKey="Terry, Jr" uniqKey="Terry J">JR Terry</name></author><author><name sortKey="Bogacz, R" uniqKey="Bogacz R">R Bogacz</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Haidar, I" uniqKey="Haidar I">I Haidar</name></author><author><name sortKey="Pasillas Lepine, W" uniqKey="Pasillas Lepine W">W Pasillas-Lepine</name></author><author><name sortKey="Panteley, E" uniqKey="Panteley E">E Panteley</name></author><author><name sortKey="Chaillet, A" uniqKey="Chaillet A">A Chaillet</name></author><author><name sortKey="Palfi, S" uniqKey="Palfi S">S Palfi</name></author><author><name sortKey="Senova, S" uniqKey="Senova S">S Senova</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Mccarthy, M" uniqKey="Mccarthy M">M McCarthy</name></author><author><name sortKey="Moore Kochlacs, C" uniqKey="Moore Kochlacs C">C Moore-Kochlacs</name></author><author><name sortKey="Gu, X" uniqKey="Gu X">X Gu</name></author><author><name sortKey="Boyden, Es" uniqKey="Boyden E">ES Boyden</name></author><author><name sortKey="Han, X" uniqKey="Han X">X Han</name></author><author><name sortKey="Kopell, N" uniqKey="Kopell N">N Kopell</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Faye, G" uniqKey="Faye G">G Faye</name></author><author><name sortKey="Faugeras, O" uniqKey="Faugeras O">O Faugeras</name></author></analytic></biblStruct></listBibl></div1></back></TEI><pmc article-type="abstract" xml:lang="en"><pmc-dir>properties open_access</pmc-dir>
<front><journal-meta><journal-id journal-id-type="nlm-ta">BMC Neurosci</journal-id><journal-id journal-id-type="iso-abbrev">BMC Neurosci</journal-id><journal-title-group><journal-title>BMC Neuroscience</journal-title></journal-title-group><issn pub-type="epub">1471-2202</issn><publisher><publisher-name>BioMed Central</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="pmc">4697613</article-id><article-id pub-id-type="publisher-id">1471-2202-16-S1-P24</article-id><article-id pub-id-type="doi">10.1186/1471-2202-16-S1-P24</article-id><article-categories><subj-group subj-group-type="heading"><subject>Poster Presentation</subject></subj-group></article-categories><title-group><article-title>Incremental stability of delayed neural fields: a unifying framework for endogenous and exogenous sources of pathological oscillations</article-title></title-group><contrib-group><contrib contrib-type="author" corresp="yes" id="A1"><name><surname>Is. Detorakis</surname><given-names>Georgios</given-names></name><xref ref-type="aff" rid="I1">1</xref><xref ref-type="aff" rid="I2">2</xref><email>georgios.detorakis@lss.supelec.fr</email></contrib><contrib contrib-type="author" id="A2"><name><surname>Chaillet</surname><given-names>Antoine</given-names></name><xref ref-type="aff" rid="I1">1</xref><xref ref-type="aff" rid="I2">2</xref></contrib></contrib-group><aff id="I1"><label>1</label>University Paris Sud, Orsay, Paris, 91400, France</aff><aff id="I2"><label>2</label>LSS, Supélec, Gif sur Yvette, Paris, 91190, France</aff><pub-date pub-type="collection"><year>2015</year></pub-date><pub-date pub-type="epub"><day>18</day><month>12</month><year>2015</year></pub-date><volume>16</volume><issue>Suppl 1</issue><supplement><named-content content-type="supplement-title">24th Annual Computational Neuroscience Meeting: CNS*2015</named-content><named-content content-type="supplement-editor">Gennady Cymbalyuk and Anthony Burkitt</named-content><named-content content-type="supplement-sponsor">The publication charges for this supplement were funded by the Organization for Computational Neurosciences. The Supplement Editors declare that they have no competing interests.</named-content></supplement><fpage>P24</fpage><lpage>P24</lpage><permissions><copyright-statement>Copyright © 2015 Is. Detorakis and Chaillet</copyright-statement><copyright-year>2015</copyright-year><copyright-holder>Is. Detorakis and Chaillet</copyright-holder><license license-type="open-access" xlink:href="http://creativecommons.org/licenses/by/4.0"><license-p>This is an Open Access article distributed under the terms of the Creative Commons Attribution License (<ext-link ext-link-type="uri" xlink:href="http://creativecommons.org/licenses/by/4.0">http://creativecommons.org/licenses/by/4.0</ext-link>), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The Creative Commons Public Domain Dedication waiver (<ext-link ext-link-type="uri" xlink:href="http://creativecommons.org/publicdomain/zero/1.0/">http://creativecommons.org/publicdomain/zero/1.0/</ext-link>) applies to the data made available in this article, unless otherwise stated.</license-p></license></permissions><self-uri xlink:href="http://www.biomedcentral.com/1471-2202/16/S1/P24"></self-uri><conference><conf-date>18-23 July 2015</conf-date><conf-name>24th Annual Computational Neuroscience Meeting: CNS*2015</conf-name><conf-loc>Prague, Czech Republic</conf-loc></conference></article-meta></front><body><sec><title></title><p>Neural fields are integro-differential equations that have been extensively used to model spatiotemporal evolution of neocortical areas (see [<xref ref-type="bibr" rid="B1">1</xref>] for a detailed review). Time-delayed neural fields have also been a matter of investigation since they take into account axonal delays [<xref ref-type="bibr" rid="B2">2</xref>]. On the other hand, time-delay finite dimensional systems have been used in models of Parkinson's disease: delays have been shown to play a possible role in the generation of pathological neural oscillations linked to motor symptoms of Parkinson disease in a firing-rate model of basal ganglia [<xref ref-type="bibr" rid="B3">3</xref>,<xref ref-type="bibr" rid="B4">4</xref>]. Nonetheless, these models fail at rendering the spatial distribution of the neural activity of the populations involved. Two possible mechanisms for the onset of pathological oscillations in basal ganglia have been investigated in the literature. The first one, the "endogenous" mechanism, hypothesizes that dopamine depletion tends to increase the synaptic gains between the excitatory neurons of the subthalamic nucleus (STN) and the inhibitory neurons of the external segment of globus pallidus (GPe), thus generating an instability that translates into sustained oscillations. The second one, the "exogenous" mechanism, explains these oscillations onset by a diffusion of spontaneous oscillations from external structures (such as Striatum) to the GPe-STN network [<xref ref-type="bibr" rid="B5">5</xref>].</p><p>The main goal of this work is to deepen this analysis by providing theoretical conditions under which a network of time-delayed neural field equations is incrementally stable. We believe that incremental stability constitutes an instrumental framework to investigate both the mechanisms evoked above. Indeed, by considering constant inputs to the basal ganglia, incremental stability ensures convergence to a unique equilibrium configuration, thus ruling out the possibility of "endogenous" mechanism for oscillations onset. On the other hand, incremental stability guarantees entrainability to periodic inputs (meaning convergence to a T-periodic solution in response to any T-periodic input), and can thus be useful to unravel the mechanism of pathological diffusion from external structures in the "exogenous" scenario.</p><p>Relying on the Razumikhin-Lyapunov approach here we derive these sufficient conditions for incremental stability of delayed neural fields. This theoretical framework thus complements the Krasovskii-Lyapunov approach already used in the literature to address the stability of delayed neural fields equations [<xref ref-type="bibr" rid="B6">6</xref>]. Simulations confirm our theoretical expectations and demonstrate that interconnected neural fields can exhibit sustained oscillations, according to either the "endogenous" or the "exogenous" mechanism, depending on the strength of the synaptic weights between the excitatory (STN) and the inhibitory (GPe) populations. The derived theoretical results thus seem to constitute a fertile ground for further investigations based on experimental data, to discriminate between the "endogenous" and the "exogenous" hypotheses for Parkinsonian sustained oscillations in the STN-GPe network.</p></sec></body><back><sec><title>Acknowledgements</title><p>This work has received support from ANR JCJC SynchNeuro and from the iCODE institute project funded by the IDEX Paris-Saclay, ANR-11-IDEX-0003-02.</p></sec><ref-list><ref id="B1"><mixed-citation publication-type="journal"><name><surname>Bressloff</surname><given-names>PC</given-names></name><article-title>Spatiotemporal dynamics of continuum neural fields</article-title><source>Journal of Physics A: Mathematical and Theoretical</source><year>2011</year><volume>45</volume><issue>3</issue><fpage>033001</fpage></mixed-citation></ref><ref id="B2"><mixed-citation publication-type="journal"><name><surname>Veltz</surname><given-names>R</given-names></name><name><surname>Faugeras</surname><given-names>O</given-names></name><article-title>Stability of the stationary solutions of neural field equations with propagation delays</article-title><source>The Journal of Mathematical Neuroscience</source><year>2011</year><volume>1</volume><issue>1</issue><fpage>1</fpage><lpage>28</lpage><pub-id pub-id-type="pmid">22655751</pub-id></mixed-citation></ref><ref id="B3"><mixed-citation publication-type="journal"><name><surname>Nevado Holgado</surname><given-names>AJ</given-names></name><name><surname>Terry</surname><given-names>JR</given-names></name><name><surname>Bogacz</surname><given-names>R</given-names></name><article-title>Conditions for the Generation of Beta Oscillations in the Subthalamic Nucleus-Globus Pallidus Network</article-title><source>Journal of Neuroscience</source><year>2010</year><volume>30</volume><issue>37</issue><fpage>12340</fpage><lpage>12352</lpage><pub-id pub-id-type="pmid">20844130</pub-id></mixed-citation></ref><ref id="B4"><mixed-citation publication-type="journal"><name><surname>Haidar</surname><given-names>I</given-names></name><name><surname>Pasillas-Lepine</surname><given-names>W</given-names></name><name><surname>Panteley</surname><given-names>E</given-names></name><name><surname>Chaillet</surname><given-names>A</given-names></name><name><surname>Palfi</surname><given-names>S</given-names></name><name><surname>Senova</surname><given-names>S</given-names></name><article-title>Analysis of delay-induced basal ganglia oscillations: the role of external excitatory nuclei</article-title><source>International Journal of Control</source><year>2014</year><volume>80</volume><issue>8</issue><fpage>1936</fpage><lpage>1956</lpage></mixed-citation></ref><ref id="B5"><mixed-citation publication-type="journal"><name><surname>McCarthy</surname><given-names>M</given-names></name><name><surname>Moore-Kochlacs</surname><given-names>C</given-names></name><name><surname>Gu</surname><given-names>X</given-names></name><name><surname>Boyden</surname><given-names>ES</given-names></name><name><surname>Han</surname><given-names>X</given-names></name><name><surname>Kopell</surname><given-names>N</given-names></name><article-title>Striatal origin of the pathologic beta oscillations in Parkinson's disease</article-title><source>PNAS</source><year>2011</year><volume>108</volume><issue>28</issue><fpage>11620</fpage><lpage>11625</lpage><pub-id pub-id-type="pmid">21697509</pub-id></mixed-citation></ref><ref id="B6"><mixed-citation publication-type="journal"><name><surname>Faye</surname><given-names>G</given-names></name><name><surname>Faugeras</surname><given-names>O</given-names></name><article-title>Some theoretical and numerical results for delayed neural field equations</article-title><source>Physica D</source><year>2010</year><volume>239</volume><issue>9</issue><fpage>561</fpage><lpage>578</lpage></mixed-citation></ref></ref-list></back></pmc></record>Pour manipuler ce document sous Unix (Dilib)
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