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An astro-neural-field model with application to cortical spreading depolarization.

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Title: An astro-neural-field model with application to cortical spreading depolarization.
Authors: Baspinar E; MathNeuro Team, Inria Branch of the University of Montpellier, Montpellier, France. emre.baspinar@inria.fr., Avitabile D; MathNeuro Team, Inria Branch of the University of Montpellier, Montpellier, France.; Department of Mathematics, Vrije Universiteit Amsterdam, Amsterdam, The Netherlands.; Amsterdam Neuroscience - System and Network Neuroscience, Amsterdam, The Netherlands., Nouveau C; MathNeuro Team, Inria Branch of the University of Montpellier, Montpellier, France., Desroches M; MathNeuro Team, Inria Branch of the University of Montpellier, Montpellier, France., Campillo F; MathNeuro Team, Inria Branch of the University of Montpellier, Montpellier, France. fabien.campillo@inria.fr., Mantegazza M; Université Côte d'Azur, Valbonne-Sophia Antipolis, France.; CNRS UMR7275, Institute of Molecular and Cellular Pharmacology (IPMC), Valbonne-Sophia Antipolis, France.; Inserm U1323, Valbonne-Sophia Antipolis, France.
Source: Journal of computational neuroscience [J Comput Neurosci] 2026 Sep; Vol. 54 (3), pp. 559-576. Date of Electronic Publication: 2026 Jul 28.
Publication Type: Journal Article
Language: English
Journal Info: Publisher: Springer US Country of Publication: United States NLM ID: 9439510 Publication Model: Print-Electronic Cited Medium: Internet ISSN: 1573-6873 (Electronic) Linking ISSN: 09295313 NLM ISO Abbreviation: J Comput Neurosci Subsets: MEDLINE
Imprint Name(s): Publication: New York : Springer US
Original Publication: Boston : Kluwer Academic Publishers, 1994-
MeSH Terms: Cortical Spreading Depression*/physiology , Astrocytes*/physiology , Neurons*/physiology , Models, Neurological* , Cerebral Cortex*, Potassium/metabolism ; Membrane Potentials/physiology ; Migraine Disorders/physiopathology ; Humans ; Animals ; Nonlinear Dynamics
Abstract: We present a novel astro-neural-field population model with application to migraine-related cortical spreading depolarization. The model is composed of four spatio-temporal state variables: excitatory and inhibitory membrane potentials, astrocytic potassium uptake recruitment, and extracellular potassium concentration. Extending a previous neural field model, we incorporate activity-dependent astrocytic potassium clearance via a nonlinear term coupled to astrocyte dynamics. The astrocyte transfer function, like its neural counterpart, exhibits three regimes governed by extracellular potassium, capturing its effect on clearance. This yields a more comprehensive framework, better fits experimental data, and provides new insights into the mechanisms of cortical spreading depolarization.
(© 2026. The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.)
Competing Interests: Declarations. Conflict of interest: The authors declare no competing interests.
References: Comput Biol Med. 1996 Mar;26(2):133-41. (PMID: 8904287)
Nat Neurosci. 2006 Sep;9(9):1142-9. (PMID: 16921370)
J Cereb Blood Flow Metab. 2011 Jan;31(1):17-35. (PMID: 21045864)
J Neurophysiol. 1982 Jul;48(1):217-37. (PMID: 7119846)
Brain. 2012 Jan;135(Pt 1):259-75. (PMID: 22120143)
J Comput Neurosci. 2019 Dec;47(2-3):125-140. (PMID: 31620945)
PLoS Comput Biol. 2021 Jul 27;17(7):e1009239. (PMID: 34314446)
Geroscience. 2020 Feb;42(1):57-80. (PMID: 31820363)
Biophys J. 1972 Jan;12(1):1-24. (PMID: 4332108)
Brain. 1994 Feb;117 ( Pt 1):199-210. (PMID: 7908596)
J Theor Biol. 2009 May 21;258(2):219-28. (PMID: 19490858)
Int J Mol Sci. 2021 May 26;22(11):. (PMID: 34073593)
Front Neurosci. 2019 Aug 22;13:892. (PMID: 31507365)
World Neurosurg. 2020 Feb;134:50-57. (PMID: 31655239)
Cephalalgia. 2012 Jan;32(2):116-24. (PMID: 22174359)
Lancet Neurol. 2010 Apr;9(4):413-24. (PMID: 20298965)
J Physiol. 1999 Sep 1;519 Pt 2:415-25. (PMID: 10577057)
J Comput Neurosci. 2001 Jan-Feb;10(1):99-120. (PMID: 11316343)
J Comput Neurosci. 2018 Apr;44(2):203-217. (PMID: 29210004)
Sci Rep. 2025 Sep 24;15(1):32749. (PMID: 40993139)
Cephalalgia. 2009 Mar;29(3):308-13. (PMID: 19220312)
Stroke. 2002 Dec;33(12):2738-43. (PMID: 12468763)
Biophys J. 2016 Jul 26;111(2):452-462. (PMID: 27463146)
PLoS Biol. 2005 Mar;3(3):e68. (PMID: 15737062)
Brain Res. 2004 Mar 5;999(2):167-74. (PMID: 14759495)
J Math Neurosci. 2013 May 29;3(1):7. (PMID: 23718283)
J Neurosci. 2003 Oct 29;23(30):9888-96. (PMID: 14586018)
Nat Rev Neurosci. 2014 Jun;15(6):379-93. (PMID: 24857965)
PLoS Comput Biol. 2010 Aug 26;6(8):. (PMID: 20865153)
Exp Neurol. 1984 May;84(2):249-58. (PMID: 6714339)
Kybernetik. 1973 Sep;13(2):55-80. (PMID: 4767470)
Phys Rev E. 2017 Dec;96(6-1):062409. (PMID: 29347421)
Int J Mol Sci. 2021 Jul 13;22(14):. (PMID: 34299111)
Cephalalgia. 2019 Apr;39(4):477-488. (PMID: 29986598)
Cells. 2025 Oct 31;14(21):. (PMID: 41227353)
Cephalalgia. 2009 Oct;29(10):1115-24. (PMID: 19735537)
J Neurosci. 2008 Jul 16;28(29):7273-83. (PMID: 18632931)
J Comput Neurosci. 2024 May;52(2):145-164. (PMID: 38607466)
J Cereb Blood Flow Metab. 2016 Nov;36(11):1965-1977. (PMID: 26661217)
Nat Commun. 2022 Nov 21;13(1):7136. (PMID: 36414629)
Biophys J. 1978 Aug;23(2):257-76. (PMID: 687764)
Biol Rev Camb Philos Soc. 2006 Nov;81(4):457-81. (PMID: 16848916)
PLoS Comput Biol. 2025 Jun 4;21(6):e1013099. (PMID: 40465585)
Brain Res. 1996 Nov 18;740(1-2):268-74. (PMID: 8973824)
Grant Information: ANR-15-IDEX-01 Agence Nationale de la Recherche; LabEx ICST ANR- &&-LABX-0015-01 Laboratory of Excellence "Ion Channel Science and Therapeutics
Contributed Indexing: Keywords: Astrocyte; Migraine; Neural field; Spreading depolarization
Substance Nomenclature: RWP5GA015D (Potassium)
Entry Date(s): Date Created: 20260728 Date Completed: 20260918 Latest Revision: 20261008
Update Code: 20261008
DOI: 10.1007/s10827-026-00948-3
PMID: 42518050
Database: MEDLINE
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  Data: <searchLink fieldCode="AU" term="%22Baspinar+E%22">Baspinar E</searchLink>; MathNeuro Team, Inria Branch of the University of Montpellier, Montpellier, France. emre.baspinar@inria.fr.<br /><searchLink fieldCode="AU" term="%22Avitabile+D%22">Avitabile D</searchLink>; MathNeuro Team, Inria Branch of the University of Montpellier, Montpellier, France.; Department of Mathematics, Vrije Universiteit Amsterdam, Amsterdam, The Netherlands.; Amsterdam Neuroscience - System and Network Neuroscience, Amsterdam, The Netherlands.<br /><searchLink fieldCode="AU" term="%22Nouveau+C%22">Nouveau C</searchLink>; MathNeuro Team, Inria Branch of the University of Montpellier, Montpellier, France.<br /><searchLink fieldCode="AU" term="%22Desroches+M%22">Desroches M</searchLink>; MathNeuro Team, Inria Branch of the University of Montpellier, Montpellier, France.<br /><searchLink fieldCode="AU" term="%22Campillo+F%22">Campillo F</searchLink>; MathNeuro Team, Inria Branch of the University of Montpellier, Montpellier, France. fabien.campillo@inria.fr.<br /><searchLink fieldCode="AU" term="%22Mantegazza+M%22">Mantegazza M</searchLink>; Université Côte d'Azur, Valbonne-Sophia Antipolis, France.; CNRS UMR7275, Institute of Molecular and Cellular Pharmacology (IPMC), Valbonne-Sophia Antipolis, France.; Inserm U1323, Valbonne-Sophia Antipolis, France.
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  Data: <searchLink fieldCode="MM" term="%22Cortical+Spreading+Depression%22">Cortical Spreading Depression*</searchLink>/<searchLink fieldCode="MM" term="%22Cortical+Spreading+Depression+physiology%22">physiology</searchLink> <br /><searchLink fieldCode="MM" term="%22Astrocytes%22">Astrocytes*</searchLink>/<searchLink fieldCode="MM" term="%22Astrocytes+physiology%22">physiology</searchLink> <br /><searchLink fieldCode="MM" term="%22Neurons%22">Neurons*</searchLink>/<searchLink fieldCode="MM" term="%22Neurons+physiology%22">physiology</searchLink> <br /><searchLink fieldCode="MM" term="%22Models%2C+Neurological%22">Models, Neurological*</searchLink> <br /><searchLink fieldCode="MM" term="%22Cerebral+Cortex%22">Cerebral Cortex*</searchLink><br /><searchLink fieldCode="MH" term="%22Potassium%22">Potassium</searchLink>/<searchLink fieldCode="MH" term="%22Potassium+metabolism%22">metabolism</searchLink> ; <searchLink fieldCode="MH" term="%22Membrane+Potentials%22">Membrane Potentials</searchLink>/<searchLink fieldCode="MH" term="%22Membrane+Potentials+physiology%22">physiology</searchLink> ; <searchLink fieldCode="MH" term="%22Migraine+Disorders%22">Migraine Disorders</searchLink>/<searchLink fieldCode="MH" term="%22Migraine+Disorders+physiopathology%22">physiopathology</searchLink> ; <searchLink fieldCode="MH" term="%22Humans%22">Humans</searchLink> ; <searchLink fieldCode="MH" term="%22Animals%22">Animals</searchLink> ; <searchLink fieldCode="MH" term="%22Nonlinear+Dynamics%22">Nonlinear Dynamics</searchLink>
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  Data: We present a novel astro-neural-field population model with application to migraine-related cortical spreading depolarization. The model is composed of four spatio-temporal state variables: excitatory and inhibitory membrane potentials, astrocytic potassium uptake recruitment, and extracellular potassium concentration. Extending a previous neural field model, we incorporate activity-dependent astrocytic potassium clearance via a nonlinear term coupled to astrocyte dynamics. The astrocyte transfer function, like its neural counterpart, exhibits three regimes governed by extracellular potassium, capturing its effect on clearance. This yields a more comprehensive framework, better fits experimental data, and provides new insights into the mechanisms of cortical spreading depolarization.<br /> (© 2026. The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.)
– Name: Abstract
  Label: Competing Interests
  Group: Ab
  Data: Declarations. Conflict of interest: The authors declare no competing interests.
– Name: Ref
  Label: References
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(PMID: <searchLink fieldCode="PM" term="%2231820363%22">31820363)</searchLink><br />Biophys J. 1972 Jan;12(1):1-24. (PMID: <searchLink fieldCode="PM" term="%224332108%22">4332108)</searchLink><br />Brain. 1994 Feb;117 ( Pt 1):199-210. (PMID: <searchLink fieldCode="PM" term="%227908596%22">7908596)</searchLink><br />J Theor Biol. 2009 May 21;258(2):219-28. (PMID: <searchLink fieldCode="PM" term="%2219490858%22">19490858)</searchLink><br />Int J Mol Sci. 2021 May 26;22(11):. (PMID: <searchLink fieldCode="PM" term="%2234073593%22">34073593)</searchLink><br />Front Neurosci. 2019 Aug 22;13:892. (PMID: <searchLink fieldCode="PM" term="%2231507365%22">31507365)</searchLink><br />World Neurosurg. 2020 Feb;134:50-57. (PMID: <searchLink fieldCode="PM" term="%2231655239%22">31655239)</searchLink><br />Cephalalgia. 2012 Jan;32(2):116-24. (PMID: <searchLink fieldCode="PM" term="%2222174359%22">22174359)</searchLink><br />Lancet Neurol. 2010 Apr;9(4):413-24. (PMID: <searchLink fieldCode="PM" term="%2220298965%22">20298965)</searchLink><br />J Physiol. 1999 Sep 1;519 Pt 2:415-25. (PMID: <searchLink fieldCode="PM" term="%2210577057%22">10577057)</searchLink><br />J Comput Neurosci. 2001 Jan-Feb;10(1):99-120. (PMID: <searchLink fieldCode="PM" term="%2211316343%22">11316343)</searchLink><br />J Comput Neurosci. 2018 Apr;44(2):203-217. (PMID: <searchLink fieldCode="PM" term="%2229210004%22">29210004)</searchLink><br />Sci Rep. 2025 Sep 24;15(1):32749. (PMID: <searchLink fieldCode="PM" term="%2240993139%22">40993139)</searchLink><br />Cephalalgia. 2009 Mar;29(3):308-13. (PMID: <searchLink fieldCode="PM" term="%2219220312%22">19220312)</searchLink><br />Stroke. 2002 Dec;33(12):2738-43. (PMID: <searchLink fieldCode="PM" term="%2212468763%22">12468763)</searchLink><br />Biophys J. 2016 Jul 26;111(2):452-462. (PMID: <searchLink fieldCode="PM" term="%2227463146%22">27463146)</searchLink><br />PLoS Biol. 2005 Mar;3(3):e68. 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(PMID: <searchLink fieldCode="PM" term="%2229347421%22">29347421)</searchLink><br />Int J Mol Sci. 2021 Jul 13;22(14):. (PMID: <searchLink fieldCode="PM" term="%2234299111%22">34299111)</searchLink><br />Cephalalgia. 2019 Apr;39(4):477-488. (PMID: <searchLink fieldCode="PM" term="%2229986598%22">29986598)</searchLink><br />Cells. 2025 Oct 31;14(21):. (PMID: <searchLink fieldCode="PM" term="%2241227353%22">41227353)</searchLink><br />Cephalalgia. 2009 Oct;29(10):1115-24. (PMID: <searchLink fieldCode="PM" term="%2219735537%22">19735537)</searchLink><br />J Neurosci. 2008 Jul 16;28(29):7273-83. (PMID: <searchLink fieldCode="PM" term="%2218632931%22">18632931)</searchLink><br />J Comput Neurosci. 2024 May;52(2):145-164. (PMID: <searchLink fieldCode="PM" term="%2238607466%22">38607466)</searchLink><br />J Cereb Blood Flow Metab. 2016 Nov;36(11):1965-1977. (PMID: <searchLink fieldCode="PM" term="%2226661217%22">26661217)</searchLink><br />Nat Commun. 2022 Nov 21;13(1):7136. (PMID: <searchLink fieldCode="PM" term="%2236414629%22">36414629)</searchLink><br />Biophys J. 1978 Aug;23(2):257-76. (PMID: <searchLink fieldCode="PM" term="%22687764%22">687764)</searchLink><br />Biol Rev Camb Philos Soc. 2006 Nov;81(4):457-81. (PMID: <searchLink fieldCode="PM" term="%2216848916%22">16848916)</searchLink><br />PLoS Comput Biol. 2025 Jun 4;21(6):e1013099. (PMID: <searchLink fieldCode="PM" term="%2240465585%22">40465585)</searchLink><br />Brain Res. 1996 Nov 18;740(1-2):268-74. (PMID: <searchLink fieldCode="PM" term="%228973824%22">8973824)</searchLink>
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  Data: <i>Keywords: </i>Astrocyte; Migraine; Neural field; Spreading depolarization
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