Beyond global synchrony: Equivalence between Kuramoto oscillators and Wilson-Cowan model for large scale brain networks

Ahmed H. Abd-Elrazik, Felipe A. Torres, Mónica Otero, Caroline A. Lea-Carnall, Wael El-Deredy

Producción científica: Capítulo del libro/informe/acta de congresoContribución a la conferenciarevisión exhaustiva

Resumen

Oscillations are ubiquitous in the nervous system, from single neurons to whole brain networks. The link between neural oscillations and cognition and behaviour is actively investigated by cognitive and computational neuroscience. Biophysically motivated computational models, such as Wilson-Cowan [W-C], have contributed to the understanding of the dynamics of oscillatory neuronal networks. W-C describes mean field interactions between excitatory/inhibitory neural populations. Using Malkin's Theorem we show the equivalence, under certain conditions, between the W-C model and the Kuramoto oscillators, with the advantage that the latter comprises fewer parameters. We construct a thirty-two nodes network of Kuramoto oscillators, coupled using two options: homogeneous (same strength in all connections) and heterogeneous (different values of coupling strengths). We characterized the Kuramoto network synchrony by measuring the Kuramoto order parameter, and the frequency spectrum of each oscillator using Welch's periodograms. We characterized those two features as a function of number of nodes, their intrinsic frequency, and the global coupling parameter. Using variable intrinsic frequency between oscillators, we found that as we increase the number of nodes of the system, the global synchrony becomes dependent on the global coupling strength. Also, as global coupling increases, the frequency spectrum of each oscillator converges to the mean intrinsic frequency, similar to the case when the intrinsic frequency is equal for all nodes. We conclude that the Kuramoto order parameter alone is not enough of characterizing network dynamics, and that a distribution of intrinsic node frequency is important to generate the sort of network dynamics observed in brain imaging data.

Idioma originalInglés
Título de la publicación alojada18th International Symposium on Medical Information Processing and Analysis
EditoresJorge Brieva, Pamela Guevara, Natasha Lepore, Marius G. Linguraru, Leticia Rittner, Eduardo Romero Castro
EditorialSPIE
ISBN (versión digital)9781510662544
DOI
EstadoPublicada - 2023
Evento18th International Symposium on Medical Information Processing and Analysis - Valparaiso, Chile
Duración: 20222022

Serie de la publicación

NombreProceedings of SPIE - The International Society for Optical Engineering
Volumen12567
ISSN (versión impresa)0277-786X
ISSN (versión digital)1996-756X

Conferencia

Conferencia18th International Symposium on Medical Information Processing and Analysis
País/TerritorioChile
CiudadValparaiso
Período09/11/2211/11/22

Nota bibliográfica

Funding Information:
Further author information: (Send correspondence to WED.) A.H.A.: [email protected], F.A.T.: [email protected], M.O.: [email protected], C.LC.: [email protected], WED.: [email protected] This work is supported by ANID, Chile: Anillo ACT210053, FONDECYT REGULAR 1201822, FONDECYT POST-DOCTORADO 3210508, BASAL FB210008, and BASAL FB0008.

Funding Information:
The authors acknowledge the financial support of ANID Chile: ANILLO ACT210053, FONDECYT 1201822, FONDECYT Postdoctorado 3210508, BASAL FB210008 and BASAL FB0008.

Publisher Copyright:
© 2023 SPIE.

Áreas temáticas de ASJC Scopus

  • Materiales electrónicos, ópticos y magnéticos
  • Física de la materia condensada
  • Informática aplicada
  • Matemáticas aplicadas
  • Ingeniería eléctrica y electrónica

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