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Biological Cybernetics

, Volume 113, Issue 5–6, pp 561–577 | Cite as

Investigating the role of gap junctions in seizure wave propagation

  • Laura R. González-RamírezEmail author
  • Ava J. Mauro
Original Article
  • 48 Downloads

Abstract

The effect of gap junctions as well as the biological mechanisms behind seizure wave propagation is not completely understood. In this work, we use a simple neural field model to study the possible influence of gap junctions specifically on cortical wave propagation that has been observed in vivo preceding seizure termination. We consider a voltage-based neural field model consisting of an excitatory and an inhibitory population as well as both chemical and gap junction-like synapses. We are able to approximate important properties of cortical wave propagation previously observed in vivo before seizure termination. This model adds support to existing evidence from models and clinical data suggesting a key role of gap junctions in seizure wave propagation. In particular, we found that in this model gap junction-like connectivity determines the propagation of one-bump or two-bump traveling wave solutions with features consistent with the clinical data. For sufficiently increased gap junction connectivity, wave solutions cease to exist. Moreover, gap junction connectivity needs to be sufficiently low or moderate to permit the existence of linearly stable solutions of interest.

Keywords

Traveling waves Seizure termination Gap Junctions 

Mathematics Subject Classification

35C07 37N25 45K05 92C20 

Notes

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Departamento de Formación Básica Disciplinaria, Instituto Politécnico NacionalUnidad Profesional Interdisciplinaria de Ingeniería Campus HidalgoSan Agustín TlaxiacaMexico
  2. 2.Department of Chemistry and BiochemistryUniversity of Notre DameNotre DameUSA

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