title: Designing a planar vector field to investigate the role of a slow variable in an enhanced mean-field model during general anesthesia.
abstract: Local mean-field models (MFMs) describe regional brain activities by some connected differential equations. In an overall view, constituting variables of these differential equations can be divided to very fast, fast and slow variables. In this article we propose a method that can be used to determine role of a slow variable in behavior of MFMs. Very fast variables can be adiabatically removed from the equations. Isoclines of fast and slow variables and their corresponding vector field can provide valuable information about model behavior and role of the slow variable in it. The vector field of our interested MFM that is an enhanced MFM designed specially for general anesthesia, is a 3D field (one slow and two fast variables) and it is not so convenient for visually inspecting the role of the slow variable in this model. To afford this problem we design a 2D (planar) vector filed that only considers the slow variable and one of the fast variables.
authors.affiliation: LTSI INSERM U 642, Univ., de Rennes I, France. brhnam.molaee-ardekani@univ-rennes1.fr
authors.forename: Behnam
authors.initials: B
authors.lastname: Molaee-Ardekani
authors.forename: Mohammad-Bagher
authors.initials: MB
authors.lastname: Shamsollahi
authors.forename: Lotfi
authors.initials: L
authors.lastname: Senhadji
authors.forename: Bijan
authors.initials: B
authors.lastname: Vosoughi-Vahdat
authors.forename: Eric
authors.initials: E
authors.lastname: Wodey
mesh_terms: D000465:Algorithms; D000768:Anesthesia, General; D000777:Anesthetics / Q000627:therapeutic use; D003198:Computer Simulation; D006801:Humans; D008564:Membrane Potentials; D008954:Models, Biological; D008959:Models, Neurological; D015233:Models, Statistical; D008962:Models, Theoretical; D009474:Neurons; D012107:Research Design; D012815:Signal Processing, Computer-Assisted; D013569:Synapses
chemical_list: D000777:Anesthetics