title: Neuronal models in infinite-dimensional spaces and their finite-dimensional projections: Part II.
abstract: Application of comparison theorem is used to examine the validitiy of the "lumped parameter assumption" in describing the behavior of solutions of the continuous cable equation U(t) = DU(xx)+f(U) with the discrete cable equation dV(n)/dt = d*(V(n+1) - 2V(n) + V(n-1)) + f(V(n)), where f is a nonlinear functional describing the internal diffusion of electrical potential in single neurons. While the discrete cable equation looks like a finite difference approximation of the continuous cable equation, solutions of the two reveal significantly different behavior which imply that the compartmental models (spiking neurons) are poor quantifiers of neurons, contrary to what is commonly accepted in computational neuroscience.
authors.affiliation: Department of Differential Equations, Faculty of Applied Mathematics, AGH University of Science and Technology, Al. Mickiewicza 30, 30-059 Cracow, Poland. brzych@agh.edu.pl
authors.forename: S
authors.initials: S
authors.lastname: Brzychczy
authors.forename: H
authors.initials: H
authors.lastname: Leszczyński
authors.forename: R R
authors.initials: RR
authors.lastname: Poznanski
mesh_terms: D000200:Action Potentials / Q000502:physiology*; D000818:Animals; D002451:Cell Compartmentation / Q000502:physiology*; D006801:Humans; D008959:Models, Neurological; D009474:Neurons / Q000502:physiology*; D017711:Nonlinear Dynamics; D013569:Synapses / Q000502:physiology