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We integrate our model cells into a continuum model for excitable tissue using a nonlinear parabolic second order partial differential equation, which we discretize in time using finite differences and in space using finite elements.
The canonical model for excitable media are the well-known FitzHugh Nagumo equations [26] with diffusion in the activator variable: ε ∂ u ∂ t = u − 1 3 u 3 − v + ∇ 2 u, ∂ v ∂ t = u + β. (1).
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The original ventricular model along with the new Purkinje structural model then can be used as a domain in which cardiac model equations may be solved, yielding models for isolated excitable ventricular and Purkinje systems.
In the example, we consider the classical model of excitable membrane by Morris and Lecar (1981).
We examine the problem of parameter estimation in mathematical models of excitable cell cardiac electrical activity using the well-known Beeler Reuter (1977) ionic equations for the ventricular action potential.
Such oscillations have been measured in neurons and agree with simulations using models of excitable cells [4], [5].
In a parallel track, the Physiome Project is building on over half a century of molecular modeling of excitable cells that used ordinary and partial differential equations and is also using finite element lattices for geometric modeling of complete human organs.
In fact, it turned out for excitable elements that the main two classes of excitability are actually amenable to direct analysis in a two-dimensional phase plane by identifying in the conductance-based model fast and slow processes and grouping these into dynamics of just two lump variables [4, 5].
The model is stimulated with external pulse stimuli and can generate nonlinear integrate-and-fire and resonant responses typical for excitable neuronal cells (all-or-none).
For excitable six- to 10-year-olds, 29-31 October, northernstage.
There are doggy diapers for "excitable urination" and incontinence.
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Justyna Jupowicz-Kozak
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