Propagation in Spatially Extended Reaction Diffusion Systems
Omschrijving
Propagation of functional or pathological ionic
disturbances in biological systems plays an important
role in normal regulatory mechanisms and in disease.
For example, potassium diffusion in brain tissue is
involved in spreading excitation. Models of this
type of phenomenon often take the form of a
reaction-diffusion system in one spatial dimension
with continuous dynamic variables. This text examines
propagation in three spatial dimensions through a
network of discrete dynamic elements coupled by
diffusion.
Conditions permissive of pulse origination and
propagation can be determined analytically for
systems in one spatial dimension. However, in three
spatial dimensions or in dynamic systems containing
discontinuities, explicit solutions may not exist.
Instead, the local dynamics of the excitable system
at a point in space are analyzed. The effective
diffusive flux or current at a point is interpreted
as a slowly varying parameter. The bifurcation
structure of the dynamics with respect to this
parameter and the effect of waveform on the time
course of the parameter are examined. Propagation
results when an excursion at a point produces a
diffusion current sufficient to move its resting
neighbor above some threshold value. The formation of
a pulse back depends on the stability of equilibria
of the local dynamics. Propagation in some cases may
also depend on the geometry of the wavefront.
Predictions are verified by numerical simulation
using a software package developed by the author. A
three dimensional lattice allows for description of
the local dynamics at nodal elements and diffusion
between elements and throughout the lattice.
Ik heb een vraag over het boek:
‘Potassium Waves and Neural Excitation - Hahn, Philip, Alexander, Sir James (UT Southwestern)’.
Vul het onderstaande formulier in.
We zullen zo spoedig mogelijk antwoorden.
