Excitable Media
Excitable media are spatially distributed systems which have the ability to propagate signals without damping. For example, a forest fire travels as a wave from its
initiation point, and regenerates with every tree it ignites. This is in contrast to passive wave propagation, which is characterized by a gradual damping of signal
amplitude due to friction. An example of passive wave propagation is sound waves passing through air.
An impulse over a certain threshold initiates a wave of activity moving across the excitable media. As each element undergoes an excursion from steady state, it
causes its neighbors to move over threshold at a rate determined by the diffusion coefficient (a `passive' property of the media), and the rate of rise of the diffused
species of the excited element (a `active' property of the media).
The propagation of electrical activity in cardiac muscle involves the interaction of different ion species across a combination of active and passive ion channels and
diffusion of charge through a heterogeneous substrate with dynamically changing conductances.
Despite complexity inherent in conduction at microscopic
scales, the heart can be approximated as a continuous excitable media.
A variety of cardiac tachycardias have been attributed to formation of large
scale patterns of excitation such as the formation and break up of spiral waves.
In our laboratory
we map conduction
in cultured monolayers of cardiac tissue. The monolayer can be thought of as an
excitable media with heterogeneities. We use general theories on excitable media
to model our results.
For more background on excitable media follow these links to relevant sections of my thesis. (Please note that the figures are not
linked to the thesis document.)
Excitable Media Overview
Mathematical Models
Mathematical Models: Cellular Automata
Bursting Cellular Automata
Spiral Waves
The Heart as an Excitable Medium
Reentry
The Monolayer as a Model System
Spiral Wave Formation
Spiral Wave Destruction
Continuum Considerations: Heterogeneity Issues
Great resources on excitable media can be found in the links page.
