Defibrillation of cardiac muscle by the application of a large brief current is used routinely in hosptials to
save hundreds of
lives daily. Although this technique was discovered in the late
1940's and has been steadily improved since then, until recently there has been no theory
describing how or why defibrillation works. In fact, previous theory
predicted that it cannot work, even though it obviously does.
Within the last few years a theory describing the mechanism of
defibrillation has been proposed. This theory exploits the spatial
inhomogeneity of the normal heart. However, a substantial controversy
remains about the nature of the most important inhomogeneities, with one
view favoring large scale inhomogeneities, such as anisotropy and
changes in fiber direction, and another favoring
small scale inhomogeneities.
In this talk, I will describe this proposed mechanism for cardiac
defibrillation and use homogenization theory to
develop a mathematical model that shows when it works and why it
fails. I will also
demonstrate why there is a crucial dependence on the spatial scale of
inhomogeneity.