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Applied
Math Seminar
Quarter 2001
3:15 - 4:15 p.m.
Sloan Mathematics Corner
Building 380, Room 380-C
Friday, December 7, 2001
James Keener
Mathematics Department
University of Utah
The Importance of Microstructure in Defibrillation
Abstract:
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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.
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