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Mathematical Medicine and Biology Advance Access originally published online on March 14, 2008
Mathematical Medicine and Biology 2008 25(1):21-36; doi:10.1093/imammb/dqn002
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© The author 2008. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Shortening of cardiac action potential duration near an insulating boundary

John W. Cain

Department of Mathematics and Center for the Study of Biological Complexity, 1001 West Main Street, Virginia Commonwealth University, Richmond, VA 23284-2014, USA

David G. Schaeffer{dagger}

Department of Mathematics and Center for Nonlinear and Complex Systems, Duke University, Box 90320, Durham, NC 27708-0320, USA
{dagger} Email: dgs{at}math.duke.edu

Received on November 30, 2006. Revised on January 4, 2008. Accepted on January 19, 2008.

It is known, from both experiments and simulations, that cardiac action potentials are shortened near a non-conducting boundary. In the present paper, this effect is studied in a simple, two-current ionic model, with propagation restricted to a 1D fibre. An asymptotic approximation for the dependence of action potential duration on distance to the boundary is derived. This estimate agrees well with simulations.

Keywords: action potential duration; insulating boundary; 1D cable


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