V.N. Biktashev
Submitted to PRL: 2002/04/08. Accepted: 2002/08/27. Reference: Phys Rev Letters 89(16):168102, 2002
An excitation wave in cardiac tissue will fail to propagate if the transmembrane voltage at its front rises too slow and does not excite the tissue ahead of it. Then the sharp voltage profile of the front will dissipate, and subsequent spread of voltage will be purely diffusive. This mechanism is impossible in FitzHugh-Nagumo type systems. Here a simplified mathematical model for this mechanism is suggested. The model has exact traveling front solutions, and gives conditions for the front dissipation. In particular, a front will dissipate if it is not allowed to propagate faster than a certain nonzero speed. This critical speed depends only on the properties of the fast sodium channels. The inactivation gates of these channels play a crucial role in the front dissipation, even if their dynamics are by an order of magnitude slower than those of the voltage.
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