This mathematical model demonstrates that excitation fronts in cardiac or nerve tissue will dissipate if propagation speed falls below a certain threshold, highlighting the critical role of Na inactivation gates.
Alerts modelers to minimum speed thresholds for front stability; leaves open experimental validation of Na inactivation effects in tissue.
An excitation wave in nerve or cardiac tissue may fail to propagate if the temporal gradient of the transmembrane voltage at the front becomes too small to excite the tissue ahead of it. A simplified mathematical model is suggested, that reproduces this phenomenon and has exact traveling front solutions. The spectrum of possible propagation speeds is bounded from below. This causes a front to dissipate if it is not allowed to propagate quickly enough. A crucial role is played by the Na inactivation gates, even if their dynamics are by an order of magnitude slower than the dynamics of the voltage.
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V. N. Biktashev (2003) studied this question.
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