Abstract
Cardiac waves can fail to propagate when the membrane potential of the cells in the wavefront rises too slowly. The sodium channel inactivation gates play an important role in this process of propagation block. Simple models including inactivation gates can have travelling waves of constant form with two possible velocities. A stability analysis demonstrates that the slower velocity is always unstable, and in limited parameter regimes the faster velocity can also be unstable. Waves with the lower velocity propagate a finite distance before they dissipate due to this instability and this distance is calculated. The distance can be large suggesting that they might be seen in certain pathological conditions. The analytical results are compared with numerical simulations of the simplified model and a detailed cardiac ionic model.
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Hinch, R. Stability of cardiac waves. Bull. Math. Biol. 66, 1887–1908 (2004). https://doi.org/10.1016/j.bulm.2004.05.004
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DOI: https://doi.org/10.1016/j.bulm.2004.05.004