Key result
Mathematical modeling using the Morris-Lecar system demonstrated that the stability of one-dimensional spiral waves, and thus the propensity for wave reflections, is most sensitive to variations in calcium and potassium conductances.
Why the study?
Reflected waves induced by action potentials interacting with cardiac tissue heterogeneities are linked to cardiac arrhythmias, but their generation is not well understood.
Computational modeling demonstrates that the existence and stability of 1D spiral waves dictate the propensity for reflected action potentials, providing a mechanistic basis for reflection-mediated cardiac arrhythmias.
When propagated action potentials in cardiac tissue interact with local heterogeneities, reflected waves can sometimes be induced. These reflected waves have been associated with the onset of cardiac arrhythmias, and while their generation is not well understood, their existence is linked to that of one-dimensional (1D) spiral waves. Thus, understanding the existence and stability of 1D spirals plays a crucial role in determining the likelihood of the unwanted reflected pulses. Mathematically, we probe these issues by viewing the 1D spiral as a time-periodic antisymmetric source defect. Through a combination of direct numerical simulation and continuation methods, we investigate existence and stability of a 1D spiral wave in a qualitative ionic model to determine how the systems propensity for reflections are influenced by system parameters. Our results support and extend a previous hypothesis that the 1D spiral is an unstable periodic orbit that emerges through a global rearrangement of heteroclinic orbits and we identify key parameters and physiological processes that promote and deter reflection behavior.
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Dodson et al. (2021) studied Cardiac arrhythmia. Parameter variation in Morris-Lecar model was evaluated on Unstable eigenvalue of the 1D spiral wave. Mathematical modeling using the Morris-Lecar system demonstrated that the stability of one-dimensional spiral waves, and thus the propensity for wave reflections, is most sensitive to variations in calcium and potassium conductances.
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