Spiral Wave Dynamics in a Bursting Media

Tanya, Radha Rani (2023) Spiral Wave Dynamics in a Bursting Media. Masters thesis, Indian Institute of Science Education and Research Kolkata.

Text (MS dissertation of Radha Rani Tanya (18MS129)) Thesis_18MS129.pdf - Submitted Version Restricted to Repository staff only Download (14MB)

Abstract

Cardiac Arrhythmias can be caused by spiral waves of action potential which rotate at frequencies greater than the frequency of the natural pacemaker cells. In experiments conducted on chicken embryo myocytes, we observe spontaneous initiation of spiral waves under low potassium concentrations, and observe parabolic bursting at the cell level under high potassium concentrations. Based on the analysis of the experimental data, it was shown that the parabolic bursting happens due to the circle - circle mechanism with Saddle ode on an Invariant circle (SNIC) bifurcations in the fast subsystem, caused by the dynamics of the slow subsystem. Based on this, we proposed that the Extended Morris Lecar model is a good fit for the cell level processes. To explain the spontaneous initiation of spiral waves in the tissue, we first look at various mechanism of functional re-entry using the monodomain formulation. In particular, we look at action potential restitution heterogeneity across the tissue and demonstrate that such heterogeneities can initiate spiral wave activity. In particular, for spiral waves to continue propagating and persisting in a medium with single static heterogeneity, it is essential that the slope of the Action Potential Restitution (APD) restitution curve of the heterogeneous curve be greater than 1. In case the slope of the APD restitution curve in all regions is lesser than 1 for the stable pacing cycle length, spiral waves may be initiated,but will not be able to sustain or propagate. In media with dynamic heterogeneities, or with multiple heterogeneous regions, we observe that spiral wave initiation and break up can happen even if the regions have flat APD restitution curve. Therefore, we demonstrate another computational model which discredits the APD restitution hypothesis, showing that spiral wave formation and breakup are not always limited to regions where the APD restitution curve has a slop greater than 1. We also show the possible mechanisms by which spiral waves can breakup, specifically break ups due to interactions with heterogeneous regions of the tissue and self interactions. Finally to demonstrate the agreement between the simulation model and the experiment, we show the spiral tip meander patterns of both agree, and are circular in nature. Thus we conclude that the medium has dynamic regions of heterogeneity which have APD restitution slopes lesser than 1, allowing formation of stable spirals across the tissue.

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