VULNERABILITY IN EXCITABLE BELOUSOV-ZHABOTINSKY MEDIUM FROM 1D TO 2D

Mechanisms for initiating rotating waves in 1D and 2D excitable media were compared and parameters affecting wavefront formation were analyzed. The time delay between two sequentially initiated wavefronts (a conditioning wave followed by a test wave) was varied in order to induce rotating waves, a protocol similar to that utilized in cardiac muscle experiments to reveal vulnerability to rotating wave initiation. We define the vulnerability region, VR, as the range of time delays between conditioning and test waves where the test waves evolves into a rotating wave. The smaller the VR, the more resistant the heart is against origination of dangerous cardiac arrhythmias. Heterogeneity of cardiac muscle is widely recognized as the prerequisite for rotating wave initiation. We have identified the VR in homogeneous 2D excitable media. In the Belousov-Zhabotinsky (BZ) reaction with immobilized catalyst and in the Oregonator model of this reaction, a properly timed test wave gives rise to rotating waves. The VR was increased when the size of the perturbation used for test wave creation was increased or when the threshold for propagation was decreased. Increasing the dimensionality of the medium for 1D to 2D results in diminishing of VR.