Executive Summary : | The interest in the dynamics of two-dimensional spiral waves and their three-dimensional counterparts, called scrolls, has enormously increased over the years. This is primarily because of their analogy with several complex biological phenomena. It is well known that the generation of spiral and scroll waves in the mammalian heart often leads to cardiac arrhythmias, which are serious clinical conditions characterized by abnormal heart beat. The situation becomes worse, when the vortices meet different types of heterogeneities in the highly inhomogeneous myocardial tissue and get anchored to them. Such anchoring, referred to as pinning in the terminology of nonlinear dynamics, generally increases the life span of the undesired waves and in extreme cases may even prevent their disappearance from the medium. Thus, detailed knowledge of the mechanisms of the pinning processes is crucial for the control and removal of the waves in the cardiovascular system. However, in vivo studies are not often feasible, if not impossible, because the heart is a delicate and complicated physiological organ. Therefore, information is usually extracted from simpler analogous systems. The Belousov-Zhabotinsky reaction is such a system. Under appropriate conditions, it can sustain spiral and scroll waves and have many behavioural similarities with a mammalian heart. This reaction-diffusion system is thus serves as the cleanest and simplest model of cardiac wave propagation. For studying pinning processes, heterogeneities are introduced into the BZ system, which is otherwise homogeneous unlike cardiac tissue. This proposed work is aimed at the study of the dynamics of three-dimensional scroll waves in chemical excitable media using impermeable, inert heterogeneities of arbitrary and complex shapes. The experimental study will be conducted using the BZ-reaction and that will be accompanied by numerical simulations of reaction-diffusion equations. The choice of 3D-waves and arbitrarily shaped obstacles has been made keeping in view the anisotropic, thick, inhomogeneous cardiac tissue, where anatomical obstacles like scar tissues, coronary vessels are abundant. These anatomic obstacles can be of complex irregular shapes and a wide range of sizes. As most of the earlier works in this area involved very symmetrical spherical anchors or simple regular geometries like squares, rectangles or cylinders, further investigation is necessary that takes into account the complexity arising from the irregular shape, unequal sizes, and different angular orientations of not-so-symmetric obstacles. These aspects are planned to be investigated in detail as part of the proposed project using obstacles of different shapes and sizes. |