ABSTRACT
As mentioned earlier in this book, the dynamical spatial patterns in excitable media, such as spiral and scroll waves, can become unstable in certain conditions and give rise to a state characterized by spiral turbulence, corresponding to spatiotemporal chaos. As mentioned in Chapter 1, such spatiotemporally chaotic states have been implicated in clinically significant disturbances of the natural rhythm of the heart [Gray et al. 1998; Witkowski et al. 1998], e.g., fibrillation. Ventricular fibrillation in particular is lethal as it results in complete loss of coordination of activity between different regions in the heart [Winfree 1987]. The resulting cessation of the mechanical pumping action necessary for blood circulation leads to a drastic fall in blood pressure. If not treated immediately death follows within a few minutes. However the conventional methods of defibrillation require the application of large electrical shocks that are undesirable for a variety of reasons. Developing low-amplitude control schemes involving as few control electrodes as possible is an exciting challenge and has potential clinical relevance [Christini et al. 2001; Gauthier et al. 2002; Pumir et al. 2007]. As mentioned in Chapter 9, devising such control using low voltages or current has to take into account the special features of excitable media like the existence of a refractory period and activation threshold. The amplitude and timing of the control signal needs to be appropriately chosen so that it results in the desired response from the medium. Note that the excited state is meta-stable, and the cell eventually recovers to the resting state associated in different biological systems with a characteristic resting transmembrane potential (≃ −84 mV for cardiac myocytes). Thus, the control of spatiotemporal chaos in excitable media may be viewed as essentially a problem of synchronizing the excitation phase of every cell, so that the entire system returns to the resting state, resulting in the termination of all activity.
