Prevalence of Rate-Dependent Behaviors in Cardiac Muscle

Spatiotemporal complexity can degrade the performance of dynamical systems. Recent research has focused on the control of complexity in biological systems, where a loss of performance can be deadly [1]. In cardiac function, for example, it is advantageous to suppress the spatiotemporal disorganization of ventricular fibrillation that prevents blood from being pumped throughout the body. Chaos control techniques [2] have shown the potential to modify temporal disorganization in spatially extended cardiac tissue using small electrical perturbations. To optimize the design of these control techniques it is essential to determine the types and prevalence of spatially localized dynamical behaviors that have been correlated with the initiation of spatiotemporal complexity in the heart [3,4]. In this Letter we investigate in vitro the response of small pieces of bullfrog (Rana catesbeiana) cardiac muscle to periodic electrical stimulation to determine the prevalence of different rate-dependent behaviors. Under various conditions of periodic electrical stimulation (pacing), M stimuli can elicit N responses (M:N behavior). A wide range of these responses have been observed depending on the type of cardiac tissue, animal species, or stimulus parameters, such as frequency [5], amplitude [6], and shape [7]. We concentrate on rate-dependent behaviors in cardiac muscle because of the wide range of excitation rates that occur in both healthy and pathological cardiac tissue. In addition, we explore the range of dynamical behaviors in a large number of animals to determine the relative prevalence of different dynamical states because control protocols must be able to deal with every behavior occurring in