Photon-Scanning Approach to Control Spiral Wave Dynamics in the Heart.

Self-organizing spiral electrical waves are produced in the heart during fatal cardiac arrhythmias. Controlling these waves is therefore an essential step in managing the disease. Here we present an effective method for controlling cardiac spiral waves using optogenetics.

Pulsed low-energy stimulation initiates electric turbulence in cardiac tissue.

Interruptions in nonlinear wave propagation, commonly referred to as wave breaks, are typical of many complex excitable systems. In the heart they lead to lethal rhythm disorders, the so-called arrhythmias, which are one of the main causes of sudden death in the industrialized world. Progress in the treatment and therapy of cardiac arrhythmias requires a detailed understanding of the triggers and dynamics of these wave breaks.

External forcing and feedback control of nonlinear dissipative waves.

The dynamics of traveling waves in a nonlinear dissipative system are studied analytically and numerically. Spatiotemporal forcing and feedback forcing are applied to the traveling waves in a phase-separated system undergoing chemical reactions. The stability of the traveling waves and interesting, unexpected behavior, including the reversal of the propagation direction are analyzed in one dimension.

Selection mechanism for rotating patterns in weakly excitable media.

Two types of patterns rigidly rotating within a disk of a weakly excitable medium are studied using the free-boundary approach. The patterns are spots moving along the boundary of the disk and spiral waves rotating around the disk center. The study reveals a selection mechanism that uniquely determines the shape and the angular velocity of these patterns as a function of the medium excitability and the disk radius.

Wave front interaction model of stabilized propagating wave segments.

A wave front interaction model is developed to describe the relationship between excitability and the size and shape of stabilized wave segments in a broad class of weakly excitable media. These wave segments of finite size are unstable but can be stabilized by feedback to the medium excitability; they define a separatrix between spiral wave behavior and contracting wave segments. Unbounded wave segments (critical fingers) lie on the asymptote of this separatrix, defining the boundary between excitable and subexcitable media.

Resonance attractors of spiral waves in excitable media under global feedback.

The dynamics of spiral waves on a circular domain is studied by numerical integration of an excitable reaction-diffusion system with a global feedback. A theory based on the Fourier expansion of the feedback signal is developed to explain the existence and the stability of resonance attractors of spiral waves on domains of different sizes. The theoretical analysis predicts the existence of a discrete set of stable attractors with radii depending on the time delay in the feedback loop.

Instabilities of the resonance attractor for spiral waves in an excitable medium.

During an experimental study of the resonance attractor for spiral waves in the light-sensitive Belousov-Zhabotinsky reaction, strong deviations of the attractor trajectories from circular orbits are observed if the time delay in the feedback loop becomes relatively long. A theory is developed that reduces the spiral wave dynamics under a long-delayed control to a higher order iterative map. Then the observed deviations are explained to be a result of instabilities appearing due to the Neimark bifurcation of the map.

External forcing of spiral waves.

The effect of an external rhythm on rotating spiral waves in excitable media is investigated. Parameters of the unperturbed medium were chosen, such that the organizing spiral tip describes meandering (hypocyclic) trajectories, which are the most general shape for the experimentally observed systems. Periodical modulation of excitability in a model of the Belousov-Zhabotinsky (BZ) reaction forces meandering spiral tips to describe trajectories that are not found at corresponding stationary conditions.