Response function framework for the dynamics of meandering or large-core spiral waves and modulated traveling waves.

In many oscillatory or excitable systems, dynamical patterns emerge which are stationary or periodic in a moving frame of reference. Examples include traveling waves or spiral waves in chemical systems or cardiac tissue. We present a unified theoretical framework for the drift of such patterns under small external perturbations, in terms of overlap integrals between the perturbation and the adjoint critical eigenfunctions of the linearized operator (i.e., response functions). For spiral waves, the finite radius of the spiral tip trajectory and spiral wave meander are taken into account. Different coordinate systems can be chosen, depending on whether one wants to predict the motion of the spiral-wave tip, the time-averaged tip path, or the center of the meander flower. The framework is applied to analyze the drift of a meandering spiral wave in a constant external field in different regimes.

Filament Tension and Phase Locking of Meandering Scroll Waves.

Meandering spiral waves are often observed in excitable media such as the Belousov-Zhabotinsky reaction and cardiac tissue. We derive a theory for drift dynamics of meandering rotors in general reaction-diffusion systems and apply it to two types of external disturbances: an external field and curvature-induced drift in three dimensions. We find two distinct regimes: with small filament curvature, meandering scroll waves exhibit filament tension, whose sign determines the stability and drift direction. In the regimes of strong external fields or meandering motion close to resonance, however, phase locking of the meander pattern is predicted and observed.

Spiral wave stability in cardiac tissue with biphasic restitution.

Human ventricular tissue as well as several animal ventricular preparations show a biphasic shape of the action potential duration restitution curve, with a local maximum at low diastolic intervals. We study numerically how the location and properties of this nonmonotonicity affect the stability of spiral waves. We find that, depending on the slopes of the ascending and of the descending parts of the restitution curve, we can have either stable rotation of the spiral wave or spiral breakup. We identify two types of spiral breakup: one due to a steep positive slope and another due to a steep negative slope in the restitution curve. We discuss the differences in their manifestation and possible implications. We also find that increasing the slope of the descending part of the restitution curve increases the meandering of the spiral wave, due to the repeated occurrence of conduction blocks near the spiral wave tip.

Transition from ventricular fibrillation to ventricular tachycardia: a simulation study on the role of Ca(2+)-channel blockers in human ventricular tissue.

We study the effect of blocking the L-type Ca(2+)-channel on fibrillation in simulations in two-dimensional (2D) isotropic sheets of ventricular tissue and in a three-dimensional anisotropic anatomical model of human ventricles, using a previously developed model of human ventricular cells. Ventricular fibrillation (VF) was obtained as a result of spiral wave breakup and consisted of a varying number of chaotically wandering wavelets activating tissue at a frequency of about 6.0 Hz. We show that blocking the Ca(2+)-current by 75% can convert ventricular fibrillation into a periodic regime with a small number of stable spiral waves, ranging from six in 2D sheets of 25 x 25 cm to a single spiral in the anatomical model of human ventricles. The dominant frequency during this process changed to about 10.0 Hz in the 2D simulations, but to only 5.0 Hz in the whole heart simulations where a single spiral wave anchored around an anatomical obstacle. We show that the observed effects were due to a flattening of the electrical restitution curve, which prevented the generation of wave breaks and stabilized the activation patterns.

A computationally efficient electrophysiological model of human ventricular cells.

Recent experimental and theoretical results have stressed the importance of modeling studies of reentrant arrhythmias in cardiac tissue and at the whole heart level. We introduce a six-variable model obtained by a reformulation of the Priebe-Beuckelmann model of a single human ventricular cell. The reformulated model is 4.9 times faster for numerical computations and it is more stable than the original model. It retains the action potential shape at various frequencies, restitution of action potential duration, and restitution of conduction velocity. We were able to reproduce the main properties of epicardial, endocardial, and M cells by modifying selected ionic currents. We performed a simulation study of spiral wave behavior in a two-dimensional sheet of human ventricular tissue and showed that spiral waves have a frequency of 3.3 Hz and a linear core of approximately 50-mm diameter that rotates with an average frequency of 0.62 rad/s. Simulation results agreed with experimental data. In conclusion, the proposed model is suitable for efficient and accurate studies of reentrant phenomena in human ventricular tissue.