Dynamics of bound states of same-chirality spiral waves

In silico thermal control of spiral wave dynamics in excitable cardiac tissue

Self-organizing spiral waves of excitation occur in many complex excitable systems. In the heart, for example, they are associated with the occurrence of fatal cardiac arrhythmias such as tachycardia and fibrillation, which can lead to sudden cardiac death. The control of these waves is therefore necessary for the treatment of the disease. In this letter, I present an innovative approach to control cardiac arrhythmias using low (nonfreezing) temperatures. This approach differs from all previous established techniques in that it involves no drugs, no genetic modification, no injection of foreign bodies, no application of voltage shocks (high or low, single or pulsed), and no curative damage to the heart. It relies on regional cooling of cardiac tissue to create a transient inhomogeneity in the electrophysiological properties. This inhomogeneity can then be manipulated to control the dynamics of the reentrant waves. This approach is, to my knowledge, the most sustainable theoretical proposal for the treatment of cardiac arrhythmias in the clinic.

Markov modeling of phase singularity interaction effects in human atrial and ventricular fibrillation

Atrial and ventricular fibrillation (AF/VF) are characterized by the repetitive regeneration of topological defects known as phase singularities (PSs). The effect of PS interactions has not been previously studied in human AF and VF. We hypothesized that PS population size would influence the rate of PS formation and destruction in human AF and VF, due to increased inter-defect interaction. PS population statistics were studied in computational simulations (Aliev-Panfilov), human AF and human VF. The influence of inter-PS interactions was evaluated by comparison between directly modeled discrete-time Markov chain (DTMC) transition matrices of the PS population changes, and M/M/∞ birth-death transition matrices of PS dynamics, which assumes that PS formations and destructions are effectively statistically independent events. Across all systems examined, PS population changes differed from those expected with M/M/∞. In human AF and VF, the formation rates decreased slightly with PS population when modeled with the DTMC, compared with the static formation rate expected through M/M/∞, suggesting new formations were being inhibited. In human AF and VF, the destruction rates increased with PS population for both models, with the DTMC rate increase exceeding the M/M/∞ estimates, indicating that PS were being destroyed faster as the PS population grew. In human AF and VF, the change in PS formation and destruction rates as the population increased differed between the two models. This indicates that the presence of additional PS influenced the likelihood of new PS formation and destruction, consistent with the notion of self-inhibitory inter-PS interactions.

Spatial symmetry breaking determines spiral wave chirality

Chirality represents a fundamental property of spiral waves. Introducing obstacles into cardiac monolayers leads to the initiation of clockwise-rotating, counterclockwise-rotating, and pairs of spiral waves. Simulations show that the precise location of the obstacle and the pacing frequency determine spiral wave chirality. Instabilities predicted by curves relating the action potential duration and the pacing frequency at different spatial locations predict sites of wave break initiation and, hence, spiral wave chirality.

Selection of multiarmed spiral waves in a regular network of neurons

Formation and selection of multiarmed spiral wave due to spontaneous symmetry breaking are investigated in a regular network of Hodgkin-Huxley neuron by changing the excitability and imposing spatial forcing currents on the neurons in the network. The arm number of the multiarmed spiral wave is dependent on the distribution of spatial forcing currents and excitability diversity in the network, and the selection criterion for supporting multiarmed spiral waves is discussed. A broken spiral segment is measured by a short polygonal line connected by three adjacent points (controlled nodes), and a double-spiral wave can be developed from the spiral segment. Multiarmed spiral wave is formed when a group of double-spiral waves rotate in the same direction in the network. In the numerical studies, a group of controlled nodes are selected and spatial forcing currents are imposed on these nodes, and our results show that l-arm stable spiral wave (l = 2, 3, 4,...8) can be induced to occupy the network completely. It is also confirmed that low excitability is critical to induce multiarmed spiral waves while high excitability is important to propagate the multiarmed spiral wave outside so that distinct multiarmed spiral wave can occupy the network completely. Our results confirm that symmetry breaking of target wave in the media accounts for emergence of multiarmed spiral wave, which can be developed from a group of spiral waves with single arm under appropriate condition, thus the potential formation mechanism of multiarmed spiral wave in the media is explained.

Interaction of multiarmed spirals in bistable media

We study the interaction of both dense and sparse multiarmed spirals in bistable media modeled by equations of the FitzHugh-Nagumo type. A dense one-armed spiral is characterized by its fixed tip. For dense multiarmed spirals, when the initial distance between tips is less than a critical value, the arms collide, connect, and disconnect continuously as the spirals rotate. The continuous reconstruction between the front and the back drives the tips to corotate along a rough circle and to meander zigzaggedly. The rotation frequency of tip, the frequency of zigzagged displacement, the frequency of spiral, the oscillation frequency of media, and the number of arms satisfy certain relations as long as the control parameters of the model are fixed. When the initial distance between tips is larger than the critical value, the behaviors of individual arms within either dense or sparse multiarmed spirals are identical to that of corresponding one-armed spirals.

Collision-based spiral acceleration in cardiac media: roles of wavefront curvature and excitable gap

We have previously shown in experimental cardiac cell monolayers that rapid point pacing can convert basic functional reentry (single spiral) into a stable multiwave spiral that activates the tissue at an accelerated rate. Here, our goal is to further elucidate the biophysical mechanisms of this rate acceleration without the potential confounding effects of microscopic tissue heterogeneities inherent to experimental preparations. We use computer simulations to show that, similar to experimental observations, single spirals can be converted by point stimuli into stable multiwave spirals. In multiwave spirals, individual waves collide, yielding regions with negative wavefront curvature. When a sufficient excitable gap is present and the negative-curvature regions are close to spiral tips, an electrotonic spread of excitatory currents from these regions propels each colliding spiral to rotate faster than the single spiral, causing an overall rate acceleration. As observed experimentally, the degree of rate acceleration increases with the number of colliding spiral waves. Conversely, if collision sites are far from spiral tips, excitatory currents have no effect on spiral rotation and multiple spirals rotate independently, without rate acceleration. Understanding the mechanisms of spiral rate acceleration may yield new strategies for preventing the transition from monomorphic tachycardia to polymorphic tachycardia and fibrillation.

Resonant drift of two-armed spirals by a periodic advective field and periodic modulation of excitability

The drift behavior of two-armed spirals induced by periodic advective field and periodic modulation of excitability is investigated. It is shown that the two-armed spirals controlled by periodic advective field and periodic modulation of excitability drift in completely different ways. For periodic advective field, the two tips of the two-armed spiral drift in the same direction and the two-armed spiral is stable. While for periodic modulation of excitability, the two tips drift in the opposite direction and the two-armed spiral splits into two single-armed spirals. Analytical results based on a kinematic theory of rotating spirals in weakly excitable media are consistent with the numerical results.

Stabilization of multiarmed spiral waves by circularly polarized electric fields

The influence of circularly polarized electric fields (CPEFs) on the stability of multiarmed spiral waves is investigated. It is shown that CPEFs can change the period of the multiarmed spirals. The average period is an important quantity of multiarmed spiral and it must be larger than a threshold for stable multiarmed spiral. After a counter-rotating CPEF with suitable amplitude and period is applied, the average period of the multiarmed spiral may increase, which stabilizes the multiarmed spiral.