Intermittent trapping of spiral waves in a cardiac model

Exploring the Synthesis of Self-Organization and Active Motion

Proteins, genetic material, and membranes are fundamental to all known organisms, yet these components alone do not constitute life. Life emerges from the dynamic processes of self-organization, assembly, and active motion, suggesting the existence of similar artificial systems. Against this backdrop, our Perspective explores a variety of chemical phenomena illustrating how nonequilibrium self-organization and micromotors contribute to life-like behavior and functionalities. After explaining key terms, we discuss specific examples including enzymatic motion, diffusiophoretic and bubble-driven self-propulsion, pattern-forming reaction-diffusion systems, self-assembling inorganic aggregates, and hierarchically emergent phenomena. We also provide a roadmap for combining self-organization and active motion and discuss possible outcomes through biological analogs. We suggest that this research direction, deeply rooted in physical chemistry, offers opportunities for further development with broad impacts on related sciences and technologies.

Spatially Conserved Spiral Wave Activity During Human Atrial Fibrillation

BACKGROUND

Atrial fibrillation is the most common cardiac arrhythmia in the world and increases the risk for stroke and morbidity. During atrial fibrillation, the electric activation fronts are no longer coherently propagating through the tissue and, instead, show rotational activity, consistent with spiral wave activation, focal activity, collision, or partial versions of these spatial patterns. An unexplained phenomenon is that although simulations of cardiac models abundantly demonstrate spiral waves, clinical recordings often show only intermittent spiral wave activity.

METHODS

In silico data were generated using simulations in which spiral waves were continuously created and annihilated and in simulations in which a spiral wave was intermittently trapped at a heterogeneity. Clinically, spatio-temporal activation maps were constructed using 60 s recordings from a 64 electrode catheter within the atrium of N=34 patients (n=24 persistent atrial fibrillation). The location of clockwise and counterclockwise rotating spiral waves was quantified and all intervals during which these spiral waves were present were determined. For each interval, the angle of rotation as a function of time was computed and used to determine whether the spiral wave returned in step or changed phase at the start of each interval.

RESULTS

In both simulations, spiral waves did not come back in phase and were out of step." In contrast, spiral waves returned in step in the majority (68%; P=0.05) of patients. Thus, the intermittently observed rotational activity in these patients is due to a temporally and spatially conserved spiral wave and not due to ones that are newly created at the onset of each interval.

CONCLUSIONS

Intermittency of spiral wave activity represents conserved spiral wave activity of long, but interrupted duration or transient spiral activity, in the majority of patients. This finding could have important ramifications for identifying clinically important forms of atrial fibrillation and in guiding treatment.

A possible new cardiac heterogeneity as an arrhythmogenic driver

Atrial fibrillation (AF) is the commonest cardiac arrhythmia, affecting 3 million people in the USA and 8 million in the EU (according to the European Society of Cardiology). So, why is it that even with the best medical care, around a third of the patients are treatment resistant. Extensive research of its etiology showed that AF and its mechanisms are still debatable. Some of the AF origins are ascribed to functional and ionic heterogeneities of the heart tissue and possibly to additional triggering agents. But, have all AF origins been detected? Are all accepted origins, in fact, arrhythmogenic? In order to study these questions and specifically to check our new idea of intermittency as an arrhythmogenesis agent, we chose to employ a mathematical model which was as simple as possible, but which could still be used to observe the basic network processes of AF development. At this point we were not interested in the detailed ionic propagations nor in the actual shapes of the induced action potentials (APs) during the AF outbreaks. The model was checked by its ability to exactly recapture the basic AF developmental stages known from experimental cardiac observations and from more elaborate mathematical models. We use a simple cellular automata 2D mathematical model of N × N matrices to elucidate the field processes leading to AF in a tissue riddled with randomly distributed heterogeneities of different types, under sinus node operation, simulated by an initial line of briefly stimulated cells inducing a propagating wave, and with or without an additional active ectopic action potential pulse, in turn simulated by a transitory operation of a specific cell. Arrhythmogenic contributions, of three different types of local heterogeneities in myocytes and their collaborations, in inducing AF are examined. These are: a heterogeneity created by diffuse fibrosis, a heterogeneity created by myocytes having different refractory periods, and a new heterogeneity type, created by intermittent operation of some myocytes. The developmental stages (target waves and spirals) and the different probabilities of AF occurring under each condition, are shown. This model was established as being capable of reproducing the known AF origins and their basic development stages, and in addition has shown: (1) That diffuse fibrosis on its own is not arrhythmogenic but in combination with other arrhythmogenic agents it can either enhance or limit AF. (2) In general, combinations of heterogeneities can act synergistically, and, most importantly, (3) The new type of intermittency heterogeneity proves to be extremely arrhythmogenic. Both the intermittency risk and the fibrosis role in AF generation were established. Knowledge of the character of these arrhythmogenesis agents can be of real importance in AF treatment.

Meander pattern of spiral wave and the spatial distribution of its cycle length

One of the most interesting dynamics of rotating spiral waves in an excitable medium is meandering. The tip of a meandering spiral wave moves along a complex trajectory, which often takes the shape of an epitrochoid or hypotrochoid with inward or outward petals. The cycle lengths (CLs) of a meandering spiral wave are not constant; rather, they depend on the meandering dynamics. In this paper, we show that the CLs take two mean values, outside T^{out} and inside T^{in} the meandering trajectory with a ratio of T^{in}/T^{out}=(n+1)/n for the inward and (n-1)/n for the outward petals, where n is the number of petals in the tip trajectory. We illustrate this using four models of excitable media and prove this result. These formulas are shown to be suitable for a meandering spiral wave in an anatomical model of the heart. We also show that the effective periods of overdrive pacing of meandering spiral waves depend on the electrode location relative to the tip trajectory. Overall, our approach can be used to study the meandering pattern from the CL data; it should work for any type of dynamics that produces complex tip trajectories of the spiral wave, for example, for a drift due to heterogeneity.

The physics of heart rhythm disorders

The global burden caused by cardiovascular disease is substantial, with heart disease representing the most common cause of death around the world. There remains a need to develop better mechanistic models of cardiac function in order to combat this health concern. Heart rhythm disorders, or arrhythmias, are one particular type of disease which has been amenable to quantitative investigation. Here we review the application of quantitative methodologies to explore dynamical questions pertaining to arrhythmias. We begin by describing single-cell models of cardiac myocytes, from which two and three dimensional models can be constructed. Special focus is placed on results relating to pattern formation across these spatially-distributed systems, especially the formation of spiral waves of activation. Next, we discuss mechanisms which can lead to the initiation of arrhythmias, focusing on the dynamical state of spatially discordant alternans, and outline proposed mechanisms perpetuating arrhythmias such as fibrillation. We then review experimental and clinical results related to the spatio-temporal mapping of heart rhythm disorders. Finally, we describe treatment options for heart rhythm disorders and demonstrate how statistical physics tools can provide insights into the dynamics of heart rhythm disorders.

Rotational synchronization of pinned spiral waves

Coupled rotors can spontaneously synchronize, giving rise to a plethora of intriguing dynamics. We present here a pair of spiral waves as two synchronizing rotors, coupled by diffusion. The spirals are pinned to unexcitable obstacles, which enables us to modify their frequencies and restrain their drift. In experiments with the Belousov-Zhabotinsky reaction, we show that two counterrotating spiral rotors, pinned to circular heterogeneities, can synchronize in frequency and phase. The nature of the phase synchronization varies depending on the difference in their characteristic frequencies. We observe in-phase and out-of-phase synchronization, lag synchronization, and phase resetting across the experiments. The time required for the two spirals to synchronize is found to depend upon the relative size of their pinning obstacles and the distance separating them. This distance can also modify the phase lag of the two rotors upon synchronization. Our experimental observations are reproduced and explained further on the basis of numerical simulations of an excitable reaction-diffusion model.