Spatial symmetry breaking determines spiral wave chirality

Control of the chirality of spiral waves and recreation of spatial excitation patterns through optogenetics

Spiral waves lead to dangerous arrhythmias in the cardiac system. In 2015 Burton et al. demonstrated the reversal of the spiral wave chirality through the rotating spiral-shaped illumination on the optogenetically modified cardiac monolayers. We show that this process entails the recreation of a spiral wave. We show how this methodology can be used to control and create the desired spatial excitation pattern. We found that the control is sensitive to the area of illuminated region but independent of the phase difference of the existing spiral wave and the applied spiral-shaped light. We also discovered that our methodology can temporarily resynchronize a turbulent system. The results offer numerical evidence for the control of spatial pattern in biological excitable systems with optogenetics.

Thermal effects on cardiac alternans onset and development: A spatiotemporal correlation analysis

Alternans of cardiac action potential duration represent critical precursors for the development of life-threatening arrhythmias and sudden cardiac death. The system's thermal state affects these electrical disorders requiring additional theoretical and experimental efforts to improve a patient-specific clinical understanding. In such a scenario, we generalize a recent work from Loppini et al. [Phys. Rev. E 100, 020201(R) (2019)PREHBM2470-004510.1103/PhysRevE.100.020201] by performing an extended spatiotemporal correlation study. We consider high-resolution optical mapping recordings of canine ventricular wedges' electrical activity at different temperatures and pacing frequencies. We aim to recommend the extracted characteristic length as a potential predictive index of cardiac alternans onset and evolution within a wide range of system states. In particular, we show that a reduction of temperature results in a drop of the characteristic length, confirming the impact of thermal instabilities on cardiac dynamics. Moreover, we theoretically investigate the use of such an index to identify and predict different alternans regimes. Finally, we propose a constitutive phenomenological law linking conduction velocity, characteristic length, and temperature in view of future numerical investigations.

Programmed Locomotion of an Active Gel Driven by Spiral Waves

Active media that host spiral waves can display complex modes of locomotion driven by the dynamics of those waves. We use a model of a photosensitive stimulus-responsive gel that supports the propagation of spiral chemical waves to study locomotive transition and programmed locomotion. The mode transition between circular and toroidal locomotion results from the onset of spiral tip meandering that arises via a secondary Hopf bifurcation as the level of illumination is increased. This dynamic instability of the system introduces a second circular locomotion with a small diameter caused by tip meandering. The original circular locomotion with large diameter is driven by the push-pull asymmetry of the wavefront and waveback of the simple spiral waves initiated at one corner of gel. By harnessing this mode transition of the gel locomotion via coded illumination, we design programmable pathways of nature-inspired angular locomotion of the gel.

Spreading of perturbations in myosin group kinetics along actin filaments

Global changes in the state of spatially distributed systems can often be traced back to perturbations that arise locally. Whether such local perturbations grow into global changes depends on the system geometry and the spatial spreading of these perturbations. Here, we investigate how different spreading behaviors of local perturbations determine their global impact in 1-dimensional systems of different size. Specifically, we assessed sliding arrest events in in vitro motility assays where myosins propel actin, and simulated the underlying mechanochemistry of myosins that bind along the actin filament. We observed spontaneous sliding arrest events that occurred more frequently for shorter actin filaments. This observation could be explained by spontaneous local arrest of myosin kinetics that stabilizes once it spreads throughout an entire actin filament. When we introduced intermediate concentrations of the actin cross-linker filamin, longer actin was arrested more frequently. This observation was reproduced by simulations where filamin binding induces persistent local arrest of myosin kinetics, which subsequently spreads throughout the actin filament. A spin chain model with nearest-neighbor coupling reproduced key features of our experiments and simulations, thus extending to other linear systems with nearest-neighbor coupling the following conclusions: 1) perturbations that are persistent only once they spread throughout the system are more effective in smaller systems, and 2) perturbations that are persistent upon their establishment are more effective in larger systems. Beyond these general conclusions, our work also provides a theoretical model of collective myosin kinetics with a finite range of mechanical coupling along the actin filament.

Spatiotemporal correlation uncovers characteristic lengths in cardiac tissue

Complex spatiotemporal patterns of action potential duration have been shown to occur in many mammalian hearts due to period-doubling bifurcations that develop with increasing frequency of stimulation. Here, through high-resolution optical mapping experiments and mathematical modeling, we introduce a characteristic spatial length of cardiac activity in canine ventricular wedges via a spatiotemporal correlation analysis, at different stimulation frequencies and during fibrillation. We show that the characteristic length ranges from 40 to 20 cm during one-to-one responses and it decreases to a specific value of about 3 cm at the transition from period-doubling bifurcation to fibrillation. We further show that during fibrillation, the characteristic length is about 1 cm. Another significant outcome of our analysis is the finding of a constitutive phenomenological law obtained from a nonlinear fitting of experimental data which relates the conduction velocity restitution curve with the characteristic length of the system. The fractional exponent of 3/2 in our phenomenological law is in agreement with the domain size remapping required to reproduce experimental fibrillation dynamics within a realistic cardiac domain via accurate mathematical models.

Double-wave reentry in excitable media

A monolayer of chick embryo cardiac cells grown in an annular geometry supports two simultaneous reentrant excitation waves that circulate as a doublet. We propose a mechanism that can lead to such behavior. The velocity restitution gives the instantaneous velocity of a wave as a function of the time since the passage of the previous wave at a given point in space. Nonmonotonic restitution relationships will lead to situations in which various spacings between circulating waves are possible. In cardiology, the situation in which two waves travel in an anatomically defined circuit is referred to as double-wave reentry. Since double-wave reentry may arise as a consequence of pacing during cardiac arrhythmias, understanding the dynamic features of double-wave reentry may be helpful in understanding the physiological properties of cardiac tissue and in the design of therapy.

Controlling excitable wave behaviors through the tuning of three parameters

Excitable systems are a class of dynamical systems that can generate self-sustaining waves of activity. These waves are known to manifest differently under diverse conditions, whereas some travel as planar or radial waves, and others evolve into rotating spirals. Excitable systems can also form stationary stable patterns through standing waves. Under certain conditions, these waves are also known to be reflected at no-flux boundaries. Here, we review the basic characteristics of these four entities: traveling, rotating, standing and reflected waves. By studying their mechanisms of formation, we show how through manipulation of three critical parameters: time-scale separation, space-scale separation and threshold, we can interchangeably control the formation of all the aforementioned wave types.

Spiral wave initiation in excitable media

Spiral waves represent an important example of dissipative structures observed in many distributed systems in chemistry, biology and physics. By definition, excitable media occupy a stationary resting state in the absence of external perturbations. However, a perturbation exceeding a threshold results in the initiation of an excitation wave propagating through the medium. These waves, in contrast to acoustic and optical ones, disappear at the medium's boundary or after a mutual collision, and the medium returns to the resting state. Nevertheless, an initiation of a rotating spiral wave results in a self-sustained activity. Such activity unexpectedly appearing in cardiac or neuronal tissues usually destroys their dynamics which results in life-threatening diseases. In this context, an understanding of possible scenarios of spiral wave initiation is of great theoretical importance with many practical applications.This article is part of the theme issue 'Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (part 2)'.

Spiral wave initiation in excitable media

Spiral waves represent an important example of dissipative structures observed in many distributed systems in chemistry, biology and physics. By definition, excitable media occupy a stationary resting state in the absence of external perturbations. However, a perturbation exceeding a threshold results in the initiation of an excitation wave propagating through the medium. These waves, in contrast to acoustic and optical ones, disappear at the medium's boundary or after a mutual collision, and the medium returns to the resting state. Nevertheless, an initiation of a rotating spiral wave results in a self-sustained activity. Such activity unexpectedly appearing in cardiac or neuronal tissues usually destroys their dynamics which results in life-threatening diseases. In this context, an understanding of possible scenarios of spiral wave initiation is of great theoretical importance with many practical applications.This article is part of the theme issue 'Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (part 2)'.

Demonstration of cardiac rotor and source mapping techniques in embryonic chick monolayers

Excitable media, such as the heart, display propagating waves with different geometries including target patterns and rotors (spiral waves). Collision of two waves leads to annihilation of both. We present algorithms for data processing and analysis to identify the core of rotors. In this work, we show that as the spatial sampling resolution decreases it becomes increasingly difficult to identify rotors-there are instances of false negatives and false positives. These observations are relevant to current controversies concerning the role of rotors in the initiation, maintenance, and treatment of cardiac arrhythmias, especially atrial fibrillation. Currently some practitioners target the core of rotors for ablation, but the effectiveness of this procedure has been questioned. In view of the difficulties inherent in the identification of rotors, we conclude that methods to identify rotors need to first be validated prior to assessing the efficacy of ablation.

Nonlinear diffusion and thermo-electric coupling in a two-variable model of cardiac action potential

This work reports the results of the theoretical investigation of nonlinear dynamics and spiral wave breakup in a generalized two-variable model of cardiac action potential accounting for thermo-electric coupling and diffusion nonlinearities. As customary in excitable media, the common Q₁₀ and Moore factors are used to describe thermo-electric feedback in a 10° range. Motivated by the porous nature of the cardiac tissue, in this study we also propose a nonlinear Fickian flux formulated by Taylor expanding the voltage dependent diffusion coefficient up to quadratic terms. A fine tuning of the diffusive parameters is performed a priori to match the conduction velocity of the equivalent cable model. The resulting combined effects are then studied by numerically simulating different stimulation protocols on a one-dimensional cable. Model features are compared in terms of action potential morphology, restitution curves, frequency spectra, and spatio-temporal phase differences. Two-dimensional long-run simulations are finally performed to characterize spiral breakup during sustained fibrillation at different thermal states. Temperature and nonlinear diffusion effects are found to impact the repolarization phase of the action potential wave with non-monotone patterns and to increase the propensity of arrhythmogenesis.

Geometrical factors in propagation block and spiral wave initiation

Many theoretical and experimental studies indicate that a propagation block represents an important factor in spiral wave initiation in excitable media. The analytical and numerical results we obtained for a generic two-component reaction-diffusion system demonstrate quantitative conditions for the propagation block in a one-dimensional and a two-dimensional medium due to a sharp spatial increase of the medium's excitability or the coupling strength above a certain critical value. Here, we prove that this critical value strongly depends on the medium parameters and the geometry of the inhomogeneity. For an exemplary two-dimensional medium, we show how the propagation block can be used to initiate spiral waves by a specific choice of the size and shape of the medium's inhomogeneity.

Varieties of reentrant dynamics

Experiments were carried out in monolayer tissue cultures of embryonic chick heart cells imaged using a calcium sensitive fluorescent dye. The cells were grown in annular geometries and in annular geometries with an isthmus connecting antipodal region of the annulus. We observed a large number of spatially different patterns of propagation consisting of one or more circulating waves. As well, we also observed rhythms in which rotors embedded in the annuli generated propagating pulses. These results demonstrate that many different patterns of excitation can be present in cardiac tissue with simple geometries.

Fast propagation regions cause self-sustained reentry in excitable media

Self-sustained waves of electrophysiological activity can cause arrhythmia in the heart. These reentrant excitations have been associated with spiral waves circulating around either an anatomically defined weakly conducting region or a functionally determined core. Recently, an ablation procedure has been clinically introduced that stops atrial fibrillation of the heart by destroying the electrical activity at the spiral core. This is puzzling because the tissue at the anatomically defined spiral core would already be weakly conducting, and a further decrease should not improve the situation. In the case of a functionally determined core, an ablation procedure should even further stabilize the rotating wave. The efficacy of the procedure thus needs explanation. Here, we show theoretically that fundamentally in any excitable medium a region with a propagation velocity faster than its surrounding can act as a nucleation center for reentry and can anchor an induced spiral wave. Our findings demonstrate a mechanistic underpinning for the recently developed ablation procedure. Our theoretical results are based on a very general and widely used two-component model of an excitable medium. Moreover, the important control parameters used to realize conditions for the discovered phenomena are applicable to quite different multicomponent models.

Determining conduction patterns on a sparse electrode grid: Implications for the analysis of clinical arrhythmias

We present a general method of utilizing bioelectric recordings from a spatially sparse electrode grid to compute a dynamic vector field describing the underlying propagation of electrical activity. This vector field, termed the wave-front flow field, permits quantitative analysis of the magnitude of rotational activity (vorticity) and focal activity (divergence) at each spatial point. We apply this method to signals recorded during arrhythmias in human atria and ventricles using a multipolar contact catheter and show that the flow fields correlate with corresponding activation maps. Further, regions of elevated vorticity and divergence correspond to sites identified as clinically significant rotors and focal sources where therapeutic intervention can be effective. These flow fields can provide quantitative insights into the dynamics of normal and abnormal conduction in humans and could potentially be used to enhance therapies for cardiac arrhythmias.

Optical control of excitation waves in cardiac tissue

In nature, macroscopic excitation waves^1,2 are found in a diverse range of settings including chemical reactions, metal rust, yeast, amoeba and the heart and brain. In the case of living biological tissue, the spatiotemporal patterns formed by these excitation waves are different in healthy and diseased states^2,3. Current electrical and pharmacological methods for wave modulation lack the spatiotemporal precision needed to control these patterns. Optical methods have the potential to overcome these limitations, but to date have only been demonstrated in simple systems, such as the Belousov-Zhabotinsky chemical reaction⁴. Here, we combine dye-free optical imaging with optogenetic actuation to achieve dynamic control of cardiac excitation waves. Illumination with patterned light is demonstrated to optically control the direction, speed and spiral chirality of such waves in cardiac tissue. This all-optical approach offers a new experimental platform for the study and control of pattern formation in complex biological excitable systems.