Unpinning of rotating spiral waves in cardiac tissues by circularly polarized electric fields

Theory and experiments of spiral unpinning in the Belousov-Zhabotinsky reaction using a circularly polarized electric field

We present the first experimental study of unpinning an excitation wave using a circularly polarized electric field. The experiments are conducted using the excitable chemical medium, the Belousov-Zhabotinsky (BZ) reaction, which is modeled with the Oregenator model. The excitation wave in the chemical medium is charged so that it can directly interact with the electric field. This is a unique feature of the chemical excitation wave. The mechanism of wave unpinning in the BZ reaction with a circularly polarized electric field is investigated by varying the pacing ratio, the initial phase of the wave, and field strength. The chemical wave in the BZ reaction unpins when the electric force opposite the direction of the spiral is equal to or above a threshold. We developed an analytical relation of the unpinning phase with the initial phase, the pacing ratio, and the field strength. This is then verified in experiments and simulations.

Removal of spiral turbulence by virtual electrodes through the use of a circularly polarized electric field

Heart disease is the leading cause of death and is often accompanied by cardiac fibrillation. Defibrillation using the virtual electrode effects is a promising alternative compared to using the high-voltage electric shock in the clinic. Our earlier works [S. L. Murphy, K. D. Kochanek, J. Xu, and E. Arias, NCHS Data Brief 427 (2021); R. A. Gray, A. M. Pertsov, and J. Jalife, Nature 392, 75-78 (1998); F. X. Witkowski, L. J. Leon, P. A. Penkoske, W. R. Giles, M. L. Spano, W. L. Ditto, and A. T. Winfree, Nature 392, 78-82 (1998); M. Santini, C. Pandozi, G. Altamura, G. Gentilucci, M. Villani, M. C. Scianaro, A. Castro, F. Ammirati, and B. Magris, J. Interv. Card. Electrophysiol. 3, 45-51 (1999).] prove that, compared with other external electric fields, a low voltage circularly polarized electric field is more efficient in turning non-excitable defects in cardiac tissue into virtual electrodes. It, therefore, needs lower voltage to stimulate the excitation waves and causes less harm to reset the spiral turbulence of cardiac excitation for defibrillation. In this paper, we investigate the virtual electrode effect of multiple defects by the circularly polarized electric field for the removal of spiral turbulence. Considering different shapes, sizes, and distributions of multiple defects, we reveal the phase locking of stimulated excitations around multiple virtual electrodes. Furthermore, the circularly polarized electric field parameters are optimized to remove the spiral turbulence.

Optimal entrainment for removal of pinned spiral waves

Cardiac fibrillation is caused by self-sustaining spiral waves that occur in the myocardium, some of which can be pinned to anatomical obstacles, making them more difficult to eliminate. A small electrical stimulation is often sufficient to unpin these spirals but only if it is applied during the vulnerable unpinning window. Even if these unpinning windows can be inferred from data, when multiple pinned spirals exist, their unpinning windows will not generally overlap. Using phase-based reduction techniques, we formulate and solve an optimal control problem to yield a time-varying external voltage gradient that can synchronize a collection of spiral waves that are pinned to a collection of heterogeneous obstacles. Upon synchronization, the unpinning windows overlap so that they can be simultaneously unpinned by applying an external voltage gradient pulse at an appropriate moment. Numerical validation is presented in bidomain model simulations. Results represent a proof-of-concept illustration of the proposed unpinning strategy which explicitly incorporates heterogeneity in the problem formulation and requires no real-time feedback about the system state.

Theory of unpinning of spiral waves using circularly polarized electric fields in mathematical models of excitable media

Spiral waves of excitation are common in many physical, chemical, and biological systems. In physiological systems like the heart, such waves can lead to cardiac arrhythmias and need to be eliminated. Spiral waves anchor to heterogeneities in the excitable medium, and to eliminate them they need to be unpinned first. Several groups focused on developing strategies to unpin such pinned waves using electric shocks, pulsed electric fields, and recently, circularly polarized electric fields (CPEF). It was shown that in many situations, CPEF is more efficient at unpinning the wave compared to other existing methods. Here, we study how the circularly polarized field acts on the pinned spiral waves and unpins it. We show that the termination always happens within the first rotation of the electric field. For a given obstacle size, there exists a threshold time period of the CPEF below which the spiral can always be terminated. Our analytical formulation accurately predicts this threshold and explains the absence of the traditional unpinning window with the CPEF. We hope our theoretical work will stimulate further experimental studies about CPEF and low energy methods to eliminate spiral waves.

Human Pluripotent Stem Cell-Derived Cardiac Tissue-like Constructs for Repairing the Infarcted Myocardium

High-purity cardiomyocytes (CMs) derived from human induced pluripotent stem cells (hiPSCs) are promising for drug development and myocardial regeneration. However, most hiPSC-derived CMs morphologically and functionally resemble immature rather than adult CMs, which could hamper their application. Here, we obtained high-quality cardiac tissue-like constructs (CTLCs) by cultivating hiPSC-CMs on low-thickness aligned nanofibers made of biodegradable poly(D,L-lactic-co-glycolic acid) polymer. We show that multilayered and elongated CMs could be organized at high density along aligned nanofibers in a simple one-step seeding process, resulting in upregulated cardiac biomarkers and enhanced cardiac functions. When used for drug assessment, CTLCs were much more robust than the 2D conventional control. We also demonstrated the potential of CTLCs for modeling engraftments in vitro and treating myocardial infarction in vivo. Thus, we established a handy framework for cardiac tissue engineering, which holds high potential for pharmaceutical and clinical applications.

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hiPSC-CMs are seeded on aligned nanofibers to obtain 3D cardiac tissue-like constructs

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Drug assessment using CTLCs can be more robust than conventional cultures

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CTLCs can be used to model in vitro cardiac tissue engraftment

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CTLCs improve the function of rat hearts with myocardial infarction

A theory for spiral wave drift induced by ac and polarized electric fields in chemical excitable media

Spiral waves are shown to undergo directional drifts in the presence of ac and polarized electric fields when their frequencies are twice of the spiral frequencies. Here, we propose a quantitative description for the spiral wave drift induced by weak electric fields, and provide the explicit equations for the spiral wave drift speed and direction. Numerical simulations are performed to demonstrate the quantitative agreement with analytical results in both weakly and highly excitable media.

Dynamics of spiral waves rotating around an obstacle and the existence of a minimal obstacle

Pinning of vortices by obstacles plays an important role in various systems. In the heart, anatomical reentry is created when a vortex, also known as the spiral wave, is pinned to an anatomical obstacle, leading to a class of physiologically very important arrhythmias. Previous analyses of its dynamics and instability provide fine estimates in some special circumstances, such as large obstacles or weak excitabilities. Here, to expand theoretical analyses to all circumstances, we propose a general theory whose results quantitatively agree with direct numerical simulations. In particular, when obstacles are small and pinned spiral waves are destabilized, an accurate explanation of the instability in two-dimensional media is provided by the usage of a mapping rule and dimension reduction. The implications of our results are to better understand the mechanism of arrhythmia and thus improve its early prevention.

Model of electrical activity in cardiac tissue under electromagnetic induction

Complex electrical activities in cardiac tissue can set up time-varying electromagnetic field. Magnetic flux is introduced into the Fitzhugh-Nagumo model to describe the effect of electromagnetic induction, and then memristor is used to realize the feedback of magnetic flux on the membrane potential in cardiac tissue. It is found that a spiral wave can be triggered and developed by setting specific initials in the media, that is to say, the media still support the survival of standing spiral waves under electromagnetic induction. Furthermore, electromagnetic radiation is considered on this model as external stimuli, it is found that spiral waves encounter breakup and turbulent electrical activities are observed, and it can give guidance to understand the occurrence of sudden heart disorder subjected to heavily electromagnetic radiation.

Removal of pinned scroll waves in cardiac tissues by electric fields in a generic model of three-dimensional excitable media

Spirals or scroll waves pinned to heterogeneities in cardiac tissues may cause lethal arrhythmias. To unpin these life-threatening spiral waves, methods of wave emission from heterogeneities (WEH) induced by low-voltage pulsed DC electric fields (PDCEFs) and circularly polarized electric fields (CPEFs) have been used in two-dimensional (2D) cardiac tissues. Nevertheless, the unpinning of scroll waves in three-dimensional (3D) cardiac systems is much more difficult than that of spiral waves in 2D cardiac systems, and there are few reports on the removal of pinned scroll waves in 3D cardiac tissues by electric fields. In this article, we investigate in detail the removal of pinned scroll waves in a generic model of 3D excitable media using PDCEF, AC electric field (ACEF) and CPEF, respectively. We find that spherical waves can be induced from the heterogeneities by these electric fields in initially quiescent excitable media. However, only CPEF can induce spherical waves with frequencies higher than that of the pinned scroll wave. Such higher-frequency spherical waves induced by CPEF can be used to drive the pinned scroll wave out of the cardiac systems. We hope this remarkable ability of CPEF can provide a better alternative to terminate arrhythmias caused by pinned scroll waves.

Hysteresis and drift of spiral waves near heterogeneities: From chemical experiments to cardiac simulations

Dissipative patterns in excitable reaction-diffusion systems can be strongly affected by spatial heterogeneities. Using the photosensitive Belousov-Zhabotinsky reaction, we show a hysteresis effect in the transition between free and pinned spiral rotation. The latter state involves the rotation around a disk-shaped obstacle with an impermeable and inert boundary. The transition is controlled by changes in light intensity. For permeable heterogeneities of higher excitability, we observe spiral drift along both linear and circular boundaries. Our results confirm recent theoretical predictions and, in the case of spiral drift, are further reproduced by numerical simulations with a modified Oregonator model. Additional simulations with a cardiac model show that orbital motion can also exist in anisotropic and three-dimensional systems.

Wave trains induced by circularly polarized electric fields in cardiac tissues

Clinically, cardiac fibrillation caused by spiral and turbulent waves can be terminated by globally resetting electric activity in cardiac tissues with a single high-voltage electric shock, but it is usually associated with severe side effects. Presently, a promising alternative uses wave emission from heterogeneities induced by a sequence of low-voltage uniform electric field pulses. Nevertheless, this method can only emit waves locally near obstacles in turbulent waves and thereby requires multiple obstacles to globally synchronize myocardium and thus to terminate fibrillation. Here we propose a new approach using wave emission from heterogeneities induced by a low-voltage circularly polarized electric field (i.e., a rotating uniform electric field). We find that, this approach can generate circular wave trains near obstacles and they propagate outwardly. We study the characteristics of such circular wave trains and further find that, the higher-frequency circular wave trains can effectively suppress spiral turbulence.

Synchronization of networked chaotic oscillators under external periodic driving

The dynamical responses of a complex system to external perturbations are of both fundamental interest and practical significance. Here, by the model of networked chaotic oscillators, we investigate how the synchronization behavior of a complex network is influenced by an externally added periodic driving. Interestingly, it is found that by a slight change of the properties of the external driving, e.g., the frequency or phase lag between its intrinsic oscillation and external driving, the network synchronizability could be significantly modified. We demonstrate this phenomenon by different network models and, based on the method of master stability function, give an analysis on the underlying mechanisms. Our studies highlight the importance of external perturbations on the collective behaviors of complex networks, and also provide an alternate approach for controlling network synchronization.